### About the Just Intonation Ear Trainer

About 30 years ago, wanting to develop my ear to distinguish the intervals beyond those represented on a piano, I created the Just Intonation Ear Trainer. At the time, it worked only for Macintosh but had a niche popularity. After Apple's transition to OS-X, the program no longer worked, and I stopped supporting it. With the advent of the Web Audio API, it became feasible for me to resurrect this idea but now on modern browsers across different platforms.

This is currently the beta version of the new Just Intonation Ear Trainer.

### What is Just Intonation?

Just Intonation is a method of choosing musical pitches in which the pitches are related to one another by integer frequency ratios. It is different from the method of choosing pitches (the tuning system) standardized on the modern piano, which is called "equal temperament." The intervals, or distances between pitches, in equal temperament cannot be expressed by integer frequency ratios (except for the octave) because equal temperament intervals are irrational proportions. Just Intonation intervals, on the other hand, are defined by integer fractions (such as 9/8 or 8/5, conventionally the numerator is larger), though many common Just ratios are close to those of equal temperament, such as the 3/2 (perfect fifth), 4/3 (perfect fourth), 5/4 (major third), or 5/3 (major sixth). Many composers have held Just intervals as ideal, even when other demands of music (such as modulation) required compromises. Modern composers who have used Just Intonation were led by Harry Partch, who often used a scale of 43 pitches per octave, all defined by Just ratios. The Just Intonation Ear Trainer uses Partch's set of intervals (aside from the 1/1 or unison). More information on Just Intonation can be found here, here, and here.

### About me

Find out more about me or listen to some of my Just Intonation compositions.

—Bill Alves