CA1237592A - Apparatus for carrying out integral affine transformation on musical compositions - Google Patents
Apparatus for carrying out integral affine transformation on musical compositionsInfo
- Publication number
- CA1237592A CA1237592A CA000477928A CA477928A CA1237592A CA 1237592 A CA1237592 A CA 1237592A CA 000477928 A CA000477928 A CA 000477928A CA 477928 A CA477928 A CA 477928A CA 1237592 A CA1237592 A CA 1237592A
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- computer
- sound
- input
- mathematical
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- Legal status (The legal status is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the status listed.)
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Abstract
ABSTRACT OF THE DISCLOSURE
A sound sequence or musicial composition to be trans-formed is fed together with the mathematical data into a computer by means of an input unit and stored in a memory. The arithmetic-logic unit processes the input data, and the control unit passes on these data to a display device or to an acoustic playback unit according to the instructions. All the sound sequences input and computed can be passed on by the computer to an external memory.
A sound sequence or musicial composition to be trans-formed is fed together with the mathematical data into a computer by means of an input unit and stored in a memory. The arithmetic-logic unit processes the input data, and the control unit passes on these data to a display device or to an acoustic playback unit according to the instructions. All the sound sequences input and computed can be passed on by the computer to an external memory.
Description
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 ~l," ;
123759~
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.
- la -lZ3759~
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 lZ3759Z
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 -- lZ3759Z
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 ~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 , lZ3759~
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.
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 ~l," ;
123759~
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.
- la -lZ3759~
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 lZ3759Z
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 -- lZ3759Z
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 ~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 , lZ3759~
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.
Claims (6)
PROPERTY OR PRIVILEGE IS CLAIMED ARE DEFINED AS FOLLOWS:
1. An apparatus for carrying out integral affine transformations on musical compositions, comprising at least one input unit permitting the entry of musical data represen-ting a melody to be transformed and mathematical data rep-resenting mathematical operations to be performed 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 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.
2. An apparatus according to claim 1, further com-prising a monitor memory for permanent storage connected to the computer.
3. An apparatus according to claim 1, further com-prising an external memory for permanent storage connected to the computer.
4. An apparatus according to claim 1, further com-prises an x-y plotter connected to the computer.
5. An apparatus according to claim 1, wherein the input unit is a digitizing unit with a menu.
6. An apparatus according to claim 1, wherein the means for generating an acoustic output is an electronic organ.
Priority Applications (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CA000477928A CA1237592A (en) | 1985-03-29 | 1985-03-29 | Apparatus for carrying out integral affine transformation on musical compositions |
Applications Claiming Priority (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CA000477928A CA1237592A (en) | 1985-03-29 | 1985-03-29 | Apparatus for carrying out integral affine transformation on musical compositions |
Publications (1)
| Publication Number | Publication Date |
|---|---|
| CA1237592A true CA1237592A (en) | 1988-06-07 |
Family
ID=4130150
Family Applications (1)
| Application Number | Title | Priority Date | Filing Date |
|---|---|---|---|
| CA000477928A Expired CA1237592A (en) | 1985-03-29 | 1985-03-29 | Apparatus for carrying out integral affine transformation on musical compositions |
Country Status (1)
| Country | Link |
|---|---|
| CA (1) | CA1237592A (en) |
-
1985
- 1985-03-29 CA CA000477928A patent/CA1237592A/en not_active Expired
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Legal Events
| Date | Code | Title | Description |
|---|---|---|---|
| MKEX | Expiry |