[jacobvosmaer]

I'm not sure. Intuitively I would think "phase angle" means "offset into the sine wave lookup table".

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.

[HelloNurse]

What matters for FM is an instantaneous quantity: the derivative or increment of the instantaneous phase, i.e. how the phase changes from sample to sample.

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).

[ajxs]

Author here: This is one reason why I used that term. I was definitely thinking in terms of the 'phase accumulator' looking up the sin table.

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.

[joeberon]

> This is exactly why I used that term

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

[ajxs]

I've edited my post to clarify. It's a reason why I used that term. The second part of my post is not directly addressing what GP said. One of my aims in writing this article was to create something that could be interesting to read, with someone like myself as the target audience. Part of that involves using some artistic flourish.

[rcxdude]

This is exactly how direct digital synthesis works and the 'step size' is labelled 'frequency' (specifically, frequency in HZ = step size / size of table * update rate)

[joeberon]

"frequency" would mean the same thing in your weird practical analogy.