I'm reading about Algorithms in Frecuency Modulation. In most synthetizers each algorithm operator have an "Out" level knob, in carriers this knob controls the output volume. For modulators however the level knob decides the amount of change it does to the carrier.
Is this amount the Modulation Index?
Short answer: yes, I think you're understanding the concept correctly.
The modulation index is the ratio between the carrier and modulator frequency deviations. The modulation index is directly proportional to the amplitude of the modulator, and inversely proportional to the frequency of the modulator.
The formula for the modulation index is:
You've mentioned that you can set the output level for each operator on your synth. For FM radio, the amplitude of the carrier wave is constant. In music synthesizers you can adapt it to tweak sounds. That's also because you often have more complex algorithms than what's used for FM radio (one modulator+carrier only). In a DX7 you can cascade up to 6 operators, and in the FS1R and Montage you have 8.
In FM synths you'd use it to get more or fewer sideband frequencies in the resulting signal.
By the way, if you're talking about FM synths: It's mostly an implementation detail, but they don't actually modulate the frequency but the phase.
