AMusicofChanges
AlgorithmicComposition • •
StochasticMusic–anoverview o o o o o
Somedefinitions
MarkovChain
• • •
SimulatingaMarkovChain
AnExample ��=����������������������������������ℎ��������������=6��,��,…,����=��=0������=��0.2����ℎ��������������,��=1166×600.20.20.20.20.20.200.20.20.20.20.20.200.20.20.20.20.20.200.20.20.20.20.20.200.20.20.20.20.20.20
TheAppendix1:MarkovChainSimulationCode
plot(y=states,x=1:10,type="b",col="blue",ylab="State",xlab="Step",main="Simulatedstates}{for(iinstates[1]=1states=array(0)P[6,]=c(0.2,0.2,0.2,0.2,0.2,0)P[5,]=c(0.2,0.2,0.2,0.2,0,0.2)P[4,]=c(0.2,0.2,0.2,0,0.2,0.2)P[3,]=c(0.2,0.2,0,0.2,0.2,0.2)P[2,]=c(0.2,0,0.2,0.2,0.2,0.2)P[1,]=c(0,0.2,0.2,0.2,0.2,0.2)P=matrix(0,nrow=6,ncol=6)#DiscreteMarkovChainfortransition#specifyinginitialstate2:10)#Inversetransformsamplingp=P[states[i-1],]states[i]=which(rmultinom(1,1,p)==1)MarkovChain")
DerivationAppendix2:ofpitchmaterialfromonestate ��=������ ��∈0,1,2,…,11∀��=11�� �� ��()��() ��:ℝ→ℝ����,��,…,��=����������12,����������12,…,����������12=��();��∈ℝ����(��=11��)��∈0,1,2,…,11∀��=11����
References • • • •