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karplus strong mathematics and the A-188-1

2008-04-30 by Doug

Hi folks, according to my calculations, the number of BBD stages is
related to the highest possible musical note via karplus strong
synthesis as follows:

128max=G5
256max=G4
512max=G3
1024max=G2
2048max=G1
4096max=G0

Am I wrong? Here's how I got there:

1) the frequency of the karplus strong loop is the note that will be
heard as the loop attenuates. This frequency F is equal to 
F = Fs/N where Fs is the sampling rate and N is the number of samples. 

2) According to the Doepfer documentation for the A-188-1, the design
clock range of these modules is roughly 10kHz to 100kHz. I am assuming
this is the range of acceptable values for Fs. So taking Fs as 100kHz,
and N=128 (for the 128 stage BBD), the highest note that this setup
can play is 
100000Hz/128 = 781Hz or roughly a G5. The lowest note is not so much
an issue, but just for grins, 10000Hz/128= 78Hz, or roughly D#2.

3) For comparison, the 256 stage BBD will only manage 100000/256 =
390Hz, or about a G4. And it goes down an octave with each doubling of
the number of stages.

Since it appears that my guitar roughly covers octaves 1 through 4 (I
think) the 256 BBD is the ideal number of stages for plucked string
sounds.

Any advice is appreciated, especially from those who have tried BBD
modules. Thanks, Doug

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