The Kyma Language for Sound Design, Version 4.5

Markov Chain
In Kyma, the MarkovChain is a generic object, not necessarily tied to musical applications. It is a kind of
sparse, fast-food version of the classic Markov chain: instead of weighted transitions, you give it a
“training sequence” in the form of an Array, and it constructs weighted transitions based on what transitions
occur and how many times they occur in the training sequence. Once you have “trained” the object
this way, you can ask it to generate any number of sequences, each of which will be statistically related to
the original training sequence you gave it.
For example, if you evaluate the following, short program,
| chain seq |
chain :=
MarkovChain
trainingSequence: #(
what is your name
is it an animal name
or is your name one that would belong to a human
like my name is a name that would
belong to a very human being
)
chainLength: 2.
seq := chain newSequenceOfLength: 100 seed: 9008.
you might get something like this as the result:
OrderedCollection(your name is a name that would belong to a very human being)
Since the chain length is 2, every pair of words in the generated sequence is one that occurs in the original
training sequence. However, the entire chain is something new, not found anywhere in the sequence.
Each time you ask the MarkovChain for a new sequence, giving it a different seed, the result will be a
new sequence. Notice that we asked for a sequence that was 100 words long; when the MarkovChain
backs itself into a corner and can’t find any more legal transitions, it returns what it has been able to come
up with so far.
Now let’s look at a musical example. Here’s the script from the example called modified Markov chains:
| t chain dur pitchOffset seq |
MM := 160.
chain :=
MarkovChain
trainingSequence: #(
#(0 4) #(3 2) #(-5 2) #(2 4) #(3 2) #(-5 2) #(2 4)
#(3 2) #(-5 4) #(2 2) #(3 2) #(-5 4) #(2 2) #(-5 2)
#(5 2) #(-7 4) #(1 2) #(-2 2) #(1 4) #(0 0.5) #(12 4)
)
chainLength: 2.
t := 0.
1 to: 10 do: [ :i |
seq := chain newSequenceOfLength: 100 seed: i * 26.
seq do: [ :offDur |
dur := (offDur at: 2) / i.
pitchOffset := offDur at: 1.
self
keyDownAt: t beats
duration: dur beats
frequency: 1 g + pitchOffset nn + i nn
velocity: i/10.
t := t + dur]].
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