Harmonic Series Calculator
Every partial, exact Hz, cents from 12-TET, audible.
What the harmonic series is
Every pitched sound is a stack of sine waves at integer multiples of the fundamental frequency. A 110 Hz fundamental produces partials at 220, 330, 440, 550, 660 Hz and onward. Our ears fuse those into a single note with a timbre. The partials are not equally spaced in pitch — they get closer together as the series climbs — and most of them land at noticeable cent offsets from 12-TET. The seventh partial is 31 cents flat of the nearest equal-tempered pitch; the eleventh is 49 cents flat, almost exactly a quarter-tone.
What this module shows
Enter a fundamental, as a frequency in Hz or as a note name, and Calcophony lays out the full series. Each partial displays its number, exact frequency, nearest 12-TET pitch, MIDI note, and cents deviation. Every partial is playable as a sine tone so you can actually hear what a 13th partial sounds like against the 12-TET equivalent.
Modes
- Harmonic series — the overtone series rising from the fundamental.
- Subharmonic series — the mirror series descending from the fundamental (useful for spectral composition and undertone-based harmony).
Highlights
Built-in highlight groups flag partials that form the natural harmonic chord, just-intonation perfect fifths, the harmonic seventh (1:4:5:7 ratio), and every individual partial group (third, fifth, seventh, ninth, eleventh). Each group gets its own color so you can read the structure at a glance.
Who this is for
Spectral composers mapping a specific fundamental onto orchestration. Sound design and synthesis students learning why a sawtooth sounds different from a square. Brass players studying why their natural harmonics drift from equal temperament. Ear training — you learn the flat seventh partial by hearing it against a 12-TET minor seventh. For combination tones and difference frequencies between multiple input frequencies, use Spectral Calculator.