[sdiy] Question for those with musical ears

mskala at ansuz.sooke.bc.ca mskala at ansuz.sooke.bc.ca
Thu Apr 15 14:58:53 CEST 2021

On Thu, 15 Apr 2021, Mike Bryant wrote:
> Thanks - interesting read.  What I'm doing is sort of like a polyphonic
> version of that.  At the moment I use a large array of processors to
> analyse the incoming signal in 100uS time intervals and 1 cent pitch
> intervals, so 128,000,000 bins per second.  This produces tables of

Information theory limits how much meaningful timing and frequency
information you can extract from a signal when you're trying to get both
at once.  If your signal comes in with a sampling rate of 48kHz, then you
only get 48,000 numbers describing the signal per second, and it's
intuitively reasonable that you just can't extract 128,000,000 numbers
from that and have them all be useful information.  There just isn't that
much in the signal to extract.  Stuff like the Nyquist theorem and the
Gabor limit make this notion more formal; really doing the estimate
properly requires involving the signal to noise ratio as well as just the
sampling rate.  I wrote an informal article about it, mostly from the
point of view of "latency" concerns that sometimes come up with hardware
synth effects, here:

On your initial posting I considered commenting that since you can't
really get an accurate frequency measurement more than about once per
cycle - which is 262 times per second for middle C - then any glissando
that would have more than one step per cycle is information theoretically
the same as a pure smooth portamento.  I kept quiet because I didn't think
that comment would really be helpful:  it works out to minimum glissando
steps of 0.4 cents for your example of one semitone per second at middle
C, and that's clearly finer than the human ear's resolution anyway.  But
if you're talking about taking complete high-resolution spectra instead of
just a frequency measurement, at 100us intervals, then you're pushing far
beyond the information theoretic limits and this becomes the limiting
factor after all.

Matthew Skala
mskala at ansuz.sooke.bc.ca                 People before tribes.

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