31 Tone Equal Temperament

17 Tone Equal Temperament

17 tone equal temperament (17-ET) is a tuning that shares only a few things in common with 31-ET. With its modest number of divisions to the octave, only a few more than in 12-ET, 17-ET is much more like 12-ET than 31-ET, and is much less "microtonal" so to speak.

17-ET is the first tuning after 12-ET that provides a reasonable match to fifths; the fifths are actually more in-tune than in 31-ET. 17-ET matches the 11th harmonic about as closely as 12-ET matches the 5th, and 17-ET matches the 7th harmonic better than 12-ET, although still not very well. The main problem with this tuning is that the 5th harmonic is poorly matched.

One odd benefit of 17-ET is that the 13th harmonic is well-matched, making many intervals involving this harmonic well-matched as well. 17-ET is the smallest equally tempered tuning that matches both this harmonic and the 3rd well.

Relationship to Arab Music

17-ET bears some similarity to the 17-tone scale developed in the 13th century by the music theorist Safi al-Din al-Urmawi. But that system was not an equally tempered system.

17-ET captures some elements of Arab music better than 12-ET, notably, the neutral seconds and neutral thirds, and the undecimal tritones, the main intervals involving the 11th harmonic. However, traditional Arab music also contains major and minor thirds, which are poorly captured in this tuning.

So I would say that 17-ET is just as inadequate for playing Arab music as 12-ET is; it merely happens to be inadequate in a completely non-overlapping way. If the goal in choosing an equal temperament in which to play Arab music is to get a simple tuning that highlights the elements of Arab music that are absent from Western music, 17-ET might be a good choice, but for accurately representing the musical tradition in its entirety, it is not.

Weaknesses or Disadvantages of 17-ET

Advantages of 17-ET

External resources