Introduction to Computer Music by Nick Collins

Author:Nick Collins
Language: eng
Format: epub, pdf
Publisher: John Wiley Sons
Published: 2018-01-18T05:00:00+00:00

dt

=

cos

(

2

π

440

t

)

2

π

440

Use a naive Euler ordinary differential equation solver to synthesize an output solution on a sample by sample basis, say over two seconds, starting at x = 0, t = 0. (The basic Euler method is simply to update a variable x(n) by the most straightforward approximation to the derivative, a first-order difference

x

(

n

+

1

)

=

x

(

n

)

+

α

dx

dt

(

n

/

R

)

α controls how quickly you update, and one over the sampling rate R might be a good first choice for the steps in time. dx/dt is evaluated at the discrete time t = n/R). If that went well, now try and tackle

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