What is just intonation?

Just intonation is a tuning system where every interval is tuned to a simple whole-number frequency ratio (e.g. 3:2 for a perfect fifth). This produces the purest, beat-free sound for each interval, but only works well in a single key.

Why does equal temperament differ from just intonation?

Equal temperament divides the octave into 12 equal semitones using the irrational ratio 2^(1/12). This lets you play in any key without retuning, but most intervals are slightly out of tune compared to their pure just-intonation equivalents.

What does the cent deviation mean?

Cents measure the difference between just intonation and equal temperament. One cent is 1/100th of a semitone. A positive value means JI is sharper than ET; negative means JI is flatter. Values above ±5 cents are audible on sustained tones.

Which intervals are the same in JI and ET?

The unison (1:1) and the octave (2:1) are identical in both systems. All other intervals have some deviation, with the major third (−13.69 ¢) and minor third (+15.64 ¢) being the most significant in 5-limit JI.

Can I use a note name instead of a frequency?

Yes. Type a note name such as A4, C#3, or Bb4 and the calculator will resolve it to the standard equal-temperament frequency (A4 = 440 Hz) before building the just scale.

Just Intonation Calculator

Enter a root frequency to see the full just intonation scale — pure-ratio frequencies for all 12 intervals with cent deviations from equal temperament.

Root Note / Frequency

Root (Hz or note, e.g. A4)

Harmonic Limit

5-limit: classic just intonation using ratios built from primes 2, 3, and 5.

Quick Presets

Root

— Hz

Limit

5-limit

Max |Deviation|

— ¢

Interval	Ratio	JI Freq (Hz)	ET Freq (Hz)	Deviation	Diff bar

Cent Deviation: JI vs ET

−20 ¢ 0 ¢ (ET) +20 ¢

Copied!

Summary

The Just Intonation Calculator generates a complete 12-note scale from any root frequency using pure whole-number ratios. For each interval it shows the just intonation frequency, the equal temperament frequency, and the deviation in cents between the two systems.

How it works

Just intonation tunes each interval to a simple whole-number frequency ratio against the root (e.g. perfect fifth = 3:2, major third = 5:4). The calculator multiplies the root frequency by each ratio to get the JI frequency, then computes the equal-temperament frequency using f × 2^(n/12) and subtracts to find the cent deviation (1200 × log₂(JI/ET)).

Use cases

Tune acoustic instruments or synthesizers to pure harmonic intervals.
Understand why equal temperament compromises certain intervals.
Compose or analyze music in just intonation or meantone temperaments.
Explore the beating differences between JI and ET on a specific root.
Generate reference frequencies for string ensemble or choir intonation work.

Frequently Asked Questions

Last updated: 2026-06-11 · Reviewed by Nham Vu