If you scale a one cycle of cosine wave by a factor of -0.5 and offset it by 0.5 you get a "Hanning function", which goes from 0 to 1 and back to 0 as smoothly as possible. That can be used to shape the amplitude of a sound, turning it on and off smoothly, or it can be used to modulate any characteristic of the sound.
Frequency modulation is the use of one oscillator—usually but not obligatorily at a sub-audio frequency—to modify the frequency of a sound. The modulating oscillator is added to a main frequency value to create a frequency that fluctuates up and down from the central value. The result, at low modulation rates, is called "vibrato".
A single phasor~ object can serve to synchronize several different modulations. In this example, the phasor~ is scaled and applied in three different ways. On the left side of the patch, the output of the phasor~ is cubed (multiplied by itself, then multiplied by itself again) so that it's a gentle curve instead of a straight line; that curve is then scaled by a factor of 1760, offset by 220, and used as the central frequency of the cycle~ object.
This patch shows a simple method for mixing and viewing two sine tones generated by the cycle~ object.
Amplitude modulation is the use of one oscillator—usually but not obligatorily at a sub-audio frequency—to modify the amplitude of a sound. (Ring modulation, shown in Multiplication of Sine Tones, is one particular example of amplitude modulation.) The modulating oscillator is added to a main amplitude value to create an amplitude that fluctuates up and down from the central value. The result, at low modulation frequencies, is called "tremolo".
To play two tones, you need two oscillators: two cycle~ objects). To mix them together, simply add the two signals with a +~ object. (For digital signals, addition is mixing.) To control the amplitude, multiply it by some factor, using a *~ object. (Multiplication is amplification.)
This patch shows how to mix detuned oscillators with modulation.
This patch demonstrates wave interference with two cycle~ objects, and offers two ways of visualizing the audio signal, with scope~ or by creating your own scope with Jitter.
Frequency modulation refers to using the output of a low-frequency oscillator to continually alter (modulate) the frequency of another oscillator. This example provides the user control of the amplitude and frequency of both the "carrier" oscillator (the one we hear directly) and the "modulator" oscillator (the effect of which we hear indirectly). The output of the modulating oscillator is added to a constant (the main frequency), thus causing the carrier frequency to fluctuate up and down around that central frequency.
There are certain wave types that are historically used in electronic music, known as "classic" waveforms: sine, sawtooth, square, and triangle. These are the four waveforms generated by the classic Moog synthesizer oscillators, and are still quite useful in computer music.