This document summarizes a presentation on automatic music composition using answer set programming. It discusses using the ANTON system to composition melodies and harmonies by applying declarative rules. ANTON uses 191 lines of code and answer set programming to represent 28 melodic and harmonic rules to generate valid musical pieces. The system can compose for multiple voices and outputs pieces in standard music formats. Future work aims to improve performance and expand ANTON's capabilities to real-time improvisation and more complex musical structures.

1. Trends in Answer-Set-
Programming – Focus: Music
Erhard Dinhobl

2. Roadmap
• Motivation: Why Automatic Composition?
• Basics in Music
• ANTON and Music
• Basics in Answer-Set-Programming
• ANTON and Answer-Set-Programming
• Conclusion

3. Why Automatic Composition
• Is it possible? – With ANTON, yes
• melodic and harmonic composition tool
• ANTON uses declarative programming
language for rules representation
• helps composers to understand and
detect failures

4. Basics
Harmony
• „underlying sound“ of a melody –
functional parameter, the chord
structure
• define harmonic progress (history, new
melody) – i.e. cadences
Melody
• progress of notes over time
• „what we sing“

5. Basics - Genre
• style of music – different rules (added to
fundamental music)
• characteristics, culture, instruments, way
we hear
• western tonality – halftone music
interval structure smaller – Arabian-
classic, quarter-tone, microtonal
• BUT: blues (quint in between #11 and 5)

6. System ANTON
• minimal set of rules to generate/verify
music
• adding rules  improvement of quality
• Computer-Aided Composition
• „Background music“ – Elevators, Halls, …

7. Compositionprocess I
• global structure (AABA, Etude, Minuet,
…)
• melody (not overall, variations, J.S.Bach
Invetionen, W.A.Mozart Twinkle Twinkle
Little Star)
• question: „where is the next note?“
• example: „Musikalisches Würfelspiel“
• approved: mathematic models, fractals,
chaos processes, Markov-chains

8. Compostionprocess II
• David Cope „The Algorithmic Composer“
• Iannis Xenakis (example: Modulor)
• my work „Ursprungskunst“ – generate
music out of architecture and the other
way
• ornaments (Claude Debussy, Morton
Feldmann)

9. Composition III
• alternative: IRCAM (based on
PWConstraints-addon LISP and graphic
lang.)
• composition also in „improvisation music“
(jazz, baroque „figured bass“ notation)
• jazz musicians improvise over accord
structure „a standard“
• Improvisation system  Composition
system

10. Answer-Set-Programming I
• formal defined rules
• r: a1,…, aj ← b1,…, bm, not bm+1,…,
not bn
• H(r) = „head“, left-hand side
„consequence“
• B(r) = „body“, right-hand side „condition“
• if B(r) = {}  H(r) = fact, always true
• construction of answer-set in fixpoint
iterations to truth assignment of atoms

11. Answer-Set Example
• a ← b, c
Iterations:
• b←c T({}) = {c}
• c←. T({c}) = {b, c}
• T({b, c}) = {a, b, c}
d←e
T({a, b, c}) = {a, b, c}
• e←d
d & e not contained!

12. Answer-Set Programming II
• atoms: something about reality
• rules: connection between atoms;
assignment gets them to true or false 
atoms (rules fulfilled)
• choice rules: 1 { p, q, r } 2
describes, that at least 1 atom of p, q, r
but at most 2 are choosen to be true
• no negation %

13. Gelfond-Lifschitz-Reduct
• Reduce every „not“ in rules
• result: no negation in rules
• Interpretation, then check if true or false
(accept as true or delete rule)
• all facts
Example:
• all rules without neg.
a ← not b a←.
c ← not d c←.
d←b  d←b
d ← e, not a d←e
e ← d, not a e←d

14. ANTON
• with ASP model is defined due that
music is harmonic and melodic valid
(instance of rules  atoms)
• ANTON consists of 191 loc (28 melodic
and harmonic rules)
• piece with 8 notes: 3.500 atoms; 13.400
rules
• duet with 16 notes: 11.000 atoms;
1.350.000 rules

15. runtime of anton
piece for 1 voice with _length_ notes
piece for 2 voices with _length_ notes
clause learning-mechanism  better performance

16. Twenty Short Pieces (excerpt)
• verification by human
• disadvantage: only quarter notes
• advantage: due declarative prog.
order of rules processing doesn‘t
matter and rule base is extendable
… trying to get insight to Anton's
„thinking“…
0:57

17. Twenty Short Pieces (Harmony)

18. Some Example in Code
• key-rule: choosenNote(P, T, N)
„at time T, voice P plays note N“
• discrete time (quarter notes in this
example)
• may consists of more than one voice
(polyphonic)
• octave is divided in 12 intervals –
independent from temper

19. Example II
keyMode(lydian).
choosenNote(1,1,25).
choosenNote(1,2,24).
choosenNote(1,8,19).
choosenNote(1,9,20).
choosenNote(1,10,24).
choosenNote(1,14,29).
choosenNote(1,15,27).
choosenNote(1,16,25).
#const t=16.
configuration(solo).
part(1).

