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SEALSungkyunkwan EvolutionaryAlgorithm Lab
SEAL
Website report
2006.10.19
Sungkyunkwan Univ.
Aug 22, 2014
Chang Wook Ahn
SEALSungkyunkwan Evolutionary Algorithm Lab
Automatic Evolutionary
Music Composition

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Introduction
 Algorithmic Composition
 A way of composing music
using computational methods
 Evolutionary Music Composition
 Evolutionary Algorithm을 이용한 Algorithmic music
 Evolutionary Art의 음악에 대응 되는 분야

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Introduction
 Brief History
 컴퓨터의 발명 이전, Algorithmic Composition과 유사한 기법
- Mozart의 “Musical Dice Game”
- Kirnberger 와 Hydne은 Random number 사용
- Mozart, Bach, Bartok은 Fibonacci numbers와
Golden section 사용
 1980년대 이후 machine learning과 optimization technique의
인기와 함께 computer-aided composition에 대한 관심 증폭
• knowledge-based systems, neural networks,
genetic algorithms 등이 특히 많이 사용
 NEUROGEN, GenDash, GenJam, GP-Music System 등

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Categories of EC-based Composition
 자동 시스템 (Automatic System)
 Evaluate fitness by the musically meaningful criteria
• 경험적 지식 기반 룰, 음악 지식기반 룰, 기존 음악 학습 등을 활용
• Zipf의 법칙, 황금 비율, 유사성 기반 룰 등의 추가적 활용 가능
 Often, automatic system faces failure situations
• False positive: High fitness but musically not good
• False negative: Low fitness but musically good
 Consequently, the music doe not possibly reflect the user’s preference
 상호작용 시스템 (Interactive System)
 Evaluate fitness by the user’s judgment itself
 Require a lot of time and effort, and difficult to keep consistency in evaluation
Evolutionary Music
Composition System
Human
Mentor
Population of
composition
Evaluation
Listen
Filtering
(Artificial Neural
Network)

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 GA의 배열을 이용한 일반적인 멜로디 표현
 Mapping value of notes and rest
 실제 악보(music)의 유전자 표현:
4박자곡(quadruple tune)에서 8분 음표(quaver) 길이를 최소 단위로 구성한 예
5
Genetic Representation of Melody
Rest Hold … B3 C4 C#4 D4 D#4 E4 F4 F#4 G4 G#4 …
-1 0 … 59 60 61 62 63 64 65 66 67 68
-1 60 64 71 69 0 0 76 74 71 72 60 62 0 0 0 -1 64 76 74 72 0 0 71 69 67 79 77 76 0 0 0
middle

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Genetic Operators
 자동시스템에서의 유전연산자(Crossover, Mutation)
-1 69 67 70 70 0 -1 0
76 79 76 75 74 72 69 67 76 79 76 75 74 0 -1 0
67 69 67 70 70 72 69 67
Parent 1
Parent 2
Child 1
Child 2
 상호작용 시스템에서는 musically meaningful 유전 연산자를 사용
 Crossover :
교차 후 자손의 melodic interval의 크기가 최소가 되도록 하는 지점에서 교차
 Mutation :
Motif development technique (repetition , Reverse, Transpose 등)을 활용한 변이연산
Parent 1 Parent 1 Child 1 Child 2

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 Multiobjective Optimization
 MO has several conflicting objectives to be maximized
simultaneously
 Due to their interdependence
 A set of alternative solutions exists
 The solutions, known as Pareto-optimal set,
are optimal in the sense that
 no solution is superior to them overall as no objective
can be improved without degrading the others;
where indicates that x1 (Pareto) dominates x0.
 The image of the Pareto-optimal set is defined as the Pareto optimal
solutions
Multiobjective Optimization
}|)(,),(),({ 000
2
0
1 QfffF n  xxxx 
)()(:)()(: 1010
xxxx jjii ffjffi 
f1
f2
dominates
dominate
d
indifferen
t
indifferen
t}:|{ 0110
xxxx fAQ 
01
xx 
x1
x0
Pareto
optimal
Comfort Economy

