Just Intonation Calculator
Free tool to calculate just intonation scales in Hz and cents, with .scl export. No sign-up
Pick a tonic and a reference frequency (A4 = 440 Hz by default).
Choose a system (5-limit, 7-limit, Pythagorean, meantone, overtone scale) or type your own ratios, like 9/8 or 5/4.
Read the table: each degree shows its ratio, Hz, cents and the offset from equal temperament.
Press play to hear a degree or the whole scale, or hold a drone on the tonic to hear the beats.
Download an .scl file for synths and samplers, save a CSV, or copy the scale as text.
How do you calculate a just intonation scale, and how far is it from equal temperament?
In just intonation every note is a simple whole-number ratio applied to the frequency of a tonic. A major third (5/4) above 440 Hz is 550 Hz, and a perfect fifth (3/2) is 660 Hz. The difference from the piano is measured in cents: 5/4 is 386.3 cents, 13.7 cents flatter than the 400 of equal temperament, while 3/2 is 702.0 cents, about 2 cents sharper than 700. This tool does the maths for any ratio system and gives you Hz, cents and an .scl file for your synth or sampler.
What is just intonation?
Every note is a frequency. On a modern piano the octave is split into 12 identical steps (equal temperament): it lets you play in every key, but almost every interval is slightly off from the pure one. Just intonation tunes intervals as simple ratios, like 3:2 for a fifth and 5:4 for a major third. Chords sound steadier and sweeter, without the slow wobble called beating. The catch is that a scale tuned this way works best in one key only. The gap between the two systems is measured in cents: 100 cents is one equal-tempered semitone.
Made by Luca Martone, sound designer and live sound engineer based in Turin.
