Sawtooth wave
Roland System-100 model 101 sawtooth wave graph
A sawtooth wave is one of several periodic waveforms that can be generated by an oscillator or LFO.
Shape
As its name suggests, the sawtooth wave resembles the teeth of a saw, either slowly rising then quickly falling back down (also known as a ramp wave), or vice versa. As we can't hear the difference between a regular and inverted waveform, these sound the same to us.
A few oscillators (such as on the VCS3)[1] are able to seamlessly make a falling sawtooth wave, through to triangle wave, through to rising sawtooth wave, and everything in between. Most offer only one direction of sawtooth wave, and a completely separate triangle wave.
Harmonics
In terms of its harmonics, a sawtooth wave has an additional sine wave at double the frequency and half the amplitude of the fundamental one, another at three times the frequency and a third the amplitude, and so on.[2][3][4] In mathematical terms, each harmonic n has a value of 1/n.
All a sound designer needs to know is that it's rich in harmonics, second only to a particularly narrow pulse wave,[5] making it especially useful to feed into a filter or vocoder.
References
- "VCS3: The Putney manual" EMS, p. 9
- Learning Music With Synthesizers David Friend, Alan R. Pearlman, Thomas D. Piggott, 1974, pp. 10—12
- "System-100 Model 101 manual" Roland, Nov 1976, pp. 14—15
- A Foundation for Electronic Music, second edition Roland, pp. 17—18
- "The first dip from the left in the amplitude spectrum is determined by the duty cycle: the dip occurs at the D-1th harmonic [where D = a duty cycle from 0 to 1, 0.5 being square]." "Sine, Saw, Square, Triangle, Pulse: Basic Waveforms in Synthesis and Their Properties" Jan Wilczek
Periodic waveforms: Sawtooth wave
