Harmonic Series Calculator
Every partial in exact Hz, with cents from 12-TET and audio for each one.
What the harmonic series is
In a harmonic spectrum, partials occur at integer multiples of the fundamental frequency. A 110 Hz fundamental produces partials at 220, 330, 440, 550, 660 Hz and onward. Many pitched sounds approximate this closely, though some instruments include inharmonic partials. The partials are not evenly spaced in pitch; they cluster more tightly as the series climbs, and most 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, and cents deviation. Every partial is playable as a sine tone, so you can hear how a 13th partial actually sounds against its 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 sonority (partials 4:5:6:7), and every individual partial group (third, fifth, seventh, ninth, eleventh, thirteenth). Each group gets its own color so you can read the structure at a glance. Microtonal partials (7, 11, 13 and their octaves) are labelled inline with their named just-intonation ratio.
Who this is for
This module is built for anyone who works from the overtone series down. Spectral composers use it to map a specific fundamental onto orchestration, sound-design and synthesis students use it to understand why a sawtooth sounds different from a square, and brass players use it to study why their natural harmonics drift from equal temperament. It is also a direct ear-training tool: 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.