Sawtooth wave

Description

The sawtooth wave (or saw wave) is a kind of non-sinusoidal waveform. The convention is that a sawtooth wave ramps upward and then sharply drops. However, in a “reverse (or inverse) sawtooth wave”, the wave ramps downward and then sharply rises. It can also be considered the extreme case of an asymmetric triangle wave. While a square wave is constructed from only odd harmonics, a sawtooth wave’s sound is harsh and clear and its spectrum contains both even and odd harmonics of the fundamental frequency. Because it contains all the integer harmonics, it is one of the best waveforms to use for subtractive synthesis of musical sounds, particularly bowed string instruments like violins and cellos, since the slip-stick behavior of the bow drives the strings with a sawtooth-like motion. The formula in trigonometric terms is related to the period and the amplitude of the wave.

Related formulas

Variables

yxSawtooth wave (dimensionless)
aThe amplitude of the wave (dimensionless)
πpi
xX-coordinate (dimensionless)
pThe period of the wave (dimensionless)