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That's really interesting. Would you have some more information on how the Yamaham FM chips were implemented. I'm still trying to wrap my brain around what "mod

That's really interesting. Would you have some more information on how the Yamaham FM chips were implemented. I'm still trying to wrap my brain around what "modulation" is actually doing and why it sounds the way it does when one wave operates another.

klodolph 6y ago
Your basic core is the numerically-controlled oscillator, which consists of a phase accumulator and a wave shaper which converts the phase to the desired wave (basically a sine wave lookup table). phase accumulator -> wave shaper Yamaha FM just lets you add other signals to the wave shaper input: other signal -------\ (+)-> wave shaper phase accumulator --/ For example, instead of getting sin(x), you get something like sin(x + sin(x)). You start adding parameters like “a sin(b x + c sin(d x))” suddenly there are millions of possibilities. “Why it sounds that way” can get really deep if you like, but basically, as you increase the modulation level you get more harmonics, and if you increase it too much you start losing the fundamental frequency. This is one of the reasons why it’s nice to have a 6-operator FM system (like in the DX-7). With the 4-operator FM, once you turn the modulation “all the way up”, there’s nowhere to go, but with 6-operator FM you have some extra operators around for modulating modulators.
SonOfLilit 6y ago
The math is just Asin(at+Bsin(bt+...))+Csin(ct+...), where you can slowly play with A, a, B, b, ... but to get a good musical intuition try this tutorial for the Yamaha Reface DX (a modern incarnation of this algorithm, identical to the DX7 except they replaced the last two operators with a feedback unit per op instead of just one): https://www.yamahasynth.com/synths/basics-of-fm-synthesis https://www.yamahasynth.com/synths/basics-of-fm-synthesis
jim-jim-jim 6y ago
You may want to give this a read when you have the time: written by the man who discovered FM synthesis, and intended for musicians rather than mathematicians. Very eye-opening for any casual synth enthusiast--even somebody without a DX: https://libgen.is/book/index.php?md5=A0BE23E763754D12807CDD6A773AF69D https://libgen.is/book/index.php?md5=A0BE23E763754D12807CDD6... The book is long out of print so I don't think anybody would object to the link.

klodolph 6y ago

Your basic core is the numerically-controlled oscillator, which consists of a phase accumulator and a wave shaper which converts the phase to the desired wave (basically a sine wave lookup table). phase accumulator -> wave shaper Yamaha FM just lets you add other signals to the wave shaper input: other signal -------\ (+)-> wave shaper phase accumulator --/ For example, instead of getting sin(x), you get something like sin(x + sin(x)). You start adding parameters like “a sin(b x + c sin(d x))” suddenly there are millions of possibilities. “Why it sounds that way” can get really deep if you like, but basically, as you increase the modulation level you get more harmonics, and if you increase it too much you start losing the fundamental frequency. This is one of the reasons why it’s nice to have a 6-operator FM system (like in the DX-7). With the 4-operator FM, once you turn the modulation “all the way up”, there’s nowhere to go, but with 6-operator FM you have some extra operators around for modulating modulators.

SonOfLilit 6y ago

The math is just Asin(at+Bsin(bt+...))+Csin(ct+...), where you can slowly play with A, a, B, b, ... but to get a good musical intuition try this tutorial for the Yamaha Reface DX (a modern incarnation of this algorithm, identical to the DX7 except they replaced the last two operators with a feedback unit per op instead of just one): https://www.yamahasynth.com/synths/basics-of-fm-synthesis https://www.yamahasynth.com/synths/basics-of-fm-synthesis

jim-jim-jim 6y ago

You may want to give this a read when you have the time: written by the man who discovered FM synthesis, and intended for musicians rather than mathematicians. Very eye-opening for any casual synth enthusiast--even somebody without a DX: https://libgen.is/book/index.php?md5=A0BE23E763754D12807CDD6A773AF69D https://libgen.is/book/index.php?md5=A0BE23E763754D12807CDD6... The book is long out of print so I don't think anybody would object to the link.