# Triangle wave

Triangle wave

A triangle wave is a non-sinusoidal waveform named for its triangular shape.

Like a square wave, the triangle wave contains only odd harmonics. However, the higher harmonics roll off much faster than in a square wave (proportional to the inverse square of the harmonic number as opposed to just the inverse), and so its sound is smoother than a square wave and is nearer to that of a sine wave.

One simple definition of a triangle wave is

:

It is possible to approximate a triangle wave with additive synthesis by adding odd harmonics of the fundamental, multiplying every (4n−1)th harmonic by −1 (or changing its phase by $pi$), and rolling off the harmonics by the inverse square of their relative frequency to the fundamental.

This infinite Fourier series converges to the triangle wave:

:

It is also possible to approximate a triangle wave with abs() and floor():

:

Or with modulo:

:

See also

*Triangle function
*Sine wave
*Sawtooth wave
*Square wave
*Waves
*Sound

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