Hi,
I created the following picture to further illustrate the issue with running a "normal" PWM signal into a triac or a random firing or random turn-on SSR:

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I choosed a random PWM frequency (which was easy to draw) relative to the 60Hz mains but it doesn't really matter.
The triac/SSR is ON during the purple sections which, as you can clearly see, is a lot more than the 12% dutycycle of the PWM signal.

I hope this helps illustrate my point.

/Henrik.