Modulation

AM

Ring modulation

Others like single sideband are not generally used in this context

Used in practice as an audio effect

except when the modulator has DC offset, in which case FM shifts frequency, while PM shifts phase

The second one is preferable if you need to predict the final tuning of a note

DC offset can result from FM/PM when a sideband falls on frequency 0! (which can be often for harmonic spectra)

For this reason most implementations of FM are actually PM (particularly if they allow feedback or chaining of more than 2 oscillators)

Sidebands are equally spaced around the carrier

Bessel Functions of the first kind (Jx) describe the behavior of the resulting sidebands

The order of the function is the sideband number and the x value is the modulation index. The y value is the amplitude of the sideband

Modulation index

The ratio between Carrier and Modulator can help predict the output spectrum

and importantly the perceived fundamental for harmonic spectra

Upper sidebands

Lower sidebands

For the carrier to be the fundamental M > 2C or ratio 1:1

B. Truax, "Organizational Techniques for C:M Ratios in Frequency Modulation", Computer Music Journal, 1(4), 1978, pp. 39-45; reprinted in Foundations of Computer Music, C. Roads and J. Strawn (eds.). MIT Press, 1985

Having envelopes for each modulation index creates dynamic spectra

Multiple oscillators to chain modulation

Modulation feedback

The frequency of the oscillators can be fixed or linked with a factor to another oscillator