Note : Les descriptions sont présentées dans la langue officielle dans laquelle elles ont été soumises.
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SYSTEM AND METHODS FOR AUTOMATICALLY GENERATING A
MUSICAL COMPOSITION HAVING AUDIBLY CORRECT FORM
Background to the Invention
5 This invention relates, in general, to signal processing I-by an
apparatus] of an audio input
signal to split that signal into fundamental constituent data elements, and
the mathematical
functions thereof necessary to reproduce this signal as well as a plethora of
new signals,
with differing internal structural properties and differing boundary
conditions that permit,
through mapping and/or textural classification, the identification of both
permissible
10 linkages between constituent data elements and subsequent generative
output from the
identified mathematical functions, concatenated re-assembly into a different
signal with a
different structure. More particularly, the present invention relates to a
system supporting
original generative composition, not just recombination of existing material
especially in
the context of music and how an original composition can be generated to align
with and
15 reflect an emotionally descriptive narrative, such as a described scene
in a film script.
More particularly, but not exclusively, the present invention relates to a
process for
identifying and parsing, in existing tonal (as well as non-tonal) music, Form
Atoms of
varying length and where each Form Atom defines a contextually smallest
meaningful
snippet or element of musical content having both boundary conditions and
compositional
20 properties that permit automated concatenation of multiple Form Atoms into
a new
musical composition having good musical form but at least acceptable musical
form.
Summary of the Prior Art
Music in its own right does not exist because it is undetectable by science.
Rather, music
25 reflects observation by the mind that provides a response in the brain.
A profound couple
of statements but reflective of the fact that music and, more particularly,
the appreciation
of music reduces to signal processing and mental stimulation associated with
the
interpretation of a subjectively constructed journey in sound that exploits
the concepts of
"tension" and "release" as each is resolved in the mind of the listener.
Regardless of what
30 music amounts to and whether it is based on western, tribal or oriental
structures, there are
desirable physiological effects associated with music, with these effects
further affecting
emotional responsiveness and demeanour.
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Music theory has traditionally been more of a folk psychology used to name and
categorise
music, rather than a theory in a scientific sense that can predict the
effectiveness of a
passage, or the next note or chord in a piece.
'Good' music ¨ in the sense of an artistically appreciated structured
composition ¨ is music
that the mind (i.e., relevant neural pathways and centres of the brain) models
successfully
by being able to predict both an increase in tension within a musical journey
and then the
following release of that tension. Alternatively, this can be thought of as a
compositional
piece asking a question, as reflected in musical phrasing or musical
structure, and then the
compositional piece answering that question [shortly after the question has
been posed] to
permit mindful termination of a particular part within the entirety that is
the musical
journey in the composition. The question is thus a construct of tension in the
music, and
the release of a construct that correlates to an appropriate musical answer
that puts the
change in tonality into perspective. A more complete definition is provided
below for these
terms to enhance the reader's understanding of what these semantic terms mean
in a more
technical sense.
Putting the above into a psychological perspective, "good music" is recognised
through a
self-gratification process in which the mind firstly predicts what it thinks
will be delivered
by the musical journey, and when an "I was right" prediction is confirmed the
reward
system of the brain triggers to complete the reward. Whilst not wishing to be
bound by
theory, it is understood that the reward system refers to a group of
structures that are
activated by rewarding or reinforcing stimuli. When exposed to a rewarding
stimulus (such
as good music), the brain responds by increasing the release of the
neurotransmitter
dopamine. The structures associated with the reward system are found along the
major
dopamine pathways in the brain, including the ventral tegmental area ( V TA)
and the
nucleus accumbens in the ventral striatum. Another major dopamine pathway, the
mesocortical pathway, travels from the VTA to the cerebral cortex and is also
considered
part of the reward system.
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In contrast, "bad music" or bad composition or "bad form" corresponds to
reduced
reward/gratification that arises from the brain's inability to predict
anything from
seemingly/ostensibly meaningless random [musical] events, and thus the brain's
inability
to congratulate itself with a reward arising from stimulation.
A significant and unaddressed problem that has prevented the effective
automated
generation of "good" music is "form". The question is how to implement
technically a
process that does not generate randomness and which technical system is imbued
with a
technical mechanism that provides consistent evaluation of signal components
initially to
classify fundamentally compatible musical sections and then to permit those
musical
sections to be automatically selected and concatenated together seamlessly to
provide a
new generative composition; this is far from simple.
In fact, with respect to "form" composers require experience to identify
"form", and even
accomplished composers frequently have failed to appreciate acceptable form
until later
in their evolutionary compositional life. Even with the gained appreciation of
form,
composers frequently revert to templates in all their compositions. Templates
provide a
pre-structured structure on which the desired narrative is hung. A template
can, for
example, be sonata form or a rondo and other forms, as will be understood. As
a specific
example, the first movement of any symphony or concerto will share an
identical form but
a different narrative, e.g. A-B-A-B-C and then D, where A is the first subject
in the
major/dominant tonic, B is a contrasting key centre to the major/dominant
tonic and A and
B together form the "exposition", C is the conflict between A and B (which is
also known
as the "development") and D is the "recapitulation" or resolution of A and B.
"Form", in contrast with "narrative" [the latter being what one intends to
express
musically, i.e., the story between a beginning and end point as expressed by a
set of
emotional icons such as intensity swells and climaxes], is the structure of
linking musical
elements together in a musically sensible fashion that avoids discontinuity or
randomness
(in musical terms) such that a smooth transition is achieved between the
syntax of the
composite elements. Expressing "form" more tangibly but still subjectively,
"good form"
may be the syntax reflected in codes and conventions in accepted musical
compositions,
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whereas "bad form" has no obvious or known linking that makes any discernible
musical
sense between successive musical elements/phrases and, indeed, "bad form" in
music]
will fail to communicate structure because the sound signals cannot logically
be processed
by the brain.
The problem is that when any generative composition needs to adapt to follow a
narrative
that is different than that that can be laid down by an initial form template,
regardless of
whether it is human or machine-based, systems struggle to realise a generative
mechanism
that consistently achieves "good form" and thus the generation of relatively
high levels of
dopamine in the brain's reward centres. And with a failure to achieve "good
form", by
definition the composition acquires "had form" and correspondingly
identifiable
qualitative and/or measurable decreases in brain stimulation, particularly
associated with
the reward centres. Effective generative composition thus leads to a tangible
technical
effect with an associated technical assessment process. Indeed, better
generative
composition leads to increasing levels of detectable stimulation/brain
activity.
Indeed, identification of common musical traits in splice compatible musical
elements is
desirable and useful to game developers and/or advert or film trailer
producers/editors who
are tasked with rapidly compiling a suitable multimedia product that aligns
relevant music
themes, such as increasing musical intensity (in the context of an increasing
sense of
developing drama and urgency and not necessarily in the context of an absolute
audio
power output level) with video output. To provide a context for the problem of
composition in a commercial environment, the generation of an appropriate film
score is
a first example. Currently, the film director will write a narrative
reflecting the evolution
of action in a scene and will then approach a composer for a suitable
composition. The
composer will review the narrative and attempt to tailor a composition to the
narrative in
the provision of a "demo" to the client, such as a film director or game
designer.
More particularly, music for films, TV and adverts follows a similar
commissioning and
production pattern. A composer is commissioned typically by a director or
producers.
Their choice of the composer is either based on a musical showreel, or through
the fact
that the commissioner knows the composer' s specific discourse and desires it
for their
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project. Before the composer views the pictures, a temp track is typically
used to aid in the
editing process as well as to give an idea for the type of pace and mood that
the
commissioner wishes the film to have at specific points. The composer and
commissioner
then meet for what is known as a "spotting session-. In this meeting, the
parties view the
5 temp track and discuss the project in terms of where the music should
start and stop, a
process known as spotting. All other parameters for each section of self-
contained music,
or music cue, in the film are also considered. This process completes the
brief, which
consists of entry and exit timings for each cue, any hit points within the
cue, and the mood,
orchestration, and pace of the cues. [Hit points are points on the timeline
where the music
10 should "hit- the action, such as Tom being hit over the head with a
frying pan by Jerry.
From this, the composer produces a demo of the desired tracks for each cue.
These tracks
are then auditioned by the commissioners and feedback is provided for the
cue's
refinement. Once the tracks are considered to be in a satisfactory state by
all parties, they
are then recorded, or baked as it is known.
Interestingly, film composers are prone to borrow and steal ideas from
historical pieces
and those of other contemporary composers in order to satisfy various briefs,
just as John
Williams did when lifting a complete orchestral section of the closing of Mars
from
Holst's The Planets suit in his opening credits for the film Star Wars (Kurtz
& Lucas,
20 1977). Indeed, this point is openly spoken about by John Williams
himself in an interview
with David Meeker at the BFI (Meeker, 1978). Indeed, it is evidently clear
that composers
revisit scores and not only tweak them as Bach did (Ledbetter, 2002), but
completely
reform them so as to make a better temporal narrative, as was the case with
Rachmaninoff s Piano Concerto No. 4 (Norris, 2001).
This also leads to the question of the presently perceived artistic process of
composition,
although with generative composition this must necessarily technically assess
"form" and
for such "form" to be maintained sufficiently under the control of the system
intelligence
assembling the generative work.
This iterative process of film score multimedia composition may - or may not -
lead to a
composition that has "good form", and it will involve again the film director
in making a
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decision as to whether the remotely composed score is acceptable with the
requisite level
of "good form". The composer, as indicated above, is likely also to be
influenced by their
own prior compositions and, frequently, will make use of these personal
templates in
composing the "new- musical work. The use of such personal templates, which
generally
5 means that they have accepted form qualities, invariably leads to a score
that is "samey";
this is not necessarily a good thing. For example, there are noticeable common
traits in the
compositions of the main themes for the movies Superman and Star Wars since
both
were penned by John Williams.
10 In providing at least one resultant "demo" for review, the developer or
editor has already
expended considerable time in identifying potentially suitable music and then
fitting/aligning the selected music to the video. To delay having to identify
a
commercially-usable audio track, content developers presently may make use of
so-called
"temp tracks" that are often well-known tracks having rights that cannot be
easily
15 obtained, but this is just a stop-gap measure because a search is then
required to identify a
suitable commercially-viable track for which use rights can be obtained.
Further time
delays then arise from the instructing client having to assess whether the
edit fits with their
original brief. Therefore, an effective bank of cross-referenced musical
elements that are
contextually related to each other in the sense of "form" would beneficially
facilitate
20 effective generative composition for alignment with, for example, a
visual sequence or the
building of a musical program (such as occurs within film score development,
TV or
streamed advertising and "spin" classes that choreograph cycling exercise to
music to
promote work rates).
25 Interestingly, there is rarely a record of the crafting that went into
any compositional
decisions, although some do exist and provide great insight into the
compositional process
(Ledbetter, 2002)(Norris, 2001)(Cooper, 1992). Mostly, we are just left with a
single score
or performance, leading to an attitude of idolisation for the chosen notes;
that is, notes that
made it into the final manuscript that appear selected from a perfectionist
standpoint.
30 Evidence of the alternatives a composer may have taken paint a picture
of compositional
craft and choice that inevitably led to certain decisions of an arbitrary
nature. In (Meeker,
1978), John Williams states that he had 97 different versions of what became
the five-note
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theme to Close Encounters (Phillips & Spielberg. 1977). These were grouped
into four
groups of variations initially, which were reduced and further refined from
there through
discussions with the director Steven Spielberg until he arrived at the famous
five note
melody that is known. However, William's own remarks nevertheless did not stop
5 individuals writing about the apparent mathematics and physics-related
perfection of his,
and the director's, final choice for those five pitches in a particular chord,
with particular
timing and note duration. To Williams, it was clear that this was a set of
notes no better
than many others; however, they were the chosen ones that others have come to
believe
were in some sense preordained and, arguably, those with best "good form".
As another example, an interactive game provides no tailored user-experience
with respect
to the accompanying musical score. Presently, "it is what it is" for the
particular aspect of
the game or scene in a game and just reflects base programming. Should there
be an
effective generative process, then the sound experienced in terms of musical
textures can
15 provide an enhanced indication for the user as viewed from the emotional
perspective of
the on-screen avatar. For example, it would be an immersive experience for a
player to be
exposed to a user-dedicated specific musical segment that reflected growing
emotional or
physical conditions of the player' s in-game avatar. Currently, gaming systems
provide no
audible suggestion of in-game issues that the avatar is facing/experiencing
and this is to
20 the detriment of the physical player experience. The problem, however,
is that each player
journey is unique so how does a relevant tailored and meaningful sound
experience get
generated on-the-fly? And, in fact, can such a sound experience be tailored to
music that
has particular connotation and relevance to a specific user? At the moment,
any
accompanying game-related score is simply a generic path that may have no
emotional
25 connection to the player and, indeed, the score may actually not
emotionally resonate with
the player or actually may be disliked by the player.
Generative music compilers do exist. These existing systems typically use some
form of
Markov process to generate chords, but all have a series of algorithms that
produce
30 different notes across different instruments. The problem with the prior
art approaches is
that they support little if any creativity and little if any ability to
manipulate compositional
content. In fact, the prior art approaches all generally produce compositions
that sound the
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same because all generated composition is based on a fixed number of
predefined
instrumental templates. The consequence of this straight-jacketing approach is
a loss of
musical texture. This is a significant problem which diminishes usability
because of the
resultant sameness.
There are various methods for writing chord schemes that have been implemented
over
the years (C. Johnson, Carballal, & Correia, 2015; Lerdahl & Jackendoff, 1996;
Nierhaus,
2009). The aesthetic valuation for any given method is based on the
developer's artistic
requirements, justifications, post-rationalisations, or simple tolerances.
Experience in fact
shows that it can be considered acceptable for any chord to follow any other
chord given
enough context in the surrounding harmonic progression. When choosing a chord
to follow
another one, if this context is ignored and we only look for evidence of the
sequence in an
example, we find ourselves in the position whereby chord schemes simply become
a
randomised sequence.
Whilst the present invention relates to a signal processing of a sound signal
especially for
use in a generative sense, in order to provide further context it is
appropriate to provide a
working basis for the terminology that is used by musicians and which is
relevant to
specific embodiments and implementations of the invention. In this respect:
- In Western musical theory, a cadence is a melodic or harmonic configuration
that creates
a sense of resolution [finality or pause], especially since any cadence has
decreasing
emphasis. A harmonic cadence is a progression of (at least) two chords that
concludes a
phrase, section or piece of music. And a rhythmic cadence is a characteristic
rhythmic
pattern that indicates the end of a phrase. A cadence can be weak or strong
depending on
its sense of finality. While cadences are usually classified by specific chord
or melodic
progressions, the use of such progressions does not necessarily constitute a
cadence; there
must be a sense of closure as at the end of a musical phrase. Generally,
harmonic rhythm
plays an important part in determining where a cadence occurs. Cadences are
also strong
indicators of the tonic or central pitch of a passage or piece of music.
- In music, the tonic is the first scale degree of the diatonic scale (the
first note of a scale)
and the tonal centre or final resolution tone that is commonly used in the
final cadence in
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tonal (musical key-based) classical music, popular music, and traditional
music. In the do
solfege system, the tonic note is sung as do. More generally, the tonic is the
note upon
which all other notes of a piece are hierarchically referenced. Scales are
named after their
tonics: for instance, the tonic of the C major scale is the note C. The term
tonic can also
5 be referred to as a the keycentre. The local tonic, e.g., Cm or Bb,
provides both the first
and last notes of the scale.
- A triad formed on the tonic note, the tonic chord, is thus the most
significant chord.
10 - A chord is a series of pitches played in parallel with each other and
which are tied to a
keycentre. In terms of function, the mind makes use of a chord to predict
where it is in the
composition. A chord does not in its own right have any lexicological meaning
because
musical meaning is derived from the syntax, i.e., the sequence of chords.
15 - A chord scheme is a chain of chords.
- A metachord scheme are the principals of how a chord scheme is written.
- Major and minor scales are two of the most popular and commonly used
scales in western
20 music, with a set of notes each with a distinct pitch forming the scale.
Major and minor
scales are variations of the diatonic scale in which there are pitch intervals
of five full steps
and two half steps, with the relative pitch/physical displacement of the third
note
determining whether the scale is major or minor. This third note makes the
major scale
brighter and more cheerful sounding while giving the minor scale its
characteristic
25 sadness, melancholy and darkness. In a major scale, the third note is
one note higher than
the minor 3rd note. The pattern of steps in a major scale has note spacing
WWHWWWH
(where W representing transition of a whole note and H representing transition
of a half
note), whereas the pattern in a minor diatonic scale has note spacing
WHWVVHWW. In
convention Western music, any major or minor key will have seven degrees/notes
in its
30 scale, i.e., notes A to G.
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Whilst the inventive concepts ¨ of which there are many - will now be
described in
considerable detail, the following description of additional musical
terminology may
further assist.
5 Particularly in Western music, the relationship between chords is defined
by the degree of
scale. The degree of scale refers to the position of a particular note (having
a particular
pitch) on a scale relative to the tonic, i.e., the first and main note of the
scale from which
each octave is assumed to begin. In music theory, a diatonic scale is any
heptatonic scale
that includes five whole steps (whole tones) and two half steps (semitones) in
each octave,
10 in which the two half steps are separated from each other by either two
or three whole
steps, depending on their position in the scale. This pattern ensures that, in
a diatonic scale
spanning more than one octave, all the half steps are maximally separated from
each other
(i.e. separated by at least two whole steps).
15 An octave is the difference in pitch between two notes where one has
twice the frequency
of the other. Two notes which are an octave apart always sound similar and
have the same
note name, e.g., C, while all of the notes in between sound distinctly
different, and have
other note names e.g., D, E, F, etc. Notes naturally fall into groups of
twelve, which are
all one octave apart from each other. An octave thus comprises 12 equal
semitones, with
20 each semitone therefore having a frequency step in a ratio of 21/12 to
the earlier frequency.
Further, it will also be appreciated that the choice of the note within a
chord leads to its
classification. For example, a three-note chord [which incidentally is a
"triad"' can have
varying note spacing between the three notes of:
25 for a minor triad, 3 semitones followed by 4 semitones;
for major triad, 4 semitones, followed by 3 semitones;
for an augmented triad. 4 semitones, followed by 4 semitones; and
for a diminished triad, 3 semitones, followed by 3 semitones.
30 Whilst not wishing to teach your grandmother to suck eggs, a dominant
7th is where the
[piano] chord includes a fourth note that is a degree/scale note down from the
8th (i.e. the
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repeating note in the next octave), whereas a major 7th is where the chord
includes a fourth
note that is a semitone down from the 8th.
Clearly, as will be understood, a full orchestration for multiple instruments
will have
5 different scores for each instrument, with different instruments having
different numeric
representations on the Musical Instrument Digital Interface protocol (MIDI)
scale. For
example, middle C has a value of 60 (representing a real-world frequency of
261.63Hz
using contemporary tuning of A=440Hz).
10 Instruments have idiomatic restrictions. For example, a conventionally
tuned 4-string bass
guitar, the lowest MIDI value is position 28. Conversely, a violin will only
generally be
able to play two notes simultaneously with these having a lowest note having a
MIDI value
55.
15 Returning to the underlying technical problems associated with effective
automated
generative composition, another issue faced by the music industry is how best
to augment
the listener/user experience, especially on a personal/individual level.
Indeed, it has long
been recognized that the contextual relevance of or relationship between a
piece of music
and an event brings about recognition or induces a complementary emotional
response,
20 e.g., a feeling of dread or suspense during a film or a product
association arising in TV
advertising.
Tailoring a generative sound experience to a narrative articulated by an end
user having
no credentials in composition would be advantageous provided that the
composition was
25 quickly generated and of a discernible standard. However, in short, for
automated
generative composition, there is presently no effective way to assess "form"
in a sound
signal comprised from selectively linked musical phrases typically expressed
in terms of
bars, or indeed how a procedure for generative composition can be automated to
avoid
"bad form" and thus to impose the related consequences on human physiology and
state
30 of mind.
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Summary of the Invention
In overview, a generative composition system reduces existing musical
artefacts to
constituent elements termed "Form Atoms-. These Form Atoms may each be of
varying
length and have musical properties and associations that link together through
Markov
5 chains. To provide myriad new composition, a set of heuristics ensures
that musical
textures between concatenated musical sections follow a supplied and defined
briefing
narrative for the new composition whilst contiguous concatenated sections,
such as Form
Atoms, are also automatically selected to see that similarities in respective
and identified
attributes of musical textures for those musical sections are maintained to
support
10 maintenance of musical form. Independent aspects of the disclosure
further ensure that,
within the composition work, such as a media product or a real-time audio
stream, chord
spacing determination and control is practiced to maintain musical sense in
the new
composition. Further and additionally, a new and complementary but independent
technical approach structures primitive heuristics to maintain pitch and
permit key
15 transformation.
According to a first aspect of the invention there is provided a generative
composition
system, comprising: an input coupled to receive a briefing narrative
describing a musical
journey with reference to a plurality of emotional descriptions for a
plurality of musical
20 sections along the musical journey; a database comprising a multiplicity
of music data files
each generating, when instantiated, an original musical score and wherein each
original
score is partitioned into a multiplicity of identifiable concatenated Form
Atoms having
self-contained constructional properties and where each has: a tag that
describes a
compositional nature of its respective Form Atom; a set of chords in a local
tonic, and a
25 progression descriptor in combination with a form function that
expresses musically one
of a question, an answer and a statement, and wherein musical transitions
between Form
Atoms are mapped to identify and then record established transitions between
Form Atoms
in multiple original scores and such that, within the system, groups exist in
which Form
Atoms are identified as having similar tags but different constructional
properties; and
30 processing intelligence responsive to the briefing narrative and coupled
to the database,
wherein the processing intelligence is arranged to: assemble a generative
composition
having regard to the briefing narrative through selection and concatenation of
Form Atoms
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having tags that align with emotional descriptions timely required by
respective ones of
the plurality of musical sections; and select and substitute Form Atoms from
different
original scores into the generative composition, the substitute Form Atom:
derived from
any original score; and having its compositional nature aligned with the
emotional
5 descriptions.
The database may include heuristics in the form of meta-data containing
information
explaining how to reconstruct original musical artefacts as well as
alternatives thereto.
10 The Form Atom may be assembled into a string of form atoms that generate
a string of
chord schemes with associated timing.
The system can include chord spacer heuristics arranged to distribute chords
across a
stipulated time window.
The system intelligence may be arranged to process chord schemes to
instantiate textures
where texture notes are derived from chords and their associated timings.
Each Form Atom has minimal length and different Form Atoms may embody
different
20 musical durations.
In one embodiment, a subset of the tags may be semantically identical.
In another embodiment, each Form Atom never includes a tonic in a middle
section of the
25 Form Atom.
Each Form Atom will have a specific set of chords in a local tonic expressed
as interval
distance relative to the local tonic having both pitch and tonality.
30 In an embodiment, the Form Atom stores a chord type and a chord's bass.
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In an embodiment, the database store lists of Form Atoms that are linked to
lists of
preceding or following Form Atoms through Markov-chain associations that
identify,
from a corpus of artefacts, prior transitions that have worked musically with
good form.
5 Form Atoms provide harmonic structure and an ability to generate harmonic
structures
that obey compositionally good musical form.
Form Atoms may have associations to a list of mapped textural components which
define
texture for the composition and which permit, when selectively chosen and
written with
10 chord scheme chains, maintenance of textural continuity in the
generative composition.
In another aspect of the invention there is provided a method of generative
composition,
the method comprising: receiving a briefing narrative describing a musical
journey with
reference to a plurality of emotional descriptions for a plurality of musical
sections along
15 the musical journey; assembling a generative composition having regard
to the briefing
narrative through selection and concatenation of Form Atoms having tags that
align with
emotional descriptions timely required by respective ones of the plurality of
musical
sections; and selecting and substituting Form Atoms from different original
scores into the
generative composition, the substitute Form Atom: derived from any original
score; and
20 having its compositional nature aligned with the emotional descriptions;
and wherein each
original musical score is partitioned into a multiplicity of identifiable
concatenated Form
Atoms having self-contained constructional properties and where each has: a
tag that
describes a compositional nature of its respective Form Atom; a set of chords
in a local
tonic, and a progression descriptor in combination with a form function that
expresses
25 musically one of a question, an answer and a statement; and mapping
musical transitions
between Form Atoms to identify and then record established transitions between
Form
Atoms in multiple original scores and such that groups of Form Atoms exist in
which Form
Atoms are identified as having similar tags but different constructional
properties.
30 In a further aspect of the invention there is provided a method of
analysing a musical score
containing a plurality of musical sections, the method comprising: identifying
the presence
of an emotional connotation associated with a musical texture in the plurality
of sections
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and wherein the musical texture is represented by a plurality of identifiably
different
compositional properties, and wherein: i) the musical texture has an emotional
connotation; and ii) each musical texture of any musical section is expressed
musically in
terms of the presence of musical textural classifiers selected from a set
containing multiple
5 pre-defined musical textural classifiers and such that: a) different
musical sections may
include a differing subset of pre-defined musical textural classifiers; b) for
a given musical
section, each pre-defined musical textural classifier has either zero or at
least one
component to that textural classifier and wherein each component that is
present is further
tagged as either a musical accompaniment or a musical feature and where each
musical
10 textural classifier that has a component present possesses: i) either no
musical feature or a
single musical feature, and ii) one or more musical accompaniments; and c)
different
musical sections can have a common descriptor or a similar descriptor having
an
association with the common descriptor, but at the same time different musical
sections
possess differing subsets of musical textual classifiers or differing subsets
of components
15 in the musical textural classifier.
The textural classifier may be selected from a group comprising at least some
of melody,
counter-melody, harmony, bass, pitched rhythm, non-pitched rhythm and drums.
20 A musical feature is a salient musical component in musical texture; and
contains
information about musical tension and release within the musical section and
which
tension and release would be musically contextually destroyed if the musical
feature were
to be combined with another musical feature in the musical section and in the
same pre-
defined musical textual classifier. An accompaniment does not interfere with
another
25 accompaniment or a feature in any specific textual classifier of a
musical section and can
be added or removed selectively to thicken or thin the texture of the musical
section.
In yet another aspect of the invention there is provided a method of providing
texture in
an automated generative composition process, the method comprising: generating
at least
30 one chord scheme to a narrative brief, wherein the chord scheme is based
on Form Atoms
and the narrative brief provides an emotional connotation to a series of
events; and apply
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a derived texture to the at least one chord scheme to generate a composition
reflecting the
narrative brief.
The method may further comprise identifying absence of a textural narrative in
a first
5 musical section concatenated with a second music section having a texture
profile; and
filling the first musical section with at least one component that is a
musical
accompaniment or a musical feature selection wherein the at least one
component is based
on one of: history of preceding textural classifiers and a continuation of a
dominant one of
the textural classifiers, else a logical bridge between a destination subset
of pre-defined
10 musical textural classifiers based on intensity of respective subsets.
Effective generative composition, according to the various component aspects
of this
disclosure, thus leads to a tangible technical effect, particularly through
the production of
a generative work that has -good form". The embodiments achieve this through a
15 categorization process in which technical properties linked to Form
Atoms, of non-
standard varying duration, are extracted and stored relative to a descriptor
of expressive
qualities of each Form Atom. A relationship map is established between
different Form
Atoms such that the technical properties exhibited by one Form Atom can be
concatenated
with those properties of an adjacent Form Atom in a fashion where the
transition in musical
20 terms between adjacent Form Atoms has perceptibly good form. This
approach underpins
the ability to produce automated generative composition.
In still yet another aspect of the invention there is provided a database of
tagged Form
Atoms, wherein each Form Atom includes: a tag that describes a compositional
nature of
25 its respective Form Atom; a set of chords in a local tonic, and a
progression descriptor in
combination with a form function that expresses musically one of a question,
an answer
and a statement.
