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