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

• 12-ET has major and minor thirds that are not particularly in-tune, and using quarter-tones does nothing to address these shortcomings. Quarter tones thus produce a conflict--as musicians fine-tune their ears to hear and play microtonal music, the out-of-tuneness of the familiar thirds becomes more of an issue.
• Quarter tones provide a very poor match to intervals involving the 7th harmonic, such as the septimal whole tone, septimal minor third, septimal major third, and septimal tritones. These intervals are higher up in the harmonic series, making it harder to hear their relationships, and they are less familiar to most people's ears; having them be so out-of-tune makes it more likely that these intervals will sound "off" or out-of-tune to listeners, rather than sounding natural and displaying their true harmonic colors.

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.

• 31-ET provides a significant improvement to 12-ET or 24-ET in terms of the intonation of major and minor thirds. For all practical purposes, these intervals sound perfectly in tune in 31-ET to most listeners.
• 31-ET provides a much closer match to intervals involving the 7th harmonic, including the septimal whole tone, septimal major and minor thirds, and septimal tritones. Furthermore, it distinguishes between the greater and lesser septimal tritones, allowing people to use these intervals as a consonant interval implying a tonal center, rather than as an ambiguous, dissonant interval.
• Like the quarter tone system, 31-ET also provides the possibility of neutral seconds, neutral thirds, and the 11:8 harmonic ratios, and these intervals are all still usably in-tune. Like quarter tones, 31-ET matches the 12:11 neutral second more closely, making this interval harmonically familiar in 31-ET to people used to playing Arab scales in quarter tones. 31-ET can thus play Arab scales and other traditional music using these intervals just as they can be played with quarter tones.

Further Reading:

• Quarter Tone on Wikipedia - A detailed article discussing quarter tones and 24-tone equal temperament, covering instruments, scales, and individual intervals.