Präsentation for the document

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