31 Tone Equal Temperament

Why Not Quarter Tones?

Quarter tones are the most well-known and commonly used system for microtonal music in western music. The tuning produced by quarter tones is also called 24 tone equal temperament. This tuning is widely used primarily because the 12-tone equal temperament is in such wide use, and indeed, there are virtually no other systems in mainstream use. Quarter tones are easy to implement because they represent a natural division of the 12-tone scale. A musician learning quarter tones thus has only half as many intervals to learn, and has a familiar context of tuning and intonation into which to place these new intervals.

Arab music can also be understood in terms of quarter tones, and quarter tones can be used to play the scales traditionally needed to play this music.

In order to use a system other than quarter tones, most musicians would need to be convinced that the system is indeed better, in the sense that it is easier to learn, or somehow more practical or more flexible. I believe that 31-ET offers all of these advantages.

Shortcomings of Quarter Tones

31-ET Improves On Many Intervals Achievable With Quarter Tones

There are only two sets of intervals (and their inversions) that are less in-tune to their just intervals in 12-ET relative to quarter tones: fifths (and fourths), and major seconds (minor sevenths).

24-ET does better match the 11th harmonic than 31-ET, so some intervals, including 12:11 and 11:8, are matched better with quarter tones.

Further Reading: