What is equal temperament?

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.

What is just intonation?

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.

What is Pythagorean tuning?

Pythagorean tuning generates all intervals from stacked perfect fifths (ratio 3:2). Fifths sound pure, but thirds are wider than in equal temperament. 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). The difference is about 31 cents (less than a quarter tone).

AudioCalcs

Tuning Calculator — Alternative Tuning Systems

Calculate frequencies for alternative tuning systems. A4 reference pitch adjustment.

A4 Reference

Tuning System

Octave

How We Calculate This

Equal Temperament

f = A4 × 2^(n/12) where n = semitones from A4

Just Intonation

Uses whole-number frequency ratios from the root: unison (1:1), major 2nd (9:8), major 3rd (5:4), perfect 4th (4:3), perfect 5th (3:2), etc.

Cents Deviation

Cents = 1200 × log2(f_alt / f_equal)

100 cents = 1 semitone. Deviations under 5 cents are generally imperceptible.

Frequently Asked Questions

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Last updated: February 2026

All calculations are estimates based on standard formulas. Always verify results for critical applications.