[sdiy] Sine width modulation?

[Amos]

Apologies if this has been covered before, but I am curious...

Is it practical or musically useful to investigate per-cycle sinewave FM, a
la pulse-width modulation?
I envisioned an FM process such that for example, the rising/positive
portion of each sinewave cycle is at a higher frequency while the
falling/negative portion is at a lower frequency.  (or vice-versa I suppose,
for >50% duty cycle)
Would this still be considered sinusoidal?  Does it sound like anything
other than a pulse waveform with very-low-cutoff lowpass filter applied?

I feel like this is perhaps an ignorant question, but I would be grateful
for any replies on the topic.

Thanks!

[for implementation, I was thinking that a Pulse wave at the same
fundamental frequency as the sine to be modulated could be used, with the
pulse duration corresponding to the amount of frequency offset for the
positive portion of the sinewave.  The means by which the one should
influence the other (specifically how to create positive and negative
half-waves of differing frequency without artifacts) is still unclear to
me...]
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