31 Tone Equal Temperament

22 Tone Equal Temperament

Improvisations on a 22-ET guitar.

22-Tone Equal Temperament is the next smallest tuning after 31-Tone Equal Temperament (31-ET) that provides a usable match to both perfect fourths and fifths and major and minor thirds. 22-ET is arguably the most xenharmonic tuning that matches all these intervals, and the matches to minor thirds and fourth/fifths are poor enough to sound out-of-tune to the trained ear.

22-ET matches the 5th, 11th, 15th, and 17th harmonics well, and the 3rd harmonic is somewhat closely matched. The 7th harmonic is poorly matched, meaning that the few good matches to intervals involving this harmonic are an accident of mismatches to various harmonics cancelling out.

Some factors that make the 22-ET system sound xenharmonic, and make it difficult to play conventional Western music and diatonic scales in include:

Because of the last two points, if the primary motivation for exploring microtonal music is to explore harmonies involving the 7th or 11th harmonics, 31-ET would be a better choice than 22-ET. And because of the first point, if one desires to still play diatonic music in a microtonal tuning, 31-ET is also superior to 22-ET.

Summary of 22-ET Relative to 31-ET

Compared to 12-ET, 22-ET offers a glimpse of the harmonic possibilities utilizing the 7th and 11th overtones, at the expense of the loss of the familiar whole tone and possibility of constructing consonant scales and harmonies by stacking whole tones. But the selection of intervals involving the 7th and 11th harmonics, and their correspondence to the just intervals, is limited. 31-ET preserves the use of whole tones in scales, while providing a much more thorough array of harmonic possibilities involving the 7th and 11th harmonics. The only advantage that 22-ET offers is its larger interval size and lower complexity.

On a personal note, I experimented with, but abandoned writing music in 22 due to the poor intonation of fifths and minor thirds, incomplete matches to the intervals involving the 7th and 11th harmonic, and my inability to play diatonic scales in-tune enough for my tastes.

Intervals well-matched by 22-ET

External resources