In the various embodiments, a question is a chord scheme that suggests tension
requiring
30 mental settlement as indicated by notes that have appeared within a
harmony or melody
and which are questionably present because they are outside of the key centre
of the local
tonic of the Form Atom; an answer is the resolution of the question which
operates to
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resolve the presence of the questionable tones or notes from the mind's
perspective by
reinforcing the key centre of either the local tonic or any new tonic of the
answering Form
Atom; and a statement is entirely self-contained from a musical question and
doesn't imply
or induce any meaningful musical tension that requires release through
resolution, and a
5 statement is neither a question nor an answer.
Each Form Atom provides harmonic structure and an ability to generate harmonic
structures that obey compositionally good form.
10 In another aspect, there is provided a musical Form Atom in a database
containing a
multiplicity of selectable Form Atoms, each Form Atom arranged provide
harmonic
structure and an ability to generate harmonic structures that obey
compositionally good
form.
15 The present invention, amongst other things, functions to reduce chords
to their relational
position to the base tonic, while maintaining pitch relationships arising in
any transposition
between different keys/tonics. The chain of transitions is then maintained.
Putting this
differently, in any musical key in the preferred implementation, the
relationship between
chords is expressed by the degree of the scale. Thus, regardless of the
octave, in the key
20 centre of F, an F note in the scale would be expressed as a value I, a
Bb as a IV and a C as
a V. This approach therefore leads to an equivalency between chord schemes
irrespective
of the chosen tonic and is maintainable across both major and minor scales (or
any chosen
degree of scale that departs from the exemplary context of a 7-note Western
scale as used
herein). Consequently, by reducing notes within chords to their relational
position relative
25 to the base tonic means that relative constructional context of any
chord is maintained
irrespective of transposition to a different tonic. i.e., the chain of
transitions is then
maintained. Thus in the exemplary key of C major on a piano:
Middle C on the piano would have a MIDI value 60 and position I,
Db on the piano would have a MIDI value 61 and position Ilb,
30 D on the piano would have a MIDI value 62 and position II,
Eb on the piano would have a MIDI value 63 and position IIlb,
E on the piano would have a MIDI value 64 and position III,
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F on the piano would have a MIDI value 65 and position IV,
Gb on the piano would have a MIDI value 66 and position Vb,
G on the piano would have a MIDI value 67 and position V,
Ab on the piano would have a MIDI value 68 and position VIb,
5 A on the piano would have a MIDI value 69 and position VI,
Bb on the piano would have a MIDI value 70 and position Vilb,
B on the piano would have a MIDI value 71 and position VII, and
C (in the next octave and with a return to the tonic) on the piano would have
a MIDI value
72 and position I (again).
The preferred embodiments therefore work on the premise that every chord can
be
measured in the context of its local tonic/key centre by an integer, and that
relationships
can be established between chords rather than just sequencing of specific
chords.
15 Advantageously, aspects of the present invention therefore analyse and
then parse music
to deduce various heuristics permitting generation of musical textures as well
as
performance parameters and the building blocks required for assuring quality
of final
assembly/performance of processor-originating generative work. A
classification
mechanism allows for different instrumental components to be used in different
compositional contexts, thereby allowing brand new textures to be created
through
combining principals of different compositions. The beneficial result is a
generative
composition that follows a brief, i.e., a narrative provided by a client, and
which
consequently is musically relevant, formalistically variable (since, unlike
the prior art
approaches, it is not formalistically tied to a template) and which has
audibly ¨ and thus
25 reward centre rewarding - good musical form.
Beneficially, based on processing music information retrieval techniques and
analysis
supported by a processor-based system intelligence, such as a bespoke expert
system, the
present disclosure provides a multiplicity of complementary yet inventively
different
30 technical solutions. The processing mechanisms function to compress an
original musical
composition through a series of mathematical functions [having correctly
applied
parameters] that support both the reproduction of the original
composition/score as well
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as myriad other alternative generative composition that satisfy human
requirements of
predictive tension and release that stimulate the reward centre of the brain
to promote
dopamine release. In this respect, correct parameters amount to the
application of
mathematical choices based on developed core heuristics, i.e., rules, together
with a
5 sequential ordering of execution of these core heuristics. The invention
applies an Occam' s
Razor approach, i.e., generative mathematical functions should be the simplest
to support
the objective reproduction of the original musical intent, to selection of
heuristics in the
various generative aspects of the approach, such as in (a) pitch generation,
(b) pitch
transformation into a new tonic, (c) chord spacing that maintains the rate of
play of
10 generative chords in the generative composition and (d) texture
maintenance in the
generative composition. Examples of such mathematical functions, of which
there are
many disclosed in detail herein, can include the axioms that a bass note in
transposition
cannot be below the lowest note on a bass guitar or a score for a transposed
violin
component can maximally only relate to play two notes simultaneously.
Applications of the techniques of the embodiments and aspects of this
disclosure can be
employed in any music to video application, including film score, advert
production and
gaming (especially in the context of producing a user-specific musical
accompaniment
that is generated to reflect player-selected music having direct player
connotation to player
20 emotion(s)). Also, since the generative piece embodies "good form" and
originality, the
application of the technology can be applied to produce a new composition for
which lyrics
can be written.
The present invention produces alternative generative musical works that are
equally
25 satisfiable to the mind from a process that identifies compatible
musical elements from
different musical sources/scores and concatenates complementary generative
heuristics/mathematical functions.
Brief Description of the Drawings
30 The patent or application, as filed, contains/contained at least one
drawing executed in
colour. Copies of this patent or patent application publication with colour
drawing(s) will
be provided by the Office upon request and payment of the necessary fee.
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Exemplary embodiments of the present invention will now be described with
reference to
the accompanying drawings in which:
FIG. lA is a diagram illustrating composition approach in the prior art;
5 FIG. 1B is a diagram illustrating compositional approach of the present
invention.
FIG. 2A shows a prior art sketch of the final score to The High and the
Mighty;
FIG. 2B shows a prior art formal final score to The High and the Mighty;
FIG. 3 is a representation of texture classification and generative assembly
according
to an embodiment of an aspect of the present invention;
10 FIG. 4 is a representation of texture classification and generative
assembly and in
which an intermediate musical section has been unspecified and "filled" to
provide texture
continuity according to an embodiment of an aspect of the present invention;
FIG. 5 is a hierarchical task flow for the generative compositional system of
a
preferred embodiment;
15 FIG. 6 represents, according to an embodiment, assemblage of
permissible inter-
Form Atom mapping relationships;
FIG. 7 shows the Affordances of a heuristic mechanism with hierarchical and
logical
flow as practiced by the approach of embodiments of the present invention;
FIG. 8 is a schematic view of a preferred composition architecture and
methodology
20 for generative composition;
FIG. 9 shows, according to a preferred embodiment, how a single composition is
parsed into a set of trees with viable Form Atom branches;
FIG. 10 is a schematic representation of texture generation according to a
preferred
embodiment of the present invention;
25 FIG. 11 is a screen shot of a graphical user interface for a piece
annotation system
according to one embodiment of the present invention;
FIG. 12 is a chord placement chart representing a spacing heuristic for use in
one
embodiment of the present invention;
FIG. 13 is a sequential Form Atom template for use in one embodiment of the
present
30 invention;
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FIG. 14 is a portion of The Quidditch Match musical score by John Williams
annotated for reduction and analysis according to an implementation of the
present
invention;
FIG. 15 is an intervallic template representing a loop of sequence Form Atom
3, with
5 escape Form Atom 4, derived from The Quidditch Match composition
according to an
implementation of the invention;
FIG. 16 is a template representing a Form Atom 6 sequential cadence derived
from
The Quidditch Match composition according to an implementation of the
invention;
FIG. 17 is a template representing sequence and escape phrases 7 and 8 derived
from
10 The Quidditch Match composition according to an implementation of the
invention;
FIG. 18 is a musical score of a four-bar section of detache string writing
enhanced
according to one implementation of the invention with associated colour labels
that
indicate note pitch;
FIG. 19 is a musical score of the first two bars of the Prelude in C Minor by
Johann
15 Sebastian Bach modified according to one implementation of the invention
by highlighting
syntactic structures and note pitches according to a predefined colour scheme;
FIG. 20 is a table showing degrees of the scale of semiquaver 3 with relation
to the
local dominant of the corresponding bar, in an analysis of texture according
to the
invention;
20 FIG. 21 is an exemplary diagram according to an implementation of the
invention
that expresses musical notes within Bars 1 to 3 of the Bach prelude as a
numerical array;
FIG. 22 is an alternative exemplary diagram according to an implementation of
the
invention that expresses musical notes within Bars 1 to 3 of the Bach prelude
as a
numerical array;
25 FIG. 23 is another exemplary diagram according to an implementation of
the
invention that expresses musical notes within Bars 4 to 6 of the Bach prelude
as a
numerical array;
FIG. 24 is a table illustrating changes in the pattern in the bass at
semiquaver 5,
including direction of the pattern, the chord component on which the 5th
semiquaver in
30 the bass lands, and the 5th' s position in either the Treble T or bass
B;
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FIG. 25 is another exemplary diagram according to an implementation of the
invention that expresses musical notes within Bars 7 to 9 of the Bach prelude
as a
numerical array;
FIG. 26 is another exemplary diagram according to an implementation of the
5 invention that expresses musical notes within Bars 10 to 11 of the Bach
prelude as a
numerical array;
FIG. 27 is another exemplary diagram according to an implementation of the
invention that expresses musical notes within Bars 12 to 14 of the Bach
prelude as a
numerical array;
10 FIG. 28 is an image of a Wilhelm Friedemann Bach manuscript copy of
Johann
Sebastian Bach's Bar 14. C minor prelude 1, from the "Clavier-Buchlein
version";
FIG. 29 is an exemplary diagram according to an implementation of the
invention
that expresses musical notes within Bars 15 to 17 of the Bach prelude as a
numerical array;
FIG. 30 is an exemplary diagram according to an implementation of the
invention
15 that expresses musical notes within Bar 18 of the Bach prelude as a
numerical array;
FIG. 31 is a musical score representation of the Bach prelude according to an
implementation of the invention that uses color-coded heuristics showing
hierarchical flow
and highlighted points of entropy;
FIG. 32 is a musical score representation according to an implementation of
the
20 invention of all possible combinations (spanning an octave) of major and
minor triads with
C and Eb as the top extensions;
FIG. 33 is an image of a keyboard representation showing possible notes within
textures of Bars 19 and 20 of the Bach prelude according to an implementation
of the
invention.
Detailed Description of a Preferred Embodiment
The extensive nature of this application and the invention lends itself to
being broken down
into an overview, followed by explanatory sections and then followed by a
worked
example of the application of the signal processing approach and the
application of the
30 functions to a specific example. Within this application, the system may
be referred to as
the "Heresy generative system", "generative composition system", or other
appropriate
descriptive tag for a computer-implemented system that oversees a real-world
application
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of a new mathematical analysis and re-assembly approach within an applied
technical
process applying a Turing equivalency that results to an improved technical
output.
The principles behind the "Heresy generative system- revolve around a shift
from how we
5 traditionally view compositions and the composition process, and treats
music (and the
related signal processing of audio signals) as a fluid non-static entity that
never has a final
fixed state that cannot be changed.
It is important to understand the requirements involved in creating a "brief'
before
considering how each aspect of the generative system of the preferred
embodiments
interact to create a new score from existing [analysed] artefacts. The brief
itself is a set of
compositional requirements that are the backbone of the generative system. The
description will then consider the generative approach of the various
embodiments and
aspects.
The invention considers, as a corpus, potentially all compositions as a source
for analysis,
reference and input into the generative system. Through this process, the
invention
functions to extract (either through digital analysis through signal
processing by Al or
processor-based intelligence or otherwise by a musicologist) certain specific
compositional principles from a given composition or multiple compositions,
thus
allowing the invention to blend principles from different works into one
distinctive/discrete meta-composition. Applying an Occam' s Razor based
approach, these
compositional principles are expressed as a set of heuristics/rules that can
subsequently
create new generative works.
With regards to the Heresy generative system, it is understood that different
keywords in
a brief potentially have different meanings to different users. Therefore, it
is preferable
that generic terms that have little semantic meaning to the concept they are
tagging are
used, in order to give a noun to a category, whilst still allowing attachment
of one or more
30 keyword to a personal set of meta-tags that mean something to a user
alone. Natural
Language Processing "NLP" can be employed to derive a processible data for a
usable
descriptor of a musical section.
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An effective categorisation strategy may be the Estil method of vocal training
(Klimek,
2005). This abstract connotation-labelling method offers a viable alternative
to trying to
attach words with semantic meaning to music, the pitfalls of which are
highlighted in (G.
5 A. Wiggins, 1998).
The system of the invention and preferred embodiments provide a framework for
crafting
iterations in composition. It offers a way for users to state an intent (in
the form of an
inputted narrative or brief that is interpreted and correlated to heuristics
and thus salient
10 musical sections that can be concatenated together in an auditory
seamless fashion), and
then, indeed, to adjust quickly the output from this briefing specification.
In other words,
the system of the present invention offers the ability to define a set of
compositional ideas,
before auditioning them and listening to how effectively they communicate the
original
intention. Nevertheless, the chosen ones will change every time the system is
asked to
15 generate a new composition, whilst form is protected. The inventive
approach takes this
principle one step further in that it offers the ability to see which
generative expression is
potentially "wrong". More particularly, through critical analysis and
commentary of the
system's output, it is possible to identify [considering the original
intention/instruction/brief] exactly which heuristic produced a wrong chord,
note pitch,
20 length, position, voicing, voice leading, textural clash or emotional
connotation. It is then
possible to reflect this criticism in the heuristics themselves, altering how
they make their
decisions to fit better the compositional intention, iteratively refining the
heuristic
expression of the original concept. Alternatively, whilst the system can
generate perfectly
reasonable material, there are instances where this result could be better
aligned with the
25 original intent. This gives two things: firstly, a new compositional
idea that can be post-
rationally meta-tagged as a different concept; and secondly, an insight into
how close one's
original intention may be to other compositional ideas and indeed the
generative work.
The system of the present invention makes a shift of roles from traditional
film-scoring
30 methods. Where composers have traditionally relied on technological tools
by
programmers and engineers (such as streamers and click-tracks), and sequencing
software
for demoing their material; and whilst commissioners have taken a selective
role in
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choosing material presented to them, such as Steven Spielberg did with the
themes for
both Indiana Tones (Laurent, 2003) and the Close Encounters five-note motif
(Meeker,
1978), the system of the present invention shifts these roles; this is
reflected in the
comparison of approaches shown in the commissioner/user/composer/programmer
5 delineations of FIGS. lA and 1B.
With the present invention, the composers themselves become both the
programmers and
the users. Composers now use the tool to create the heuristic processes that
can be used by
other users, thus taking on the technical role of programmers, whereas the
commissioners
10 themselves can become composers, as users of the generative tool.
The approach underlying the present invention is based on an understanding of
composition, and particularly the act of composition, in a conceptually
different way,
namely: showing how the next note in the audio signals follows an earlier note
(as
15 expressed in rules associated with the generation thereof and the length
of a fundamental
musical component that expresses fundamental audio signal components of a
musical
section) a rather than what the note actually is. In this paradigm, the
principle of
composition requires a method of analysis, with iterations of generated
heuristics applied
to refine the concept for composition.
According to the present invention, a processor-based system and related
methodology
differs from systems of earlier approaches in that the present invention makes
each of the
processes, decisions and weighting factors [that go into composition] the core
on which
the system can abstract the principles for how to generate these new
compositional works.
25 Particularly, rather than using a suite of parameterised generative
systems that present
components whose compositional input is all but complete, the system of the
present
invention break downs composition from scratch and creates generative
mechanisms for
the specific piece.
30 Axiomatically, the present invention asserts that:
1. Fewer heuristics that can achieve the same result are more desirable. This
is Occam's
Razor and by making heuristics easier to understand this approach makes them
easier to
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adapt and easier to build on with future rules applied by the processors and
functionality
of the present invention.
2. A linear increase in heuristics encompasses an exponentially increasing
number of
works. In short, new compositions preferably should increasingly incorporate
past
5 analytical components, and therefore give increasing compression progress
to a universal
set of heuristics that explain previous and future compositions.
3. New heuristics must explain more than one phenomenon. If a set of new rules
only
explains one core compositional component from a specific piece, then this is
a bespoke
ruleset and should be omitted until evidence from the corpus can provide
further examples
10 of where the heuristics are appropriate. This avoids over fitting rules
to analysis of
composition, and causing bloat and noise in the pursuit of seeking a more
unified
understanding of composition. In practical terms, fewer rules will be required
to explain
new compositions by (at least) the same composer, or for those compositions
that are
connected through similarity in genre or time.
When a piece is analysed and generative heuristics are created from it, these
will have a
specific flavour, and can be considered a "pack". A heuristic pack may produce
piano
preludes in the style of Bach, or action movie music in the style of John
Powell. These
packs can then be meta-tagged with information about the intention of the
content and its
20 emotional connotation(s).
In this way, music composed by the generative framework of the present
invention never
has a generic and identifiable sound in itself, but its heuristic packs most
definitely will.
The functional tool thus reflects a generic expression of composition with a
measurable
25 output that allows for refinement towards greater simplicity and higher
diversity of output.
This in itself is significant to the compositional process especially in the
context of
automated generative composition having good form.
The present invention, as will become apparent from the more detailed
explanation below
30 and herein of the various interactive components that support automated
generative
composition, is capable of predicting the immediate path for a new composition
at a
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specific point, thereby offering a new mechanism in the field of composition
for reflection
on practice, and refinement of the categorisation of emotional connotations.
SECTION A
5 I. Meta-Composition: the Briefing Mechanism
Music is synced to film for a variety of reasons. Whilst "synced" music, i.e.,
music which
sits within the diegesis, is typically heard by the characters as part of the
story, non-diegetic
music, i.e., music that sits outside the story and comments on it, acts in a
variety of ways
to bring out certain properties of the film.
In the case of synced tracks, that is tracks that have been pre-recorded by an
artist and then
superimposed to accompany the action (pop, rap, and such the like), these
tracks are often
the starting point in the editing room and form the basis of the pace and
style of the cut.
These bring sub-cultural identities to the film, grounding it in genre, or
lending the
15 connotations of a certain culture to the film. A quintessential example
of this is the use of
"Hotel California" by the Gipsy Kings in The Big Lebowski. In the scene that
introduces
the character of Jesus Quintana (played by John Turturro), the viewer is given
a
reinterpretation of the original song, which itself has a laid-back, and
somewhat
melancholy treatment in both lyrics and musical feel. This new interpretation
has an
20 energetic and spirited quality, giving connotations that the character
Jesus views the
environment entirely differently to the narrative's discourse so far: this is
a juxtaposition
that is highlighted further by a montage of slow-motion shots that accompany
the fast-
paced music.
25 In the case of the non-diegetic music being custom written by a scoring
composer, s/he
may choose a discourse via a textural palette to achieve a specific effect
such as this
juxtaposition in the Jesus Quintana example, but will also be looking to help
the pace and
flow of the film through appropriate tempo and time signature mapping, as well
as to
follow the story on screen until preceding narrative peaks to create tension.
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Embodiments of the present invention therefore provide an interface and
functionality to
a user that allows for the briefing of the above elements. There are several
methods that
can be considered as appropriate, including but not limited to:
1. A written brief from a spotting session with time-codes for where cues will
start and
5 stop, as well as the connotations that each cue will have, complete with
any hit points that
the director/composer have agreed on.
2. A full score for the film.
3. A short score, or "sketch-, on a limited number of staffs, that contains
the basic
compositional material for orchestrators to use.
10 4. A partially graphical score used to make notes across a mapped-out
timeline that gives
the composer, or orchestrators s/he trusts, notes on the desired sound,
texture, and
harmony. In this situation, the composer's or orchestrator's ability to
interpret and
understand the directions is an intelligent parsing mechanism that the brief
relies on to
obtain a result. This discrepancy between sketch and final score is
highlighted by the
15 reconstruction of the score to The High and the Mighty as seen in FIGS.
2A and 2B.
Whilst the above list is not comprehensive, it provides an indication of the
requirements
for a tool that allows briefing. There are, however, components in the
briefing that are
significant and include some or all of:
20 1. The ability to map pace across time. This clearly points to the use
of a musical time
ruler rather than a standard minutes, seconds, and frames ruler. This ruler
should be
adaptable through tempo and time signature changes to map out the pace of, for
example,
a film or aspect of an adventure/quest game whether multi-player interactive
and
irrespective of the game being streamed or remotely accessed.
25 2. A system to specify hit points, and the associated connotation that
the hit point should
have.
3. A method for specifying textural elements and their connotations at
different points in
time.
4. A list of discourses that can be chosen, which bring with them sub-cultural
properties:
30 "Cuban Montunos", "LA Urban", etc. This may also manifest itself as the
distinctive
sound of certain composers, such as "John Barry", or of films themselves such
as "The
Bourne Identity" movies.
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5. A method of setting the compositional pace, including one or more of:
(a) The number of chords across timell.11; (b) Modulations and shifts in
tonality; and (c)
Emotional connotation keywords that can be associated with different chord
scheme
properties: (i) Use of pedal notes as chords change; (ii) The use of a cycle
of fifths to move
5 through key centres; and (iii) Functional properties of a chord scheme,
such as the
beginning or end of a cue.
The last item in this list, namely the method of setting compositional pace,
gives a hint at
the structural hierarchy that the system of the invention uses to compose
generatively, as
10 explained in more detail in Section B below. It implicitly is stating
that all pace and
compositional form comes from specifying a chord scheme and its functionality
across
time. The chord scheme's requirements are the pillar on which we build the
brief, and
hence generate output.
15 II. Chord Scheme Requirements
The complete system of the present invention is based on aspects of textural
and melodic
output as harmonic sequences of chords. It therefore uses such sequences to
form sections
of the piece and set its pace.
20 Chord schemes, in the case of the generative system of the various
embodiments and
aspects, therefore have two distinctive properties: (i) their form function,
and (ii) their
emotional connotations.
From a form perspective, the system is arranged to permit annotation of
information/stored
25 data for any given section to reflect that this data:
1. Is the current section starting, ending, or in the middle of the cue?
2. Focuses on the piece's tonic, or whether there is a need to move to a
different key centre
by the end of a section?
3. Represents a section that should be modulated, i.e., is there a need for a
local tonic in
30 the next Form Atom (see below) to be different from the local tonic of
the current Form
Atom (i.e., musical building block of potentially variable length determined
by the
surrounding context and musical properties and transitional points of the Form
Atom)?
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4. Stipulates the chord density (number of chords over musical duration) for a
given
section?
This briefing of desired form functionality of a specific section brings with
it information
5 about how the chords should be written in relation to the piece's tonic,
whether there
should be a movement, via a modulation, at that point to arrive at a new key
centre in order
to move the piece on into a different subsection of the composition/film.
Functionality in the system intelligence and its interpretational capabilities
(see below),
10 when combined with the above form function, provides the ability to set
the number of
chords within a given section, thereby allowing comprehensive shaping of the
form and
direction of the generative composition.
No matter what generative technique is used to create the form and chords of a
new piece,
15 there remains a need for the user to brief the emotional connotative
elements that the
programmer/composer wants the piece to take. Providing context, when it comes
to
expressing connotation within film composition, composers try to draw on the
plethora of
discourses and codes that are within our western culture. However, when
dealing with the
subject of lexical meaning and its description of music, little consensus
exists even from
20 individuals within the same sub-culture. This is because individuals
each have different
interpretation of their cultural coding.
In terms of reference materials in the form of nuggets of usable musical
sections, the
system is functionally arranged to reference different compositional
components'
25 connotations with meta-tags that make their reproduction easy, but which
leave their
interpretation open to the user's briefing/narrative. As indicated previously,
the briefing
may be processed using NLP techniques to cross-correlate coded musical
sections with
similar or identical language expressed in the narrative that is input to the
system. NLP
techniques are well-known. In this way, a user can bring their own
interpretation to the
30 system's ability to write a generative composition independently based
only on the brief
as input, coded and correlated to sections of music having associated
connotation, without
being hindered by a programmer's perspective on what the meta-tags associated
with or
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attached to the musical segments should always apply. Clearly, emotional
connotations
take the form of generic variable keywords (or short key phrases) which have
user specific
meaning. These are initially named as Mode I... Mode n, but can be changed
depending
on the user's preferred lexical meaning. Compositional heuristics (such as
methods for
5 creating specific chord sequences, textures, melodic contours, chord-
spacing heuristics,
note generators, and rhythm generators) have these keywords attached to them.
The
generative mechanism operates to select appropriate heuristics to create these
connotations
at each instance in the timeline where they are requested by the user.
10 111. Texture Requirements
Having established how to meta-tag connotations to specific musical generative
heuristics,
the system of the various embodiments provides a mechanism that maintains
musical
texture and particularly con strains requests for insertion of adjacent
musical components
(e.g., Form Atoms) that would clash, such as asking for seven melodies at the
same time
15 or three bass lines.
It is, however, entirely possible to have three bass lines at the same time.
John Powell' s
cue "To The Roof' from The Bourne Supremacy has exactly this: we hear a
driving bass
line in the synth bass, accompanied by the double basses playing sustained
long notes in
20 the bottom of the string texture, whilst there is a percussive effect
every bar on the final
three semiquavers of the bar and the first beat of a new bar whereby a bass
player drags
the fingers across muted strings. In isolation alone, any single one of these
bass lines would
work as a viable bass part, but here the texture calls on all three to make a
final effect that
neither contradicts the harmony nor clashes in sonic space.
The system intelligence firstly generates a set of heuristics and applies a
technical
approach to the identification and use of a set of musical components [for
instruments],
such as stings (e.g., a viola), offset horns, a harp arpeggio, pizzicato-bass.
Identification
can be achieved using Music Retrieval technologies to create a MIDI
representation of the
30 original score, or simply the original score itself stored in MIDI
format. There can be one
or more musical components that then contribute to define a set of textural
classifiers, such
as [but not limited to] melody, counter-melody, harmony, bass, pitch rhythm,
non-pitch
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rhythm and drumfbeat and other musical characteristics as will be appreciated
by the
skilled addressee. In this respect, reference is made to FIG. 3.
Each of these musical instrument components is further classified, according
to an aspect
5 of the invention associated with final assembly of a composition, to have
one of two
attributes, namely the component may either be a "feature" or an
"accompaniment-. A
[musical] feature can be considered to give temporal sense, awareness and
gravitas, i.e.,
contributing significance, to a musical section. A musical feature is thus a
salient sonic
component in the texture space of the musical section, i.e., it itself
contains information
10 about tension and release and which information would be destroyed in
the event that a
second feature co-existed in a common textural classifier even if that second
feature is
played by an entirely different instrument. An accompaniment is complementary
musical
fluff that is inessential but provides richness and tonality to a textural
classifier.
15 There is also one or more semantic descriptors associated with each
musical section, such
as a Form Atom. The descriptors will generally be derived by a musicologist
who has
critiqued a musical section of an existing piece of music and, indeed, within
an overall
corpus of musical artefacts in a library.
20 Within each musical section, a musical component or collection of
musical components
(including multiple musical components in a single textural classifier, such
as harmony)
can be grouped together and correlated/tagged with a semantic descriptor, such
as
"raunchy", "warm", "gritty/sleezy", "floaty", "pounding", "victorious",
"reminiscent",
"calm", "both smooth and reminiscent at the same time", as well as with
broader semantic
25 descriptors such as "loud", "sexy", "exciting" and more other
descriptive connotations,
including "light Spring day" and "shimmery woodwind". There are, of course,
myriad
semantic descriptions. Different musical sections may contain the same
semantic
descriptor or a similar sematic descriptor that has some common descriptive
connotations,
but then again the same semantic descriptor in different musical section may
have different
30 instrumental components and/or differing numbers of instrumental
components. The
semantic descriptors are therefore linked or associated, such as within
metadata, to the
respective musical section. Semantic descriptors can therefore be associated
with just a
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single instrument component, or otherwise assembled from a subset of
instrument
components or groups of subsets (either mutually exclusive or overlapping) of
instrument
components or from groups of textural classifiers. The granularity is user-
selectable.
