to clarify: i mean that since this is a computer program, and the car/mod frequency ratio is an integer, they are in perfect sync in the sense i meant above. that is, every time the carrier phase is zero, the modulator phase will also be zero. this will never happen in an analog circuit without some specific design choices to ensure that it happens - if you’re just taking two arbitrary analog sines there is gonna be some amount of beating between them.
e.g. ye olde buchla 259 has hard and soft primary->secondary sync options for exactly this reason. i’m sure lots of modern dual osc modules have a similar feature.
it’s pretty high, but not outrageous.
recap: sideband spacing is determined by mod frequency, there are always a (theoretically) infinite number of symmetrical sidebands, and the amplitude of each sideband in that infinite series is a (bessel) function of the mod index.
mod index = mod amp / mod freq. (in most digital FM synth scenarios, you want to parameterize mod index instead of specifying mod amplitude directly - the “meaning” of the mod amp in your patch will change completely if you change the mod frequency. ofc in analog these might be decoupled by necessity, unless the car/mod oscs coexist in a dedicated FM module.)
bessel functions are hard to get an intuitive grasp of. so we tend to fall back on rules of thumb, like: the number of (audible) sidebands is about equal to mod index + 1.
your mod. amp. goes to 15k, so index maxes out around 17, num sidebands = 18, sideband spacing is 880hz, so you have sidebands out to +16khz or so, and likewise way down to ~ -15khz. if i did that right, i think you’re ok for aliasing, but yea, understanding cycle~'s behavior with negative freqs is pretty important. (update: it appears to just work.)
i’d consider converting this to phase modulation to see the difference (or rather, total lack thereof.) though it is annoying that cycle~'s phase input is bounded to [0,1].
anyways, making a comparable analog patch doesn’t seem too hard (given that mod and car freqs are fixed), but: 1) the scaling of the mod depth will be arbitrary, 2), analog sines are never quite sines, 3) analog phase sync will not be perfect, 4) the modulation must be linear. also if carrier is not TZ this amount of modulation will not work.
