MusicReasonPitch, Tuning, Intonation, and Fret Geometry
How does this interval differ across temperaments?
Choose an interval. This tool compares its size in 12-tone equal temperament against a documented just-intonation ratio, showing the deviation in cents without treating either system as universally "correct."
Answer
Want to learn more? Tuning, Cents, Temperament, and Reference Pitch
Understand
Just intonation tunes an interval to a simple whole-number frequency ratio, which sounds maximally consonant for that one interval in that one key, but does not transfer cleanly to every other key the way equal temperament's evenly spaced compromise does. Neither system is "better" in general: they trade off consonance in specific keys against consistency across all of them.
Worked example
A pure 3:2 fifth (just intonation) is about 701.955 cents, while the 12-TET fifth is exactly 700 cents, a deviation of roughly 2 cents that most listeners cannot consciously hear in isolation but that accumulates audibly across a full cycle of fifths.
Method and limitations
12-TET cents are 100 times the semitone count. Just cents are 1200 × log2(ratio) for the documented ratio. This launch comparison set covers a handful of well-documented simple ratios; it does not attempt every historical temperament, and a just ratio's consonance is inherently key-dependent in a way this single-interval comparison cannot fully capture.
Where this actually shows up in practice
A cappella singers and unaccompanied string players routinely drift toward pure, just ratios for the harmonies they can hear ringing, since there is no fixed keyboard forcing equal temperament on them. A fretted instrument or a piano, by contrast, is built around equal temperament by construction, which is part of why the "same" interval can feel subtly different depending on the instrument producing it, even before any player error enters the picture.