Note: Descriptions are shown in the official language in which they were submitted.
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The present invention relates to an apparatus for
carrying out integral affine transformations on musical compo-
sitions. This kind of apparatus serves particularly for
teaching purposes and can be applied particularly to the
teaching of musical composition.
In the mathematics institutes of various universi-
ties and in conservatories, known compositions are analyzed
Eor more intensive study. In the analysis, parts of the com-
position are transcribed according to mathematical rules. The
basic operations used for this purpose are: rotation, reflec-
tion, translation and transvection.
Apart from these basic operations, all combinations
of these basic operations are of interest.
These analyses were made heretofore by transcrip-
tions carried out manually. The expendlture of time thus
required was enormous. Furthermore, the compositions thus
resulting are frequently compositions which are very difficult
to play or required an enormous amount of practice.
Nevertheless, simpler transcriptions of the kind
mentioned above have also been carried out by famous musicians
and composers for centuries.
It is an ob~ect of the invention to provide an appa-
ratus which carries out integral afflne transformations on
musical compositions and plays them back.
According to the present invention there is provided
an apparatus for carrying out integral affine transformations
on musical compositions, comprising at least one input unit
permitting the entry of musical data representing a melody to
be transformed and mathematical data representing mathematical
operations to be perform~d on the music data, a computer with
a memory and control unit for carrying out the mathematical
operations determined by the mathematical data on the music
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data to derive output data representing the transformed melody
and means for generating an acoustic output from said output
data of the transformed melody represented thereby.
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The invention will now be described in more detail, by
way of example only, withreference to the accompanying drawings,
in which -
Figure 1 is a block diagram of an apparatus in accor-
dance with the invention;
Figure 2 is a top view of the switchboard of the input
unit of the apparatus; and
Figure 3 is an example of an input sound sequence and a
transformed sound sequence.
As is evident from the block diagram of Figure 1, the
apparatus substantially comprises five units. Further units can
be added if desired. A computer 1 which is fed with musical and
mathematical data by an input unit 2 forms the core of the appara-
tus. The data fed in are s-tored in a memory 11 on the inside of
the computer 1. The arithmetic-logic unit 12 of the computer 1
processes the musical data fed by the input unit 2 in accordance
with the mathematical data also provided by the input unit. Fol-
lowing a control command from the input unit 2, the integral
affine transformation of the compositions fed-in which is based
on an integer matrix, is carried out and played back by a musical
instrument 3, which is electronically controlled by the control
unit 13 of the computer 1.
The electronically controlled musical instrument 3, which
serves as the acoustic output unit of the apparatus, can be, for
example, an electronic organ. Computer 1, input unit 2, and output
unit 3 constitute the minimum structure of the apparatus.
~he
Various additions toJ~minimum struc-ture of the appara-
tus simplify the operation and enhance the comprehension.
This includes, for example, a monitor 4 on which the
musical data stored in the memory 12 of the computer 1 are rendered
visible. As the desired transformation is carried out, the trans-
formed sound sequence appears on the screen of -the monitor. In
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this manner a transformation carried out can be corrected or
varied by the input of further data.
In a memory 5, outside the computer 1, the sound sequence
fed onto the transformed sound sequence can be stored permanently,
for example, on recording tape or discette, and recalled again
from the computer 1.
By means of an additional display screen, which is
associated with the input unit 2, but is not shown in the drawing,
the data input can also be rendered visible directly and checked
by the operator before being passed to the computer 1.
An embodiment of the control board of the input unit 2
is shown in Figure 2. The control board has input keyboards for
musical data and mathematical data, and operating units for play-
back.
A row of keys 21 arranged laterally on the left-hand
side has twelve keys and serves for determining the pitch. The
scale extends from c to h and takes into account all the semitones.
This provides a sound sequence c, cis, d, e, f, fis, g, gis, a,
ais (or b) and h identical to the keyboard of a piano.
The row of keys shown at the bottom of the drawing of
the control board serves for determining the desired octave. The
individual keys are numbered throughout from 1 to 8. The keyboards
21 and 22 together define the input pitch.
Finally, the data with regard to the duration of the
sound can also be input via a keyboard. The scale starts here
from a simple absolute unit of time and extends via arbitrary mul-
tiples to the maximal period of a 64 fold. With this keyboard
alone, a corresponding pause can be input. With the three key-
boards 21 to 23 described all the musical data can be input.