5 Whilst it could be possible for the system to store the texture
classifiers for each section
with each section or provide a direct record, it is preferred that the system
intelligence
applies a set of heuristics, e.g., computation parameters, to generate the
respective
attributes (having regard to historical records of what combination of
instrument
components are linked or closely associated with particular descriptors).
With automated generative composition, the inventor has identified that
instrument
components within a particular textural classifier (e.g., melody) cannot
contain more than
one instrument component that is categorised as a feature. If this were the
case, then
features in the same textural classifier would be mutually destructive.
However, this is not
15 the case for musical components that are accompaniments. Consequently, a
single textual
classifier may contain zero or a multiplicity of instrument components acting
as
accompaniments but no more than one (if any) instrument components fulfilling
the role
of a feature. Conversely, within a descriptor, multiple features may exist so
long as the
multiple features are distributed across the textural classifiers (and not
within a single
20 textural classifier.
In FIG. 3, for example, the descriptor "pounding" in musical section 4 of
"Piece 1" is
comprised from four (4) textural classifiers, namely bass, pitched rhythm, non-
pitched
rhythm and drums. It just so happens that "pounding" is actually a subset of a
more general
25 descriptor "victorious" which further includes a melody as well as a
harmony. In this
example, the semantic descriptor "pounding" actually has eight individual
instrument
components, with one being a feature component "F" in the bass textual
classifier, two
individual instrument components being accompaniments in the textural
classifier pitched-
rhythm, three individual instrument components being in the non-pitched rhythm
of which
30 one is a feature and two are accompaniments, and two individual
instrument components
being in the drums (textural classifier) on which one is a feature (such as a
floor Tom) and
one is an accompaniment (e.g., a snare). For the sake of simplicity, the
number of
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instrument components is represented in each textural classifier as either a
blank/nothing
(in absent), or the letter "F.- for a feature or one or more letter "As" to
represent the number
of instrument accompaniments. Looking now at "Piece 2-, one can see that there
is no
descriptor for its section 1, one descriptor in each of sections 2,4, 5 and 6
where the counter
5 melody in section 4 has no assigned descriptor and thus no contribution
of the connotation
"warm", and Piece 2 has two different but independent features for melody and
harmony
that both relate to the semantic descriptor "calm".
There is one further piece of information that can be derived, by the
processing system of
10 the invention, from the instruments components, namely musical
intensity. Based on a
comparison between sections, a count of the number of instances of feature and
accompaniments associated with a descriptor and/or the entire musical section
is
interpreted to provide an indication of intensity in that section. In short,
the higher the
count of components then the more intense and rich the section.
The system intelligence functions to look for commonality in descriptors
between musical
sections and, importantly, the contributory nature of the components
associated with each
of those descriptors to identify usable instrument components (or entire
descriptors) that
can complement one another across different musical sections in any future
generative
20 composition.
As intermediate summary, there may therefore be one or a multiplicity of
instrument
components and/or textural classifiers that can contribute to an overall
texture for any
musical section. Indeed, within a musical section, there may actually be zero,
one or more
25 sets of textural classifiers, with these having musical components that
are treated by the
system intelligence to be mutually exclusive or complementary and which sets
may be
isolated, partially overlaid or layered so that one textual classifier is
actually a subset of
another textural classifier.
30 Returning again to FIG. 3, looking at musical section 3, the system
intelligence thus
identifies the bass accompaniment to be usable for expressing an emotional
connotation
of one or a combination of "gritty", "sleezy" and/or "floaty". The linkages
(shown by
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dotted lines in FIG. 3) just show how, potentially, the system intelligence
can insert
musical texture derived from analysis of a musical corpus into a new
composition that
follows a briefing note pounding followed by warm and smooth followed by
victorious
and reminiscent, and with a time-varying intensity that drops between the
start of musical
5 section 1 and the end of musical section 2, then levels off during
musical section 3 before
sharply rising and then remaining constant in musical section 4 before again
sharply rising
at the start of musical section 5 before tailing off to zero intensity.
It should be noted that the musical sections are not representative of
discrete time scales
and there may, in fact, be a multiplicity of Form Atoms present within each
musical
section.
Turning to FIG. 4, there is shown a succession of musical sections 40-48 for a
first piece
of music 49 and a succession of musical sections 50-58 for a first piece of
music 59, with
15 the first and second pieces of music forming a [limited] "corpus" of
artefacts. For the sake
of explanation only, the textural classifiers 60 have been restricted to four,
namely melody,
harmony, bass and drums and are presented from the perspective of a simplified
macro
perspective (rather than with textural descriptors with sub-classifications
and more
complex inter-relationships). In FIG. 4, contributory derivative musical
components are
20 drawn or assembled into the generative composition 70 from similar
descriptors analysed
by the system and parsed from individual musical section in the corpus; the
relationship is
shown by the lines with arrow heads.
A brief has been input into the processing system of preferred embodiments,
such as
25 through touchscreen or other computer interface. The brief stipulates an
intensity pattern
62-66 for musical sections 1, 3 and 4, but no narrative for musical section 2
that must thus
be filled from all perspectives of the invention as described in totality
herein, including
texture continuity.
30 Dealing solely with the latter issue of texture continuity at this
point, the system
intelligence of the preferred embodiments firstly looks to assemble a musical
section that
is both "rough and warm". There is no corresponding overall texture having the
descriptor,
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so the processing system assembles the components of "rough" from Piece 1 and
"warm"
from Piece 2. These are entirely complementary since they have no feature in a
common.
The textual classifier and the overall intensity is high so there is no
particular need for the
system to reduce the number of accompaniments. This therefore generates:
Rough and Warm
Rough Warm Gen.Textr
Mel. AAA FA AAAFA
Harm. F A FA
Bass FA FA
Drums FA FA
Ignoring the intermediate transition in the succeeding musical section, the
third musical
section is narrated as being "exciting". There is, in this respect, a directly
corresponding
texture that can be lifted from musical section 3 of Piece 2. In musical
section 4 of the
generative work 70, there is also a corresponding pre-analysed "loud" texture
at musical
section 3 of Piece 1. However, the system recognises that adaption is required
both to fill
the unspecified space 80 between musical sections 1 and 3 and to morph the
texture in the
generative work from reflecting "exciting" to reflecting "loud".
Musical section 5 has no stipulated texture and so either represents a
termination point for
the generative composition 70 or a chance to repeat musical section 4 in
totality or with a
variation in, for example, an accompaniment. These are design parameters
executable by
the system intelligence based on heuristical instruction.
Dealing with the fill, there are four alternative processes by which fill can
be accomplished
by one or an appropriate and logical combination of:
1. Morphing from the components in a start texture to the required components
of the
texture in the destination section. This can be a simple linear interpolation
exercise;
2. Fulfil a requested intensity brief stipulated by the user;
3. Apply a Markov approach by analysing corpus of historically closest
compositions to
identify the likely or permissible transitions between textural classifiers;
and
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4. Work on the basis of selected intensity in terms of specific desired
textural classifier,
such as harmony.
In terms of user input of the preferences for unspecified musical sections, a
preferred
5 embodiment includes a GUI that includes dial-down values for one or more
user-selectable
textural classifiers. The user/programmer is thus able to set relative
intensity levels
between the multiplicity of textural classifiers, with the system intelligence
configured to
apply comparative analysis to identify suitable candidates for direct in-fill
or adaptation.
10 Looking again at the generative composition 70 and its texture needs,
since the musical
section 3 must include the prior analysed textual classification for
"exciting" in Piece 2,
there is no choice other than to maintain this exact textural structure
because the textural
classification fits. The first issue relates to the unspecified intermediate
hope at musical
section 2. It is generally desirable to maintain features from a previous
section, and it is
15 also relevant to assess the level of intensity in the texture presented
for "rough and warm";
this looks relatively high given the nature of the distribution of the
instrument components
across all textural classification and also because the resulting texture of
rough and warm
includes three features. Consequently, heuristics would generally dictate that
a variation
would be required to begin the transformation towards the texture for
"exciting" but it
20 would be beneficial from a continuity perspective to maintain a solidly
associated texture
from "warm" of Piece 2, but to reduce the accompaniment associated with purely
the rough
texture. It is noticeable that significant musical components from the "rough"
descriptor
remain, although now diminished. To move in an alternative direction, the
system
intelligence would ¨ or at least could ¨ consider retaining either
contribution from bass
25 and drums from the rough texture, with this including continuation of
either or both of the
accompaniment or feature components from the rough texture. However, in view
of the
brief drop in intensity, a fuller carry-over of the accompaniments from
musical section 1
is not preferable. However, the feed-through of the feature from the drums
through each
of the successive musical sections yields a degree of textural continuity. In
short, the
30 system intelligence looks to maintain as many contributing instrumental
components
whilst having regard to the intensity changes and avoiding conflict between
features that
would class in the same textural classification.
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In summary, again, the processing system and logic treats features within a
musical section
with a simple single rule. Any instrument component that realises a feature
within a single
textural classifier will directly conflict with another feature in the same
textural classifier
5 and so that musical situation must be avoided to preserve overall
textural space. However,
a textural classifier may have as many accompaniments as it wishes. This
provides the
ability to have multiple textural elements, whilst guaranteeing that any
specific one that
provides a salient feature to the texture will not be corrupted or interfered
with by others.
In the aforementioned example by John Powell, the synth bass would be
classified as the
10 feature, and the percussive electric muted bass and double basses as the
accompaniment.
These two auxiliary items do not conflict with the main bass part, and could
feasibly be
added to any such texture with a featured bass line; the featured bass, on the
other hand,
would not fit into any other texture that has a featured bass part.
15 An explanation of textural classifiers now follows:
Melody
The paradox of which is hierarchically more important, melody or harmony, has
been a
subject of debate for centuries. The system intelligence of the preferred
embodiment takes
20 a stance that form is generated through the flow and pace of chords;
however, it is possible
to change the connotation of a chord, or string of chords, through melodic
passing notes,
and harmonic substitutions ¨ both of which may be meta-tagged as textural
components.
Mostly, melodies are typically all classed as features, although some sparse
melodic
25 components can be considered accompaniment melodies: that is, they do
not counter a
given melody, and are not consuming the textural space that a featured melody
would. In
the event of a bass melody, the category of the heuristics would be both
tagged as melody
and bass, and as a feature. This way, there will not be a conflict of texture
in the bass
region, but certain accompaniment bass components could still be inserted into
the texture.
A textural component classified as a melody that is also tagged as a feature
may well bring
certain alterations to the scale or mode of the given texture. In the case of
the exemplary
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The Bourne Supremacy, there is a main melodic feature throughout the film that
quite often
prevalent in the celli, and revolves around a falling melodic minor scale with
a flattened
2nd. This melodic component would not sit well with any other melodic
component that
is using a natural 2nd, therefore it would alter the given mode for the
texture and any
5 accompanying melody. No other melodic feature would be able to override
this because
only one featured melodic component can be present at any given time.
Counter-Melody
This category of textural element may be linked to a melody, or simply be a
melodic
element that sits around the temporal space where a melody might sit. This
applies
typically to guitar riffs, melodic bridging features in orchestral textures,
and melodic
components that emphasis mode and tonality, but do not present a strong
melodic pattern.
Typically, a counter-melody can play with many others, so they are marked as
15 accompaniment. However, if a specific counter-melody is designed to work
in conjunction
with a melody, then this can be marked as a feature to make sure no other such
textural
elements that are interacting with a melody get in the way.
Harmony
20 A component that is tagged as a feature for harmony states that it does
something with a
chord (as known in jazz), or a chord that features multiple extensions, like a
#11 chord. As
with melodic components, components marked as harmonic features are marked as
such
because they would be deemed to interfere with each other. The issue of how to
cope with
potentially clashing requests for a melody component that wishes to alter the
given scale,
25 and harmonic components that change notes within the given chord is
discussed later.
B ass
A bass feature occupies the textural space in the bass range, with this
typical of an electric
or synth bass line. Bass components that are not features but which are marked
as
30 accompaniment will simply occupy the bass note of the chord.
Pitched Rhythm
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This is any percussive component that is pitched, such as a trip hop loop that
has tuned
components that could clash with other such tuned components. It also
incorporates
orchestral tuned percussion.
5 Non-Pitched Rhythm
This textural component is reserved for instruments such as shakers, timbale,
HiHat
patterns, etc. Examples of a feature in this space would be the type of power-
drum patterns
one hears in many modern film scores, such as at 1:17 in Rogue One (Edwards,
2016) and
throughout the cue Funeral Pyre (Crowley & Greengrass, 2004), or any other
type of
10 prominent non-pitched feature. These rolling dynamic power-drum motifs
would suffer
texturally if they were interrupted by other such non-tuned features.
Drums
This covers all rhythmic patterns that come from drum kits. If marked as
features, these
15 are drum patterns that lie out a specific groove to which other
accompanying patterns are
subservient. Non-featured drum patterns are auxiliary components such as
military drum
patterns, patterns that in themselves have connotative properties, but which
do not interfere
with the main thrust of the groove.
20 With respect to tempo and time signature changes, the approach advocated by
the
invention renders the timeline as invariant. Film is mapped out across time in
seconds and
frames. However, embodiments within relevant aspects of the invention are
arranged to
alter the tempo to create more or fewer bars on the musical ruler. Unlike
other sequencer
software (Cubase, Logic Pro, Pro Tools) in which tempo does not affect the
time ruler, the
25 functionality of the system intelligence evaluates, having regard to the
supplied narrative,
how much musical material will fit into a given requirement and then generates
a best fit
solution for the generative composition. The timeline can have multiple tempo
changes to
allow for different paces throughout a cue, and to enable the timing of
arrival at hit points.
30 SECTION B
I. Generative Functionality of the Heresy Generative Composition System
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To this point there has been a generally philosophical discussion surrounding
the ideas
that underpin the generative compositional system of the present invention.
To this point, there has been, in fact, a general explanation of the preferred
system's
5 hierarchical workflow. We now examine this hierarchy in detail, as well
as the tasks that
are performed at each level to expose the generative method of aspects of the
invention.
An initial outline is now provided on the overarching principle of how the
Heresy system
of the aspects of the present invention is embodied and functions. This
outline explains
the hierarchy for how various compositional tasks ¨ from writing chords,
through to
writing textures ¨ are handled. Secondly, the heuristic mechanism and
organisational
structure for processing logical tasks is explained. Finally, detail is
provided about the
preferred properties, functions and interactions between the components and
also the
preferred steps involved with generating a composition.
II. Heresy System Overview
FIG. 5 gives the outline for the different hierarchical layers 100 within the
Heresy system
embodying a multiplicity of complementary but independent inventive aspects.
These
layers flow from top to bottom.
Firstly, briefing elements 102-106 are requested from the user. Secondly,
these elements
102-106 are interlaced with generated elements 108 to create a complete set of
requirements that fill the timeline of the piece of music that is about to be
generated. From
here, the heuristics of the system, as interpreted and applied by system
intelligence, will
25 generate the chord schemes 110 on which the textures will operate and be
strung together.
This is achieved through a mechanism that makes use of "Form Atoms". Form
Atoms are
a meta-chord scheme and thus the principles by and starting point from which a
coherent
chord scheme is written/generated and, ultimately, a composition is created.
Each is a
30 snippet of music (i.e., a musical section) of varying duration that has
a length dependent
upon the nature of the analysed musical expression and, as such, each
represents a building
block within the generative system of the preferred embodiments. Each Form
Atom is
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derived from interpretational analysis ¨ either manual or computer-based using
WHAT ¨
from a library of existing independent compositions, and is stored as an
indexed
emotionally-described record that is accessible for future compositional use.
Form Atoms
are thus meta-chord syntactical descriptors. Each one has a small stored
snippet of chords
5 from a previously analysed work, and a generative set of heuristics that,
when run, can
produce variations of snippets with similar connotative properties as the
stored one.
The Form Atoms, such as reference numerals 120-124, include a generative set
of
heuristics that, when run, produce variations of the stored chord snippet
(extracted from
10 the earlier analysed work) to create chord schemes 128 that have a well
organised form,
narrative direction and purpose. The Form Atoms are chosen and strung together
through
a bespoke syntax mechanism. These sequential chord schemes are then used to
give a
texture generator 130 the harmonic palette on which to orchestrate music. The
final output
of the Heresy generative composition system is music 132 created from the
heuristics
15 within the texture generator.
Each Form Atom has a specific syntax internally and to each other but is self-
contained in
its nature, and each Form Atom embodies or possesses the following signal
properties,
generative characteristic or attributes:
20 1. A specific set of chords in a local tonic expressed as interval
distance relative to the
local tonic having both pitch and tonality and thus a key centre for the Form
Atom;
2. Predicates that are formed from:
(a) A form function definition based on logical operative selection between
musical
phrasing that is one of a question, an answer or a statement and, optionally,
whether the
25 Form Atom operates as a modulator that permits a change from the current
local tonic to
a new local tonic in the next Form Atom, a modulated Form Atom which indicates
the
preceding Form Atom has a different tonic, both or neither a modulating or
modulated
Form Atom (meaning that the local tonic stays the same relative to preceding
and
following Form Atoms) and, further optionally, whether the Form Atom appears
at the
30 beginning, end or neither the beginning nor the end of a particular
piece of music; and
(b) A progression descriptor establishing the nature of cadential or
sequential progression
between adjacent Form Atoms, i.e., the passage of the Form Atom scheme across
time;
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3. A generative set of heuristics/rules that support generation of a set of
chords in a chord
scheme or many different sets of chords in the same or different tonics that
achieve the
same form functions and which thus have the similar associated
emotional/musical
connotations, and heuristics that space out temporally any number of generated
chords for
5 any given length of musical time to fill the briefing space;
4. A tagged descriptive association with an emotional connotation that
articulates one or
more realistically palpable emotional response(s) experienced by a listener
when the Form
Atom is used in a chord scheme in accordance with heuristics described herein,
with such
a descriptive association providing relationships to music elements, e.g.,
chords, chord
10 timings and chord distances to their tonic. These descriptive
associations or "placeholders"
can be taken from a library so as to present consistency with terminology used
in any
narrative brief, although this is not a requirement provided association
between different
descriptors used in different parts of the system of the invention can be
resolved as
equivalent, similar or neither in semantic space; and
15 5. A smallest musical phrase that makes musical sense and which has a
describable
relationship with neighbouring Form Atoms; and optionally
6. Metatags, such as composer name, instrumentation and/or genre as examples
amongst
other more specific detail, including (for example) the name of a suite of
specific preludes
or a series of films. This allows for easier referencing to find styles in a
generative phase
20 of composition when briefing considerations are identified. This list
allows for further
Form Atom refinement from the briefing mechanism.
7. A Form Atom cannot contain a tonic in the middle of itself.
Form Atoms provide harmonic structure and the ability to generate harmonic
structures
25 that obey compositionally good form, and they store a list of textural
components in a
classified state which define texture and which permit maintenance of textural
continuity
in the generative composition.
The system, as a whole, therefore functions to generate and store lists of
Form Atoms that
30 are linked to lists of preceding or following Form Atoms through Markov-
chain
associations that identify, from a corpus of artefacts, prior transitions that
have worked
musically with good form.
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Returning to the issue predicates and what is meant by the terms question,
answer and
statement.
5 A question is a chord scheme that suggests tension requiring mental
settlement as indicated
by notes that have appeared within a harmony or melody and which are
questionably
present because they are outside of the key centre of the local tonic of the
Form Atom.
Multiple successive questions can be asked musically.
10 An answer is the resolution of the question which operates to resolve
the presence of the
questionable tones (i.e., pitch) or notes (i.e., pitch with duration) from the
mind's
perspective by reinforcing the key centre of either the local tonic or any new
tonic of the
answering Form Atom. An example of this are the opening two phrases of "The
Love
Theme" from Superman by John Williams.
A statement is entirely self-contained from a musical question and doesn't
imply or induce
any meaningful musical tension that requires release through resolution. A
statement is
neither a question nor an answer.
20 Aspects of the present invention that relates to Form Atoms thus have
appreciated that all
chords within a chord scheme relate to a local tonic, e.g., C or Cm for the
major and minor
scales of C. Moreover, the sequence of chords is less valuable than an
understanding of
relationships between chords. If you know the relationship between, say Dm and
G with a
local tonic of C, in terms of MIDI separations (i.e., chord IIminor => chord V
for Dm and
25 G) within the degree of scale, then this sequence of chords can be
repeated in any different
key centre (e.g., chord IVminor => I in the local tonic of G).
The predicates, as indicated above, also must include (as a minimum besides an
indication
of question, answer or statement treated logically by an exclusive OR
function, XOR)
30 either one of four cadential progressions (where the
sequence/displacement of chords is
not mathematically expressible) or two sequence progressions.
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Cadential progressions take one of four alternative forms and express ways to
change the
tonic. Cadential progress thus can be logically X0Red during processing to
identify one
of:
1. a tonic that appears at the beginning (Cb) of the Form Atom;
5 2. a tonic that appears at the end (Cõ) of the Form Atom;
3. a tonic that appears at both the beginning and the end (CO of the Form
Atom; or
4. the absence null appearance (Cõ) of the tonic in the Form Atom.
There the two alternative sequence progressions permit termination, with these
coining in
10 the X0Red forms of
1. an interval based sequential progression, Si. where the chord is followed
by a
mathematically expressible distanced relationship with another chord; and
2. a tonality-based sequential progression, Si, which relates to the scale of
the local tonic
and a sequence of chords which have mathematically expressible relationships
that can be
15 repeated forever and which is based on tonality of the local tonic.
Cadential progressions therefore string together as a series of chords with
relation to the
key centre of the Form Atom's tonic. The options for which chords can be
chosen from
each other is extracted from all stored analysis of previous pieces. This is
essentially a
20 range of choices found using a Markov chain, but with relation to a
given key centre. A
simple example of this might be that in the key of C we observe that Dmin or F
may come
before G7, therefore, we can choose either of them as preceding chords to G7
if the tonic
is C. We can then perform a similar action to precede this chosen chord of
Dmin or F.
25 Sequence progressions can be based on the tonality of the Form Atom's
tonic, such as the
second section of Bach's C Minor Prelude, bars 5 to 14 (see Section D), or may
ignore the
tonic altogether and simply proceed in a given interval sequence such as a
cycle of 5ths or
a rising sequence of major triads spaced in minor thirds.
30 In the case of a cadential pattern, if the tonic is present within the
Form Atom, it could be
said to be a pivot point from which we can arrive at and depart from one Form
Atom to
the next. Although a Form Atom cannot contain a tonic in the middle of itself,
this does
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not preclude the well-known culturally accepted principle of a phrase' s chord
scheme
culminating in a second inversion tonic ¨ to dominant ¨ to tonic progression.
Rather, Form
Atoms therefore have their tonic appearing in one of the four ways highlighted
above in
the cadential progressions list.
A consideration for cadential sequences is the ability to change key. In the
event of a key
change, if the new tonic features at the end of the chain of chords, then we
simply state
that it is not considered a tonic until the next atom. This means that
modulations are created
by sequences of new tonics. Unlike Form Atoms, the relationships of these
tonics are not
relative to an external datum; instead, they are categorised through emotional
tags, and
provide a component of the emotion-briefing mechanism. New tonics may appear
at any
point in a piece of music; within this mechanism, though, they will have at
least one Form
Atom sequence before they can change. It is possible that this sequence could
be one chord
only, that of the local tonic, in which case care must be taken in the
briefing mechanism
to make sure that such changes are not too frequent or else a series of random
chords may
be inappropriately produced.
In the case of sequence progressions, there are two possibilities: i) the
chord scheme is
related to the tonic, or ii) it is a regular sequence of chords which ignore
it. In both
circumstances, the sequence needs to be broken at some point. This is
accomplished by an
escape chord. Escape chords are related to the chords that immediately precede
them
irrespective of the local tonic. They are used to break the sequence and
establish a bridge
to the next Form Atom. Consequently, escape chords typically produce a change
in key
centre.
Once Form Atoms have been analysed (and thus derived) from a series of pieces
of music
and labelled with progression descriptors, Form Atoms can be strung together
like jigsaw
pieces. Any Form Atom that has the same progression descriptor as another, can
be
interchangeably substituted. We can therefore generate a series of Form Atom
inter-
relationships using the principle of Markov chains: the relationship between
any Form
Atom and the ones that precede or follow it is established by looking at their
progression
descriptors as well as the predicates. This is reflected in FIG. 6 which shows
inter-Form
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Atom relationships and a resulting Markov chain 602 having a permissible chord
scheme
construction arising from identification of form-viable concatenated Form
Atoms capable
of supporting the chord transition for identified emotional connotation. For
example, in a
limited corpus that generated the chains in FIG. 6, chord V to either chord I
or chord IV is
5 permissible but transition to chord IIrn is not because (a) there is no
established path in the
corpus, and (b) there is [implicitly] no common descriptor between the
emotional
connotations of chords V and IIm. In the case of FIG. 6, there is in fact no
established/recognised relationships to chord IIm (when appreciating that FIG.
6 is a
highly simplified view). The Form Atom transition from chord IV as a
destination is shown
10 in FIG. 6 to be from chords 11Im and V and its onward permissible
transitions to either
chord I or chord V. All these translations have been extracted by critical
analysis of the
historical corpus of music by automated use of music information retrieval
(MIR)
techniques or otherwise manually coding by a musicologist.
15 Consequently, if a Form Atom x has an example within the corpus of being
followed by a
Form Atom y, then any Form Atom with the same descriptor as y can follow x.
This can
work in any direction temporally, so we can also precede Form Atoms using the
same
technique. Finally, the weightings of any Form Atom being used are based on
how many
occurrences we find in the corpus; this provides a probability selecting and
using a specific
20 Form Atom within a new composition.
Modulation is necessary to provide a contrast between two key centres and
provide
structure across time. This allows for the application of heuristics that
align with the brief
to move the generative composition along its tonal journey. A modulator Moir
that is present
25 within a Form Atom confirms that there will be a definite transition to
a new key centre at
the end of the Form Atom. If the Form Atom is a modulated, Med, Form Atom,
then
historical analysis has identified that, at the instantiation of the modulate
Form Atom, there
has been a change in key. A modulated Form Atom therefore emphasises the
emotionally
significant perceptible changes in surrounding and context, such as when there
is a change
30 in pace or when a narrative of a film scene must change. A modulator Mor
and modulated
Med Form Atom are therefore exclusive, i.e., an ORed logical function.
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Predicate
Progression Form Function
Descriptor
Required Required Options Options
XOR XOR OR XOR
Cb Question Mor Start
C. Answer Med End
Ci Statement Mor Med Neither
C. Neither
St
Si
It is possible for any given Form Atom to have multiple form tags at the same
time, except
for those of question, answer and statement, whereby the atom can only have
one of these
at once.
There are, consequently and potentially, 6x3x4x3=216 separate lists for
predicate
combinations. The number of lists may be reduced by combining lists or
otherwise
ignoring one or more of the optional form function predicates. Each predicate
list will be
populated with Form Atoms that, from above, include contextual descriptors
linked to their
respective content that define a real-life emotional experience, feeling or
emotional
connotation that can be tied to both a briefing narrative input into the
system intelligence
(e.g., through a user interface) and, further, to semantic descriptor(s)
linked with each
texture.
