[sdiy] Favorite control laws for nonlinear waveshaping and FM

[Lanterman, Aaron]

Howdy,

Pitch and amplitude are naturally controlled with an exponential function.

What about the index of modulation in FM synthesis, or in particular the variable gain at the input to a memoryless waveshaping nonlinearity (like the Blacet Miniwave)? It seems that an "optimal" choice for the latter would depend on the waveshaping function, but maybe there's a quasi-optimum compromise that people like?

Regarding FM, the DX/TX series control laws are pretty complicated. As far as I can tell there's an exponential-ish mapping from an "output level" setting, but that's added to the envelope output, which is sort of linear-ish in the "attack" ramps and exponential-ish in the "decay" ramps. Sort of.

The main other most-famous FM synth is the Synclavier; I have idea no what it does as far as its FM control is concerned.

The only "commercial" synths I know of that included waveshaping as part of a fixed-architecture synth voice (i.e. where the designer made a particular envelope-to-control mapping) are the Buchla 300, 400, and 700, and of course applying the word "commercial" to anything Buchla is always going to need air quotes. ;) 

Buchla's envelope generators -- at least the ones I know about -- put out linear ramps, so one could take a guess as to his intent if you knew the control laws of the FM and timber modulation inputs of his various oscillators. At least in the 259 he uses a lot of vactrols for that and he doesn't seem terribly concerned with getting any particular mathematical function; I have a feeling he just twiddle resistor values and such until he got something he liked. But who knows...

- Aaron