dragan matić: genetički algoritmi i muzika

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  • Univerzitet u Novom Sadu

    Prirodno - matematiki fakultet

    Departman za matematiku i informatiku

    Genetiki algoritmi i muzika

    -master rad-

    Novi Sad, juni 2009. Matid Dragan

  • 2

    Sadraj

    Predgovor ...................................................................................................................................................... 5

    Algoritmi u muzici ......................................................................................................................................... 7

    Definicija algoritma ................................................................................................................................... 7

    Upotreba algoritama u muzici................................................................................................................... 7

    Istorijski pregled formalizovanja muzike i algoritamskog komponovanja ................................................ 8

    Algoritmi u staroj Grkoj ....................................................................................................................... 8

    Pitagorejska skala .............................................................................................................................. 9

    Jednako temperirana skala put ka formalizaciji muzike .............................................................. 10

    Moteti .................................................................................................................................................. 11

    Kanonska muzika ................................................................................................................................. 11

    Muziki toak ................................................................................................................................... 11

    Igra pomodu muzike kocke ................................................................................................................ 12

    Fux-ov algoritam ................................................................................................................................. 13

    Sonate i algoritmi ................................................................................................................................ 13

    Algoritmi u muzici u 20. vijeku ............................................................................................................ 14

    Muzika terminologija ................................................................................................................................. 15

    Algoritamsko komponovanje muzike .......................................................................................................... 18

    Naini algoritamskog komponovanja muzike ......................................................................................... 20

    Matematiki modeli ............................................................................................................................ 20

    Sistemi zasnovani na znanju ................................................................................................................ 21

    Gramatike ............................................................................................................................................ 21

    Sistemi koji ue .................................................................................................................................... 21

    Hibridni sistemi ................................................................................................................................... 22

    Genetiki algoritmi u muzici ........................................................................................................................ 23

    Genetiki algoritmi .................................................................................................................................. 23

    Osnovni dijelovi implementacije genetikih algoritama, sa aspektima upotrebe u muzici .................... 24

    Kodiranje ............................................................................................................................................. 24

    Kodiranje pojedinanih tonova ....................................................................................................... 25

  • 3

    Kodiranje nizova tonova .................................................................................................................. 25

    Primjer predstavljanja kompozicije pomodu relativnog predstavljanja tonova ............................. 26

    Fitnes funkcija ..................................................................................................................................... 28

    Automatsko odreivanje fitnesa ..................................................................................................... 29

    Mjerljivi elementi kompozicije ..................................................................................................... 29

    Kriterijumi za fitnes funkciju ............................................................................................................... 31

    Interakivno odreivanje fitnesa ...................................................................................................... 32

    Genetiki operatori ............................................................................................................................. 32

    Inicijalizacija .................................................................................................................................... 32

    Selekcija ........................................................................................................................................... 33

    Ukrtanje ......................................................................................................................................... 34

    Mutacija .......................................................................................................................................... 35

    Zamjena ........................................................................................................................................... 37

    Genetiki algoritmi i dizajniranje zvuka ...................................................................................................... 38

    Primjer optimizacije procesa kreiranja zvuka ........................................................................................ 39

    Opis jednog algoritma za optimizovanje procesa kreiranja zvuka .......................................................... 41

    Genetiki algoritmi u komponovanju muzike sopstveni primjer ............................................................. 42

    Cilj i ideja algoritma ................................................................................................................................. 42

    Softverski paket JFugue ....................................................................................................................... 43

    Neki primjeri upotrebe JFugue elemenata koji su koriteni u radu .................................................... 43

    Klasa Player ..................................................................................................................................... 43

    Klasa Pattern ................................................................................................................................... 44

    Detaljan opis algoritma opti principi funkcionisanja .......................................................................... 44

    Kreiranje jedinke ................................................................................................................................. 45

    Odreivanje fitnesa jedinke ................................................................................................................ 46

    Formiranje i organizacija populacije ................................................................................................... 49

    Genetski operatori koriteni u algoritmu ............................................................................................ 49

    Mutacije .......................................................................................................................................... 49

    Selekcija ........................................................................................................................................... 50

    Konkretno rjeenje .............................................................................................................................. 50

    Implementacija.................................................................................................................................... 51

    Klasa Jedinka osnovni elementi .................................................................................................... 51

  • 4

    Klasa Populacija osnovni elementi ............................................................................................... 52

    Glavni program ................................................................................................................................ 53

    Primjeri generisanih jedinki ................................................................................................................ 53

    Primjeri generisanih main stream kompozicija ........................................................................... 53

    Specijalni primjerci jedinki .................................