FIG. 7 provides an overview of the mechanism for generative composition
achieved by
the various aspects and combinations of embodiments, with the extent and depth
of any
combination merely varying the level of sophistication, implementation
complexity and/or
attainment of the generative signal that is eventually output. More
particularly, FIG. 7 is a
schematic overview of how heuristics are logically organised and processed.
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Independent of the tasks that the heuristics perform in accordance with the
concepts of the
present invention, FIG. 7 shows the affordances necessary for a heuristic
mechanism that
organises them; let us consider these in turn:
1. There is an ordered method for how the heuristics are processed. This is
shown in FIG.
5 7 by following the numbers attached to the task and then succeeding sub-
tasks.
2. There is an overall percentage chance of the task being performed. This is
represented
by a percentage at the front of the task box.
3. There is a branching mechanism for subtasks. The percentage chance of the
sub-tasks
being processed is used as a weighting mechanism for the probability of taking
each
10 branch.
4. There is a logical operator on the branching mechanism that allows for all
or only one
sub task to be processed. Depending on the logical operator (AND or XOR), we
process
either one or all of the sub tasks. In FIG. 7, task 7 is dependent on the XOR
branching
from task 6, and therefore task 7 is performed by either one of the sub-tasks
attached to
15 task 6. One of these sub-subtasks has a 25% chance of being processed,
the other has a
75% chance of being processed.
5. There is the ability for a task to be null, offering a branch only for
further subtasks; an
example of this can be seen in process 6 within FIG. 7.
20 The generative compositional system of the present invention is,
predominantly, a
software implemented system that is based on a bespoke expert system running
code. The
system, as will be understood, therefore includes one or more processors. This
system
intelligence will call on code stored in memory, and will retrieve, manipulate
and return
data to and from storage, such as a database or other memory storage. The
database may
25 be local to the expert system, but equally it may be remotely located
and accessible via a
wide area or local area network and appropriate network connection. Equally,
the user
interface may be a computer or other client device that provides an ability to
upload,
download and/or stream data and media content to any logically appropriate
part of the
system for reason of storage (in one or more databases), manipulation and/or
output
30 (whether streamed or downloaded or imprinted) as a playable media
product, including
but not limited to a bespoke user-centric and/or user-selected soundtrack for
an interactive
game. In short, the underlying system architecture is well-known, although the
approach
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to processing and generative composition efficiency yields manipulated audio
signal data
(whether aligned with a film brief of for its own sake and purpose) that has
improved
characteristics and qualities. The system provides a significant advance in
the field of
audio signal processing in the context of, particularly, audio composition.
Heresy's compositional output is derived from this briefing mechanism from
which two
requirements for the generative mechanism can be extracted (by, for example,
NLP or
more structured responses to specific question posed in relation to a
selectively definable
timeline). The two requirements are:
1. that the mechanism can be briefed by a non-musically skilled individual;
2. that the brief can contain information on the connotations that the
commissioner desires
at any given point in the composition.
To fulfil these requirements, the system and in particular the system
intelligence needs to
be able to generate musical output without any skilled musical input, whilst
responding to
input concerning emotional connotations. This is achieved through a
hierarchical
generative mechanism 100, in which chord schemes, textures and melodies are
created
having regard to the briefing requirements. This mechanism is represented in
FIG. 8 which
shows the three major method steps (and internal processing, including data
management
and data processing) to create a composition from a given brief. The steps
are:
1. Generate 102 Form Atoms,
2. Generate 104 Chord Schemes ¨ this component creates strings of chords that
are related
and fulfil briefing requirements. This is because they are made from related
Form Atoms'
generative heuristics.
3. Generate 106 Textures ¨ this component generates musical material for
instruments
based on the generated chord schemes and briefing requirements.
The system performs analysis on the musical corpus (or at least a portion of
it) stored in a
database 110. This results in historically stored music being broken down into
Form Atoms
and each classified in terms of both the aforedescribed predicates (or a
subset thereof) and
emotional descriptors that linked to each Form Atom to reflect associated
emotional
connotation of that Form Atom. The Form Atoms can have ancillary metadata,
such as
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genre information and composer (to name two exemplary categories). The
analysis and
classification/categorization may be manual and conducted by a musicologist
making
informed parsing of the music to identify, e.g., beginning and end points of
each Form
Atom as well as other properties and characteristics of the Form Atom (as
discussed herein
5 in terms of predicates), or otherwise the classification and assessment
may be entirely or
partially based on use of a trained AI/neural network that can import content
meaning to
extracted file properties representative of the predicates. Such Al systems
are described,
for example, in US 2020-0320398 "Method of Training a Neural Network to
Reflect
Emotional Perception and Related System and Method for Categorizing and
Finding
10 Associated Content" and other such patents in related Al technology.
The flow process that is within FIG. 8 indicates that the user brief 114 may
also influence
the pieces file. To this extent, the pieces file could simply be the entire
database, although
it would be a subset that reflects requirements for a particular genre of
work, e.g., jazz, or
15 a particular composer, e.g., Bach, and artist, e.g., Pink Floyd, to be
used in the generation
of the pieces file. This simply reduces the complexity in generating following
and
preceding chord trees or Form Atom trees.
Using a Markov chain approach, connections that extend both forwards and
backwards
20 from each Form Atom, drawn into the pieces file, are established and mapped
112.
Essentially, this tree identifies existing permissible paths/transitions
between Form Atoms
in earlier analysed musical pieces. This process is then refined in the
generation of specific
Form Atoms that align with the brief, wherein the emotional connotations
associated with
each Form Atom are resolved by the system intelligence against briefing
requirements
25 thereby to select relevant Form Atoms that are both musically
emotionally relevant and
germane in terms of underlying musical properties. The formation of trees and,
indeed, the
alignment of emotional connotation between the reference in the Form Atom and
the
stipulated user brief are generally reflected in FIG. 6. In short, viable
inter-relationship
transitions are identified in the trees and these stored for use in the
subsequent composition
30 process. Again, the Markov chains are associated with the requirements
of the brief, e.g.,
a need for raunchy heavy rock for a scene in a bar that has a stipulated start
and stop time,
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so that relationships between relevant Form Atoms align with the brief and
provide
compositional options for transitions along the composition path.
Based on a brief 114 that is input into the system, the system intelligence
selects 116 an
5 opening Form Atom 118 from Form Atoms 117 in the pieces file (or more
extensive
database), which Form Atom corresponds to the system-interpreted requirements
of the
brief. Referring again to the brief, the creation of a Form Atom string is
actioned 118,
which string may include blank periods that must be auto-filled to provide an
end-to-end
composition that does not contain breaks in audio. The process then moves onto
chord
10 scheme generation 104.
In terms of a briefing tool that permits workable input, this general
requirement for such a
tool is its ability to map pace across time, i.e., a musical time ruler.
Preferably, it should
be adaptable through tempo and time signature changes and sufficiently
receptive to allow
15 identification of:
1. Hit points;
2. Sustained features;
3. Discourse choice;
4. Chord scheme requirements, including
20 (a) Compositional pace: chords over time, modulations, tonality shifts,
(b) Emotional connotations (bass pedal, cycle of 5ths, mood tags), and
(c) Form function; and
5. Texture requirements.
25 Brief filling is a constraint satisfaction mechanism and may be achieved
by a generic
algorithm or on a more laboursome basis involving consideration and
recommendation.
The process of insertion of fill arises because the briefing mechanism allows
for a Form
Atom to be specified at any point on the timeline through the use of a Form
Atoms
requirements list. This list will more than likely contain a series of Form
Atoms that do
30 not necessarily tessellate, leaving gaps in between them. The constraint-
satisfaction
mechanism operates to fill in the gaps in the list, which is preferably
exercised through
heuristics. This gives a localised treatment of the most popular parameters
requested for
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Form Atoms. The system then fills in the gaps with atoms that have these
parameters. The
requirement for this system-centric correction or interpretation is therefore
dependent on
the extensivity of the supplied brief. In-filling of gaps will typically
consider and account
or compensate for:
5 1. the mean length and average number of chords per bar within each tempo
change in the
cue.
2. gaps with request parameters that have values.
3. truncation of the final atom and suitable adjustment parameters to achieve
fit.
4. averaged chord density per bar within a given tempo section and
particularly such that
10 chord density is set in each atom to reflect a number closest to the
average number of
chords per bar within the given tempo section.
Briefed sections will typically have properties requested by the user in the
form of
emotional connotations, form functions, and meta-tags. To reline the list of
options, we
15 prioritise in the order of form functions, then emotional functions,
then meta-tags. Firstly,
if the list contains any item or items with the required form function, we
remove all other
items in the list that do not have the appropriate form function tags. This is
then repeated
for emotional connotations, and finally for meta-data. We then chose an option
that
satisfies the greatest number of tags in general.
Although still at a level of abstraction, a chain of chord schemes contains
all the
information necessary for a harmonic map of the composition, including
position timing
between chords. From this information, it is possible to create the relevant
notes at any
given point in time, and apply them to textural elements such as harmonic and
melodic
25 parts.
From the brief 114, the tonic is selected 120, with this providing a
primary/priority tone
and available chords (with tonic pitch and tonality 1220 expressed in terms of
note
displacements between I and VII (and which includes minor offsets from the
full notes of
30 the degree of the scale). Having regard to the brief, a chord scheme is
then created 124 and
a chord scheme train 126 stored.
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Again, referring to the brief, texture generation is applied 130 following
extraction 132 of
relevant textural group files having regard to the brief and descriptor
correspondence or
similarity between the emotional connotations of the Form Atoms in the
assembled chord
scheme chains. Writing 134 of the textures chord scheme thus leads to
generation of a
5 composition which can be sent 138 to a sequencer for either audio
broadcast or storage, as
the case may be.
Returning to the issue of Form Atoms and taking a deeper look at the benefits
associated
therewith, the Inventor has realised that harmonic context is the driving
force for the
10 choices that are made compositionally. From this, the acceptability of
any given chord
followed by another chord is dependent on the harmonic context created by
neighbouring
chords and their relationship with a common tonic, with this manifesting
itself in the
mind's recognition and physical gratification. Hierarchically, whilst chords
are dependent
on their neighbours, adjacent sequences of chords also need to be self-
contained entities
15 that are related to each other. It therefore follows, following this
revelation, that sequences
can be substituted for alternative ones depending on their common harmonic
properties,
such as: do they end with a recognisable cadence to the tonic, do they feature
a tonic at the
beginning, or maybe at the end? Within the context of the invention,
recapitulating specific
chord schemes verbatim is avoided through the creation of heuristics that can
produce not
20 only the chords for any given analysed sequence, but have the logic to
produce different
varieties of chord sequences of similar or differing lengths in their place ¨
and whilst any
rules of how the sequences connect through certain specific chords may
restrict the
system's chord choices, it will ensure sound compositional flow across the
sequences.
25 Sequences are delineated and categorised through rules with respect to
the occurrence of
their tonic. Perceptually, they appear to be of similar length to a musical
phrase, although
this may not be the case. These small sequences are the aforedescribed Form
Atoms. They
are the smallest possible building block that can act as an independent
sequence whilst still
making musical sense to the listener. Form Atoms have certain properties, and
Form
30 Atoms with similar properties can be substituted for each other. An
aspect of the invention
thus defines the properties and constituent parts of a Form Atom, as well as
the mechanism
by which Form Atoms may be combined.
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If progression descriptors were to have complete free rein on the generation
of potential
chord sequences, then the result is that pieces would start and end with
progressions
generated by heuristics that fit the criteria but which come from the middle
of pieces where
the chords may be fully flowing. This would not generally make a good ending
or
beginning to a piece of music that is trying to temporally deliver a self-
contained narrative.
Form Atoms that have a start or end tag mean their heuristics are appropriate
for such a
setting.
As indicated earlier, the question and answer tags come from another important
consideration: the problem of chord sequences that involve chords from outside
the current
local Form Atom key centre. An example would be the love theme from John
William's
score to Superman (Spengler & Donner, 1978), whereby the theme's exposition is
accompanied by the following chord sequence:
Eb => F/Eb (or Eb #11 13) => Ab/Eb => Eb
Looking at this example, we can examine the consequences of keeping this chord
scheme
as a self-contained unit, or breaking it into two Form Atoms that are a
question and answer.
If the chord scheme is kept intact, then the information that is gleaned is as
follows.
1. An Eb chord can be followed by an F/Eb chord,
2. An F/Eb chord can be followed by an Ab/Eb chord,
3. An Ab/Eb chord can be followed by an Eb chord, and
4. This chord scheme can be substituted for any other chord scheme that starts
and ends
on the local tonic.
However, in contrast, the approach of the preferred embodiment considers that
this chord
scheme is a question and answer and that means it is possible and practicable
to assimilate
all of the chord information in points one through three above. From the
inventive
approach described herein, a question phrase that has the tonic at the
beginning but not the
end can be joined to an answer phrase that has the tonic at the end. This
gives us the ability
to break this chord sequence into smaller substitutable pieces, and to change
these pieces
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to introduce interest. By breaking this Superman example into two Form Atoms,
this
granularity would allow for a construction of a series of Form Atoms that
present ja, b, a,
c}. This is indeed what the original piece does. If we extend the example to
see the next
two Form Atoms, the question is repeated in the original score, but the answer
is different
5 to create new interest:
Eb => F/Eb => Ab/Eb => Eb => Eb => F/Eb => Abm => Bb7sus4
To recap, clearly this initial four bar phrase could be expressed as a chord
scheme that is
cadential with the tonic at the beginning and end, but this would miss out on
a series of
10 opportunities for generation. This creates a rule that chords must be
from the given local
tonic key centre. In the event of a chord altering a fundamental note in the
given scale, we
break the Form Atom into a size that puts this new chord, or string of chords
at the end or
beginning. This then gives the ability to pivot at this chord to a newly
implied key, or to
follow back to the local tonic via the remaining chords in the progression. We
tag the first
15 Form Atom with a form function question tag, and the second with an
answer tag. This
classification process is significant for generative composition since it
opens up greater
opportunities for variation in compositional structure that satisfies good
form.
Within the Form Atom, a preferred embodiment stores two pieces of chord
information,
20 namely the chord type and the chord's bass. An example would be Fm7/Bb.
Their specific
timing is irrelevant, because there may be more or fewer chords generated by
the atom's
heuristics depending on the briefing requirement. There are two reasons for
storing these
chords within the Form Atom. Firstly, for debugging the atom's chord-
generation
heuristics (because it is important to know what the heuristics were based
on). Secondly,
25 so that a Chord Scheme Generator can obtain a set of chord trees of
which chords precede
or follow each other.
Form Atom Heuristics
There are two sets of heuristics that are used by the Form Atom. Firstly,
there is a set to
30 generate a requested number of chords. Secondly, there is a set to space
out any given
number of chords across any given time-frame. In the case of the first set,
this is where
one may find heuristics, for example, that would generate a cycle of 5ths, or
a sequence of
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rising triads a minor third apart. There are many others that will be
understood by a
musicologist, including Markov chains of chords derived from previously
analysed works,
secondary dominant to dominant jazz progressions such as a III-VI-II-V-I
progression or
a VI-VII-III-VI-II-V-I progression, or a series of chords that are separated
by a single
5 integer difference, such as a series of falling major triads that are all
a major third apart.
In the case of the second set, there may be a specific effect that is created
from how the
chords are spaced. For example, in the central chord scheme to the song "La
Grange" by
ZZ Top, as used in the film Armageddon (Bruckheimer & Bay, 1998), there is a
clear
intent to keep on the tonic for as long as possible and then to emphasise the
two other
10 chords in progression by placing them on the third and fourth beats,
respectively, of the
final bar of the phrase. This common I => bIII => IV Form Atom has a plethora
of
alternative timings in other songs that also feature it: "Dragonfly" by Ziggy
Marley,
"Starman" by David Bowie, or "Back In The USSR" by The Beatles, to name but a
few.
All of these alternative timings have different emotional connotations. This
emphasises
15 the importance of chord-spacing heuristics, the importance of applying
an appropriate and
relevant descriptor of emotional connotation to the Form Atom and the
uniqueness of the
timing that they bring to the personality of any given Form Atom.
In the generation of Form Atoms, the point is made again that there are two
sub-tasks,
20 namely the generation of chord trees that looks at analysed compositions
to create forwards
and backwards pointing Form Atom trees, and the creation of Form Atoms in
which there
is a selection of a viable path of Form Atoms from the given chord trees
taking into account
briefing requirements that affect the decision-making process. Form Atom trees
are
formed in terms of both forward and backwards paths to address varying levels
of input
25 detail provided in the briefing narrative. One tree contains options for
Form Atoms that
can follow the one we are generating from, whereas the other contains options
for Form
Atoms that can precede it. Both will typically have multiple branches and both
reflect
identified musical progression in terms, for example, of whether a sequence of
cadences
makes sense. This is a qualitative determination based on a quantitative
assessment.
When iterating through all Form Atoms of the analysed work, Form Atoms with
identical
meta-tags for form functions and progression descriptors are placed into the
same list.
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Each preceding and following atom from this one goes into the respective
options list for
forwards and backwards for that list. Then, when a Form Atom is generated, a
choice from
these lists creates a neighbouring atom. This allows generation of a meta-
structure for the
chord scheme of the composition that will make coherent musical sense.
FIG. 9 shows how a single composition is parsed into a set of trees, and the
preceding and
following options that can be selected for any given atom generated from the
lists. End
and start form functions do not affect the Form Atoms' listing, but all other
categories are
considered. Given six different progression descriptors, and three different
sets of form
functions, this gives an exemplary number of 216 possible lists to reflect
every
corn hi nation.
Chord Schemes
Armed with a repository of Form Atoms, the generative composition process
moves to a
phase of chord scheme generation. A chord schemes, as the name suggests, is a
grouping/concatenation of chords that are formed from Form Atoms having
musical
properties based on Predicates, as described herein.
Chaining together of chord schemes provides a harmonic map for the generative
composition. It is only possible to move to the compositional phase once this
harmonic
map is in hand, in which third stage notes are actually generated and texture
applied to
reflect the briefing requirements.
The requirements for each chord scheme come from a requirements list. Once we
have
generated a Form Atom for every item in the requirements list, we use the
heuristics of the
Form Atoms in conjunction with the properties of the requirements list to
create chord
schemes. A chord scheme consists of the following properties:
1. A tonic ¨ this is the tonic for the chord scheme's local context. It is set
from the previous
chord scheme' s new tonic property, or in the event of this being the first
chord scheme,
the piece's tonic.
2. A new tonic ¨ in the event of the chord scheme modulating, this is set the
new key, and
will become the next chord scheme's local tonic.
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3. A list of chords ¨ this is a list of chords which are expressed through the
following
properties:
(a) Pitch ¨ this is the root of the chord.
(b) Bass ¨ this is the bass note that the chord is over.
5 (c) Chord type ¨ this gives a type of chord. Types are used later when
creating sets of
pitches from which to choose notes. Types are defined by the analyst for the
purposes of
their own musical generation heuristics. Examples might include maj, min7,
dom7 b9,
myWeirdChordTypel, myWeirdChordType2.
(d) Position ¨ each chord has a local relative position within the chord
scheme that is
10 measured from the beginning of the chord scheme which itself is treated
as an epoch.
Rather than an absolute position (which would measure the chord's position
from the
beginning of the piece), this allows the chord scheme to be moved back and
forth in time
by the user if requirements are moved or reordered.
15 Generating Chord Schemes
Having outlined the type on information that a chord scheme contains, the
generation of
any given chord scheme for the new composition, given a set of briefing
requirements and
associated Form Atoms, is a combination of the following factors:
1. Tonality and key ¨ these are affected by the overall emotional requirements
stipulated
20 in the brief.
2. Position ¨ each chord scheme starts at a certain position, measured in
bars.
3. Length ¨ each Form Atom has a specific length on the piece's timeline.
4. Chord density ¨ this is the number of chords within the chord scheme.
5. Form Atom ¨ this is the Form Atom associated with the requirement from the
25 requirements list. This Form Atom contains the heuristic information we
need to generate
the chord scheme, and is selected based on the requirement's emotional
connotations, form
requirements, and meta-tags.
Referring again to FIG. 8 and its outlined process, an initial key centre for
the composition
30 is firstly chosen. This is referred to as the tonic, but it is only
relevant to the initial Form
Atom. The composition piece is free to deviate from this key centre depending
on which
Form Atoms have been selected to reflect the briefing requirements. Secondly,
through an
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iterative process through each pairing of Form Atom and its associated brief
requirement,
the system processes respective chord-generation heuristics, followed by their
chord-
spacing heuristics. The chord-generation heuristics produce the number of
chords that the
requirement has in its associated property. The chain of chords are then
spaced by
5 heuristics depending on how many chords there are, and the effect that
the Form Atom
wants to produce from its chord spacing.
To initiate the creation of chord schemes, a key and tonality for the
composition is selected
as a start point. This is done just before the chord scheme generation. In
short, the tonic
10 note may be randomised by the generative system. The major/minor
tonality of the piece
is determined on the basis of an overall assessment of emotional connotation
requests in
the brief, cross-referenced with analysed pieces that most feature these
emotional
connotations. Therefore, the analysed compositions that include/feature the
most relevant
connotations influence the tonality the greatest.
Heuristics
Heuristics performed by the system are generated by analysis, such as by a
musicologist
although technical approaches are also alternative or complementary, e.g., the
use of a
genetic algorithm to evolve fewer more accurate heuristics based on fitness
functions that
20 test both Occ am' s Razor (that fewer are axiomatically better) and
accuracy in that the
heuristics can explain more of the original artefact's note pitches, lengths
and positions.
These heuristics look for pattern recognition and unusualness in audio
components and
musical structures to generate a rule that has the fewest number of rules that
are able, from
a given chord, to generate at least one later chord or a succession of later
chords to
25 reproduce the original analysed chord scheme in the original musical
artefact. In short, the
heuristic is a mathematical explanation. This is the basis on which, given a
Form Atom
database as a starting point and then a set of textures having aligned
emotional connotation
which are similar and preferably align with those linked to Form Atoms,
composition can
be achieved.
Any musical score can be explained by pitch, position and duration for the
notes. Other
dimensional properties are also generally relevant, e.g., "volume" that
relates to the
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loudness or softness of the performance style which can itself take a number
of forms,
such as staccato, etc. Every musical score can therefore be described or
represented using
something akin to the MIDI protocol, i.e., a series of on-off switches over
time. Indeed, in
providing context for an implementing embodiment, in real terms each 8-bit
MIDI
5 envelope is tied to a pulse, and running through a multiplicity of such
pulses sequentially
generates the performance of the musical score. A series of mathematical
functions
realised in a Turing equivalent musical programming language can, when
combined,
ordered and programmed with correct parameters, generate the original score
from which
these functions were derived. Moreover, the same functions can generate
alternatives and
10 acceptable but different scores. For example, the rule may need to
explain how to generate
a note in the bass from a chord in a specific bar in the treble, and then for
there to be
selected parameters to be identified that, when applied to the rule, achieve
realisation with
the original analysed musical notes in the original score. Furthermore, this
rule can now
be used in other contexts to generate acceptable bass notes even if given
different chords.
15 This particular rule may be assigned a suitably descriptive name, e.g.,
"very basic bass
generation for triad in major key" for identification and re-use purposes. The
requirement
may be, for example, looking at a chord in the treble, we want the bass to be
the same pitch
but in a lower octave (closest to the bottom possible pitch of a bass guitar).
The linguistic
explanation for the correct mathematical function may be "in selecting the
next bass note,
20 look at all notes in the chord of interest and choose the closest one of
those notes (in terms
of MIDI separation) to the bass note in the previous bar. In this instance,
the correct
parameters may relate to the MIDI note separation distances in the original
chord in the
treble as expressed in terms of the degree, e.g. I, Ill, IV.
25 The way in which the generative compositional system of the various
embodiments and
aspects of the invention works requires heuristics to be used to create chord
schemes,
textures, fill-in briefing requirements, for the storage of historical
information on analysed
pieces, and how to plug certain heuristic files into each other. The system
therefore
develops a generic mechanism that is capable of producing an ordered
processing of
30 abstract tasks.
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This section describes this processing and model mechanism, before considering
the
different primitive heuristics within the system that allow for the creation
of rhythms,
pitches, stored analysis, chords, and chord spacing. Primitive heuristics give
the analyst
the ability to input their analysis without having to write code.
These processing and model mechanisms allow for the ordered processing of
heuristics,
as well as the nesting of heuristics into groups that can be copied and moved
within the
processing flow. It also offers the ability to branch both conditionally and
unconditionally,
as well as to set the probability that certain heuristics or branches of
heuristics may be
processed. This is all achieved using the principle of hypernodes.
Primitive heuristics give an analyst the ability to input analysis without
having to write
code, and are functionally configured to allow for the creation of rhythms,
pitches, chords
and chord spacing for use or analysis as a consequence of them having
predefined
mathematical functions in a Turing equivalent musical programming language.
Heuristics Framework ¨ Hypernodes
A hypernode is a building block that allows for hierarchical processing and
storing of
heuristics. It has the following properties:
1. An ordered list of hypernodes (that supports recursive nesting).
2. A logical operator to describe how the list should be processed.
3. A probability ¨ this is a number that represents the chance of the hypemode
being
processed.
4. A name ¨ this allows us to name the hypernodes so when listed we can keep
track of
them.
5. A musical element.
A set of heuristics starts off with one single hypernode. This node in turn
contains a list of
hypernodes that can have musical elements attached. A musical element contains
a specific
heuristic, and any other data that needs to be stored with it. Every hypernode
has a logical
operator attached to it, either an XOR or an AND. If it is an AND, then each
hypernode in
the list is processed in the list order; if the probability of the hypernode
is less than 1, then
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a random number generator is used to assess whether the item will be processed
or skipped.
In the event of an XOR list, then only one hypernode is selected from the list
to be
processed, its likelihood depending on the relative probabilities of each item
in the list.
5 Hypernode Processing
The type of musical element attached to the hypernode will affect how the
hypernode is
processed. There are different iterative steps that the processor will take
depending on this
information. These are the types of musical elements that exist within the
generative
musical composition system of the present invention:
10 1. Drum ¨ this is a rhythm-generating heuristic, not necessarily
associated with drums but
with all rhythm in general.
2. Form Atom ¨ this contains information about chords from repertoire that has
been
analysed and input into the system. Form Atoms are used to create a meta-m ap
of the chord
schemes of a piece, as described in detail above.
15 3. Heuristic ¨ this is a catch-all for any heuristic that is not
specifically defined as a pitch-
type heuristic. This includes chord and chord-spacing heuristics, as well as
heuristics for
filling in and completing the omitted parts of a given brief.
4. Pitch ¨ this is a specific type of heuristic that is associated with
creating pitch
information based on a given chord scheme.
20 5. Texture adapter ¨ a texture adapter is specifically associated with a
texture group.
Texture adapters tie pitch, rhythm, and MIDI routing information together.
6. Texture group ¨ a texture group ties texture adapters to meta-tags that can
be used by
the user.
25 Whilst all of the above musical elements in a hypernode structure will
be processed for
every Form Atom, the pitch heuristics will be processed for every chord within
a Form
Atom's chord scheme. This means that textures are processed only once, but
pitch
information associated with chord changes is processed for every chord.
30 Heuristic Components
A heuristic has only three elements that are stored within it: a name, a
description (so that
the analyst can see what the heuristic does), and a procedure, or method, that
is run when
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the heuristic is invoked/instantiated. This means that heuristics do not
contain any pre-
programmed data. If a heuristic needs data to be stored with it, then this is
held in the
musical element that contains the heuristic. However, a heuristic does not
rely on data
being created for it. This is because all other data is dynamically created
and cannot be
5 relied on to be available at the point of processing. This may be due to
branching, or
statistical chance from probabilities not generating material as expected.
