The Yamaha AN1x Synthesizer mailing list

Jim,

>when you mention the others had 4 or 6 operators...does the AN1x have only 
>one?

OK, it's time for a class of FM 101 ... ;^)  Please pardon me if I end up 
talking down to you; I'm going to assume that you are an FM novice.

The Yamaha DX-series had four or six "operators" -- oscillators, in classic 
synth jargon.  Thus, the AN1x is a two-operator FM synth.  (A one-operator 
FM synth is not FM at all; at least one operator has to be the base wave or 
"carrier," while one or more additional operators modulate it.)  The math 
involved is complicated, but if a sine wave is modulated by another sine 
wave, the result has some of the original wave's frequency, but also 
harmonics related to the multiplied product of the two frequencies, plus 
some artifacts related to the sum and difference of the frequencies.  In 
theory, any sound can be recreated by multiplying a sine wave by a series 
of other sine waves of specific frequencies; that was the essence of John 
Chowning's work at Stanford U., which was the basis of the Yamaha FM scheme.

On the DX-series, all of the operators were sine waves; on some of the 
later Yamaha synths, the operators could be other shapes.  If you want to 
convert the AN1x to classic FM synthesis, set the wave shape to square, and 
the Edge control of both VCOs to "0", and you've got sine waves.

The method of combining the operators -- i.e., who does what to whom -- was 
called an "algorithm."  In a two operator FM setup, there are only two 
possible algorithms:  the two oscillators in parallel, which is really not 
FM at all; and one oscillator modulating the other one, which is what the 
AN1x does when in FM mode.  If I remember correctly, in four-operator 
synthesis, there are eight unique, useful algorithms, and in 6-operator 
synthesis there are 32.  By combining the two scenes, the AN1x can actually 
create four-operator synthesis, but only in relatively simple algorithms; 
it cannot create a scenario where VCO1 is modulated by VCO2, which is in 
turn modulated by VCO3, etc.  In addition, there is only one VCA EG in each 
AN1x scene, while the DX-series provided each operator with its own EG.

Most of the time, classic FM synthesists would divide a sound into two 
parts;  the steady-state sound, and the "stuff" -- I didn't make that term 
up! -- composed of the attack transients and overtones that make the 
instrument unique, like the picking attack of a guitar, or the spit of a 
trumpet.  Two-operator sine-wave FM is pretty much sufficient to create the 
steady-state part, but the "stuff" often requires 4-5 additional sine 
modulators.

Complex-wave FM obeys the same principles as sine-wave FM, but the results 
are a little harder to keep track of, since a wave like a sawtooth or pulse 
is composed of a series of harmonically-related sine waves.  While 
two-operator sine wave FM is considered insufficient to make "interesting" 
sounds, two-operator complex-wave FM is more than sufficient.  In practice, 
you may have to decrease the edge of the modulator wave (and the carrier, 
too) to keep the result from becoming too rich in high harmonics.

Wow, this was longer than I hoped!  I hope it helps you a little.  If you 
have any more questions, contact me off-line, so we don't waste any more 
time on the list.

Regards,

-BW

--
Bruce Wahler
Design Consultant
Ashby Solutions"
www.ashbysolutions.com
CloneWheel Support Group moderator
978.386.7389  voice
978.776.0096  fax
bruce@...