[sdiy] Thoughts on drum synth

[Matt Jones]

One interesting drum synthesis method hasn't been
mentioned here: the modified Karplus-Strong method.

Essentially, this method uses a delay line with
a two-point average, followed by a probabilistic
phase inversion. In digital terms, the system
is described by the equation: 

Y[t] = +0.5*( Y[t-p] + Y[t-p-1] ) probability b
     = -0.5*( Y[t-p] + Y[t-p-1] ) probability 1-b

(here Y[t] is the output at time t, p is the length
of the delay line)

Varying p will change the decay time of the 
resulting sound, while varying b will change the
sound from pitched (b=1) to unpitched (b=1/2) and
back (b=0).

This could also be done with an analog delay and 
some simple comparator circuitry, although the 
original was designed for digital synthesis.

Equivalently, the entire thing could probably be
fit into an FPGA, possibly several times for 
multiple drums.

For those who want to check out the original paper
(very interesting, a bit mathematical):

Karplus and Strong, 'Digital Synthesis of
Plucked-String and Drum Timbres'
Computer Music Journal, Vol 7 No 2 p 43-55

Also check out (in the same issue)

Jaffe and Smith, 'Extensions of the Karplus-Strong
Plucked-String Algorithm' CMJ V7N2 p 56-69

  --mdj



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