Therefore, a
series of data maps are associated with different heuristics. These contain
any dynamically
generated data that any given heuristic may rely on to run its primary
function.
10 The heuristic maps have the following properties:
1. Composition ¨ the composition itself, which includes information on:
(a) The requirements list ¨ containing briefing information from the user.
(b) Time signature ¨ of the composition.
(c) Chord schemes ¨ which are attached to each Form Atom.
15 (d) Staffs ¨ the music information that has been created and is ready
for the sequencer.
2. A spare Heresy map to provide the heuristic with an ability to send
information forwards
in time to other heuristics, or to itself when it is processed again.
3. Drum-heuristic-specific information:
(a) A Black List ¨ for drums that should not be processed if this heuristic
has been
20 processed. This is useful to stop things like kick-drum patterns
overwriting already written
kick-drum patterns.
(b) Drum ¨ the drum that is being processed. Drums have a plethora of
properties that are
discussed below.
(c) A processed drum list ¨ this is a list of drums that have been processed.
Some of these
25 may affect the notes that are processed for the heuristic in question.
4. A list of generated pitch information ¨ this is the chord-specific pitch
information of
notes that Heresy wishes to use when certain drums trigger.
5. A number representing the current Form Atom that is being processed ¨ this
allows for
surrounding atoms to be considered for things like their local tonic, and
chord schemes.
30 6. A number representing the specific chord within the given Form Atom.
7. A flag list ¨ this may be used as yes/no triggers for this and future
heuristics.
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Primitive Pitch Heuristics
Having now established the mechanism by which heuristics are processed and how
they
pass data between each other, it is now possible to consider the different
types of primitive
heuristics and how they create musical output.
There are two different types of primitive heuristics, i.e., predefined
mathematical
functions with variable parameters, associated with pitch:
1. Core heuristics ¨ these deal specifically with pitch information and are
broken down
further into three sub categories:
(a) Pitch generators ¨ these generate pitch/frequency information, preferably
represented
in MIDI representational form.
(b) Pitch transformers ¨ these heuristics change the pitch of notes and
chords, i.e., provide
an offset which is an integer in a MIDI scale hut not in frequency scale where
each tonic
in successive octaves is frequency doubled.
(c) Pitch storers ¨ these heuristics create storage areas in memory for notes
and Flags.
These can be considered simply to be physical storage locations for data.
2. Logical Operators ¨ these heuristics allow for conditional flow control
through "If Then
Else" type mechanisms, as well as checking whether certain conditions are
true, such as
note pitches, flags, and chord types being of a certain value. They can also
check if note
pitches are within a certain range. Essentially, these are branching functions
for sub-
routines.
Pitch-generating heuristics can gather pitch information from three different
sources: from
a number that is abstractly stated by the analyst; from a specific inversion
position in a
chord from the chord scheme; or from an idea staff. An idea staff is a named
list of pitch
locations, and is set up by the analyst in a separate heuristic list in the
hypernode structure.
Whilst pitch information can be gathered from any of the three mentioned
sources, all
generated pitch information is stored in idea staff pitch locations.
There are two different pitch-generator heuristics. The first is called a note
picker. This
heuristic simply asks what the source note is, and where the destination for
the note is.
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There is the option to randomise the selection from the source if a chord or
idea staff is
selected. If a randomisation were not possible, then then the note picker
would take the
exact value from identified ideas staff value at position 0 in the list of
pitch locations.
However, with randomisation specified, it will take a value from any of the
notes stored
5 in the "treble" ideas staff. These literal note values will change every
time the chord
changes, but this picker will always point to this location. There is also a
bar offset for
notes sourced from either idea staffs or chords. This means it is possible to
obtain pitch
information from neighbouring and nearby chords and ideas staffs, and from the
pitch
values associated with them. In this example, the bar offset is not specified,
so the pitch
10 information will come from the idea staff notes associated with the
current chord number
in the chord scheme_
If the source is chosen to be a chord, then the note number would select a
value in the
chord from the bass, e.g., in a major chord "1" would give the major third and
"2" would
15 give the perfect fifth, "3" may give a major 7th or wrap back around to
give the tonic an
octave higher, depending on the chord that is generated at the time. The
integer gives a
literal value for whatever number is specified.
The alternative pitch-generation primitive heuristic is called a Voice Leader.
In this
20 generative heuristic, a reference pitch is selected from which to voice
lead. This note to
lead gives a reference to a note from one of the predefined three sources
(idea staff, chord,
number). The note to be created is then chosen from a second reference source,
typically
a chord or ideas staff. The analyst can then specify if they want the note to
lead upwards,
downwards, or in both directions from the first reference note. If they choose
both, then
25 the closest note will be found. It is possible to specify that the note
should be forced to
change pitch in the event of the note appearing in the second reference chord;
this is an
example of another rule (of many). If the analyst wishes the note not to
wander too far
from the initial pitch of a note selected using this heuristic, then this can
be specified as a
range. This range is then stored in the data map and passed on to the
heuristic the next time
30 it is written. If it ever attempts to generate a note out of range, it
then has a record of what
the initial pitch was and how to voice lead from this value instead. This
stops the voice
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leader heuristic creating melodies and scales that wander off out of idiomatic
range for the
instrument they are writing for.
It is important to note that the note picker and voice leader generative
heuristics are never
5 picking prewritten notes unless their integer option is selected. This
means that the pitches
that are chosen will be dependent on the harmony in the composition at the
point of
creation.
There are two types of storage heuristics. One creates a named idea staff with
a set number
10 of storage positions; the other is a flag that can be turned on and off
during the processing
iteration. If the analyst wishes to store any information, then they need to
create idea staffs
or flags to do this by way of these functions.
Branching and logical operations are achieved by a set of logical operator
heuristics. The
15 IfYhenElse heuristic presents a set of three hypernodes. The first "if"
hypernode checks
for a given condition via equality heuristics. There are four different
equality heuristics.
They can check if a specific note is of a certain pitch, or if a note is
within a range of
pitches, or whether a chord is of a certain type, or if a flag is in existence
and turned on or
off. If the condition is met, the "then" hypernode is used; if not, the "else"
hypernode is
20 used.
Finally, the last set of primitive generative heuristics are transformers.
There are three
specific ones. The first two are note and chord transposers. These are capable
of
transposing a note or an entire chord in pitch by a source value from one of
the mentioned
25 three sources: an abstract number, an inversion position, or from an
idea staff. The third
one is an alternative retrospective voice leader. It will take a note in a
given position with
a given pitch, and it will move it up or down by octaves until it is within an
octave of a
destination reference note. This is an effective way of removing compound
intervals in
created pitch material.
Primitive Rhythm Heuristic ¨ Drum
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Although there are potentially many alternative mechanisms for generating the
rhythmic
qualities of melodies and textures from pitch information, a preferred
embodiment uses a
single primitive rhythm heuristic. This heuristic applies a rhythmic
triggering mechanism
for the pitch values found in idea staffs created using the pitch heuristics
mentioned in the
5 previous section.
The properties of the heuristic are stored in what is referred to as a drum.
The drum
information is stored in the musical element alongside this primitive rhythm
processing
heuristic. These musical elements with attached drum data sit in hypernode
structures just
10 like other musical elements, meaning that they are processed in a
hierarchical order. This
means that drums can potentially influence each other as to how they are
triggered through
their generated and observed output. Whilst drums are indeed used to make drum
patterns,
their ability to trigger the pitch notes of idea staffs means they have a much
more powerful
use than that of just creating untuned percussion patterns.
The drum has a name for future reference within the context of the processing
mechanism.
This drum's name will be referred to by other drums in the same hypernode
structure to
affect their trigger probabilities. There is a resolution that is defined for
the drum. This in
turn sets the resolution for two grids: firstly, the probabilities for whether
the drum will
20 trigger or not; and secondly, the velocity value if the drum triggers.
Each probability can
have a value that can be set between 0% and 100%; velocities have a MIDI range
between
1 and 127. If a note triggers, then the associated velocity is used. The
velocities can be
randomised around this value by a set range.
25 The probability in specific grid positions can be influenced by other
drums that have been
processed already and triggered. In this case, there are settable velocities
for a note should
it eventually get triggered. These preprocessed drums may appear in one of two
lists.
Firstly, there is a not list of drums that negatively affects grid
probabilities. If triggered at
a given position, these preprocessed drums mean the current drum should not
trigger, even
30 if the probability is 100%. This is useful in circumstances such as the
unidiomatic
triggering of a closed Hi-Hat and an open Hi-Hat at the same time. In this
example, an
analyst may set the closed Hi-Hat to play on all quaver beats, unless an open
Hi-Hat has
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been triggered. The open Hi-Hat would be processed first in the hypernode
structure, and
the closed Hi-Hat would be processed afterwards with the open Hi-Hat in its
not list.
Secondly, there is an attractor list of drums that, if triggered, increases
the local probability
grid area of our current drum. Whether the attraction adds this probability
number to the
5 grid position to the "left", "on", or to the "right" of the triggered
grid position is set in the
drum properties. This is useful if the user wishes certain notes to be fired
next to other
notes. For example, in the case of semiquaver snare ghosting, an analyst may
wish to
increase the chance of a ghost note occurring on a surrounding 2nd or 4th
semiquaver if a
kick drum or snare drum is triggered on a neighbouring quaver. The kick drum
and snare
10 drum may contribute 30% each to the probability of a ghost happening,
thus substantially
increasing the likelihood of a trigger.
Drums have a pitch value. This pitch value can equate to a literal MIDI pitch,
or a store
position in an idea staff. Depending on whether the analyst wishes the drum
pitch
15 parameter to trigger a specific MIDI note or an idea staff pitch
position's value, different
rhythm adapters are used at a later stage when the rhythm and pitch heuristics
are plugged
into each other (such as needed to provided texture).
The drum can be forced to produce a set number of notes, or a range of notes,
thus meaning
20 that statistical flukes that result in sparse, or too busy, rhythmic
patterns can be avoided.
If the drum is only being used as a method to attract or silence other drums
through the
attractor and not lists, then it can be set to mute. This means that it will
not have an output
pitch of its own, but it will still be used in the processing mechanism.
25 The length of time that the given probability grid spans is set by a
loop-length parameter.
This way, a grid of 16 spread over four beats is effectively semiquavers but
spread over
eight beats is quavers. It is also possible to say how many times the pattern
will occur, or
loop around, and whether the pattern happens at the beginning or end of a Form
Atom, or
the beginning or end of a chord change within the Form Atom. This gives a
powerful way
30 to create intricate textures as chords and Form Atoms change.
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Finally, the triggered pitch notes are given a length in bars, beats, and
fractions of a beat
via associated length properties.
Textures
5 There has already been some considerable discussion of the structure and
or effect of
texture, particularly in relation to FIGS. 3 and 4. Returning to the point
made earlier on
extending them again, users achieve textures through specifying emotional
connotations.
These connotations are, in one embodiment, checked against what is known as a
file of
texture groups. We will now consider how texture groups are made. The workflow
for
10 creating a texture group file that contains this information is
represented in FIG. 10.
Texture descriptors will eventually be aligned with corresponding descriptors
for relevant
Form Atoms.
The creation of texture components is the physical output of the generative
system of the
15 preferred embodiment since, prior to texture overlay, there is simply a
chord scheme chain.
Having considered how to classify texture components and link them to a brief,
heuristics
for pitch and rhythm, and how to form a harmonic map for our composition using
Form
Atoms and assembled chord schemes, FIG. 10 provides an overview of the
processing
involved to combine all this information and techniques to understand how
textures are
20 specified, constructed, requested by the user, and realised by the
system.
The workflow involved with the programming of any given analysis of texture
typically
follows the following structure:
1. Create pitch data through core heuristics (explained above).
25 2. Create rhythm data through drum heuristics (explained above).
3. Create a rhythm processor to aggregate desired kits.
4. Create an orchestrator to apply internal storage and external MIDI mapping
for rhythm
processors.
5. Create a texture group that attaches core files containing pitch data, to
orchestrators that
30 contain rhythm and mapping data, through a texture adaptor.
6. Attach meta-tags to the texture group.
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Examining the process steps in more detail:
1. The analyst (or program logic and system intelligence as the case may be)
starts by
creating a set of heuristics that will create pitches that are placed into
idea staffs. These
heuristics are programmed into a hypernode structure that is stored in a core
file.
2. Next, the analyst creates a series of drum heuristics. These hypernodes are
stored in a
kit file.
3. It is feasible that there may be various different drums across different
kits that the
analyst may wish to use in order to create a desired rhythm. Therefore, kit
files are
processed in what is known as a kit processor. This uses a specific heuristic
that allows
for a kit file, and associated kit from within that file, to be processed.
This kit-processing
heuristic sits in a processor file.
4. A map is created of where the eventual note information will go, both in
terms of the
generative system's internal structure and storage, as well as external MIDI
mappings for
attached VST instruments. Before applying texture, the system has only created
abstract
snippets of musical material, principally in the form of Form Atoms with
related
processing to provide chord scheme chains. Texture overlay is where
orchestration takes
place for a specific range, instrument, and placement onto staffs at a
specific point in the
score. It is feasible that the orchestrator may wish to use various triggered
notes many
times, for different instruments (in musical terms, what we know as
"doubling"). This is
specified in an orchestrator file, which contains hypernodes that tie together
rhythm
processors, with external MIDI mappings, and internal staffs for storage of
MIDI
information.
There are two main heuristics that come into play when we create an
orchestrator. Firstly,
it is necessary to define where to store internally the information that is
generated. This is
achieved with a staff-creator heuristic. The staff-creator heuristic will
place generated
material onto a number of staffs. Whilst the ability to have more than one
staff is not
essential, it is useful for displaying the material to the user in a way that
differentiates this
material from other staffs, as well as when debugging the heuristics that
create the
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material. The staffs that are created have name properties; a length in bars,
beats, and
fractions of a beat; a time signature that is appropriate for the material
that will be written
for it; and an offset measured in bars, beats and fractions of a beat. The
offset is applied to
the absolute position of any material. This way we can move pickups at the
beginning of
5 phrases, and drum fills at the end, across the adjoining bar lines in
order to make positive
and negative anacruses. Secondly, a rhythm-adaptor heuristic is required to
map
rhythmically generated material from a processor file, to staffs, and a MIDI
channel, a core
note, and an idea staff.
10 As an example, the rhythm processor called "pianos", with hypernode
processor called
"my Bach piano right hand", will be providing triggers for notes that will
request a pitch
value from idea staff "treble" at storage position "3". It will take all
pitches generated from
the idea staff and create MIDI notes for them on channel "11", with an
internal destination
staff for all this MIDI information that is named -Piano (right hand)". The
internal
15 destination staff will provide any information about rhythmic offset. If
a pitch position is
not specified, then it is assumed that the drum is requesting a literal MIDI
pitch. This is
how percussion patterns are created. If an ideas staff is not specified, then
it is assumed
that all the pitches will have the same MIDI and staff routing.
20 These orchestrators will work on any given pitch information that is
generated in step 1
above; however, we may wish these triggers to work on pitches generated by a
variety of
different core files. Consequently, we now create a texture-adaptor heuristic
to tie pitch
data, to orchestrator data. A texture adaptor is given two components: a
specific core pitch
hypernode generator from a core file, and a orchestrator hypernode from an
orchestrator
25 file. This texture-adaptor heuristic is placed into a hypernode
structure that is part of a
texture group.
5. A texture group has a hypernode that contains texture adaptors and meta-
data that the
analyst wishes to associate with the texture adaptor's output. This data
contains the
30 briefing components that a user may specify and includes:
(a) Element types ¨ these are the texture functions listed and discussed
herein.
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(b) Texture Connotations ¨ these are the abstract keywords that associate
emotional
connotation, as discussed herein.
(c) Discourse Associations ¨ this is the meta data connotations regarding
composer and
discourse discussed herein.
5 (d) Purpose ¨ this is to indicate whether the element components are
features or
accompaniment.
Texture Generator
Previously, a system for inputting musical textures into the generative system
has been
10 described. Like the Form Atoms requirements list describe above, the
system also has a
texture requirements list. In fact, the system will only write music where
there is
simultaneously a texture requirement in the texture requirements list and
chord scheme
requirement in the Form Atom requirements list. These are required to provide
the
necessary linkage between identical, semantically equivalent or semantically
satisfactorily
15 close emotional connotations that can be musically linked from selection
of Form Atoms
that fit the entirety of the brief.
Earlier, there was described a mechanism by which any gaps in Form Atoms
Requirements
List was filed. In a preferred embodiment, the system is arranged, in view of
a lack of
20 relevant direction in the brief, to continue the current texture meta-
tag requests until a new
one arises with the arrow of time. This feeds back into the texture
requirements list so that
the user can delete or change the texture as they see fit in between sections.
This means
they do not have to repeat texture requirements in between points of changing
texture in
the brief.
To calculate textures, the generative system of the preferred embodiment
cycles through
all chord requirements and checks if a texture requirement overlaps with it.
If so, it
processes the texture requirement whilst using the chord scheme created for
the associated
Form Atom. If the Form Atom starts early, or extends longer than the texture,
this does
30 not matter because the processor is arranged to already have composed
material if early,
and if late it will compose the remaining material onto the next cycle.
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The generative system of the present invention preferably prioritises requests
for featured
texture elements (such as harmony, melody, counter-melody, etc.) over
accompaniment
elements. It creates a list of all required elements that are features, then
checks for all
available texture groups that meet one of these requirements. This texture
group list is then
5 scored depending on how many other meta-tags the texture group can
fulfil.
As explained, there may be multiple elements within a texture group. Whilst
some of these
elements may fit the brief requirement, others will not. The texture group may
also have
metatags regarding connotations attached to it that are also relevant to the
brief. Scores are
10 cumulative. To provide a selection process, the system intelligence may
score texture
elements that are not features but which are requested as -4-1, elements
requested that are
features as +2, and groups with appropriate metatags as +4. This takes into
account
weighting towards texture groups that have satisfied the strictest criterion,
namely having
a featured element that is requested by the brief. Generally, the system is
arranged to
15 choose the highest scored texture group, whereafter there is a temporary
removal of the
satisfied elements from the brief and repeat of the process to find the next
appropriate
texture groups. This eventually fulfils all requested elements with and
without features, as
well as encouraging texture groups with the correct meta-tags for discourse
and
connotation.
Once we have selected appropriate textures, we perform two tasks. Firstly, we
add the
texture groups to a list of requirements that will be checked and prioritised
on future
texture generation cycles if their scores are matched. This way we use
repeated texture
ideas throughout the composition where possible, rather than changing texture
ideas each
25 and every time a similar requirement is encountered. Secondly, the
texture groups that
have been selected are processed by the system intelligence.
To process the texture groups, these are added into a hypemode list for
processing.
However, before proceeding, the system creates a data map that contains the
form
30 requirement items for both Form Atom and texture. An index of these is
recorded, with
the composition also added into the data map too. This is all the information
the texture
adaptors need to process the texture group.
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SECTION C: ANALYSIS METHOD
Earlier, the reasoning behind compositional decisions has been stated. There
has also been
a discussion concerning the preferred analysis method used to create input for
the
5 framework of the system. Whilst a full analysis of a piece of music would
disrupt the
explanation of the concepts on which the analysis is based, Section D below
gives a
detailed analysis of Bach's C minor prelude to highlight the concepts of the
inventive
approaches employed in the preferred system through a comprehensive and
practical
example.
This section will firstly offer an overview of the steps that are gone through
in order to
perform an analysis. It will then describe how the concepts of entropy and
redundancy are
utilised, before going into detail of how the analysis is performed through
the use of
examples. This chapter also offers a useful analytical tool that is part of
the Heresy
15 framework for inputting the analysis of Form Atoms from a given
composition ¨ known
as piece annotation.
Overview of Analysis Steps
Before we consider the mechanism in-depth that will allow expression of meta-
20 compositions, this section outlines the steps an analyst or analytically-
configured smart
system must undertake to obtain a set of heuristics that deliver a desired
musical result and
generative composition. In order to break any given composition down into the
heuristics
that the system needs to generate music, the system performs the following
tasks:
1. Form Overview ¨ this process is used to breakdown the piece's overall chord
scheme
25 into constituent Form Atoms.
2. Form Atom Analysis ¨ this allows categorisation of Form Atoms that have
been
identified in step one through their properties, as well as to describe any
heuristics
necessary to create the chord schemes along with their associated chord spacer
heuristics.
3. Texture Analysis ¨ groupings of musical notes that can be explained by a
self-contained
set of heuristics are called textures. Texture analysis involves highlighting
the entropy and
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redundancy that appears within the texture (see "section titled Entropy and
Redundancy"
immediately below), as well as identification and explanation for how to
generate what
Deliege (2001) calls cues.
5 For these three tasks, using Turing equivalent mathematical programming
language, a set
of provided primitive heuristics, having programmable parameters, generates
musical
textures based on the output of chord generation and spatial/temporal
heuristics which are
logically sequenced through the principle of defined Form Atoms.
10 Entropy and Redundancy
The system and approach works on the premise of explaining the most amount of
music
in a given piece with the fewest number of heuristics. This means that new
concepts may
require development of a new heuristic, whilst older ones are further
generalised where
possible. The principles of entropy and redundancy, set out in our
understanding of
15 communication theory, present tools to work towards compression of the
rule set.
Throughout the figures we highlight entropy and redundancy using a predefined
colour
scheme of red (darker tone in grey-scale printing), green (mid-tone in grey
scale) and
yellow (lightest tone). These colours help show how sets of heuristics can be
reused and
20 adapted throughout the analysis, and where we need to devise new ones to
cope with
material we have no explanation for. Whilst using this colouring mechanism in
texture
analysis, if the Form Atom analysis has patterns that can benefit from this
approach, then
this colour coding technique can be applied there too. These colours symbolise
the
following:
25 1. Green represents direct repeats of information for which there are
devised heuristics.
2. Red highlights components of the analysis for which there is no explanation
and for
which we have to create heuristics.
3. Yellow symbolises where adaptation of already created heuristics is
required, or
otherwise a change in parameters is needed to give a different result.
Form Atom Analysis
Introduction
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This section shows how to classify Form Atoms into a limited set of
progression
descriptors depending on their chord scheme's properties (as described
earlier). This
process results in interchangeable Form Atoms depending on their properties.
5 Phillip Ball defines tonal music as that which has a priority tone (Ball,
2011), with phrases
have functionality which gives the listener a temporal map based on the
priority tone. The
listener tries to predict how the phrases will bring the piece back towards
the priority tone,
which involves the process of categorisation (Deliege, 2001).
10 To achieve the input of an analysed piece, the generative system
described herein provides
a piece annotation system. For illustrative purposes, an example
implementation of this
piece annotation system is shown in FIG. 11.
Piece Annotation
15 To annotate a piece, it is qualitatively broken down into progressions
with associated
descriptors. This restricts interpretation to a set of descriptors as outlined
earlier.
As will now be appreciated, Form Atoms are musical elements that sit in a
hypernode
structure for reasons of processing, including at least one of manipulation
and use. This
20 gives the analyst the ability to structure the piece's input
hierarchically, allowing for
branches within a piece to be represented next to each other in a logical way.
This can be
useful for visualising the relationship between Form Atoms that are in
different places in
the music, such as codas and repeats, and is useful when the system and method
of the
various embodiments creates such Form Atom trees (as described above).
There is a chord list associated with each atom from the composition under
analysis. Each
chord has the properties of pitch, type, and bass (e.g., pitch=C, type=minor,
bass=C). This
string of chords gives an ordered list which can be turned into a branching
structure to give
options for different chords from, and to, other chords in a cadential
sequence. Each atom
30 has a tonic pitch and associated tonality, such as major, minor, or one
of the modes. This
tonic is needed to give context to the chord branches. If we expand on the
previous
example considered in the explanation of the local tonic, i.e., D to G with a
tonic of C, this
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is essentially a relationship that can be expressed eventually within the
system in semitones
as tonic+2 to tonic+7. The mode of the tonic is relevant because it can be
used when
generating certain sequences of chords, as well as being an important factor
in the
classification of the tonality of particular choices within a series of
branches. For example,
5 in the tonic of C major, we would expect to see an F major preceding a C
major chord
rather than the rarer F minor. In the parallel tonality of C minor, the
expectation of the F
chord's tonality is for F minor.
There are three options for progression descriptors: cadential, sequence-
intervallic, or
10 sequence-tonal. If cadential, the system intelligence can deduce from
the entered chords
how to classify the descriptor further based on the tonic's position being
either at the
beginning, end, both, or neither. This gives the generative mechanism one
component of
the jigsaw puzzle necessary to construct future chord schemes. There are two
Form Atom
properties that can have multiple entries: the emotional functions and the
form-function
15 lists:
Firstly, considering the emotional function. In the F-to-C example just
discussed, the rarer
mode of the F minor chord could be interpreted and labelled by the analyst
with the
emotional connotation "surprise". Later, if a user asks for "surprise" in the
brief
20 requirements, this Form Atom would become a potential possibility, and the
atom's
heuristics would create a chord sequence which encapsulates this surprise
quality.
Secondly, the analyst adds form-function information. As previously, the form
functions
restrict options for interchangeability. Although we described in depth the
difference
25 between statements, questions and answers, it is a general rule that,
under analysis, if a
Form Atom:
1. feels like it is loopable, then it is a statement;
2. feels like it is modulating, or that it can go to a different key centre,
then it is a question,
and it will inevitably be followed by an answer.
Each Form Atom now has its generative heuristics attached to it. These
heuristics may be
from previously written ones that are reused, or fresh ones that describe a
new chord
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scheme generative mechanism. These heuristics consists of the two components,
as again
already described above. Firstly, a hypernode that contains the pitch and
tonality chord
sequence generator. Secondly, a chord-spacer algorithm which will space the
chords that
are generated over a given musical timeframe. In this way, the number of
chords that will
5 be generated can remain independent of the timeframe in which they will
eventually sit.
This is important, because the timeframe itself may be quite changeable when
film cues
are lengthened and shortened.
Standard Chord Heuristics
10 This section describes the standard cadential heuristic and chord-
spacing heuristics. These
are our foundations for creating chord-atom heuristics, and can quite often be
used
verbatim.
Standard Cadential Heuristic
15 As a starting point for all cadential sequences, given the tonic
position from the
progression descriptor a standard approach can be used for creating chord
trees from all
the chords recorded in any analysed pieces (Nierhaus, 2009). To do this in the
context of
the invention, account must be taken of the Form Atom' s local tonic to give
the progression
context. If the number of chords to be generated is n, and in making sure that
the tonic
20 either does not appear or otherwise appears anywhere except in the
middle of the atom,
four cadential progression descriptors are produced:
1. For a desired chord scheme which has the tonic at the beginning, we
generate a chain
of chords from tonic to tonic of length n 1. We then remove the last tonic.
2. For a desired chord scheme with the tonic at the end, we repeat the process
but delete
25 the first tonic instead.
3. For a tonic-to-tonic chord scheme, we simply produce the chain of chords of
length n.
4. For a chord scheme that has no tonic at the beginning or end, we create a
chord scheme
of length n + 2 and delete both tonics. We also confirm that there is evidence
that the last
chord can cadence to the first in the corpus of analysed pieces, e.g., Dmin =>
F => G7.
Chord-Spacer Heuristics
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Chord-spacer heuristics, abbreviated CSH, spread out the available chords into
a given
number of bars. The foundation heuristic call for any given CSH hypernode
system is
termed the CSHStandard method. This method spreads out the chords depending on
how
many chords per bar the given CSH has allocated, balanced by each bar's
priority for
5 accepting a new chord. The method needs the given chord sequence, the
Form Atom's
time signature, the number of bars, and an array of numbers representing the
priority of
each bar for having chords placed in it. The method finds the highest priority
bar and
allocates it a chord, thus reducing the bar's priority number by 1. This
process is repeated
for the number of available chords.