20. Some Rules
% every note must be in the scale
#const err nik=„note not in scale".
reason(err nik).
error(P,T,err nik) :- choosenNote(P,T,N), chromatic(N,C), not key(C).
% melodic minor -> last two notes depend on direction of playing
error(P,T + 1,err ism) :- choosenNote(P,T + 1,N), chromatic(N,9),
upAt(P,T), keyMode(minor).
% voices can only meet at one time
haveMet(P,T+1) :- choosenNote(P,T,N), choosenNote(P+1,T,N), not haveMet(P,T), part(P+1).
haveMet(P,T+1) :- haveMet(P,T).
% every note, the next note must be an other (up or down)
1 { stepAt(P,T), leapAt(P,T) } 1 :- T != t.
1 { downAt(P,T), upAt(P,T) } 1 :- T != t.
% if melody does a jump, only harmonic intervals are allowed
1 { leapBy(P,T,LS) : leapSize(LS) : LS > 0 } 1 :- leapUp(P,T).
% if a voice changes of interval I the next note must be I steps
higher/lower
choosenNote(P,T + 1,N + L) :- choosenNote(P,T,N), leapAt(P,T),
leapBy(P,T,L), note(N + L).

21. ANTON
• „filling“ of bars no problem
• harmonisation no problem
• harmonisation rules (rules may be taken
from J.S.Bach Choralgesänge –
consistent rules)
• ANTON produces diff. formats (i.e.
Csound, Lilypond) and open for further
ones

22. Evaluation
musical technical
subjective by human ~200 loc for a script
(halftone  quartertone ALL libs and so on: ~800
music) loc
STRASHEELA (UC
Belfast): 8000 loc
BOL-Proc.-Script: 88000
loc

23. Work on ANTON
• better runtime performance (Anton 1.5)
• real time composition  improvisation
• composing trios and quartets (Anton 1.5)
• rhythmic composition (Anton 1.5)
• recognizing and using of global structures

24. ANTON 1.5 (no yet released)
• runtime for generating pieces for 1/2 voice(s)
with _length_ notes
0.22 0.33
1.01 1.06
2.27 2.42
4.62 4.01
0.77 1.18
3.73 3.88
16.84 14.50
29.63 82.64
old values

25. ANTON 1.5
• runtime for generating pieces for 3/4 voice(s)
with _length_ notes

26. Example from ANTON 1.5
code-remarks
style(quartet).
part(1..4).
melodicPart(1).
lowestPart(4).
#const quartetBottomNote=1.
#const quartetTopNote=68.
% from contra C
(lowest + 2 octaves 8vb) to
g’’’ (highest + 2 octaves)
4/4 or 6/4 or …??
0:26

27. Verification with lydian chromatic
concept – George Russel
• method of scale-finding for improvisation
• chord  some lydian scale = parent scale
• chord  lydian scale from note (b7, b9,
-b5, maj = tonic)
• visualisation-model of Robert M. Weiß
(worked with George Russel)
• „travelling“ through quint-circle

28. Verification with lydian chromatic concept –
George Russel II
„A Child Is Born“

29. Conclusion / Future Work
- Anton is some kind of composition
- not the overall solution
- would be useful if it works in realtime
Future work: trying to get a verification
model through my mathematical
visualisation of music in architecture

30. Reductio ad absurdum – but good
Christmas-Song „Es ist ein Roß entsprungen“ 
(A)
||: Bbmaj Eb7 | Abmaj F#7b5 | Fm7 Bb7#11 | Ebmaj Abmaj ||
(B) (A)
| Gsus :|| B-7 A-5b13 | E-7 || Bbmaj Eb7 |
| Abmaj F#7b5 | Fm7 Bb7#11 | Ebmaj Abmaj | Gsus |
| Cmaj || 0:49
- odd count of bars
- melody  some chords (arbitrary)
- most incorrect cadences
- some correct cadences
- global structure: AABA

31. Quellen
[1]
Automatic Composition of Melodic and Harmonic Music by Answer Set Programming, Georg Boenn, Martin Brain, Marina De
Vos, John ffitch, Cardiff School of Creative & Cultural Industries University of Glamorgan UK
[2]
ANTON: Composing Logic and Logic Composing, Georg Boenn, Martin Brain, Marina De Vos, John Ffitch, Cardiff School of
Creative & Cultural Industries University of Glamorgan UK
[3]
Ursprungskunst, Erhard Dinhobl, BSc-Thesis, 2008, TU Wien
[4]
Persönliche Korrespondenz mit Robert M. Weiss / Lehrgang „Lydian Chromatic Concept“ am Josef M. Hauer Konservatorium
Wr. Neustadt
[5]
Persönliche Korrespondenz mit Michael Brain, Entwickler ANTON
[6]
Das wohltemperierte Gehirn: Wie Musik im Kopf entsteht und wirkt, Robert Jourdain, Spektrum Verlag, 2001
[7]
Neue Jazz-Harmonielehre, Frank Sikora, SCHOTT, 2003
[8]
The Lydian Chromatic Concept of Tonal Organisation, George Russel, Concept Publishing Co. New York N.Y, 1953 (2001)
[9]
Automatic Composition using Anwer Set Programming, Georg Boenn, Martin Brain, Marina de Vos, John Ffitch, University of
Glamorgan, UK, 2009
[10]
389 Choralgesänge (für vierstimmigen gemischten Chor), J.S.Bach
[11]
Knowledge, Representation, Reasoning and Declarative Problem solving, Chitta Baral, University of Cambridge, 2003
[12]
Logische Programme und Antwortensemantik II, Prof. Dr. Gabriele Kern-Isberner, Universität Dortmund, 2004
[13]
Persönliche Korrespondenz mit Monika Etzelt
Feel free to contact me: Erhard Dinhobl / er@master-studios.net