On Wed, 10 Nov 2010, - wrote:
haut-parleur-doppler.pd is the original file from Martin,
[...]
Please correct me if I'm wrong somewhere.
Yes, that file is from me and not from Martin. (but that's just a few kilometres off)
The parallel up/downshifting leads to a chaotic spectrum change. With a speed of .7 ms/ms we have at the same time the signal with 30% and 170% playback speed. Which clearly has no relation to the original pitch and no harmonic relation left.
Why is that clear to you ?The apparent slowdown and acceleration of the sound goes on at the same rate as the contents of the signal itself. Therefore, you don't even have the time to hear a change of pitch... it's not even possible to detect one... there isn't one.
Suppose you have an input signal f(t). Then the output signal is f(t-b-a*f(t)). Then suppose the input signal has period k. This means f(t)=f(t+k). Then the output signal at time t+k is f(t+k-b-a*f(t+k)). But f(t+k) = f(t), so the output signal at time t+k is also f(t-b-a*f(t)) because the argument of f is modulo k. Thus the output signal has period k. Thus all the component tones of the output are harmonics of period k. This fact does not depend on a and b, it depends on the lack of nonperiodic components and differently-periodic components in the formula.
Even if I use f(t-b-tanh(a*f(t))) instead, it remains periodic because tanh of a k-period signal is a function with a k-period signal... it only depends on f(t).
The more I think about it the more fascinated I am that this results in something interesting to the ear.
It remains consonant to the ear so easily simply because it only produces harmonics.
_______________________________________________________________________ | Mathieu Bouchard ---- tél: +1.514.383.3801 ---- Villeray, Montréal, QC
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