The priority of chords for each bar is given to this heuristic by other CSHs
that are specific
to progression descriptors. All bars' priorities are set to 0 to start.
CSH Cadential Tonic at Beginning and End
15 This CSH checks the number of chords to see if it is even. If so, it de-
prioritises the first
and last bar's priority to -1 each. If this is the same bar, it will take all
the chords. If there
are two bars, then they will be treated equally. If there are more than two
bars, then this
prioritisation will decrease the chance of the first and last bars having
chords. As the first
and last chord are both tonics in this type of chord scheme, this is a way of
giving the
20 tonics more musical space to breathe and to assert themselves over the
other chords in the
chord scheme.
If there are an odd number of chords, then the first or last tonic is given
space to breathe,
and the opposite tonic is given less time. This is achieved by randomly
choosing either the
25 first or last bar and setting its priority to -1, and assigning the
opposite end a priority of 2.
This encourages space in the chord placing of one of the tonic bars, but gives
space to the
other, thus mating up for the unusual feel of an uneven number of bars. This
technique for
spacing chords is observed in works by composers noted for phrases made up out
of
uneven numbers of bars, such as Mahler (e.g., Andante third movement of the
Symphony
30 no. 6, anacrusis to bar 3 through to bar 5, 3rd beat) and Burt Bacharach
(e.g., "That's What
Friends Are For", bars 13 to 18).
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CSH Cadential Tonic at the End
This creates even priorities for all bars of 0, except the last bar, which is
given a priority
of -1 to allow the tonic to breathe.
5 CSH Cadential No Tonic
This has an even number of bar priorities: all are simply set to 0.
CSH Cadential Tonic at the Beginning
This heuristic is a copy of CSH Cadential Tonic at Beginning and End, except
that if the
10 number of bars is odd, then the prioritisation is not random: the first
bar is de-prioritised
to -1 and the last bar has its priorities increased to 2.
Actual chord spacing is then performed by a spacing heuristic that sits behind
CSHS tandard. This heuristic is termed CHS placer and places the chords on
beats based
15 on how many chords appear in the bar. This placing is represented in
FIG. 12.
From this set of limited standard heuristics, we can see the shape of a
preferred chord
generator of the generative system, or HCGen for short. This is a series of
hypernodes that
consists of a standard chord-scheme generator, spacer, and placer hypernode. A
root
20 hypernode is created, and in it we place four items:
1. Standard Cadential Heuristic.
2. CSH progression specific heuristic for prioritising bars. This varies
depending on the
progression descriptor.
3. CSH standard chord-spacer heuristic.
25 4. CSH placer heuristic.
This represents a typical hypernode structure for creating chords.
Sequential Form Atom Notation
Sequential Form Atoms can come in two varieties: interval and tonality-based
(see above).
An intervallic Form Atom moves through a series of chords that involve chords
from
outside the key centre of the local tonic, so by definition their form
function is a question.
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Sequences need to break their sequence, or they would go on forever; we call
the first
chord to vary from the sequence its escape chord. Escape chords are, by
definition, in the
following Form Atom, and this Form Atom's form function is classed as an
answer.
5 There is a standard intervallic template that we use to express the
sequence and its escape
chord. This can be seen in FIG. 13. We state how to obtain the beginning pitch
of the
sequence, and specify the tonality and any extensions that the chord may have.
We then
have two possible arrows from this chord: one to a function that changes the
pitch of the
chord in semitones and the other to an escape chord. The pitch function has an
arrow
pointing back to the chord to show the flow loop. The escape chord will have
pitch,
tonality, and extension information.
The sequential Form Atom template of FIG. 13 lays out the pitch for the
initial chord, how
the chord is altered through iterations, and the escape chord and associated
relationship
15 and properties.
A musical example of how the Intervallic Template works for Template 1 can be
seen
below in the Section titled Form Atom 4.
20 Form Atom Analysis Example
In this section, by way of an example, a precise code brief is specified for a
section of film
score from -The Quidditch Match" by John Williams for Harry Potter and the
Philosopher's Stone (Heyman & Columbus, 2001), the score and a reduction and
analysis
of which is shown in FIG. 14.
This demonstrates how we can break down the composition into appropriate Form
Atoms
that fit the predefined progression descriptors. Due to differing frame rates
for different
movie formats, this section of music is best found at 6:39s of the commercial
release of
the soundtrack. It concerns the build-up of tension towards the final capture
of the Snitch,
30 which Harry Potter swallows and then spits out at bar 27. The analysis
is high level and
coding-language independent. Double bar lines depict each Form Atom.
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Form Atom 1 (cadential): bars 1 to 4
This Form Atom functions as a perfect cadence in the key of C minor. Due to
its initial
tonic (albeit in second inversion) and final dominant G chord, it feels
clearly loopable and
therefore is classified as a statement. The bass movement is worthy of future
analysis with
regards to how bass movement can be generated in a scalic fashion; however,
this
movement is not relevant to the immediate study of the chord scheme.
To produce this phrase we use HCGen with a cadential tonic at the beginning
bar plioritiser
heuristic. The space given to the tonic, and placement of the chords in
general through this
phrase in this phrase (two chords in the final bar), reflects how our standard
chord spacer
works.
Form Atom 2 (cadential): bars 5 and 6
This phrase contains a tonic minor chord and an Abm which follows it. This Abm
seems
to pose a musical question which requires a response if the key centre of C
minor is to be
maintained. If we take this phrase in isolation and ask if it is loopable, it
would not be a
completely offensive cadence to go from the Abm to C minor; however, the Abm
is not in
the key centre due to the Cb. This is therefore more appropriate to classify
it as a question
Form Atom. The treatment of this question in the score is to accent these two
chords with
a harsh accent. This would warrant an emotional connotation tag: "Chase
Starts", or maybe
"Power Tutti". These statements are clearly personal to the analyst, and
reveal a distinctive
set of personal aesthetics with which different analysts may argue. This is
fine, so long as
the analyst can challenge themselves with the output and stand by the
generative results as
what they expect from their work. There should also be a consistent use of
emotional
connotation words. If the analyst wishes, the words can be non-emotionally
descriptive,
such as mode 1, to allow for the user to make their own associations with the
analyst's
modes.
To produce this phrase we use HCGen with an adapted CSH cadential tonic at
beginning
and end. In our adapted version, we would specify that the tonic bar is
prioritised and the
last bar containing question chords (i.e., those not from this key centre) is
de-prioritised to
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build their tension through having more time on the foreign chord.. This means
setting the
first bar's priority to 2 and the last's to -1.
Form Atom 3 (cadential): bars 7 and 8
5 This section would sound familiar to anyone who knows the works of John
Williams: it is
the same diminished sequence that is repeated as a build-up of tension in the
Star Wars
(Kurtz & Lucas, 1977) scores. To this end, and considering it has followed a
question, we
can expect this to be an answer phrase. Confirming this, we can see that this
is effectively
a secondary dominant to dominant progression (II to V) in the current key of C
minor.
10 This will automatically give Heresy a link from a bV1 minor chord to the
diminished 11
chord, therefore any section ending or starting in either of these can call on
the other as a
link.
Likewise, these chords can be strung together within a cadential section.
We attach the standard HCGen to this Form Atom, selecting cadential no tonic
as the
progression descriptor.
Form Atom 4 (sequential): bars 9 to 12
20 This is our first sequential phrase in the piece so far, its intervallic
template can be seen in
FIG. 15, which represents a loop of sequence Form Atom 3, with escape Form
Atom 4 in
The Quidditch Match. It is based on a dominant 7 b9 chord which rises in
semitones. This,
by definition, is a question phrase because it requires an escape phrase to
answer it, thereby
bringing it to a halt. It is worth noting that this chord section could just
as easily start on
25 any chord from within a range of approximately -4 to +1 semitones (Eb 7
b9 to Ab 7 b9),
and still be effective; however, the repeat of the previous phrase's G 7 b9
helps to ground
the beginning of the chromatic rise in this build up and give it a starting
context. The
previous G could of course be generated differently, so we would tend to say
that in the
heuristic we create, the start of this chord should be a repeat of the last
chord in the previous
30 generated chord scheme associated with the previous Form Atom.
Form Atom 5 (sequential): bars 13 and 14
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This contains the escape chord for Form Atom 4, hence this is an answer
phrase. This
escape phrase's chord is minor and its pitch is +5 semitones from the last
sequence chord.
The 9 #11 13 chord in bar 14 serves as the climactic point of the escape
phrase. This is a
useful example of how to build a chord function based on embellishment of our
current
5 chord. Our heuristics are labelled with the emotional connotation
"embellishment", which
when asked for will call the chord creation and spacing heuristics that
follow.
Heuristically, we would describe this chord sequence as a number of local
tonics. The first
tonic is a plain triad, the last tonic is a fully suspended chord with a #11th
and 13th over
10 the third of the chord in the bass, creating a first inversion. Any
tonics in between these
two points alter one note to adapt towards the final state. The number of
tonics is dependent
on the number of bars. We use two chords per bar until the last bar where we
have the final
prescribed chord. If we run out of alterations hut still have chord spaces to
fill, we change
the latter chords in the sequence to occupy one bar rather than half a bar.
Form Atom 6 (cadential): bars 15 to 18
If at bar 15, Harry Potter had fallen off his broomstick and broken his neck,
we would have
been happily content with the self-contained build up that Williams has
delivered so far:
the escape function could resolve to an Abm chord and effectively finish the
cue. However,
20 as Harry pulls out of his steep dive and loses his adversary in the race
to be the sole flyer,
we are given an anticipation of success and the build up to a win.
To continue building the tension, Williams chooses to lift out of the Em #11
13 to Eb/G.
This gives us a new way to resolve from an answer phrase in a way which does
the opposite
25 of conclusion. Eb is established as the new key. Still, the piece could
end here on a Lydian
melody and fade calmly to a final repeated chord of Eb. However, at bar 17,
the chord
scheme intensifies yet again with the arrival of the Em to 2nd inversion B
chords.
This reveals a new type of sequential movement that could be extended beyond
its current
30 one cycle with immediate escape, namely that of rising pairs of chords
in semitones. This
is shown in FIG. 16 ¨ Form Atom 6 sequential cadence from The Quidditch Match.
This
takes the chord from the last chord in the previous Form Atom and looks at its
tonality,
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major or minor. If major, the first chord in this new bar is a minor first
inversion 1 chord
whose root is semitone higher. If minor, then this is a first inversion major
chord of the
same root. This pattern then repeats until the escape chord is needed.
5 The escape chord is related to a minor resolution as +7 semitones, and to
the major as +8
semitones. The escape chord is in the second inversion and is a major chord.
A standard chord spacer of cadential no tonic will give the desired spacing.
10 Form Atom 7 (sequential): bars 19 to 22
This two-chord phrase can be interpreted as a sequence which escapes after its
first
iteration. It could, however, be elongated to lengthen the time taken
throughout the build
up. This pattern is represented in FIG. 17¨ sequence and escape phrases 7 and
8 from The
Quidditch Match.
Form Atoms 8 and 9 (cadential): bars 23 to 26
Form Atom 8 in bars 23 and 24 (and its repeat as Form Atom 9 in bars 25 and
26), functions
as an escape chord to Form Atom 7, and gives us a new tonic of Bb. It is
apparent that
John Williams uses second inversion chords as escape chords, with the tonality
giving a
20 distinctive flavour. This is the beginnings of gathering enough evidence
to investigate a
more common mechanism for predicting appropriate escape chords based on second
inversions and the relationship to the last chord in the sequence, but we
would need to see
more examples of this in other works to be sure there was a pattern.
25 Texture Analysis Example
We have looked at the various primitive pitch and rhythm heuristics (above,
subsection
titled "Primitive Pitch Heuristics"). In this section we illustrate how one
can create a
texture using them. See in Section D below a far more in-depth analysis of
Bach's C Minor
prelude, placed there in order not to interrupt the discussion. We shall
procedurally step
30 through the process outlined in the earlier subsection titled
"Textures".
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For this section we shall create a generative version of the detache string
writing seen in
the score in FIG. 18. This figure shows the entropy, redundancy, and
development of
heuristics through the red (note E in treble, first bar), green (all other
notes except) and
yellow (base note and other notes in triad of first chord of first bar)
colouring system.
The score in FIG. 18 is a four-bar section of detache string writing with
associated colour
labels for note pitch. This would be orchestrated across violins 1 and 2,
violas, celli, and
double basses doubling the celli and sounding an octave below.
This style of writing is typical of many Hollywood thriller and spy scores
such as The
Bourne Supremacy (Crowley & Greengrass, 2004) and Armageddon (Bruckheimer &
Bay,
1998). From an analytical perspective it is worth investigating why this
technique is
associated with certain semiotics within films in which it features ¨ so
popular that it has
become a cliché. It is typically used to add gritty tension to action scenes.
It underpins
adrenaline-fueled chases with action starts in full swing. For this reason, it
tends to be
orchestrated in the lowest range possible for the instruments at hand, and
this in itself
normally means that the rhythmic pattern is given room in the texture to be
the main
feature, un-obfuscated by other instrumentation in this rhythm or pitch area.
This requirement for the strings to be as low as possible gives us a useful
starting point.
Because the chords are closed in the violins and violas, the pitch-depth
restriction falls on
the second violin. The heuristics to do this will be created for the second
violins without
being based on previous heuristics, consequently the second violin's first
note pitch is
coloured red. In this case, this means restricting the second note from the
top of the texture
to being as close to their bottom G as possible without going below it. The
first violins
then play an inversion above this, and the violas play an inversion below.
Both of the
pitches for first notes for the first violin's and the viola's are
developments of the heuristics
created for the second violin's, consequently they are coloured yellow.
The basses and celli simply are playing in unison as low as possible. They are
therefore
following a similar procedure to the second violin, but their lowest note is
MIDI Cl (36).
Consequently, they can use the same heuristics developed for the second violin
but with a
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different parameter for their lowest pitch. We therefore colour their pitch
yellow for the
first note. All the pitches for the rest of the notes in the example are
created using exactly
the same heuristics as their first note pitch, hence their note heads are
coloured green.
5 It is worth noting that if a chord appears one quaver before a chord
change, then the new
chord is anticipated, or pushed, resulting in a pre-emptive upbeat. This can
be seen at the
end of bar 1, when the chord changes to that of bar 2 a quaver early. For this
reason, we
will need to calculate not only the pitches necessary for any given chord, but
also for the
immediately following chord. Then, when the rhythm generator has created the
placements
10 for the chords, if a chord is a quaver away from a chord change, we can
apply the pitch of
the following chord. This push will be calculated in the rhythm adaptor,
whereby the latter
can tell if a chord change is coming in a quaver's time, and if so, how to
change selection
from the current chord position's pitches to the next chord position's
pitches.
15 Step 1: Pitches
The hypemode structure for the pitch component of the analysis is as follows:
Our first hypernode is an AND hypemode, which will process all elements in the
list given
a probability of 100%.
20 1. 100% ¨ CORE: Setup Ideas Staff
This sets up an idea staff with the name Strings with 5 pitch storage
positions for the
current chord, and 5 for the next chord, giving 10 positions in total. When
the texture
adaptor detects the presence of a chord change a quaver after the current
triggering, it will
add 5 onto its array position search, thus choosing the pitches for the chord
to come.
2. 100% ¨ AND hypemode: "violin 2"
2.1 100% ¨ CORE: Voice Leader
(a) This voice leads from a fixed number of MIDI G2 (55).
(b) The direction is up and it does not have to change from the G2.
30 (c) The chord to reference is the chord scheme in this bar.
(d) The destination for the pitch data is Strings position 2.
2.2 100% ¨ CORE: Note Picker
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The next heuristic will repeat the process of the first heuristic in 2.1, but
will have a 1-bar
offset in its chord to reference, thus choosing a pitch from the chord to
follow. However,
in the event of the current chord being the last chord in the chord scheme, we
will not have
any data to look for. The rhythm adaptor will still look for a note in this
array position if
5 there is a quaver triggered at the end of a Form Atom. Therefore, this is
a preemptive
heuristic to cope with this situation. This simply initialises position 6 of
the Strings array
with a copied value from 2.
2.3 100% ¨ CORE: Voice Leader
As mentioned, this heuristic is identical to the heuristic in 2.1, but has a 1-
bar offset in its
10 chord to reference, thus choosing a pitch from the chord to follow.
3. 100% ¨ AND hypemode: "violin 1"
3.1 100% ¨ CORE: Voice Leader
(a) This voice leads from violin 2 upwards in our current bar to the next note
available in
15 the chord.
(b) The direction is up and it is forced to change from the violin 2
reference.
(c) The chord to reference is the chord scheme in this bar.
(d) The destination for the pitch data is Strings position 1.
3.2 100% ¨ CORE: Note Picker
20 As with the preemptive heuristic in violin 2, this initialises position
5 of the Strings array
with a copied value from 1.
3.3 100% ¨ CORE: Voice Leader
This heuristic is identical to the heuristic in 3.1, but has a 1-bar offset in
its chord to
reference, thus choosing a pitch from the following chord.
4. 100% ¨ AND hypemode: "violas" 4.1. 100% ¨ CORE: Voice Leader
(a) This voice leads from violin 2 downwards in our current bar to the next
note available
in the chord.
(b) The direction is down and it is forced to change from the violin 2
reference.
30 (c) The chord to reference is the chord scheme in this bar.
(d) The destination for the pitch data is Strings position 3.
4.2 100% ¨ CORE: Note Picker
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The preemptive heuristic: it initialises position 7 of the Sirings array with
a value copied
from 3.
4.3. 100% ¨ CORE: Voice Leader
This heuristic is identical to the heuristic in 4.1, but has a 1-bar offset in
its chord to
5 reference, thus choosing a pitch from the following chord.
5. 100% ¨ AND hypemode: "bass"
5.1 100% ¨ CORE: Voice Leader
(a) This voice leads from a fixed number of MIDI Cl (36).
10 (b) The direction is up and it is not forced to change from the
reference.
(c) The chord to reference is the chord scheme in this bar.
(d) The destination for the pitch data is Strings position 5.
5.2 100% ¨ CORE: Note Picker
A preemptive heuristic: it initialises position 10 of the Strings array with a
value copied
15 from 5.
5.3 100% ¨ CORE: Voice Leader
This heuristic is identical to the heuristic in 5.1, but has a 1-bar offset in
its chord to
reference, thus choosing a pitch from the following chord.
20 6. 100% ¨ AND hypemode: "celli"
6.1 100% ¨ CORE: Note Picker
This note copies the bass at position 5. (It will sound an octave higher when
orchestrated
on the celli.)
6.2 100% ¨ CORE: Note Picker
25 This note copies the bass at position 10.
This will give us all the pitch information necessary to create our textures.
Step 2¨ Rhythm
Now we need to consider rhythm. There are two chords in each bar. The first
appears in
30 beat 1, either on the 1st or the 2nd quaver. The second attack point, or
stab, appears either
on the + of beat 2 or 4. The rhythmic hypemode in the kit's file looks like
this:
1. 100% ¨ XOR hypemode: "I or 1+"
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This node will chose between whether the first stab in the bar conies on the
first quaver of
the first beat or on the second quaver of the first beat.
1.1 50% ¨ AND hypemode: " I -
1.1.1 100% ¨ DRUM: 1Violins 1
5 (a) This is the drum template from which we will copy all other drums.
(b) Grid resolution = 8. 100% chance of triggering on the first beat with a
velocity of 122.
Velocity is randomised by 10 (122 gives a range of 117 to 127). Loop length is
4 beats.
Length is one quaver. Pitch is set to position 1 (this is the position in the
Strings idea staff).
1.1.2 100% ¨ DRUM: 1Violins 2
10 Copy of drum Violins 1. Pitch is set to position 2.
1.1.3 100% ¨ DRUM: 1Viol as
Copy of drum Violins 1. Pitch is set to position 3.
1.1.4 100% ¨ DRUM: lCelli
Copy of drum Violins 1. Pitch is set to position 4.
15 1.1.5 100% ¨ DRUM: 1Double Basses
Copy of drum Violins 1. Pitch is set to position 5.
1.2 50% ¨ AND hypemode: " 1 +"
1.2.1 100% ¨ DRUM: 1+Violins 1
In short, this node contains copies of all the drums in heuristic 1.1, but the
probability grid
20 is 100% on the second quaver of the bar, not on the first. It is worth
noting that the name
of the drums is different (incorporating a + sign), so that the NOT and
attractor lists can
show a differentiation if necessary between these similarly named drums.
1.2.2 100% ¨ DRUM: 1+Violins 2
1.2.3 100% ¨ DRUM: 1+Violas
25 1.2.4 100% ¨ DRUM: 1+Celli
1.2.5 100% ¨ DRUM: 1+Double Basses
2. 100% ¨ XOR hypemode: "1 or 1+"
This node will chose between whether the second stab in the bar comes on 2+ or
on 4+.
30 2.1 50% ¨AND hypemode: "2+ "
2.1.1 100% ¨ DRUM: 2+Violins 1
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These heuristics are copies of all the drums in heuristic 1.1, but the
probability grid is
100% on 2+.
2.1.2 100% ¨ DRUM: 2+Violins 2
2.1.3 100% ¨ DRUM: 2+Violas
5 2.1.4 100% ¨ DRUM: 2+Celli
2.1.5 100% ¨ DRUM: 2+Double Basses
2.2 50% ¨ AND hypemode: "4+"
2.2.1 100% ¨ DRUM: 4+Violins 1
These heuristics are copies of all the drums in heuristic 1.1, but the
probability grid is
10 100% on 4+.
2.2.2 100% ¨ DRUM: 4-i-Violins 2
2.2.3 100% ¨ DRUM: 4+Violas
2.2.4 100% ¨ DRUM: 4+Celli
2.2.5 100% ¨ DRUM: 4+Double Basses
15 These heuristics are processed by a custom rhythm adaptor. This adaptor
checks if the next
chord or end of phrase is a quaver away from any given triggered quaver. If
so, it adds 5
to the pitch position. This selects the next bar's notes from the Strings idea
staff.
SECTION D
20 I. Contextual analysis of Bach C minor Prelude to Generate Heuristic for
the Generative
System of Embodiments and Aspects of the Present Invention
DC.1 Abstract
The purpose of this study is to analysis the Bach prelude with a view to
creating a set of
25 exemplary heuristics capable of reproducing the analysed work as well as
many others.
Contextually, this analysis offers a way to turn qualitative musical data into
quantitative
empirical data, and demonstrates the validity and approach described above in
terms of
the treatment of chord transposition/manipulation, chord construction and note
generation.
The abstraction of the algorithms is essentially based on expert qualitative
opinion. These
algorithms have a multitude of parameters and criteria which can be changed
with
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observable results. This gives a way to measure the effectiveness of each
assertion, and to
create a bank of heuristics which give consistent musical results and work in
all contexts.
D.2 Introduction
5 Whilst identifying and developing a simple set of heuristics that
reproduce the piece in its
entirety, these algorithmic processes are able to produce a wide variety of
quality material,
too.
Like any other, the application of this analytical method is subjective and
iterative.
10 However, its findings provide a road map for an empirically measurable
set of heuristics
which can he used to test the validity of the analysis. Through this method, a
road map is
identified to take qualitative analysis and turn it into a set of heuristics
which can be judged
quantitatively.
15 The piece under consideration is the first 24 bars of Bach' s C minor
prelude from the first
book of the Well Tempered Clavier (1722). This contains data for three
algorithms which
are obtainable from the first 24 bars' data. These bars constitute the vast
majority of the
first version of the piece, after which it jumps from bar 25 to bar 35 and
ends with one bar
of C major, totalling 27 bars (Ledbetter, 2002, p. 152).
The following study is broken into four areas: three for texture heuristics
and one for
phrase analysis.
D.3 Analysis Method
25 Throughout the analysis syntactic structures and note pitches are
highlighted. The purpose
is to establish what is purely entropic and redundant, as well as what is
developed material.
FIG. 19 shows the typical structure of entropic, redundant and developed
material in the
first two bars, using the predefined colour scheme of red to indicate
"entropic" (darkest
shading, position of notes 1 to 3 in bar 1 and position of notes in positions
2 to 4 in treble
30 of bar 2), green to indicate "redundant" (mid-coloured shading, position
of note 4 in bar 1
and all remaining notes in bar 1 and bar 2 except those expressly identified
as red or
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yellow) and yellow to indicate "developed" (lightest shading and first note in
both treble
and base in bar 2).
D.4 Form Overview
5 With regards to the piece in hand, (Bruhn, 1993) breaks it down into four
structural
sections:
1. bars 1-4 (perfect cadence in C minor)
2. bars 5-14 (modulation to Eb major)
3. bars 15-18 (modulation back to C minor)
10 4. bars 18-38 (complex, extended cadence in C)
The analysis makes use of more dynamic fluidity in the functionality of any
given section.
This section shows that the piece divides into three different variations of
the same
algorithmic process. Section 1 is the first variant of this process from bar 1
to bar 18.
15 Section 2 is the second variant present in bars 19 and 20. Section 3 is
the third variant that
lasts from bar 21 to bar 24. These sections each have a different algorithmic
processes to
produce their material and provide insight into the structure of the Bach
prelude. From a
formal point of view, each of these sections is capable of breaking down into
more modular
components.
With the entirety of the generative compositional system of the present
invention, form is
elastic and dictated by refining a set of brief requirements based on the
structure of the
multi-media product, such as a film, for which it is composing. Described are
processes
that detail how chord sections may be lengthened and shortened through the use
of
25 different briefing requirements.
D.5 Phrase Analysis
The purpose of this phrase analysis is to define three distinct and different
sets of heuristics
that will generate chord schemes and form pieces.
D.5.1 Phrase 1 (cadential): bars 1 to 4
This phrase functions as a loopable statement which emphasises the key centre
of C minor.
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It demonstrates that the 1V dim can be used as a cadence chord to the local
tonic.
D.5.2 Phrase 2 (sequence): bars 5 to 12
Conventional analysis attributes this section to the harmonisation of a
falling scale using
5 the first inversion major chord to third inversion dominant 7th, figured
bass as 6-3 to 6-4-
2 (Ledbetter, 2002). It would be possible to consider this as a cycle of 5ths,
except that the
Ab to D7 chords in bars 5 and 6 do not follow a strict cycle of 5ths pattern.
The following therefore applies an approach that is more than conventional
analysis can
10 offer, namely a set of logical heuristics to explain both the choice of
major or minor
harmony, and the choice of these chords' roots that lie outside the strict
cycle of 5ths. This
approach is deemed necessary because this avoids the system from being allowed
just to
generate any chord in an ad hoc fashion in order to harmonise melody and thus
to avoid
being pushed out of the realms of tonal music where there would be a loss of
the priority
15 tone or key centre.
The evaluation does, however, need to be able to categorise specific chord
schemes if new
ones are generated based on compositional principles described herein.
20 There are several readings that are possible for the chord scheme
between bars 5 and 14.
They do follow an intervallic relationship in the melodic minor scale, that of
rising 3 scale
steps for each new chord until the chord scheme has returned to Ab (equivalent
to a falling
cycle of 5ths within the given scale). This could be interpreted as a sequence
phrase, but
this still does not offer a generative structure that would produce the D7
chord. A more
25 interesting reading is that of the principle of the tritone
substitution. Known in jazz, this is
where a dominant 7th that is a tritone (or augmented fourth) away from a
dominant 7th,
can be used in place of the dominant 7th. This supports a transposition from
Ab => D7 =>
Gm. However, if the Ab is functioning as a tritone substitution to elongate
the D7, then
switching these chords around should result in the piece still sounding quite
natural, as if
30 there was an extended cadence to Gm. This simply is not the case and
sounds awkward
when played by the algorithm in tests.
