Just Intonation, Part 1 Music Technology Pages Return to MusicWords Home

Just Intonation, Part 2: What exactly is just intonation, anyhow?

Just intonation is a tuning system -- or rather, a family of tuning systems -- in which the intervals are mathematically pure. The familiar scale that we all learned growing up, which is called the 12-tone equal-tempered scale, is a rather artificial tuning system that's the result of a compromise. Intervals in the 12-tone equal-tempered scale sound good to us because we're used to them, but in fact they're not mathematically pure.

To get a better understanding of what we mean by "pure," you'll have to read the pages on acoustic and mathematical theory. Briefly, when two sustaining tones are sounded simultaneously, and their frequencies are not related to one another in a mathematically simple way (such as a ratio of 3:2 or 5:4) the tones beat against one another. If you listen close, you'll hear a "wah-wah-wah" effect roughing up the tone color. This beating gives the interval between the two tones an unsettled quality.

All of the intervals in the 12-tone equal-tempered scale produce some beating, because the intervals in the scale are all based on what mathematicians call an irrational number -- the 12th root of 2. (This number is about 1.059464.)

The equal-tempered major third (the interval between C and E in a C major triad) produces an almost obnoxious amount of beating. We normally hear a major triad as consonant rather than harsh and ugly, but that's a learned response, not a natural one. Once you've experienced just intonation, I promise you'll never hear an equal-tempered major triad quite the same way again.

The primary appeal of just tuning systems lies in the fact that they can produce intervals that don't have beats. This gives the music a more restful, settled quality. Some would even call it a healing quality. In addition, most just intonation systems have more types of intervals than the 12-tone equal-tempered scale -- half-steps and whole-steps of several different sizes, for instance. This opens up lots of new possibilities for both melodic and harmonic expression.

If I've captured your interest, feel free to jump ahead to the page on how to set up your synthesizer.