A triangle wave is a basic kind of 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.

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 $\backslash pi$), 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:

$x\_\backslash mathrm\{triangle\}(t)\; =\; \backslash frac\; \{8\}\{\backslash pi^2\}\; \backslash sum\_\{k=1\}^\backslash infty\; \backslash sin\; \backslash left(\backslash frac\; \{k\backslash pi\}\{2\}\backslash right)\backslash frac\{\; \backslash sin\; (kt)\}\{k^2\}$

See also

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

Onda triangular | Sóng tam giác