Additive Synthesis

[mystran]

If I'm not mistaken, the "SHO" is an example of semi-implicit euler and it is symplectic but only first-order accurate. It doesn't conserve energy exactly, but IIRC in fixed-point the oscillation does cancel the error accumulation. I seem to remember it doing this in floating-point too, at least assuming a specific rounding mode, but I can't seem to find good reference either way for the floating-point case. [Here's some fun discussion.]

Don't take my word for the following (I didn't verify it in any way) but intuitively, I'd guess the phase-quadrature is essentially off by about half a sample.

[shabby]

Interesting stuff mystran. I'm going to look at the phase issue on the weekend, if it's out by .5 sample maybe use v before adjusting it for position:

p+=v;
cosv=v/(dt*2*pi);
v-=p*dts;

[mystran]

Interesting stuff mystran. I'm going to look at the phase issue on the weekend, if it's out by .5 sample maybe use v before adjusting it for position:

p+=v;
cosv=v/(dt*2*pi);
v-=p*dts;

That adjusts the phase by one full sample.

[aciddose]

It won't stay in-phase with an ideal phase accumulator, there is non-zero error. If you're generating several harmonics this way they will drift out of phase over time as opposed to generating each scaled from a single phase accumulator.

Same issue as rotation matrices, recomputing the matrices from a rotation vector will be stable because error does not accumulate.

Rotations obviously are worse because the error not only accumulates but does so non-linearly, so rotation matrices can "explode". While that doesn't happen in this case you'll still end up out of phase and the error is dependent upon all of frequency, amplitude and phase.

[Ichad.c]

https://soundcloud.com/shabtronica/synthr-dtapeloader

That's uber-nasty - I like it!