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 Fundamentally, music evaluation contains multi-objective aspect
 기존 적합도 평가 방법의 문제점
• 𝐹𝑖𝑡𝑛𝑒𝑠𝑠 = 𝑤0 ∗ 𝑓𝑖𝑡𝑛𝑒𝑠𝑠_0 + 𝑤1 ∗ 𝑓𝑖𝑡𝑛𝑒𝑠𝑠_1 + 𝑤2 ∗ 𝑓𝑖𝑡𝑛𝑒𝑠𝑠_2
• 가중치 (𝑤0, 𝑤1, 𝑤2) 결정 문제, Convex일 경우에만 유효
• Only one solution is focused w.r.t. the used weights
 Thus, the concept of Pareto Optimality is used for the fitness evaluation
 어떤 해로부터도 지배되지(dominated) 않는 개체들의 집합은 1st Front가 됨
 Pareto Optimality에 기반한 Multi-objective GA를 이용한 멜로디 작곡
 음악 안에 존재하는 Trade-off 관계의 평가 척도: Stability and Tension
 Pareto optimal set 으로 다수의 솔루션(음악)을 제시
Multi-objective Fitness
f2
1st front2nd front
3rd front
f1

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Fitness Evaluation
 Multi-objective fitness function
 Chord는 Chord tone과 Non-chord tone(Tension note + Avoid note )으로 구성
 코드 안에서 Chord tone은 안정감을 주며, 반대로 Non-chord tone은 긴장감 형성
 Fitness 1은 Chord ton, Fitness 2는 Non-chord tone과 밀접하게 연관되어 있음
 Fitness = maximize (Fitness 1, Fitness 2)
C Key
Chord
tone
Tension
note
Avoid
note
C C,E,G D,A,B F
Dm D,F,A E,G,C B
Em E,G,B A,D F,C
FM F,A,C G,B,D,E -
G G,B,D A,E,F C
Am A,C,E B,D,G F
Bmb5 B,D,F# E,G,A C
Fitness 1 Fitness 2
1. Chord tone +50 -10
2. Tension note
Tension Note -20 +50
At strong beat -50 -30
3. Resolved tension +10 +30
4. Avoid note -30 -5
5. Non-scale note -40 -20
6. Motion
Stepwise +10
Stepwise After leap +20
7. Interval
Perfect +10 -5
Greater than octave -20
 Diatonic chords of the C major key  Fitness evaluation parameters

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Chord progression Rhythm sequence
Initialize population
popul
ation
Copy
Genetic
operations
New
popul
ation
Copy
1
2
3
4
1
2
Reassign rank
Stop?
Set of melodies
User’s choice
Final composition
Rejected
Yes
No
Flowchart of the proposed system
Assign rank

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50
100
150
200
250
300
350
400
450
500
0 200 400 600 800 1000
11
 Two extreme cases
 Evolution of the Pareto front
f1
f2 1 2 3 4 5 6 7 합
1)
f1 600 -20 10 0 0 170 30 790
f2 -120 50 30 0 0 170 -15 115
2)
f1 400 -100 50 0 0 170 20 540
f2 -80 250 150 0 0 170 -10 480
 Fitness values
Experiment 1 – 4 bar melody composition
1)
2)
C F G C
C F G C

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 Evolution of the Pareto front
f1
f2 1 2 3 4 5 6 7 합
1)
f1 550 -40 20 0 0 150 60 740
f2 -110 100 60 0 0 150 -30 170
2)
f1 450 -80 40 0 0 190 0 600
f2 -90 200 120 0 0 190 0 420
 Fitness values
1)
2)
Am F C G
0
50
100
150
200
250
300
350
400
450
0 200 400 600 800
Am F C G

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C C F G F C G C
Am F C G F C G C
C C F G F C G C
Am F C G F C G C
Fitness 1: 2760 81% Chord tone
Fitness 2: 855 13% Non-chord tone, 6% Rest
Fitness 1: 1890 63% Chord tone
Fitness 2: 1900 31% Non-chord tone, 6% Rest

SEALSEAL
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Thank you for listening!

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