Your piano is deliberately out of tune. Equal temperament trades perfectly pure intervals for the freedom to play in every key — see exactly what it costs.
Equal Temperament vs Just IntonationLive
the compromise of tuning
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Just intonation tunes intervals to pure whole-number frequency ratios, which sound perfectly consonant but only in one key. Equal temperament divides the octave into 12 identical steps so every key works, at the cost of every interval except the octave being slightly out of tune. The bars show that compromise in cents.
Reading this result: The equal-tempered fifth sits at 392.0 Hz versus the pure 3:2 fifth at 392.4 Hz — only about 2 cents flat, which the ear forgives; the major third, however, runs a far more audible 14 cents sharp, the price of making every key playable.
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How it works
Just intonation tunes intervals to pure whole-number frequency ratios that sound flawlessly consonant, but only in one key. Equal temperament splits the octave into twelve identical semitones so every key is equally usable, leaving each interval except the octave slightly detuned. The chart shows that deviation in cents — a hundredth of a semitone.
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The math, the assumptions, real-world uses, or a code translation — explained for this exact simulation.
Is this equal temperament just intonation tool really free?▾
Yes. Equal Temperament vs Just Intonation runs entirely in your browser using your device's own compute, so local use is free forever. You only pay Compute Tokens if you scale a job to the cloud.
Do I need to install anything?▾
No. Everything runs client-side in a modern browser — no downloads, no license, no account required to start.
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How accurate are the results?▾
The solver uses established numerical methods, but results are for research and educational purposes and should be validated against experiment or professional review before you rely on them.