Tuning Calculator — Alternative Tuning Systems

Equal temperament divides the octave into 12 equal semitones, each with a ratio of 2^(1/12) = 1.0595. This means every key sounds equally in tune (or equally slightly out of tune). It became the standard Western tuning because it allows free modulation between all keys.

Just intonation uses simple frequency ratios (3:2 for a fifth, 5:4 for a major third, etc.) to create pure-sounding intervals. The result is beatless, perfectly consonant intervals in one key, but other keys sound increasingly out of tune. It is used in choral music, barbershop and some world music traditions.

Pythagorean tuning generates all intervals from stacked perfect fifths (ratio 3:2). Fifths sound pure, but major thirds are wider than in equal temperament (and minor thirds narrower). It was the standard tuning in Western music from antiquity through the medieval period. It works well for monophonic and parallel-fifth music.

A432 tuning sets A4 to 432 Hz instead of the standard 440 Hz. Proponents claim it sounds warmer and more natural. There is no scientific evidence for health or spiritual benefits. Some orchestras historically tuned lower (e.g. Baroque pitch around A415, roughly one semitone below A440). The difference between A432 and A440 is about 32 cents (less than a quarter tone).

This calculator uses 9/5 for A# in the just (major) scale — the greater just minor seventh, a perfect fifth (3/2) stacked on a minor third (6/5), about 1017.6 cents above the root. Some 5-limit chromatic tables instead use 16/9, the lesser (Pythagorean) minor seventh of two stacked perfect fourths, about 996.1 cents. Both are valid just minor sevenths; the choice differs by about 21 cents. Equal temperament sits between them at exactly 1000 cents.