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The preferred reading is to use a sequence phrase method that can be applied
to any
developmental section of a piece in a minor key. By choosing a random place
within the
descending melodic minor scale and then creating a descending scale from that
note,
repeating every note for a chord change. E.g.: Ab, G, G, F, F, Eb; or D, C, C,
Bb, Bb, Ab,
5 Ab. Wherever a semitone is encountered within the scale, a tritone
substitution is made to
the dominant to harmonise the pattern, and whenever a tone is encountered a
simple II V7
progression is used. The scale is then discarded as it is only used to
generate the chord
sequence.
10 This can be expressed in the following pseudo-code:
Ilmake an array that contains the tonic minor scale
descending
int[7] scale = tonic _melodic minor descending;
//create a list of chords to hold all generated chords
15 List<Chord> chordList;
//randomly choose a starting position in the scale
int positionInScale = random(7);
//loop this bit until you have enough chords
while (notAtEscapeTime)
20 // if the current scale note is a semitone away from the preceding note
if (scale[positionInScale] - scale[positionInScale+1] == semitone)
// do tritone to dom7
chordList.add: withPitch: scale[positionInScale], mode: major
chordList.add: withPitch: scale [positionInScale+1] +7, mode: dom7
25 else
// do minor II to dom7
chordList.add: withPitch: scale[positionInScale], mode: minor
chordList.add: withPitch: scale [positionInScale+1] + 7, mode: dom7
30 // move on to next not in descending scale
positionInScale++ mod 8
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D.5.3 Phrase 3 (cadential): bars 13 to 14
The phrase 2 sequence requires an escape phrase, which occurs at bars 13 and
14 as a
perfect cadence to the relative major, Eb. This sequence is generated from a
scale from the
relative minor. Therefore, the escape phrase can be focused on the specific
key of the
5 relative major without worrying about what was going on in the sequence
beforehand. This
makes for some rather interesting yet viable escape relationships, such as if
the generative
mechanism were to have finished on a scale position of D in the key of C using
the pseudo
code above.
10 This would mean the last two chords in the "chordList" would be Bbm and
Eb7. Using the
proposed escape mechanism we would get: Bbm => Eb7 => Bb7 => Eb.
D.5.4 Phrase 4 (cadential): bars 15 to 16
This phrase acts as a question in the relative minor of Eb major, the original
key centre of
15 C minor. This gives a way of modulating from the relative major through
the use of the
relative major's supertonic dom7th, which, if we were to interpret the root as
Eb, could
also be classed as the relative major 9 #1113. This chord then calls the Bb7h9
(see Section
D.6.2 for the reason this chord classification), which is connected to the
following answer
phrase.
D.5.5 Phrase 5 (cadential): bars 17 to 18
This is the answer phrase to question phrase 4. It functions as a cadence to
the tonic minor
from the supertonic diminished (see Section D.6.2 for the reason for this
chord
classification).
D.5.6 Phrase 6 (sequential): bars 19 to 20
This phrase reveals the second set of heuristics which are an adaptation of
the first. This,
by definition, means that it is a self-contained section since it acts as a
build-up to the
escape phrase at bar 21. The phrase currently features a chord scheme which
moves from
30 the subdominant minor to the second inversion tonic via a rising
diminished chord. These
chords have a tonic C minor chord superimposed at the top of their voicing.
There are two
ways to handle this. Firstly, create two chords at this point in time and give
rules for their
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voicings. Secondly, give the C minor notes context within the existing chords.
This second
approach would result in bar 19 represented as Fm7 and bar 20 as F#dim;
however, the use
of the B on the third semiquaver makes these chords unlikely candidates for
the bars'
textures. The heuristics used to embellish the texture appear to be based on C
minor and
5 clearly persist throughout the phrase. Therefore, the first reading of
two superimposed
chords makes more sense. This specific example of Fm and F# dim is a
conventional way
to arrive at a cadential six-four; however, this common invention requires
explanation in
the shape of heuristics.
10 Section 2 (D.7) considers that this two-bar phrase appears to be playing
on the fact that
the first two notes of the tonic triad, C and Eh here, can he extensions for
many other
chords that would have these as higher notes within the chord ¨ or extensions.
To create
this sequence pattern of chords we can use the following pseudo code:
15 cCds I I = array for the chord scheme;
no0fChords = number of desired chords;
newChord = new chord holder;
for(i = 0; i < no0fChords; i++){
if (i = 0){
20 newChord = findChordWith( {C, Eb , 2 , true, cCds } ;
else{
if (currentChords[i-1] has one extensions below){
newChord = findChordWith({C, Ebb 2 , true, cCds ;
if (c urrentChords[i-1] has two extensions below){
25 50% newChord findChordWith( {C, Eb } , 3 , false, cCds 0 ;
or newChord = findChordWith( [C, Ebl , 2 , true, cCds 1;
1 if (currentChords[i-1] has three extensions below){
50% newChord = findChordWith({C, Eh}, 3 , false, cCds} ;
or newChord = findChordWith({C, EN, 2 , false, cCds} ;
30 1
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cCds. add (newChord)
Here, findChordWith() is a function that returns a major or minor chord with
any number
of extensions (7ths, 9ths, etc.); it can also return a diminished chord. (An
Ab5 can be
potentially returned in this case as an Adim.)
As with all heuristics generated through this method of analysis, there is a
core qualitative
judgement made by the analyst which produces the analyst's first attempt in
attempting to
define methods which can generate as wide a variety of musical ideas as
possible whilst
ensuring they remain musically acceptable. These heuristics are therefore
refined
qualitatively by the analyst passing judgement on the return of the musical
ideas that the
rules produce. This can be through either dry runs or actual computation. The
purpose of
these refinements is to point towards a musically acceptable result as
perceived by the
predefined audience. How the analyst decides to define the audience therefore
affects the
compositional judgement that is made. Different opinions may be able to
contextualise
different verities of returned output. In the case of this specific phrase, an
analyst with in-
depth experience of jazz may perceive certain returned chords as
substitutions, therefore
subconsciously giving them a viable context that a different analyst would
not. It is
conceivable that a good composer would be able to offer a context to justify
any
combination of intervals, given sufficient scope to orchestrate and prepare
the given chord
through its surrounding syntax. Given a large enough sample set of pieces from
any
particular period, the evolution of heuristics offers increasing insight into
the development
of codes and conventions from one point in musical history to another.
In the case of this analysis, the stance taken is that the results sound
idiomatic for the piece
in question. This qualitative approach of listening to the returned values and
assessing
them through perception can offer a bulwark against criticisms such as that
articulated by
Ball (2011, p. 69), who suggests that "it's a common habit of musical
iconoclasts who seek
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'theoretical' justifications for their experiments ... to use abstract
reasoning that takes no
account of how music is actually heard".
Here, Ball is referring to the auditory-cognitive processes that a mind goes
through when
5 listening to music. The pitfalls of creating a scientific theory for
music without taking into
account a model of the cognitive process is highlighted by Wiggins et al.,
(2010, p. 237).
They argue that, "because music, and in particular musical structure, only has
existence in
the mind, the very notion of a scientific theory of Music, distinct from mind,
is suspect"
and "To study the thing itself [music], we need access to the implicit, or
tacit, knowledge
10 used by music analysts ¨ the structures that are inferred and
experienced by listeners and
other active musicians ¨ and to the processes that build them".
The exemplary study expressed herein provides a basis for definitions of these
tacit
processes, and explains the cognitive theory behind them.
In the case of this Phrase 6, we have two notes multiplied by two chords
giving four
possibilities. The two chords always feature the 3rd degree of the scale to
highlight its
harmony and the point of this section is to use the lowest extensions in the
chord which is
building down from the Eb. It is therefore irrelevant for this method to
return any chord
20 which alters the 5th. If this were to be the case, then the 3rd and 5th
without the root would
be a chord in the list that was already usable. The alternative voicing of the
root and 5th
would leave an ambiguity as to the tonality of the chord in question. This is
not the case
in Phrase 3 where extensions are sought at the top of the chord, but in this
context there is
no other supportive evidence for voicing or voice-leading. It would also seem
unidiomatic
25 to combine intervals which do not create a third relationship of some
kind, such as a natural
7th to a flattened 9th. Consequently, the approach of the invention returns
extensions
which are bound to allow major and minor thirds only through the:
(a) 7th being major or minor
(b) 9th being flattened (if 7th is minor) or natural
30 (c) 11th being natural or sharpened (if 9th is natural)
(d) 13th being natural
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The method also takes an array of notes which will make the top extensions of
the chord
it will return. It takes an integer to state how many extensions below these
notes it will
include to make the chord. It takes a Boolean to decide whether it can use
chords with
fewer extensions than this integer. It accepts an array of chords in which it
checks whether
5 the chord it has generated exists or not.
D.5.7 Phrase 7 (sequential): bars 21 to 24
This phrase is interpreted as two phrases repeated. The first acts as an
escape phrase to
sequence phrase 6 through bars 21 and 22. It would be possible to loop these
two bars, but
10 they feel as if they require embellishment throughout the repeat with
rising extensions (as
in fact the piece does in bars 23 and 24). The need to embellish a repeated
phrase is how
an answer phrase is described: one that, if repeated, appears to be building
to a climactic
release of a cadence resolution.
15 This phrase is generated by creating a series of chords that are all
cadences to the tonic, in
a way which gives a rising melody by creating an initial tonic-chord texture
and choosing
a melody note which is the closest viable option to the top of the main
texture. (This
viability is based on the note being far enough away from the main texture to
become a
cue (Deliege, 2001) as is discussed later.) The subsequent choice is a cadence
chord to the
20 tonic and repeat of the tonic texture whilst selecting the treble's
first note of the bar to be
the next available note above the previous bar's top note from the cadence
chord's various
possibilities. Each time there is a return to the tonic chord, the next
extension upwards for
the treble's first note (in the previous cadence chord's bar) is used. This
may cause the
next down note of the texture from the top melody note to fall more than an
octave away
25 from the melody note in position 1 of the treble. However, by re-voicing
the texture to be
higher the texture is brought to within the octave boundary of the top note in
the right hand
at position 1. The bass figuration stays the same unless it ends up starting
on the same
interval as the treble texture, in which case it moves one inversion higher to
offer a
harmonic alternative.
This states that the texture's voicing is dependent on the melody. This does
not stray from
traditional thinking, in that the octave span is idiomatic for the instrument.
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D.5.8 Phrase 8 (cadential): 35 till end
The current analysis is not concerned with the embellishment of the dominant
ending for
this piece. Suffice to say, the previous sequence phrase requires an escape
phrase. The
5 escape phrase in this context is a tonic chord for two bars. This is in
keeping with the
original version of the piece which cut to bar 35, (Ledbetter, 2002).
D.6 Section 1: Bars 1 ¨ 18
D.6.1 Initial Observations
10 1. Evidence of a self-contained syntagm (or sign at the very least) is
from the fact that each
bar contains a complete copy of the first half in the second half. This only
changes in bar
18, where the bass moves in a downward step from C through Bb to Ab. This
exception
can be considered within its localised context later in the analysis. Further
redundancy can
be found in the fact that the last three pitches of each second beat are the
same as the last
15 three note pitches of the first beat. On top of this, each 4th
semiquaver within the first beat
of each bar is a copy of the 2nd. This, combined with the fact that each 3rd
and 4th beat is
a copy of the first two beats, means that there is only a need to explain the
relationships
between four notes in each bar algorithmically. The rest of the bar can be
generated from
this material.
2. From the four notes in question in each bar, semiquavers 1, 2 and 5 are
notes of the
chord for the bar (with one exception at bar 14).
3. Bass notes on the first semiquaver appear to represent a pedal throughout
most of the
25 piece; these bass notes change in certain bars but not others.
Conventional readings put
this pedal note down to a chromatic note within the bar for which most
analyses provides
little more than an acknowledgment (Bruhn, 1993; Ledbetter, 2002). It would
not be
appropriate to leave such a compositional statement as this unexamined if the
underlying
algorithm is to be effective. Rather, it is necessary to establish how this
note stays the
30 same, what happens to change it and what influences the note's pitch
when it does change.
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4. There are non-chord notes which appear at semiquaver 3. These notes do not
necessarily
fall on the scale notes for the given key of C minor. The 2nd bar demonstrates
this with
the E natural in the top (right) hand. In fact, it appears as the leading note
for the bar's
chord of F minor. Ledbetter (2002) suggests that Bach used chapter VI of
Niedt's
5 Handleitung zur Variation (Niedt, 1989) in order to arrive at this
figuration.
However, Niedt's book does not offer any explanation for the note's
naturalisation. This
chapter contains rules to obtain "stronger harmony- when voice leading. The
second
chapter states rules for the setup and successful resolution of consonant and
dissonant
10 intervals, including definitions of both, but these rules do not offer a
set of heuristics for
the appropriate selection of notes in a way which can be abstracted from the
post-
rationalisation of a choice which has been made. The nature of these rules is
merely
suggested in Bach's writing (including his abilities to break them), hut they
do not give us
an explanation for the pitch choices of the notes in question. A system of
heuristics is
15 therefore needed to be obtained through analysis to decide how to
generate their pitches.
This set of heuristics should be able to be given parameters to alter the
emotional stimulus
of the music whilst maintaining its human aesthetic properties.
5. The pattern of direction within bars of the figuration changes in places.
In various bars
20 Bach chooses to alter the pattern of how the figuration works in the
left hand. This requires
explanation in order to calculate when pattern alterations are needed, and
which variants
are appropriate.
6. Bach's implied melody falls outside of the main texture where other notes
form the
25 figuration. Deliege (2001) explains this phenomenon through the
principle of cue
abstraction. Based on the concept of grouping within gestalt psychology, the
mind
separates these notes from the main texture, giving them a sense of
continuation with a
melodic function. The following considers how to reproduce this
algorithmically.
30 D.6.2 The Texture
From point 3 in the initial observations, taking the E natural in bar two as a
local leading
note to the bar's chord of F, an explanation for the note's pitch is derived.
This asserts that
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the note is derived from the dominant of the F minor chord, C major. If we
consider the G
which also appears below the E natural in this bar, this is consistent with
the C major
chord. By therefore stating that all notes in this 3rd semiquaver position in
every bar are
from the bar's chord's dominant or dominant 7th, an interesting pattern
emerges from the
5 rest of the bars in the piece (not including diminished chords, which we
shall consider
separately). Each dominant chord is guaranteed to have a 5th degree of the
scale. The other
note is either the 3rd to give the dominant chord, or the flattened 7th to
give a dominant
seventh. Furthermore, this 5th is always preceded and followed by the 3rd of
the bar's
current chord. This pattern can occur in either the bass or the treble. While
this 5th is
10 harmonised by a 3rd or a 7th note from the local dominant chord of the
bar, 3rds are
preceded and followed by roots in the bar's current chord and 7ths by 5ths.
This is
essentially a different way of looking at voice leading: the main chord of the
bar must
feature a 3rd to give it its mode. This observation of how the pattern works
in this piece is
simply stating that the 3rd always moves down to the 5th of the local dominant
and back
15 (underlined as 3-5-3 in the analysis), and likewise for the 1 st-3rd-
1st and 5th-7th-5th
relationships. FIG. 20 shows the bass and treble notes within the dominant
chord related
to the given bar's root.
The following analysis shows a simplified version of the movement and degrees
of each
20 note in the relevant first five semiquaver positions. The notes on the
third semiquaver are
in relation to the bar's local dominant. The arrows to separate chords show
the hierarchical
flow. Cm => G7 means that the Cm asks for the G7. In algorithmic terms, this
is actually
the opposite; the G7 needs to "see" the Cm chord to know what dominant chord
it should
be. This is simply to say that the G7' s pitch is dependent on the Cm.
The red-coloured (darkest shade) notes show the entropic nature of the new
observed
pattern. For example, in bar two, the 3-5-3 structure is now redundant and
the 1-3-1 is
entropic and unrelated as a development to bar one's 5-7-5. This is therefore
red (see C.3).
Further to this, in bar three both become redundant and the b3 is a
development, therefore
30 shown in yellow (lightest shade). In essence, we establish heuristics to
cope with the initial
patterns that are found. Progress through the piece sees adaptation of the
heuristics or
generation of new heuristics to cope with the new entropic material that is
encountered
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and the material that cannot be explained by the heuristics as they are (at
this point of this
exemplary analysis).
Bar two contains an entropic bass note with regards to the chord's root;
however, this is
5 clearly a development of the pedal from bar one because the chord has
changed. The notes
appearing in semiquaver five are a chord note below the previous note. This is
redundant
since this has already been seen in bar one. By bar two, the pitch direction
arrows in the
analysis become completely redundant in nature, thus proving the applied
methodology.
10 Bar three is the first diminished chord out of two in the considered
section. This chord
changes the fundamental nature of how we express interval positions.
Initially, these
diminished bars appear to function as dominants, calling a relative minor to
the root note
of the diminished chord in semiquaver three, instead of the major. This is not
redundant,
it is a new development of the original compositional concept, hence it is
coloured yellow
15 (lightest shade) in the diagram. Treating these diminished chords as
dominants with their
local dominant appearing on the third semiquaver is in keeping with the
principle of
secondary dominants.
However, classifying the fifth degree of the scale as a flattened fifth, as
well as calling the
20 sixth degree a sixth does not make any sense whilst talking about an
even-interval chord,
such as a diminished chord. It would be possible to make any bar featuring a
diminished
chord an exception, with its own local rules, but this would lead to creating
ad hoc rules.
This is undesirable as the new rule will simply act as a sticking plaster over
the troubling
statistical data at hand. However, by simplifying the interpretation of note
positions within
25 chords to simply be positions within a given array of notes, the chords
can be re-expressed
as arrays. Therefore, the root, third and fifth of a C minor chord simply
become [0],[1] and
[2] of an array. The actual values contained in the array's positions are
populated by a
minor chord function which returns the pitches as in integer notation:
{0,3,7}. We can
therefore consider 6ths and 7ths as the same thing: occupants of position [3]
of the chord
30 array. (This also allows use of different harmonic systems for
generation based on the
algorithmic processes which develop from this analysis, such as quartal
harmony.)
Consequently, Bars 1, 2 and 3 become expressed as array positions as shown in
FIG. 21.
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Whilst this simplification to the rule set means that we can deal with
challenging
extensions with ease by simply putting them into a given array position, it
makes the
musical interpretation of the analysis a little too abstract and difficult.
Therefore, it is better
5 to express the analysis in terms of note positions within the chord, such
as 3rd, 5th, etc.
(bearing in mind the computational array structure that this will eventually
fit into). See
FIG. 22.
This adaptation still does not help us cope with the harmonic independence the
bass obtains
through its leading note mechanism, but examination of more diminished chords
establishes a pattern_ As is seen in this analysis, the bass follows its own
array rather than
that of the main chord. This is generally prevalent throughout many styles of
composition
and is represented in lead sheets by using a forward-slash to denote that the
chord is over
a bass which may seem independent of the notes that appear within the chord.
15 Consequently, this is not an ad hoc rule, but simply a fact of how music
is notated, if not
conceived. It is feasible to imagine any note working in the bass of a
diminished chord.
The initial assumption, then, is that diminished chords take the bass note of
the following
bar as their bass, thus creating or continuing a pedal.
20 The interpretation of bar three being an Fdim is simply that this mates
the chord fit into
the pattern of having the 3rd and 5th or 5th and 7th of the dominant in the
3rd semiquaver
position, albeit a minor version of the dominant. Simply through interpreting
the chord as
an Fdim, there is no need for an ad hoc rule to cope with the 2nd, 3rd and 4th
semiquaver
notes. If the chord scheme is played without a pedal bass but a root bass,
conventional
25 reading would make this note a B or G in this bar. However, the chosen
reinterpretation of
Fdim would make the bass an F. This sounds perfectly acceptable. This is a
simple
example of computational analysis pointing towards a reinterpretation of the
score for no
other reason than to simplify the model without cost to the intricacies within
the data.
30 With reference to FIG. 23, Bar four starts with a repeat of the melody
note in bar one. The
repeat of this pitch is the first time that a repeat of a melody note is seen
in the composition.
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We shall consider this new, and consequently entropic, concept as more
evidence for how
the melody flows becomes apparent throughout the analysis.
Bar 4 gives us our first alteration to the figuration pattern seen in the
first three bars. In
5 practical terms, this is simply because the chosen interval jump from the
1st to 2nd
semiquaver in the bass means that if the downward pattern continued then the
bass note at
semiquaver 1 would be repeated in semiquaver position 5. The requirement for
this note
to rise is therefore a development of the material at hand and coloured
yellow. This
happens in 10 out of the 24 bars analysed. The table in FIG. 24 shows the
fifth semiquaver
10 in the bass and the chord component on which it lands. There appears to
be no correlation
between the chords' local dominant 5th (in semiquavers position 3) being in
the bass or
treble and the upward or downward movement of the 5th bass semiquaver.
The pattern goes up in the bars listed below for the following reasons:
15 4: To avoid repeating the 1st semiquaver.
10: To make sure the 7th in the bass is not confused as having a voice leading
relationship with the 1st semiquaver leading to a new cue (Deliege, 2001)
being identified
by the ear through the scale step oscillation of these two notes.
11: There is no reason except for the fact that the preceding and following
bars change
20 the movement pattern. This is a choice from Bach and entropic with
regards to heuristic
considerations.
12: To avoid repeating the 1st semiquaver.
14: To avoid repeating the 1st semiquaver, (this is a hint
at a new method of producing
notes at this position which will be considered later).
25 17: Similar to bar 10, there would be only a scale step between the 1st
and 5th
semiquavers and this could lead to a bass melody being interpreted by the
listener.
19: To avoid repeating the 1st semiquaver.
21: Generated by the bar 14 method, which produces such
notes at this position.
23: Generated by the bar 14 method.
30 24: Generated by the bar 14 method.
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A simple heuristic can thus be derived that produces the note at semiquaver 5
without a
pattern change and then checks to see whether it is within a tone of the bass
note at
semiquaver 1. If it is, then the pattern change triggers. The only exception
to this is the
aesthetic choice that Bach makes at bar 11.
Bar six raises the question of whether the dominant 7th D chord is simply a
dominant to
preserve the bass pedal. Ledbetter (2002) describes the first inversion major
chord to third
inversion dominant 7th (figured: 6-3 to 6-4-2) in this piece as a standard way
of
harmonising a descending scale. The reason why this question is important here
is to
ascertain whether the chord is created due to the bass movement, or whether
the pedal is
created due to the choice of chords. We currently choose to read this as the
chords creating
the bass, because this simplifies the heuristics. The bass note now falls
within the chosen
or generated chord, rather than the chord being generated ad hoc from the
descending bass
scale.
With reference to FIG. 25, Bars 7, 8 and 9 offer no new information apart from
the melody
in semiquaver 1, so much so that it is interesting to note that bars 8 and 9
are complete (yet
transposed) copies of bars 6 and 7. This is an important aesthetic observation
because the
heuristics we define will be capable of creating multiple different versions
and voicings in
such circumstances. It is important to note how Bach uses complete redundancy,
repeating
his voicing and textural decisions to give form to the listener's temporal
predictions.
There are two possible readings of bar 11: that of an Eb chord or a Cm7 chord.
Minor 7th
chords are indeed prevalent throughout Bach' s work, (such as in the 3rd beat
of the 22nd
Prelude in this suite in Bb minor). By using the Cm7 version, we do not need
to encounter
a 1-3-1 relationship in the bass in the first section's heuristics, but just
the predictable 3-
5-3 and 5-7-5 relationships. However, minor 7th chords do not feature in this
piece's
discourse because they simply do not appear as the main chord in any other
bar. If the
deciphered heuristics which are generated from this analysis are fed versions
of this piece's
chord scheme with both a Cm7 and Eb chord in this bar, then the voicings and
arrangements played by the Eb chord sound far more natural and appropriate. We
therefore
choose to read this bar as version 1 lb for algorithmic reasons but appreciate
that it is
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actu ally version 1 la. In truth, this simplifies the preferred construction
of the heuristics
whilst enabling the feed of the Eb chord into the chord scheme. The only
consequence is
that this specific bar's voicing will not be possible. This could be developed
in any later
versions of the heuristics as more patterns are discovered and better
generalisations are
5 made, but is irrelevant to the extent that this analysis proves the
underlying approach to
analysis and generative composition based on the methodology described herein.
As previously mentioned, there is no functional requirement for the bass in
semiquaver
position 5 to rise in bar 11. This decision by Bach remains an entropic
problem during the
10 certain stages.
With reference to FIG. 27, Bar 12 splits the mind's interpretation between a
Cmb6 chord
and an Abrnaj7/C chord. If we consider this to he an Abmaj7/C pattern, then
the 3-5-3
relationship breaks down for the first time to give 7-5-7 in the treble and 5-
3-5 in the bass.
15 If we call this chord Cmb6, then the initial b6 in the right hand can be
accommodated by
treating it as a 4th element in an array, just like a 7th. However, the b6 in
the bass in
semiquaver 5 makes the jump through the available 5th (as we go from the 3rd
in
semiquaver 4 to b6 in semiquaver 5), which is problematic considering we do
not see this
behaviour in the rest of the piece. In other versions of the pattern break
that make the bass
20 in this position rise instead of fall in order to avoid creating a
salient cue in the bass, we
see the arpeggio at semiquaver 5 feature the next note from the bar's chord
that is above
semiquaver 4. Here it climbs from the [2] array position through to the [4].
This ambiguity
is clearly desired by Bach as we sense the repeated b6 jumping out as if it
were a cue. This
creates an effect that sounds like the piece's rhythm has double-timed in this
specific bar.
25 This need for a new audible cue could be handled as a specific case
which arises at the
point of a modulation: at this point, the movement towards Eb in bar 14. This
seems
acceptable in regards to the important position of this pivot chord, but does
mean that the
algorithm will have to be sensitive to points of modulation. This bar also
resets the bass
pedal back to the tonic through the jump of a perfect fourth. This is entropic
considering
30 the bass's falling movement in the piece so far.
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Bar 14 introduces a completely new idea in the bass by moving stepwise up to
the fourth
degree of the bar's chord. This is completely out of character with the piece
so far, which
uses intervals from the given chord in this position, and hints at the
algorithm which
develops in later sections of the piece.
If this chord had a Bb instead of the Ab on semiquaver 5, there would be no
entropy here.
As an aside, it is worth noting that the score version from which we take
modern
interpretations of this piece is known as The Wagner-Volkmann Autograph. This
copy was
made in 1732, ten years after the pieces were composed in 1722. The original
manuscript
is believed to be lost, leaving this as the only known copy of the first
manuscript in Bach's
own handwriting (Palmer, 1994). However, Bach's son Wilhelm Friedemann made a
copy
of the earliest forms of the first 11 preludes with various small corrections
made by Bach's
hand, a version known as The Clavier-Buchlein version. Owned by Yale
University, this
version clearly shows that Bach initially had the Bb instead of the Ab at this
5th
semiquaver position. This can be seen in FIG. 28.
The above suggests that Bach changed the note at this point in the piece on a
later revision
to reflect the processes that he employs later on in the piece. (These
processes simply use
the sub-dominant in position 5 in a similar way that the dominant is used in
position 3.)
Heuristically, this means we can separate this specific Ab occurrence from the
first section
under analysis, and consider it using the heuristics that we obtain from
phrase 3 in which
this figuration becomes more prevalent.
With reference to FIG. 29, Bar 16 introduces an interesting dilemma for the 3-
5-3
relationship. If this bar is interpreted as a Ddim chord, then the C and Eb in
position 3 bear
no relevance to the dominant A of D.
Despite the Bb not actually appearing in the bar at all, the C and Eb leave
only two
possibilities if the 3-5-3 relationship is to be maintained: the dominant must
be either F7
or Ab. Ab makes no musical sense because it would imply the bar is the chord
of Db. F7
sustains the pattern of the 3-5-3 whilst making musical sense as the dominant
to Bb7b9.
