How to compensate for frequency shift in exponential FM. Bernie Hutchins' Electronotes patch quoted in and cribbed from Allen Strange.
Exponential audio-rate FM is great for klangorous tones. Unlike linear FM, however, it's hard to patch dynamically. Changing the index results in a churning sound. The more you modulate the carrier, the greater the pitch shift.
Bernie Hutchins' patch counteracts this detuning by simultaneously pulling the frequency of the carrier down with an inverse envelope:
The modulator is patched to the carrier via a VCA. An envelope opens the VCA. The envelope is multed to a second VCA or ring modulator and multiplied by itself. The result is inverted and patched to the carrier.
Here's how it sounds: bernie1
With and without the compensation CV: bernie2
I'd tried this previously, as a work-around for my VCOs which don't have linear FM capability, but didn't get it to work satisfactorily. My mistake was to send the full inverted envelope to the carrier - it needs tweaking to find the right level. Don't expect to be able to set high indices. I found I couldn't push the envelope much above 2-3 volts before the compensation CV itself became apparent. Similarly, short envelopes seem to work better than e.g. joystick sweeps.
Despite its limitations, this patch offers a method for dynamic timbal control of VCOs that aren't capable of linear FM. It's a bit fiddly, but as Allen Strange writes, it's certainly worth a try.