Use the free tool below: your data never leaves your browser — all work happens on your device, and nothing is uploaded to any server.
What just intonation is
Just intonation is a way of tuning in which every interval is a simple whole number ratio. The octave is 2/1, the perfect fifth is 3/2, the major third is 5/4, and the major sixth is 5/3. These ratios are not arbitrary: they come from the harmonic series, the natural overtones of a vibrating string or column of air. When two notes form a simple ratio, their overtones line up, and the interval sounds smooth and beat free, with no wavering or roughness.
That smoothness is the great appeal of just intonation, and it is why choirs, string quartets and barbershop singers drift toward it naturally. When singers hold a chord, they adjust by tiny amounts until the beating stops, and the chord locks into place. That locked sound is just intonation, found by ear rather than by theory.
The problem just intonation cannot solve
Just intonation has one serious flaw: a just scale only fits one key. The ratios that make C major sound pure make other keys sound wrong, because the same note has to serve different ratios in different keys. The classic example is the wolf fifth: stack just fifths to build a scale, and one interval comes out badly out of tune, howling like a wolf, because the arithmetic of simple ratios does not close into a neat circle.
This is why keyboards and fretted instruments use equal temperament instead. Equal temperament divides the octave into twelve equal semitones, each 100 cents, so every key sounds equally acceptable and none sounds perfect. It is a compromise, and like most compromises, it works everywhere and delights nowhere. Just intonation is the opposite: perfect in one key, unusable in distant ones.
Just intervals and their deviations
The calculator shows each just interval in cents and its distance from the nearest equal tempered note. The just fifth, 3/2, is 701.96 cents, only 1.96 cents sharper than equal temperament, so it sounds almost the same. The just major third, 5/4, is 386.31 cents, 13.69 cents flatter than equal temperament, a difference any trained ear hears clearly. The just minor third, 6/5, is 315.64 cents, 15.64 cents sharper than equal temperament.
These deviations explain why a piano third sounds brighter and slightly restless compared with a choir third, which sounds warm and settled. Neither is wrong: they are different tunings, and the ear can learn to enjoy both. Knowing the numbers helps you understand what you are hearing.
How to use the calculator
Enter the root frequency, for example 261.63 Hz for middle C, and pick an interval ratio. The calculator shows the just interval in cents, the nearest equal tempered interval, the deviation in cents, and the resulting frequency. It also lists the full just major scale from your root, with every ratio, its cents value, its frequency, and its deviation from equal temperament.
Try the just major scale from C and compare it with a piano. The thirds and sixths will differ most, the fifths and fourths least. That pattern is the whole story of temperament in one table: the intervals built from small ratios are close to equal temperament, and the ones built from the ratio 5 are further away.
Where just intonation lives today
Just intonation never died: it lives wherever pitch is flexible. Choirs, string players, trombonists and singers use it constantly, adjusting by ear. Barbershop harmony is built on just intervals, especially the pure third and the barbershop seventh, which is the ratio 7/4, far from any piano note. Some modern composers write in just intonation deliberately, using retuned instruments or electronics to explore its colours.
Electronic music makes just intonation easy to explore, since a synthesiser can retune instantly. The calculator is a starting point: pick a ratio, hear it in your head or on an instrument, and compare it with the equal tempered version. The difference is small in numbers and large in feeling.
Common mistakes
The most common mistake is assuming just intonation is simply better. It is purer in one key and worse across keys, and the right choice depends on the music. Another mistake is confusing just ratios with equal tempered intervals: a just third is not the same pitch as a piano third, even though both are called major thirds. Finally, do not try to force a fixed pitch instrument into just intonation: the instrument was built for equal temperament, and fighting it produces worse results than accepting the compromise.
Use the calculator to learn the numbers, then listen. The ratios are exact, but the feeling they produce is the real lesson, and it only arrives through the ear.