Chapter Four: Synthesis
2. Waveforms
Waveforms determine the spectral content output by an audiorate oscillator. In subtractive synthesis, an oscillator is normally at the beginning of the audio chain. The waveform output by the oscillator is selected for its spectral characteristics. Filters farther down the audio chain then 'subtract' or modify frequencies in that spectrum. Additive synthesis relies on many oscillators chained together, each normally producing a sine wave (which produces only the fundamental frequency) with their outputs being summed, to build up a timbre from scratch. Both methods are still very much in use in digital synthesis applications.
Early modular synthesizers, such as the Moog modular models, c. 1967, provided the user a choice of four basic waveforms on their oscillators, believing they offered a good variety of choices for the subtractive synthesis process. It is important when studying the characteristics of these waveforms to take into account not only the partials each form produces (see Chapter One) , but also the strength of those partials. These two factors combined form what we consider timbre and together are called the waveform's spectrum. As discussed in Chapter One, the fact that these are periodic waveforms means that they will have harmonic partials. Below is a chart indicating these spectra for the four basic waveforms (p# = partial number, 'relative strength' is relative amplitude in relationship to the fundamental).
Waveform 
Shape 
Spectrum 
Relative Strength 
sine wave 
fundamental only, no additional harmonics 
n/a 

triangle wave 
odd partials only (1,3,5,7...) 
1/p#^{2} (one over the partial # squared) (3rd partial=1/9, 5th partial=1/25, etc.) 

sawtooth wave 
all partials 
1/p# (one over the partial number) Sawtooth, sometime called a ramp wave, can be an 'up' or 'down' ramp, which doesn't effect spectrum unless mixed with another wave 

pulse wave 
duty cycle = x:y With x = 1, all integer multiples of y are missing from the spectrum. A square wave has a duty cycle of 1:2 and has only oddnumbered partials 
1/p# (one over the partial number) 
1  2