Amplitude Modulation (AM) Synthesis is performed by combining two signals together. A source audio signal, the carrier, is multiplied by an unipolar modulation signal. A unipolar signal is a signal that contains only positive values (usually between 0 and 1). This process alters the carrier signal in one of two ways: 1) The modulation signal can be used as an envelope which is applied to the carrier signal to determine the audio signal's amplitude over time. 2) The modulation signal can be used to quickly cycle the carrier signal's amplitude to create two additional frequencies known as sidebands, forming harmonic or non-harmonic sounds.
Ring Modulation (RM) Synthesis is like AM Synthsis except that it uses a bipolar modulation signal (positive and negative values). RM synthesis is used by vocoders which are often used to effect a human voice's sound signal to create a "robotic" sounding variation.
Frequency Modulation (FM) Synthesis produces an output signal by oscillating the frequency of a source oscillator's signal. This process can generate fairly complex output containing multiple frequencies/sidebands with only two oscillators, requiring minimal computations.
I created a max patch that uses frequency and ring modulation:
Download maxMSP file
The patch uses different combinations of phasor, cycle, and triangle waves to generate sounds.
To listen to sample clips from this patch, click here and navigate to the audio links under "week 3."