Just intonation or pure intonation is any musical tuning in which the frequencies of notes are related by ratios of natural numbers.
Any interval tuned in this way is called a pure or just interval.
The simple-ratio intervals upon which Just Intonation is based are the fundamental constituents of melody and harmony. They are what the human auditory system recognizes as consonance. The significance of whole-number ratios has been recognized by musicians around the world for at least five thousand years.
Just Intonation is not a particular scale, nor is it tied to any particular musical style. It is, rather, a set of principles which can be used to create a virtually infinite variety of intervals, scales, and chords which are applicable to any style of music.
Just intonation was born in Europe in the second half of the 15th century.
Vibrational modes of an ideal string, dividing the string length into integer divisions, producing harmonic partials f, 2f, 3f, 4f, etc. (where f means fundamental frequency):