MusicReasonProduction, Synthesis, and Audio Math
What harmonics does this waveform ideally contain?
Choose a waveform family, a fundamental frequency, and a harmonic limit. This tool shows the ideal Fourier-series harmonic locations and relative amplitudes for that mathematical waveform, not a recorded instrument's actual spectrum.
Answer and Play
Want to learn more? Frequency, Sampling, Nyquist, and Spectra
Understand
A real instrument's spectrum departs from these ideal shapes in every practical case: resonance, material, and playing technique all reshape the amplitudes and add inharmonicity a pure mathematical waveform never has. This tool describes the textbook ideal only, useful for understanding why a square wave sounds hollow (only odd harmonics) while a sawtooth sounds fuller (every harmonic present).
Worked example
A sine wave has only its fundamental, no harmonics at all. A square wave at 220 Hz contains energy at 220, 660, 1100, 1540 Hz, and so on, the odd multiples only, each roughly proportional to 1 divided by its harmonic number.
Method and limitations
Each family follows its standard Fourier-series amplitude rule: sine has only the fundamental; square and triangle contain odd harmonics only (square decaying as 1/n, triangle decaying faster as 1/n²); sawtooth contains every harmonic, decaying as 1/n. Playback is limited to safe listening bounds and starts only after your gesture.
Why these four shapes specifically
Sine, square, sawtooth, and triangle are the four classic building-block waveforms synthesizer oscillators are built around, precisely because each has a clean, well-known harmonic recipe worth understanding on its own terms. Real analog and digital oscillators approximate these ideals with their own quirks and band-limiting compromises, which is part of why two synths' "square wave" settings rarely sound identical even though both are chasing the same ideal shape shown here.