1. V EXPERIMENTS
V.1 (Thu Apr 12) Synthesis—a computer-aided jazz composition—I: principles

2. Here, we illustrate the theory on the jazz CD „Synthesis“ which I recorded in Its entire structure, in harmony, in rhythmics, and in melodics, was deduced and constructed by use of the composition software presto® (written for Atari computers, but now also working on Atari emulations on Mac OS X), and starting from the 26 classes of three-element motives.
This composition (a grant from the cultural department of the city of Zurich) was not recognized as a computer-generated music by the jazz critics. Only the piano part was played by myself, the entire bass and percussion part was played by synthesizers, driven by the presto® application via MIDI messages.
During the production of this composition (Synthesis is a four-part, 45-minute piece), I never felt inhibited in my piano playing, in the contrary, it was a great pleasure to collaborate with complex structures of rhythm or melody, objects of a complexity that human percussionists would never be able to play from a score.

3. Here, we illustrate the theory on the jazz CD „Synthesis“ which I recorded in Its entire structure, in harmony, in rhythmics, and in melodics, was deduced and constructed by use of the composition software presto® (written for Atari computers, but now also working on Atari emulations on Mac OS X), and starting from the 26 classes of three-element motives.
This composition (a grant from the cultural department of the city of Zurich) was not recognized as a computer-generated music by the jazz critics. Only the piano part was played by myself, the entire bass and percussion part was played by synthesizers, driven by the presto® application via MIDI messages.
During the production of this composition (Synthesis is a four-part, 45-minute piece), I never felt inhibited in my piano playing, in the contrary, it was a great pleasure to collaborate with complex structures of rhythm or melody, objects of a complexity that human percussionists would never be able to play from a score.

4. Principles for Synthesis
External data
Synthesis of Styles
Application of MaMuTh
Synthesis of Human performance and CAC (ComputerAssistedComposition)  HCI (HumanComputerInteraction)
Overall architecture

5. Principles for Synthesis
Exterior data
Synthesis of Styles
Application of MaMuTh
Synthesis of Human performance and CAC (ComputerAssistedComposition)  HCI (HumanComputerInteraction)
Overall architecture

6. Grant from City of Zürich 1990, 10 k$
concert for piano, 2 percussions, and e-bass
4 months composition of pc + e-b
2 months of completion with piano
CD recording in one day
with exception of small part in movement 2 no cutting
performance live with interactive multimedia at the International Jazz Festival of Zürich 1991

7. Principles for Synthesis
Exterior data
Synthesis of Styles
Application of MaMuTh
Synthesis of Human performance and CAC (ComputerAssistedComposition)  HCI (HumanComputerInteraction)
Overall architecture

8. Synthesis of Styles
Rock Jazz  Miles Davis: Bitches Brew (NYC 1969)
Free Jazz  Cecil Taylor: Live in the Black Forest (1979)

9. Principles for Synthesis
Exterior data
Synthesis of Styles
Application of MaMuTh
Synthesis of Human performance and CAC (ComputerAssistedComposition)  HCI (HumanComputerInteraction)
Overall architecture

10. Application of MaMuTh
music theory for composition: - modulation theory (+ from known analyses) - classification of motives (+ from known analyses: Schubert‘s setting of Stolberg‘s poem „Lied zu singen auf dem Wasser, für meine Agnes“)
Syntagmatic composition methods: - Boolean operations on sets of notes - Local-global structures (manifolds)
paradigmatic methods: - transformations of single note sets - grids of motives - deformation (morphing, alteration, quantization)
Performance theory of tempo curve hierarchies

11. Principles for Synthesis
Exterior data
Synthesis of Styles
Application of MaMuTh
Synthesis of Human performance and CAC (ComputerAssistedComposition)  HCI (HumanComputerInteraction)
Overall architecture

12. Synthesis of Human performance = following the computer while playing! and CAC (ComputerAssistedComposition) = Dialog with composed structures ~ kind of schizophrenic poietic-aesthesic behavior  HCI (HumanComputerInteraction)

