Hi,
I just read about Markov chains and how they can be applied to selecting pitches using probability. One thing I'm wondering is how we assure that our note selection matches the distribution of probability.
Let's say our current note was C4.
For the next note:
P(D4) = 0.3 P(E5) = 0.2 P(F4) = 0.5
Would we simply generate a random number R (0..1) and say:
if R < 0.3 then nextNote -> D4 elsif R < (0.3 + 0.2) then nextNote -> E5 else then nextNote -> F4
I only ask, because if our random number function wasn't well-distributed, we might actually see higher probabilities for certain notes than we've intended.
Simply put, what is the most effective, efficient, and accurate way to select the next state based on a list of note-probability pairs connected to the current state?
I'm all right with math, but probability is not one of the areas I'm very strong in. If anyone has a simple way of explaining this, I'd greatly appreciate it.
I can see that markov chains could be applied to far more things than pitch (modulation, rhythm, structure, etc.), so I want to get at least a decent grasp on how we implement them reliably before I start going nuts with the idea.
-Johnny
Hi Johnny
I think you got it all right. A useful abstraction for Markov chains
is the list-wrandom object in the list-abs collection. Also see the
c_markov and c_markovanal objects in the rj-library. They provide both
analysis and generation of markov processes.
Ciao
Frank
On 20.11.2010, at 19:43, Johnny Ferguson hyperflexed@gmail.com wrote:
Hi,
I just read about Markov chains and how they can be applied to
selecting pitches using probability. One thing I'm wondering is how
we assure that our note selection matches the distribution of
probability.Let's say our current note was C4.
For the next note:
P(D4) = 0.3 P(E5) = 0.2 P(F4) = 0.5
Would we simply generate a random number R (0..1) and say:
if R < 0.3 then nextNote -> D4 elsif R < (0.3 + 0.2) then nextNote -> E5 else then nextNote -> F4
I only ask, because if our random number function wasn't well- distributed, we might actually see higher probabilities for certain
notes than we've intended.Simply put, what is the most effective, efficient, and accurate way to select the next state based on a list of note-probability pairs connected to the current state?
I'm all right with math, but probability is not one of the areas I'm very strong in. If anyone has a simple way of explaining this, I'd greatly appreciate it.
I can see that markov chains could be applied to far more things than pitch (modulation, rhythm, structure, etc.), so I want to get at
least a decent grasp on how we implement them reliably before I
start going nuts with the idea.-Johnny
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-
Frank -
Johnny Ferguson