trends in answer set programming

7/28/2019 Trends in Answer Set Programming

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Trends in Answer-Set-

Programming Focus: Music

Erhard Dinhobl


2/31

Roadmap

Motivation: Why Automatic Composition?

Basics in Music

ANTON and Music Basics in Answer-Set-Programming

ANTON and Answer-Set-Programming

Conclusion


3/31

Why Automatic Composition

Is it possible? With ANTON, yes

melodic and harmonic composition tool

ANTON uses declarative programminglanguage for rules representation

helps composers to understand and detect

failures


4/31

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


5/31

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)


6/31

System ANTON

minimal set of rules to generate/verify

music

adding rules improvement of quality

Computer-Aided Composition

Background music Elevators, Halls,


7/31

Compositionprocess I

global structure (AABA, Etude, Minuet,)

melody (not overall, variations, J.S.Bach

Invetionen, W.A.Mozart Twinkle TwinkleLittle Star)

question: where is the next note?

example: Musikalisches Wrfelspiel approved: mathematic models, fractals,

chaos processes, Markov-chains


8/31

Compostionprocess II

David Cope The Algorithmic Composer

Iannis Xenakis (example: Modulor)

my work Ursprungskunst generatemusic out of architecture and the other

way

ornaments (Claude Debussy, MortonFeldmann)


9/31

Composition III

alternative: IRCAM (based onPWConstraints-addon LISP and graphiclang.)

composition also in improvisation music(jazz, baroque figured bass notation)

jazz musicians improvise over accord

structure a standard Improvisation system Composition

system


10/31

Answer-Set-Programming I

formal defined rules

r: a1,, aj b1,, bm, not bm+1,,not bn

H(r) = head, left-hand sideconsequence

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


11/31

Answer-Set Example

a b, c

b c

c . d e

e d

d & e not contained!

Iterations:

T({}) = {c}

T({c}) = {b, c}T({b, c}) = {a, b, c}

T({a, b, c}) = {a, b, c}


12/31

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 %


13/31

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

all rules without neg. a not bc not d

d b

d e, not a

e d, not a

a .

c .

d b

d e

e d

Example:


14/31

ANTON

with ASP model is defined due thatmusic is harmonic and melodic valid(instance of rules atoms)

ANTON consists of 191 loc (28 melodicand harmonic rules)

piece with 8 notes: 3.500 atoms; 13.400

rules duet with 16 notes: 11.000 atoms;

1.350.000 rules


15/31

runtime of anton

piece for 1 voice with _length_ notes

piece for 2 voices with _length_ notes

clause learning-mechanism better performance


16/31

Twenty Short Pieces (excerpt)

verification by human

disadvantage: only quarternotes

advantage: due declarative prog.

order of rules processing doesnt

matter and rule base is extendable

trying to get insight to Anton's

thinking

0:57


17/31

Twenty Short Pieces (Harmony)


18/31

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


19/31

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).


20/31

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 ofplayingerror(P,T + 1,err ism) :- choosenNote(P,T + 1,N),chromatic(N,9), upAt(P,T), keyMode(minor).% voices can only meet at one timehaveMet(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 allowed1 { leapBy(P,T,LS) : leapSize(LS) : LS > 0 } 1 :- leapUp(P,T).% if a voice changes of interval I the next note must be Isteps higher/lowerchoosenNote(P,T + 1,N + L) :- choosenNote(P,T,N), leapAt(P,T),leapBy(P,T,L), note(N + L).


21/31

ANTON

filling of bars no problem

harmonisation no problem

harmonisation rules (rules may be takenfrom J.S.Bach Choralgesnge

consistent rules)

ANTON produces diff. formats (i.e.Csound, Lilypond) and open for further

ones


22/31

Evaluation

musical

subjective by human(halftone quartertone

music)

technical

~200 loc for a script

ALL libs and so on: ~800

locSTRASHEELA (UCBelfast): 8000 loc

BOL-Proc.-Script: 88000

loc


23/31

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


24/31

ANTON 1.5 (no yet released)

runtime for generating pieces for 1/2 voice(s)

with _length_ notes

0.22

1.01

2.27

4.62

0.33

1.06

2.42

4.01

0.77

3.73

16.84

29.63

old values

1.18

3.88

14.50

82.64


25/31

ANTON 1.5

runtime for generating pieces for 3/4 voice(s)

with _length_ notes


26/31

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


27/31

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. Wei

(worked with George Russel) travelling through quint-circle


28/31

Verification with lydian chromatic concept

George Russel II

A Child Is Born


29/31

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 mathematicalvisualisation of music in architecture


30/31

Reductio ad absurdum but good

Bbmaj Eb7 Abmaj F#7b5 Fm7 Bb7#11 Ebmaj Abmaj||: ||

B-7 A-5b13 E-7:|| ||

|| |

| |Bbmaj Eb7

Abmaj F#7b5 Fm7 Bb7#11 Ebmaj Abmaj|| | |

(A)

(B)

| Gsus

(A)

Gsus |

| Cmaj ||

- odd count of bars

- melody some chords (arbitrary)- most incorrect cadences

- some correct cadences- global structure: AABA

Christmas-Song Es ist ein Ro entsprungen

0:49

Q ll


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Quellen

[1]

Automatic Composition of Melodic and Harmonic Music by Answer Set Programming, Georg Boenn, Martin Brain, Marina DeVos, 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 ofCreative & Cultural Industries University of Glamorgan UK

[3]

Ursprungskunst, Erhard Dinhobl, BSc-Thesis, 2008, TU Wien[4]

Persnliche Korrespondenz mit Robert M. Weiss / Lehrgang Lydian Chromatic Concept am Josef M. Hauer KonservatoriumWr. Neustadt

[5]

Persnliche 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 ofGlamorgan, UK, 2009

[10]

389 Choralgesnge (fr 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, Universitt Dortmund, 2004

[13]

Persnliche Korrespondenz mit Monika Etzelt

Feel free to contact me: Erhard Dinhobl / [email protected]

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