> As convoluted as this sounds, it makes more sense when visualised: [1]
...but does it??
[1] https://ajxs.me/static/img/articles/dx7_technical_analysis/f...
Notice how, when the modulator wave is at its top the FM wave is very short, and when the modulator wave is at its bottom the FM wave is very long.
FM = adjust the frequency (width) of the carrier based on the absolute value of the modulator.
[1] https://web.eecs.umich.edu/~fessler/course/100/misc/chowning...
I think in this case the clearest explanation is the equations + graphs:
1. modulator(t) = sin(t)
2. carrier(t) = sin(t*4)
3. result(t) = sin(t*4 + d modulator(t)/dt) = sin(t*4 + cos(t))
EDIT: it's wrong, see below
If you step through the lookup table with constant size steps, you would get a sine wave. If the steps are not constant size then you get a distorted sine wave. The "rate of change of the phase angle" would then be the step size.
What is usually called frequency, and has the same value in boring cases like an unvarying sinusoid, is the inverse of the period of the resulting sound as someone would hear it, which is not instantaneous and needs on the order of one period's worth of samples (usually more) to estimate, for a certain definition of period (e.g. interval between zero crossings) or a certain mathematically reasonable calculation (e.g. estimating the frequency of the strongest component from a fixed-length window of past samples).
Everyone is absolutely right that this is the same as frequency. I think I was used that particular poetic flourish to emphasise how complicated the academic, mathematic explanation is, in contrast with the diagram. Quite likely I picked up that exact phrasing of "phase angle" from some academic literature in particular.
That's a lie, because:
> I think I was used that particular poetic flourish to emphasise how complicated the academic, mathematic explanation is, in contrast with the diagram
is a totally different to what the person you are replying to said
In an AM radio signal, the frequency of the carrier is constant; the amplitude of the audio modulates the amplitude of the carrier.
In an FM radio signal, the amplitude of the audio modulates the frequency of the carrier. That's the difference!
In musical terms, I very much like some analog, and some FM, synthesizers. But certainly, back in the day, getting some rich sounds out of FM synths was a lot cheaper than analog. (Just in terms of the cost of patch cords alone ;-) Without Chowning there wouldn't have been a synthpop era!