frequency modulation synthesis

Fm synthesis is one of the nicest synthesis techniques, since it doesn't require heavy computations to achieve good results. It is best at synthesizing brass-like sounds, and with some refinements you can obtain realistic results.

The idea is to modulate an oscillator's (called carrier) frequency by another oscillator (surprisingly called modulator).

Frequency Modulation introduces a certain number of sidebands (new frequencies in the spectrum) on each side of the carrier, at frequencies:

                  modulation rate
                        |
  modulation           (x)<--+
    index   ------+    /|    |
                   \  / |    |
                    (x) |    |
                    _v__v_   |
                   | osc  |  |
                   `\____/'  |
                       |     |
                       v     |
      amp --+  +------(+)<---+- freq (note)
           _v__v_
          | osc  | 
          `\____/'
              |
              v

the modulation rate controls the frequency of the modulator, if it is an integer, the final spectrum is harmonic, if it is a real number, the final spectrum is inharmonic.

the modulation index controls the amount of modulation we bring to the carrier. If over 1.0, the sidebands appear to steal power from the carrier frequency, if 0.0, there is no modulation.