Square vs triangle wave: odd harmonics done two ways
Square and triangle both have only odd harmonics, but the triangle's harmonics decay much faster, so it sounds softer. Same pitch, same harmonic series, different character because of the decay rate.
Buzz versus mellow, both using only odd harmonics.
Square and triangle waves both contain only odd harmonics, but they sound nothing alike. A square wave's harmonics fall off slowly (1/n), so the upper harmonics stay strong and the tone reads as bright and buzzy. A triangle wave's harmonics fall off faster (1/n-squared), so the upper harmonics fade quickly and the tone reads as soft and mellow. Same pitch, same harmonic series, completely different character because of the rate of harmonic decay.
By TechCompare · Updated
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Side-by-side specs
| Spec | Square wave | Triangle wave |
|---|---|---|
| Fundamental frequency | Same | Same |
| Harmonic content | Odd harmonics | Odd harmonics |
| Harmonic decay rate | 1/n (slow) | 1/n-squared (fast) |
| RMS at peak 1.0 | 1.0 (better on this spec) | 0.577 |
| Character | Buzzy, bright | Mellow, soft |
| Best for | Synth leads, chiptune | Pads, soft modulation |
How they differ
Both shapes are built from odd harmonics - the fundamental plus the third, fifth, seventh, and so on. The square wave amplitudes follow 1/n (one over the harmonic number), so the third harmonic is at one-third the fundamental amplitude. The triangle wave amplitudes follow 1/n-squared, so the third harmonic is at one-ninth the fundamental amplitude. That faster decay is what makes the triangle wave softer - the upper harmonics that give the square wave its buzz are negligible. A triangle wave is also closer to a sine in perceived loudness at the same peak amplitude (RMS 0.577 versus 0.707 for sine, 1.0 for square), so it sits between the two extremes in both timbre and loudness.
Verdict
The triangle wave is a square wave with most of its upper harmonics suppressed. Use a square wave when you want buzzy character, a triangle wave when you want the same odd-harmonic structure but softer, or a sine when you want no harmonics at all.
Hear square vs triangle at 440 HzWhich should you pick?
Choose Square wave
Pick a square wave when the buzzy, brass-like character is what you want: synth leads, chiptune patches, harmonic-distortion tests.
Choose Triangle wave
Pick a triangle wave when you want the odd-harmonic flavor without the harshness: synth pads, soft flute-like tones, gentle modulation sources.
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Frequently asked questions
Why do square and triangle waves sound different despite both having only odd harmonics?
Which is louder at the same peak amplitude, square or triangle?
When should I use a triangle wave instead of a square?
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