13. presto® http://tamw.atari-users.net/presto.htm
Here, we illustrate the theory on the jazz CD „Synthesis“ which I recorded in Its entire structure, in harmony, in rhythmics, and in melodics, was deduced and constructed by use of the composition software presto® (written for Atari computers, but now also working on Atari emulations on Mac OS X), and starting from the 26 classes of three-element motives.
This composition (a grant from the cultural department of the city of Zurich) was not recognized as a computer-generated music by the jazz critics. Only the piano part was played by myself, the entire bass and percussion part was played by synthesizers, driven by the presto® application via MIDI messages.
During the production of this composition (Synthesis is a four-part, 45-minute piece), I never felt inhibited in my piano playing, in the contrary, it was a great pleasure to collaborate with complex structures of rhythm or melody, objects of a complexity that human percussionists would never be able to play from a score.

14. Here, we illustrate the theory on the jazz CD „Synthesis“ which I recorded in Its entire structure, in harmony, in rhythmics, and in melodics, was deduced and constructed by use of the composition software presto® (written for Atari computers, but now also working on Atari emulations on Mac OS X), and starting from the 26 classes of three-element motives.
This composition (a grant from the cultural department of the city of Zurich) was not recognized as a computer-generated music by the jazz critics. Only the piano part was played by myself, the entire bass and percussion part was played by synthesizers, driven by the presto® application via MIDI messages.
During the production of this composition (Synthesis is a four-part, 45-minute piece), I never felt inhibited in my piano playing, in the contrary, it was a great pleasure to collaborate with complex structures of rhythm or melody, objects of a complexity that human percussionists would never be able to play from a score.

15. Here, we illustrate the theory on the jazz CD „Synthesis“ which I recorded in Its entire structure, in harmony, in rhythmics, and in melodics, was deduced and constructed by use of the composition software presto® (written for Atari computers, but now also working on Atari emulations on Mac OS X), and starting from the 26 classes of three-element motives.
This composition (a grant from the cultural department of the city of Zurich) was not recognized as a computer-generated music by the jazz critics. Only the piano part was played by myself, the entire bass and percussion part was played by synthesizers, driven by the presto® application via MIDI messages.
During the production of this composition (Synthesis is a four-part, 45-minute piece), I never felt inhibited in my piano playing, in the contrary, it was a great pleasure to collaborate with complex structures of rhythm or melody, objects of a complexity that human percussionists would never be able to play from a score.

16. Here, we illustrate the theory on the jazz CD „Synthesis“ which I recorded in Its entire structure, in harmony, in rhythmics, and in melodics, was deduced and constructed by use of the composition software presto® (written for Atari computers, but now also working on Atari emulations on Mac OS X), and starting from the 26 classes of three-element motives.
This composition (a grant from the cultural department of the city of Zurich) was not recognized as a computer-generated music by the jazz critics. Only the piano part was played by myself, the entire bass and percussion part was played by synthesizers, driven by the presto® application via MIDI messages.
During the production of this composition (Synthesis is a four-part, 45-minute piece), I never felt inhibited in my piano playing, in the contrary, it was a great pleasure to collaborate with complex structures of rhythm or melody, objects of a complexity that human percussionists would never be able to play from a score.

17. piano
Here, we illustrate the theory on the jazz CD „Synthesis“ which I recorded in Its entire structure, in harmony, in rhythmics, and in melodics, was deduced and constructed by use of the composition software presto® (written for Atari computers, but now also working on Atari emulations on Mac OS X), and starting from the 26 classes of three-element motives.
This composition (a grant from the cultural department of the city of Zurich) was not recognized as a computer-generated music by the jazz critics. Only the piano part was played by myself, the entire bass and percussion part was played by synthesizers, driven by the presto® application via MIDI messages.
During the production of this composition (Synthesis is a four-part, 45-minute piece), I never felt inhibited in my piano playing, in the contrary, it was a great pleasure to collaborate with complex structures of rhythm or melody, objects of a complexity that human percussionists would never be able to play from a score.

