Interval & Tuning Comparison
The same interval, six tuning systems, side by side.
Why intervals differ across tuning systems
A perfect fifth in 12-tone equal temperament is 700 cents. In Pythagorean tuning it's 701.955 cents (the 3:2 ratio). In quarter-comma meantone it's 696.578 cents, because you've narrowed every fifth to make the major third lock into a pure 5:4. The differences are small on paper and huge in practice — a just-intonation major third beats zero times per second with the fundamental, a 12-TET major third beats about 10 times at concert A.
What the comparison tool shows
Pick an interval (by name, by ratio, or by cents), pick a reference pitch (e.g. A4 = 440 Hz), and the module tabulates every supported tuning system. Each row shows the interval size in cents, the defining ratio, the decimal expansion of that ratio, the deviation from 12-TET, and the expected beat frequency between the two pitches at the chosen reference. Differences are small; the table is the only place you can see them all at once.
Tuning systems supported
- 12-TET — modern equal temperament, the default.
- Just intonation (5-limit) — pure ratios up to the prime 5.
- Just intonation (7-limit) — extends to the harmonic seventh ratio (7:4).
- Pythagorean — stacked perfect fifths, pure fifths and fourths, thirds wander.
- Quarter-comma meantone — narrowed fifths to land a pure 5:4 major third.
- Werckmeister III — well-tempered, plays in every key with slightly different colors.
Input modes
- By name — minor second through octave, including tritone.
- By ratio — e.g. 3:2, 7:4, 81:64. The calculator resolves to the nearest named interval for display.
- By cents — arbitrary cent values, including microtonal intervals.
Who this is for
Early-music ensembles calibrating continuo instruments. Composers working in just intonation or xenharmonic tunings. Theorists explaining the syntonic comma to students who think a major third is always a major third. Piano tuners studying historical temperaments before tuning a harpsichord. For real-time pitch detection in any of these temperaments, use Strobe Tuner.