The mathematical functions to be carried out are also
distributed over three keyboards. Approximately at the centre of
the control board, five keys 24 are arranged in the form of a
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cross. The four keys forming the arms of the cross are provided
with arrows indicating the direction of translation. Depending
on the design, the extent of the translation can be performed
either by a corresponding number of actuations of the corresponding
key or by means of the key set 25, which contains all the digits
from 0 to 9. The meaning of these coordinate data will be explained
hereafter.
The small square key set 26 comprising four keys serves
for the input of a matrix. The integer values of the matrix are
in turn put in via the key set 25, taking into account the sign.
By means of the matrix, all the rotations, reflections, and trans-
vections can be carried out. All the rotations occur about a
coordinate point so that the desired function of the reflection
axis about the reflection point, or the point of rotation the
function must still be completed by a corresponding translation.
Finally, the actuation of the output unit will be des-
cribed. For this purpose a key 27 with a loud-speaker symbol is
provided at the centre of the cross-shaped key set 24 mentioned
hereinbefore and by means of which the note sequence input and
transformed can be played back at any time. The tempo of play-
back can be influenced by means of the shift register 28.
An image of a system of coordinates visible on the dis-
play screen of a monitor 4 is shown in Figure 3. On the x axis,
the number 88 relates to setting times for sounds which are indi-
cated as coordinates. In order to avoid cluttering the drawing,
only every third coordinate scheme line has been plotted. Each
plotted square thus corresponds to three standard time intervals.
The standard time intervals in these coordinates correspond to
freely selectable time intervals, wherein the settings of the
sounds follow each other as soon as the music is played back.
The y coordinates 1 to 88 indicate the pitch correspond-
ing to the 88 keys of a piano keyboard. Each coordinate unit in
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~he y direction thus corresponds to a semitone. Each square of
the plotted coordinate lines corresponds to three semitones.
In Figure 3, the sound a tno reference to the note a)
has the length of a unit sound interval and the sound b has twice
the length, i.e., two unit sound intervals. In the Bach Invention,
the sound a corresponds to a 1/16 note and the sound b to a 1/8
note.
The notes of the firt two strokes of the Invention No. 1
of J.S. Bach (Schmieder Verzeichnis 772) has been represented by
a solid line (sound sequence I). The same sound sequence reflec-
ted about the coordinate point 44/44 has been represented by a
dotted line (sound sequence II). The sound sequence II was dis-
placed in the vertical and horizontal directions to the sound
sequence III.
The sound sequences I and III can be played back as a
continuous sound sequence by actuating the key 27. The sound
duration can be symbolized on the display screen by the length.
However, in contrast to the notes, the sound duration has not been
represented as an absolute value, but it has been represented only
as a relative value. For the shortest sound, the computer simply
takes the value 1 of a unit time interval and all the other sounds
are an integer multiple thereof. The absolute sound duration is
adjusted by the shift register 28 and can thus be varied arbitr-
arily. The relations of the sound duration are maintained.
The input sound sequences and the transformed sound
sequences can be stored as desired by means of the operating func-
tion keys 29. Furthermore, individual notes or portions of the
sound sequence and the entire sound sequence can be erased by
means of the "reset" keys. The two keys 29' and 29" characteri-
zed by arrows permit shifting of the sound time into one or theother direction.
In order to simplify the control of the input muslcal
,
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data , optical indicator elements 30 are provided on the con-trol
board. The three data visi~le by means of the 7-segment display
are the sound time (x value in the system of coordinates), the
pitch (y value in the system of coordinates) and the sound dura-
tion.
However, apart from the described embodiment, the latter
can also be operated with other inputs and control devices. Thus,
for example, the monitor can be replaced by an x-y plotter which
displays the input sound sequence and transformed.
Furthermore, it is possible to feed in the input directly
by means of a digitizing device. These coordinate-determining
devices can be obtained from various manufacturers. These devices
comprise a digi-ti~inq plate with a transmitter or receiver and,
attachable at any point of the digitizing plate, a menu field via
which all the additional information such as sound time, sound
duration, sound time, tempo, transformation type and opera-ting
functions can be input by scanning with the aid of a scanning
pen.
