> imagine it's two-dimensional vector synthesis like a Prophet VS.  one
> dimension is some other timbre parameter with a minimum and a maximum
> (no wrap around).
>
> so, in the other dimension, imagine having say, 6 identical wavetables
> except the 2nd harmonic is offset by 60 degrees in phase between
> adjacent wavetable vector points in that dimension.  all other
> harmonics are exactly the same.  so as you crossfade from wavetable 0
> to 1, that 2nd harmonic advances 60 degrees, as you crossfade from
> wavetable 1 to 2, the 2nd harmonic advances another 60 degrees. 
> wavetable 6 and wavetable 0 are exactly the same.  as you crossfade
> from wavetable 5 to 6 you're advancing the final 60 degrees back to
> the original phase of wavetable 0. 
>
That makes sense, I'll have to try it. Six wavetables for the detuned
partial seems like a good number, and I can see that you would not want
too few of them. But what's the reasoning behind how many to use?

> now, if all of the other harmonics remain the same phase for all 6
> wavetables, moving around between them does not detune those
> harmonics.  but if you go around that circle (in the positive
> direction) one complete loop, the 2nd harmonic made one more cycle
> than it would have otherwise if the vector location was stationary. 
> if you whip around that loop 50 times per second, the 2nd harmonic
> will be detuned higher by 50 Hz.  if you whip around that loop in the
> opposite direction, you will be detuning that 2nd harmonic lower in
> frequency.
>
> the application where this might be useful might be with piano tones
> or some other natural instrument with sharpened higher harmonics (like
> above the 9th or 12th harmonic).  it's a different (and cheaper) way
> of doing it than employing what they call "group additive synthesis"
> where the higher harmonics are put into a different set of wavetables
> and run in a different wavetable oscillator that runs at a slightly
> sharp fundamental.
>

On the other hand, I find group additive synthesis conceptually simpler
when dealing with inharmonic partials.

What is the maximum detuning a partial can have with the wavetable
method? Intuitively I would guess it's the same as the fundamental
frequency, so the harmonic k could be tuned down to (k-1) or up to (k+1)
at most, is that right?

Risto




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