18. Local Score hidden parameters visible parameters
Here, we illustrate the theory on the jazz CD „Synthesis“ which I recorded in Its entire structure, in harmony, in rhythmics, and in melodics, was deduced and constructed by use of the composition software presto® (written for Atari computers, but now also working on Atari emulations on Mac OS X), and starting from the 26 classes of three-element motives.
This composition (a grant from the cultural department of the city of Zurich) was not recognized as a computer-generated music by the jazz critics. Only the piano part was played by myself, the entire bass and percussion part was played by synthesizers, driven by the presto® application via MIDI messages.
During the production of this composition (Synthesis is a four-part, 45-minute piece), I never felt inhibited in my piano playing, in the contrary, it was a great pleasure to collaborate with complex structures of rhythm or melody, objects of a complexity that human percussionists would never be able to play from a score.

19. start window target window
Here, we illustrate the theory on the jazz CD „Synthesis“ which I recorded in Its entire structure, in harmony, in rhythmics, and in melodics, was deduced and constructed by use of the composition software presto® (written for Atari computers, but now also working on Atari emulations on Mac OS X), and starting from the 26 classes of three-element motives.
This composition (a grant from the cultural department of the city of Zurich) was not recognized as a computer-generated music by the jazz critics. Only the piano part was played by myself, the entire bass and percussion part was played by synthesizers, driven by the presto® application via MIDI messages.
During the production of this composition (Synthesis is a four-part, 45-minute piece), I never felt inhibited in my piano playing, in the contrary, it was a great pleasure to collaborate with complex structures of rhythm or melody, objects of a complexity that human percussionists would never be able to play from a score.

20. Here, we illustrate the theory on the jazz CD „Synthesis“ which I recorded in Its entire structure, in harmony, in rhythmics, and in melodics, was deduced and constructed by use of the composition software presto® (written for Atari computers, but now also working on Atari emulations on Mac OS X), and starting from the 26 classes of three-element motives.
This composition (a grant from the cultural department of the city of Zurich) was not recognized as a computer-generated music by the jazz critics. Only the piano part was played by myself, the entire bass and percussion part was played by synthesizers, driven by the presto® application via MIDI messages.
During the production of this composition (Synthesis is a four-part, 45-minute piece), I never felt inhibited in my piano playing, in the contrary, it was a great pleasure to collaborate with complex structures of rhythm or melody, objects of a complexity that human percussionists would never be able to play from a score.

21. Principles for Synthesis
Exterior data
Synthesis of Styles
Application of MaMuTh
Synthesis of Human performance and CAC (ComputerAssistedComposition)  HCI (HumanComputerInteraction)
Overall architecture

22. Overall architecture
form
instrumentation: - grand piano (Steinway concert grand) - synthesizers (MIDI-driven by Atari Mega ST4)
technological realization of above principles via the presto sofware
unifying material

24. classes of n-element motives M Í Ÿ122
retrogrades
.5 (fourth mult.)
.7 (fifth mult.)
onset
pitch
transposition
in pitch + time
inversions
The classification of all possible concept types and the instances within one fiexed type is a ‚wild‘ problem. Let us just look at all isomorphism types of three-element motives with pitch modulo 12 and onset modulo 12 in the integer valued coordinate spaces. Here, isomorphism means that one is allowed to reflect, shift or rotate a given motive. The ‚orbits‘ of these isomorphism actions are the classes, there are 26 of them. I shall come back to this example below when discussing a jazz CD.
classes of n-element motives M Í Ÿ122

25. ...+ 2024.x5 + 216.x4 + 26.x3 + 5.x2 + x + 1 = cycle-index polynomial
x^144 + x^ x^ x^ x^ x^ x^ x^ x^ x^135 +
x^ x^ x^ x^ x^130 +
x^ x^ x^ x^126 +
x^ x^ x^ x^122 +
x^ x^ x^119 +
x^ x^ x^116 +
x^ x^ x^113 +
x^ x^ x^110 +
x^ x^ x^107 +
x^ x^ x^104 +
x^ x^102 +
x^ x^100 +
x^ x^98 +
x^ x^96 +
x^ x^94 +
x^ x^92 +
x^ x^90 +
x^ x^88 +
x^ x^86 +
x^ x^84 +
x^ x^82 +
x^ x^80 +
x^ x^78 +
x^ x^76 +
x^ x^74 +
x^ x^72 + …. …
x x x3 + 5.x2 + x + 1 = cycle-index polynomial
In order to count all classes of motives of n elements in onset modulo 12 and pitch modulo 12, one has to use Polya‘s enumeration theory. This theory gives you a polynomial in the indeterminate x, and the coefficient of power x^n is the number of isomorphism classes of motives with n elements. The figure shows the Polya polynomial. You can see the number 26 appearing at the bottom part of the formula for power x=3. One sees that the number of classes of 72-element motives is extremely large, even compared to the number of stars in a galaxis. So musical creativity is not likely to be restricted by the list of all possible structures in the formal framework.
Quite generally, when one works with these formalizations, even as a working jazz musician, their explicit and precise structures never kill creativity, but rather give it a drive of references and dynamic transformers, we come back to this below when discussin a jazz CD. =
72 elements
average number of stars in a galaxy = 1011

26. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18
The classification of all possible concept types and the instances within one fiexed type is a ‚wild‘ problem. Let us just look at all isomorphism types of three-element motives with pitch modulo 12 and onset modulo 12 in the integer valued coordinate spaces. Here, isomorphism means that one is allowed to reflect, shift or rotate a given motive. The ‚orbits‘ of these isomorphism actions are the classes, there are 26 of them. I shall come back to this example below when discussing a jazz CD. 19 20 21 22 23 24 25 26
classen of 3-element motives M Í Ÿ122

28. percussion instruments 2nd movement

29. Poetical Production via Baudelaire 3rd Movement Melodic Germ
26 Motif Classes
Poetical Production via Baudelaire
3rd Movement
CORRESPONDENCE
GLUING
SYMMETRIES
Melodic Germ
Rhythms and Their Modulations
1st Movement
SELECTION REFLECTIONS
ORNAMENTS
Variations via Messiaen Grids 2nd Movement
DECOMPOSITION ALTERATIONS ORNAMENTS
Fractal Refinement 4th Movement
SELECTION DILATION ORNAMENTS REFINEMENT
Bass Licks All Movements
SELECTION
SYMMETRIES

30. Here, we illustrate the theory on the jazz CD „Synthesis“ which I recorded in Its entire structure, in harmony, in rhythmics, and in melodics, was deduced and constructed by use of the composition software presto® (written for Atari computers, but now also working on Atari emulations on Mac OS X), and starting from the 26 classes of three-element motives.
This composition (a grant from the cultural department of the city of Zurich) was not recognized as a computer-generated music by the jazz critics. Only the piano part was played by myself, the entire bass and percussion part was played by synthesizers, driven by the presto® application via MIDI messages.
During the production of this composition (Synthesis is a four-part, 45-minute piece), I never felt inhibited in my piano playing, in the contrary, it was a great pleasure to collaborate with complex structures of rhythm or melody, objects of a complexity that human percussionists would never be able to play from a score.

31. Here, we illustrate the theory on the jazz CD „Synthesis“ which I recorded in Its entire structure, in harmony, in rhythmics, and in melodics, was deduced and constructed by use of the composition software presto® (written for Atari computers, but now also working on Atari emulations on Mac OS X), and starting from the 26 classes of three-element motives.
This composition (a grant from the cultural department of the city of Zurich) was not recognized as a computer-generated music by the jazz critics. Only the piano part was played by myself, the entire bass and percussion part was played by synthesizers, driven by the presto® application via MIDI messages.
During the production of this composition (Synthesis is a four-part, 45-minute piece), I never felt inhibited in my piano playing, in the contrary, it was a great pleasure to collaborate with complex structures of rhythm or melody, objects of a complexity that human percussionists would never be able to play from a score.

32. Here, we illustrate the theory on the jazz CD „Synthesis“ which I recorded in Its entire structure, in harmony, in rhythmics, and in melodics, was deduced and constructed by use of the composition software presto® (written for Atari computers, but now also working on Atari emulations on Mac OS X), and starting from the 26 classes of three-element motives.
This composition (a grant from the cultural department of the city of Zurich) was not recognized as a computer-generated music by the jazz critics. Only the piano part was played by myself, the entire bass and percussion part was played by synthesizers, driven by the presto® application via MIDI messages.
During the production of this composition (Synthesis is a four-part, 45-minute piece), I never felt inhibited in my piano playing, in the contrary, it was a great pleasure to collaborate with complex structures of rhythm or melody, objects of a complexity that human percussionists would never be able to play from a score.