# phase mod x freq mod equivalence

do any of you know how to convert a FM index to a phase mod index equivalent considering they both have the same carrier and modulator frequency? Is it even possible?

This is in respect for sound synthesis and I'm talking about one sinusoid modulating another sinusoidal oscillator.

I'm being able to get very similar sounds with these parameters:

FM: carrier freq 200Hz, modulator freq 480Hz, index 400*

• this means the carrier freq oscillates 400Hz up then back to original frequency and then down 400Hz and back 480 times a second

Phase Mod: carrier freq 200Hz, modulator freq 480Hz, index pi/4 **

** this index means the phase goes up 1/8 of a cycle and then back, down the same amount and back to the original point

FM and Phase Mod are clearly two independent processes, but I've seen people mention it can be equivalent, but I've never read anything that would tell me how to get the same results with both. So I don't know if it can really be done even if it sounds practically the same thing or if I just got lucky.

thanks

• okay, so think of $$\sin( \theta(t) ) = \sin\left( 2 \pi \int_0^t f(u) \ du + \theta(0) \right)$$ or $$\sin\left( 2 \pi \int_0^t I \cdot x(u) \ du + \theta(0) \right)$$ where $x(t) \le 1$ is your modulating signal. and $I$ is the modulation index. – robert bristow-johnson Aug 28 '14 at 20:48