[PD] Pitch envelope

[Matt Barber]

I think it would help me to think of the problem if you could say what
you wanted the envelope itself to look/sound like. Is this a
continuous glissando (in frequency? pitch?) from low to high? Does it
go up then down then up again? Or any of these possibilities? Does it
matter more what transpositions are involved or what the timing of the
contour is? All of this matters.

For instance let's say you had a 1000ms sample, and you want the
result of this process to start out an octave lower than the original
for a period of time, and then you want it to jump suddenly to an
octave higher than the original at some point, such that the total
time of this event is 1000ms. Then your timing is determined for you
-- you spend 666.667 ms for the octave lower (chewing up 1/3 of the
original), and then 333.333 ms for the octave higher (chewing up the
remaining 2/3 of the original).

But let's say you just want the sound to start some unspecified
interval lower than original and then exactly halfway through the
1000ms you leap up to some interval higher than written -- this is a
very different problem and it has multiple solutions (that is, it
depends on the value of at least one of the intervals). You can start
with an octave lower (0.5 playback speed) and then jump at 500ms to a
perfect fifth higher (1.5 playback speed). Or you could start a just
major third lower (0.8 playback speed) and then jump at 500ms to a
just minor third higher (1.2 playback speed).

This is true but a little more complicated with glissandi -- it
matters a lot whether you care more about the timing or more about the
intervals of transposition, and if you care about the intervals it's
important whether you're thinking of interval in terms of frequency
difference or in terms of pitch (the base-2 log of frequency ratios,
i.e. "fractions of an octave" or "semitones" or what have you). The
"linearity" of the continuous change will have everything to do with
whether you're thinking of frequency or the pitch measurement.

I haven't thought this through but I'm pretty sure that a linear
envelope on frequency will have the same timing as the average of the
endpoint playback speeds -- in the above example, going from 0.5x to
1.5x at 500ms would be the same as linearly changing from 0.5x to 1.5x
over the whole 1000ms -- so long as the mean is 1.


Matt



>
> Herm.. not sure,
>
> What I mean is this. If I have a sample of 1000ms, and a breakpoint envelope of
> 1000ms duration, the two will stay the same length as long as I don't make any
> points on the graph (i.e. the transpose envelope stays at 0 all the way
> through).
>
> With a transposing sampler, as soon as the transposition is increased the time
> of the sample playback is decreased, so the transposition envelope will not
> finish before the sample is played out. Similarly, if the transposition envelope
> is goes down, the transposition envelope will finish before the sample does.
>
> What I am looking for is a mathematical way to calculate the length of a
> transposition envelope relative to its effect on a finite-length sample, and so
> to derive a length for the envelope that will allow the envelope  and the sample
> to play out over the same duration.
>
>
> The transposition will continuously change the length of the sample, and so from
> my limited knowledge of mathematics I reckon it will take some integration of
> the breakpoint envelope to calculate this number. I'm just not sure how to do
> this.
>
> Best,
> Ed
>
>
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