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The Bb chord functions perfectly within the chord scheme by linking to the F7
in the
previous bar. (Audibly, this bar and the next remain highly chromatic.)
Although we could
use the lack of a 1st degree in bar 16 to suggest that the first array
position could hold the
b9, it is more consistent to expand the array to incorporate a 5th position
which contains
5 the b9.
Bar 17 contains the second diminished chord that we have experienced within
the piece so
far, (accepting bar 17's reading). The 3 5 3 relationship points to yet
another secondary
dominant (minor dominant) at semiquaver 3, as experienced in the first
diminished chord
10 of bar 3. This conventionally would signify a dominant function for the
diminished chord.
The only relationship we can see this bass note has in the pieces is that of
the bass note in
the next bar. This does however lead to a simple heuristic with regards to
diminished
chords: that they contain the bass note of the following bar's chord.
15 With reference to FIG. 30, Bar 18 contains movement in the bass which is
noted in the
Autograph, Kirnberger, Gerber and Walther manuscripts (Palmer, 1994). Only the
Kroll
edition leaves this Bb note as a C (Ledbetter, 2002). Originally believed to
be a copying
error, this has later been poorly justified in the name of consistency. This
is clearly a cue
that is being established by Bach to end the section and emphasize the move to
F minor in
20 bar 19. This chord ends the section in question.
This linking movement in the bass will be ignored with regards to the current
heuristics,
which we will develop for bars 1 ¨ 18, due to a lack of examples for how this
cue is utilised.
Any heuristic to create the Bb at semiquaver 9 would be an ad hoc rule without
further
25 supporting evidence. The 4th degree of the scale in the bass at
semiquaver 5 is further
evidence of the shift towards the algorithmic processes of the following
sections, just as
in bar 14. Further evidence to confuse any interpretation is that this F at
semiquaver 5 is
written as a repeated C in the Clavier-Buchlein version, thus emphasising the
cue which
is occurring in the bass movement.
D.6.3 Heuristics for Section 1: Bars 1 to 18
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The following commentary numbers the notes in the bass and treble by array
positions [0]
to [15] to signify the 16 semiquaver positions within the bar.
D.6.3.1 H1.0: Calculate Bass at [0]
5 The pedal note: the entropic nature of the notes in the bass in each
bar's first position
means we need a generative heuristic to create these possibilities. By looking
at the
availability of the current pedal note within the bar's chord and the pitch
value that the
note takes, it is possible to calculate this bass by checking if the bass note
of the previous
bar falls within the current bar's chord. If the note does not, the next
closest available note
10 is selected from the chord which is below or above the previous bar's
bass note. (This
direction in pitch, be it up or down, is arbitrary and means we can initialise
it from
connotation requests through briefing elements processed by an overseeing form
generator.) There is an exception for diminished chords which are used to end
sections:
they simply use the note in the bass of the bar to which they are cadencing.
This means
15 that there needs to be two passes whilst creating the piece. The first
pass is to establish the
bass notes as described without the diminished clause. The second pass is to
then change
the diminished chords' bass notes to look at that of the following bar, rather
than that of
the one preceding them. Without this double pass, the heuristic would have a
null pointer
when it reached a diminished chord.
This pattern continues until the bass is over half an octave from its origin.
In this piece's
case, the tonic C is the origin, meaning that the F# which is 6 semitones
below this C is
the reset position. When a bass note is generated that falls below this, the
pattern is reset
and the nearest note within the current chord to the initial starting bass
note on the tonic is
25 used. This can be seen when at bar 12 the note jumps from bar 11's bass
of G to the original
tonic of C. In the piece at hand, the pedal switches; rather than always
falling, it chooses
the closest note that is either higher or lower. From bar 6 to 7 it falls from
C to Bb, whereas
from bar 12 to 13 it rises from C to D.
30 D.6.3.2 H1.1: Calculate Bass at [11
There are 13 cases out of 18 where this note is the 3rd of the chord; if not
then it is the 5th
of the chord. For variety's sake during the initial investigation of how
heuristics sound,
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(before we introduce overriding aesthetic heuristics which manage choices), we
can
simply make this a 50/50 scenario. This makes the heuristic simple: make bass
[1]
randomly the 3rd or 5th above the bass in [0].
5 D.6.3.3 H1.2: Calculate Bass at [2]
If the bass hand note at [1] is the 5th, then make this the 7th of the
dominant 7th. If this is
not the case, then bass [1] must be the 3rd: we therefore make [2] the 5th of
the dominant.
Either way, we transpose [2] below the bass at [1].
D.6.3.4 H1.3: Calculate Bass at [4]
As shown in the explanation for FIG. 24, this note attempts to be the chord
position below
the value in [3] (which is a copy of [11) unless it comes within a tone of the
value at
position 101 and risks making a cue in the bass. In this event it rises to the
next available
15 chord position.
D.6.3.5 H1.4: Calculate Treble at [1]
If the bass at [1] is the 5th, then treble [1] equals the 3rd chord not in a
voicing that puts it
above the bass's 5th at position [1].
Else there is a 50/50 chance that this is the root, or 1st, above the bass.
Else this is the 5th.
25 If it is the fifth, then we check to see if it is possible to transpose
this value up an octave
from its current pitch as seen in bars 4, 10, 11 and 12. If the previous bar's
treble at [1] is
a tone or less away from the new value at the current bar's treble [1], then
we perform the
transposition up an octave from its current pitch. (This is a simple and
initial voice-leading
ad hoc rule which will need a more universal and thorough refactoring when
aesthetic
30 heuristics are introduced later.)
D.6.3.6 H1.5: Calculate Treble at [2]
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If the treble at [1] is the 1st and the chord is diminished, then make this
the minor 3rd of
the local dominant.
Else if the treble at [1] is the 1st and the chord is not diminished, then
make this the 3rd of
5 the local dominant.
Else if the treble at [1] is the 3rd, then make this the 5th of the local
dominant.
Else if the treble at [1] is the 5th, then make this the 7th of the local
dominant 7th.
D.6.3.7 H1.6: Calculate Treble at [4]
We make this the next extension in the chord below the value in treble [1]. If
this value is
equal to or below bass [4], then get the next extension above bass [4]. This
is to avoid
crossing counterpoint lines, with which the ear copes poorly. This is
something that Bach
15 is sensitive to as pointed out by Ball (2011, p. 148) with an example
from the E major
Prelude in Book 2 of the We// Tempered Clavier. This shows how Bach avoids the
sonic
equivalent of a Gestalt-style continuation, by making sure the voices do not
cross paths.
D.6.3.8 H1.7: Calculate Treble at [0]
20 The melody note is never more than an octave above the lowest note in
the bar's treble,
nor is it equal to or below the last note in the previous bar (which is the
same as treble [1]
in the previous bar). Consequently, we choose a random note from the available
notes in
the bar's chord which meets both requirements.
25 D.6.3.9 H1.8: Copy the Bass and Treble to Fill Positions
The values at positions [3], [5] and [7] equal the values in [1].
The values at positions [6] equal the values in [2].
30 The second half of the bar is a copy of the first.
D.6.3.10 Unexplained Entropic Considerations
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The score in FIG. 31 shows the different heuristics in action through the use
of colour
coding. Solid arrows are pointers to other notes which provide information for
the final
pitch of the note in question. Dashed arrows show pointers to notes whose
values are
assessed but not used due to heuristic considerations.
This final overview gives a clear impression of the hierarchy of the section
in hand. Nearly
all notes flow return to the initial bass note in bar 1. The melody at each
treble position [0]
builds on the previous bar, trying to distinguish themselves from the value at
treble
position [15], with their options restricted to the range of notes an octave
above the lowest
note in their current bar. We can see the bass note the diminished chords
created on the
first pass before overwriting it on the second: the first pass's arrows are
dashed and the
second are solid. This visualisation shows exactly how the entropic red
(darker shading)
content cannot be linked to the currently understood hierarchy. This is where
the heuristics
currently break down.
The two main points where this is a serious issue are in bar 14, where the
heuristics would
choose a Bb over the published Ab at position [4] in the bass, and bar 18
where the special
case bass pattern occurs ¨ the only point in the piece where the first and
second halves of
the bar contain different material. All three of these notes are notably the
only three which
are different in the Clavier-Buchlein version compared to the autograph copy
from which
we have our modern editions. As well as these two salient points in the score,
on a lesser
scale the current heuristics do not account for the voicing of 5-3-5 in bar 12
if we use the
Ab/C version of the chord, the only point of possible breakdown of the 3-5-3
pattern.
Similarly, we are incapable of producing the double position jump at bass
position [5] if
we express this bar as Cmb6. Apart from these cases, the entropic components
mainly
highlight a lack of aesthetic judgement in the decision-making processes of
the heuristics.
The rising bass at semiquaver 5 in bar 11 cannot be created without an
overriding aesthetic
heuristic which looks at decisions made in the surrounding bars. In both of
these more
trivial cases, if we randomise the firing of heuristics which are capable of
producing these
values, then both become possible. However, it does not seem sensible to do so
simply
because of the 1 in 25 times these examples occur.
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Voice leading in the melody may similarly require aesthetic heuristics. A lack
of
repeatability in decisions from one bar to the next makes the output
unnecessarily over-
entropic for human listening. This is a further example of a lack of purely
aesthetic
5 decision-making heuristics. Such heuristics would simply repeat decisions
in a more
predictable pattern, such as in groups of two bars, but this would restrict
the current
system's output possibilities.
D.7 Section 2: Bars 19 ¨20
10 The following two sections are based on developing the core texture of
the tonic minor
figuration.
In Section 2, Bach achieves this by inverting the initial semiquaver in the
treble to appear
below the treble and bass figurations in the other positions but [0], sitting
with the bass
15 note as a distinctive chord and salient cue. The choices Bach has made
by using an Fm7
to F# diminished are recognisable as a common preparation for a cadential 6 4.
However,
we need to express how to choose such selections algorithmically and in a way
which
gives enough scope for a variety of generative results. The question,
therefore, is what note
pairings can sit below such a texture and add to it in an interesting way? Can
the notes be
20 random and still give a sense of harmonic movement towards, or around,
the tonic of bar
21? Simple keyboard experiments show that this is not the case. The use of
random
intervals makes no harmonic sense (unless it is a conventional harmonic
fluke). However,
the use of any chord which has C and Eb in the top of the texture does, such
as an Ab chord
followed by an F7 chord.
Taking the C and Eb as the top extensions, it is possible to build a variety
of chords below
C minor which can incorporate these two notes at the top of the chord for the
texture in
Sections 2 and 3. The score of FIG. 32 shows the possible combinations of
major and
minor thirds which produce chords in descending order of pitch.
Notably, the score in FIG. 32 shows all possible combinations (spanning an
octave) of
major and minor triads with C and Eb as the top extensions. Rules exclude
certain bars:
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red X chords are unavailable through D5.6 pseudo code, purple X chords are
excluded due
to texture limitations.
A good question to ask at this point is why the chords are triadic in form?
Why not
5 incorporate 4ths or 5ths to create chords such as the second inversion C
minor chord we
are moving towards at bar 21? Many of these combinations produce either the
chords we
have already given, or chords which make no conventional sense. Adding 4ths
below many
of the chords above simply produces a different inversion of the given chord.
Likewise,
incorporating 5ths, in other words removing certain notes to make holes in the
chord
10 voicing, either misses out a major and minor third to produce a more
harmonically bare
voicing, or produces dissonance due to a clash between a perfect fifth and any
chord made
of two major, or two minor thirds. An example of this would be adding a B a
perfect fifth
below an F# diminished chord. In essence, the diatonic scale, which the "7
from 12"
system of western harmony has currently evolved into precludes use of the more
obtuse
15 chords which can be made from random choices of major and minor thirds.
This is before
we even consider introducing 4ths and 5ths, which exponentially increases the
chord' s
abstractness, or simply ratify the chord we have already hit upon with the
incorporated
thirds through luck. It would seem that any of the chords in the score of FIG.
32 which fit
within the diatonic scale make sense. Although the E augmented chord (E #5
maj7) could
20 be considered an altered chord based on the Locrian natural minor mode
(Levine, 1995, p.
70), the top Eb (or major 7th) does not appear in the mode, so consequently
this chord
does not sound like a viable option. Neither do the more obscure Db augmented
chords,
as we are too close to obscuring the sound of a C minor components with the Db
chord
below it.
Balzano (1980) has previously shown that the diatonic system offers a unique
number of
every type of interval within the scale. The interval relationships cannot be
mapped
through direct transposition; however, the brain seems to realise this, and
this is the trick
that Bach seems to be using in Section 2. This method of finding chords
through extensions
30 is then inverted for Section 3, whereby the initial chord seems to
embellish upwards from
the pedal G. The pseudo code within the phrase analysis (Section D.5.6) offers
a viable
way of selecting appropriate chords from the array of possibilities. Given
this approach,
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we can eliminate certain chords as highlighted in red in the score of FIG. 32.
If we consider
the available space for this new cognitive cue to exist in, then we are
offered limited
possibilities for these cues' placement, as shown through the two alternative
voicings of
the C and Eb texture in the keyboard representation of FIG. 33, which shows
possible
5 notes within the textures of bars 19 and 20.
In all cases, the cue notes must appear at least a minor third away from any
other notes
within the main texture or a melodic cue is established. If the semiquavers at
position [4]
travel outwards from the main texture (treble rising and bass falling), then
we are given
10 maximum availability for the treble notes at positions 101 and 181.
However, the notes in
the bass cannot repeat the pitch of treble position [0], nor fall more than an
octave below
the pitch of the highest note in the bass throughout the rest of the
figuration (the final
requirement being a stylistic observation of the range of voicings throughout
the given
piece). This gives a trade-off in the bass: if the pitch rises at position
141, then there is more
15 room for the bass but less for the treble.
This dilemma reveals one of the first cases of iterative recomposition that
the system must
employ. If a desired chord scheme is required, then the chord texture may have
to be
rewritten to incorporate it. If rewriting the chord texture cannot accommodate
the desired
20 chord scheme, then the chord scheme must be rewritten. This iterative
process of
negotiation offers a potentially descriptive insight into the compositional
process. For the
given example's textures, the chords in the score of FIG. 32 that are not
available are
crossed out in purple.
25 This leaves six possible chords which can all be used in a random order
(excluding the
F#dim which can only be 2 extensions maximum below C and Eb). These chords
cannot
be repeated, so this section can potentially be embellished for six bars with
the current
available textures.
30 D.7.1 Initial Observations of Section 2
1. In this section, as in the following section, the main texture of
semiquavers [1] and [3]
are based on the first two notes of the tonic triad: C and Eb. In this
section, there is a 50%
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chance that the C will appear in the bass and the Eb will appear in the
treble, and vice
versa.
2. Semiquaver positions [4] no longer involve a neighbouring extension from
the bar's
5 chord, but an alternative voicing of the chord used at position [0] or
[2]. If position [4] is
copying the chord at position [2], this chord is inevitably the dominant of
the featured
chord in the figuration: C minor global tonic. If position [4] is not copying
position [2],
then the 5th and 7th are used instead of the 3rd and 5th which appear at [2].
If the chord
at position [4] is the one at position [0] then we select alternative notes
from the first
10 instance of the chord and randomise the direction of the arpeggio
movement. Having
alternative notes can only happen for the two positions if there are four
notes in the given
chord, such as the diminished in this case, or else a note from a normal triad
would have
to be repeated by necessity. Although statistical information to support these
assertions is
limited, this interpretation gives a large generative potential.
3. This type of figuration is new, reversing the movement direction of
neighbouring notes
at position [4] from the ones we have in the heuristics for Section 1. Rather
than falling at
position [2] as in the first set of algorithms for bars 1 to 18, the option
exists to rise at
position [2] and then fall at position [4]. This offers a vast plethora of
generative
20 possibilities compared to the first section's somewhat rigid pattern.
This means that the
system and its methodology is creating algorithmic components which are
generating
original textures without any evidence of the textures ever having existed.
4. There is nothing stating that this section, based on these developed rules,
could not be
25 extended further to increase the length of this build up. If the chord
chosen for position [0]
never repeats, the figuration should never become a different cue from the
overall build
up in tension that this section is creating, and therefore it should be
extendable. The full
range of available chords are not equally effective, depending on whether they
extend
below the C and Eb by one, two or three extensions.
D.7.2 Heuristics for Section 2: Bars 19 to 20
D.7.2.1 H2.0: Calculate Bass at [1]
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This is initially 50% randomly the tonic below C3 or the 3rd of the tonic
chord below C3.
(This ignores any voice leading from the previous phrase in preference of an
appropriate
range for the current voicings.)
5 D.7.2.2 H2.1: Calculate Bass at [2]
This heuristic extends H1.2:
If the bass at [1] is the 5th, then make this the 7th of the dominant 7th (of
the featured
chord in the main figuration), below bass at [1].
If the bass at [1] is the 3rd, then make this the 5th of the dominant 7th
below bass at [1].
Adding to this:
If the bass at [1] is the 1st, then make this the 3rd of the dominant 7th
below bass at [1].
15 D.7.2.3 H2.2: Preparation for H2.3
This heuristic places a value in the bass at position [0] which is either 1 or
2 (50%/50%)
chord-component positions below the bass at position [1]. This value will now
randomise
a given probability tree branch for H2.3.
20 D.7.2.4 H2.3: Calculate Bass at [4]
50% of the time this follows H1.3 (which requires the note generated by H2.2).
The other 50% we make [4] the next chord-component position of the dominant
7th above
the dominant 7th' s related note at [2].
D.7.2.5 H2.4: Calculate Treble at [1]
If the bass at [1] is the root of the prevailing chord, then make treble at
[1] 3rd plus an
octave.
30 Else make treble at [L] the root, but in the octave that gives a pitch
above the bass at [1].
D.7.2.6 H2.5: Calculate Treble at [2]
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Copy of H1.5.
D.7.2.7 H2.6: Calculate Treble at 141
50% of the time we make this the next extension in the chord above the value
in treble
5 position 111.
The other 50% we make [4] the next chord-component position of the dominant
7th above
the dominant 7th' s related note at [2].
10 D.7.2.8 H2.7: Check availability of pitches for notes from the extension
chord.
This heuristic checks the pitch range available for the notes in position 101
in both the
treble and bass, where we intend to place chord notes from chords featured in
the score of
FIG. 32. This process is highlighted in the keyboard representation of FIG.
33. Obtain an
integer range from a minor third below the treble's lowest note and a minor
third above
15 the bass's highest note.
Check that the desired second chord's 1st or 3rd appear in this range (the
chord elements
are referred to here as "1" and "2" respectively).
20 Obtain an integer range from a minor third below the bass's lowest note
and an octave
below the bass's highest note.
If one note out of "1" and "2" is available in the middle range, then check
the other is
available in this range.
If both "1" and "2" are available in the middle range then check that at least
one of them
is available in this range.
In the case of all notes being placeable, then distribute them appropriately
in treble and
30 bass positions [01. (This will overwrite the temporary value in bass
[01.)
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Else return to H2.0 and start again whilst keeping an array of the created
values for all
H2.x heuristics so far. Only store the values if they change.
This means that when we have four different versions of the output, if H2.7
still has not
5 been satisfied, we need to request an alteration to the chord scheme and
then we reset the
storage array and start again from H2Ø
(The distribution logic should reflect the following:
If one note out of "1" and "2" is available in the middle range then place it
here and the
10 other in the lower obtained range below the bass.
If one note out of "1" and "2" is available in the bottom range then place it
here and the
other in the middle obtained range in between bass and treble.
If both are available then randomly assign one to each range.)
15 D.7.2.9 H2.8: Copy the Bass and Treble to fill positions.
Copy of H1.8.
D.8 Section 3: Bars 21 ¨24
Whereas Section 2 used C and Eb to extend chords downwards, this section uses
the C and
20 Eb texture as a basis for cadencing and extending extensions upwards.
The phrase analysis
in Section C.5.7 is capable of generating a chord scheme which provides the
cadential,
build up.
D.8.1 Initial Observations
25 1. This section contains a repeating texture in a similar way to the H2
set. There is a higher
chance that the treble and bass at position [4] will use the dominant 7th of
the bar's chord
to obtain their pitches.
2. The use of the diminished chord over the G pedal in bar 22 at position [4]
shows that
30 the cadence chords generated by the phrase analysis rules do not just
have be the dominant.
They can in fact be any chord that is conventionally one cadence position away
from the
tonic. We can discover candidate chords by gathering evidence from this piece
in general,
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as well as other works of the time. The featured cadence chords here are an F
sharp
diminished seventh and a dominant b9. The dominant 7th b9 features highly
throughout
the rest of the climax (which is excluded from this analysis) from bar 25 to
the end.
5 D.8.2 Heuristics for Section 3: Bars 21 to 24
D.8.2.1 H3.0: Calculate Bass at [0]
This is the dominant above the initial bass tonic in bar 1, bass position [1]
of the piece.
(This ignores the possibility of modulation for the current study.)
10 D.8.2.2 H3.1: Calculate Bass at Ill
Extends H2Ø If this is the second bar of the section, simply copy the pitch
calculated by
this heuristic in the previous bar.
D.8.2.3 H3.2: Calculate Bass at [2]
15 Copy of H2.1
D.8.2.4 H3.3: Calculate Bass at [4]
Copy of H2.3
20 D.8.2.5 H3.4: Calculate Treble at [1]
Extends H2.4. If this is the second bar of the section, simply copy the pitch
calculated by
this heuristic in the previous bar.
D.8.2.6 H3.5: Calculate Treble at [2]
25 Copy of H1.5.
D.8.2.7 H3.6: Calculate Treble at [4]
Copy of H2.6
30 D.8.2.8 H3.7: Calculate Treble at [0]
This finds the pitch, in any octave, of the next available note from the bar's
chord which
is closest to the previous bar's pitch in this position. For the initial pitch
of the first bar,
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take the pitch position which is the next above the highest note in the treble
texture for the
bar.
D.8.2.9 H3.8: Copy the Bass and Treble to fill positions.
5 Copy of H1.8.
D.9 Results
It is important to note that we are not advocating that Bach' s choices were
restricted to one
note only. We are saying quite the opposite: that he was faced with multiple
choices, but
10 we generalise the majority of them with this algorithmic analysis of
what he chose. The
validated approach, reflected in the analysis, relies on this diversity of
choices to give us
the flexibility of generative composition based on the principles we have
abstracted.
The previously unexplained Ab in bar 14 can easily be accounted for if we
consider the
15 latter heuristics for Sections 2 and 3. Randomly introducing these
heuristics in place of
earlier ones gives us the ability to explain these notes. A set of aesthetic
heuristics which
observe and copy random choices from neighbouring bars, as well as having the
ability to
interchange heuristics from other sections randomly. would produce the
original score.
20 It is noticeable throughout latter sets of heuristics that previous ones
are being reused and
extended more and more frequently. This points towards an object-orientated
approach for
heuristic data representation. The extension of H1.2 for H2.1 shows that we
should be able
to override methods to add functionality, calling their super-type methods for
any previous
logic.
D.10 Conclusions
We have implemented a system of colouring entropic, redundant and developed
material
which shows us when to generate heuristics as well as giving us their
functional purpose.
Entropic (red/darker tone) markings in the analysis require generative
heuristics which
30 create fresh material; redundant (green/mid-tone) markings require copy
heuristics to fill
out the generative material and developed (yellow-lightest tone) material
shows the need
for function heuristics which alter the output of generative heuristics. We
have three sets
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of heuristics which can account for all but two notes in the original piece as
well as many
alternatives.
We have shown that Bach's earliest version of the prelude in the Clavier-
Buchlein
5 manuscript agrees with the general heuristics derived here from the first
section, removing
the entropic thorns in the side of the opening section's analysis in bars 14
and 18. This
shows that we have created a set of rules which are closely compatible with B
ach' s original
compositional approach to this piece.
10 Unless specific arrangements are mutually exclusive with one another,
the various
embodiments described herein can be combined to enhance system functionality
and/or to
produce complementary functions or system that support the effective
identification of
user-perceivable similarities and dissimilarities. Such combinations will be
readily
appreciated by the skilled addressee given the totality of the foregoing
description.
15 Likewise, aspects of the preferred embodiments may be implemented in
standalone
arrangements where more limited functional arrangements are appropriate.
Indeed, it will
be understood that unless features in the particular preferred embodiments are
expressly
identified as incompatible with one another or the surrounding context implies
that they
are mutually exclusive and not readily combinable in a complementary and/or
supportive
20 sense, the totality of this disclosure contemplates and envisions that
specific features of
those complementary embodiments can be selectively combined to provide one or
more
comprehensive, but slightly different, technical solutions. In terms of the
suggested
process flows of the accompanying drawings, it may be that these can be varied
in terms
of the precise points of execution for steps within the process so long as the
overall effect
25 or re-ordering achieves the same objective end results or important
intermediate results
that allow advancement to the next logical step. The flow processes are
therefore logical
in nature rather than absolute. The functional architectures of the drawings
may be
implemented independently of one another, as will be understood, so that the
resulting
system is a distributed system potentially dispersed via a wide area network,
such as the
30 Internet. Architecturally, realization of aspects of the system, such as
but not limited to
texture classification as described herein [as a basis for final automated
musical
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composition] can be implemented using technologies such as the Java Expert
System Shell
"JESS" and, more typically, a bespoke expert system.
Aspects of the present invention may be provided in a downloadable form or
otherwise on
5 a computer readable medium, such as a CD ROM, that contains program code
that, when
instantiated, executes the link embedding functionality at a web-server or the
like.
The doctoral thesis of Joseph Michael William Lyske titled "Meta Creation for
Film
Scores", contemporaneously and first published on 31 March 2021 by the School
of
10 Electronic Engineering and Computer Science, Queen Mary, University of
London, is
incorporated in its entirety herein by reference.
The invention disclosed herein is applicable to any musical scale and any
cultural
precondition, not just Western music which has been used as an exemplary
format.
As disclosed herein, whilst the Form Atom provides an extremely important
building
block upon which generative composition can be based, the totality of the
disclosure
includes multiple independent (but related) aspects that, together, provide a
comprehensive implementation having considerable detail, including the use of
the
20 hypemode framework. For example, from a composition perspective, the
classification
and manipulation of textures is highly significant. For example, stand-alone
technical
solutions are related to the process by which chord spacing is determined, as
well as how
primitives are developed and employed within the context of building a
generative system.
25 It will, of course, be appreciated that the above description has been
given by way of
example only and that modifications in detail may be made within the scope of
the present
invention. For example, whilst the generative system has been expressed in the
context of
Western music having a particular degree of scale, the techniques are
commutable to other
styles and metres.
The analysis technique, coupled with the generative framework, gives a
foundation for
looking at music hierarchically in a way that leads to effective output. This
is not only a
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useful method of creating aesthetically functional generative film composition
and game
scores that can, in fact, be orchestrated personally by the user provided that
they are given
access to the system via an interface and a database containing Form Atoms
meta-tagged
to artists and songs of their personal liking.
Completely autonomous solutions are feasible, based on the given hierarchy, in
which
computers analyse works and compose music based on analysis. For example, a
trained
artificial intelligence mechanism, such as deep learning neural networks and
generative
algorithms with associated fitness functions, can learn how to select
appropriate primitives
based on a score. This approach leads to more efficient ways to create ever
smaller sets of
heuristics [Occam's Razor] that can generate the same standard of output from
the same
set of analysed compositions. The only thing then left for humans potentially
to do would
he to meta-tag the emotional concepts, although even this task can he made the
subject of
Al networks (such as those in described in US 2020-0320398 and related works)
that close
the semantic gap and which make use of NLP or file properties to correlate to
with
emotional perception. The skilled person will thus understand which aspects of
the system
intelligence may benefit for different forms of processor.
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