One vibrating string sounds not one pitch but a stack: whole-number multiples of
the fundamental. That stack is where intervals come from — the octave is 2:1, the fifth 3:2, the
major third 5:4 — and it's the yardstick every tuning system is measured against. Each card below
is one partial: its frequency, and how far it lands from the nearest piano key. Green partials are
the ones 12-ET keeps; the amber and red ones (7, 11, 13…) are the notes equal temperament
lost.
This one diagram explains half the site: the additive synth
builds timbre by summing exactly these partials; the subharmonic
synth runs the series downward; brass players play the series itself (bugle calls are partials
2–6); the just-intonation page tunes by its ratios; and the
7th harmonic's missing 31¢ is why barbershop "blue" sevenths sound so locked when singers find
them by ear.