31 Tone Equal Temperament

19 Tone Equal Temperament

19 Tone Equal Temperament(19-ET) is the tuning that is most similar to 31-ET. Both are meantone tunings. Because 19-ET has so many fewer divisions of the octave, and because its smaller interval width is bigger, relative to 31-ET, it is easier to work with. 31-ET thus must offer considerable advantages over 19-ET in order to justify its use.

Some of the weaknesses of 19-ET, when compared to 31-ET are as follows:

Summary of 19-ET relative to 31-ET

19-ET is much easier to use and learn than 31-ET. 19-ET opens up many but not all of the harmonic possibilities involving the 7th harmonic, but does not touch the 11th harmonic, whereas 31-ET opens up the full range of harmonies involving the 7th harmonic, and many involving the 11th harmonic. 19-ET, however, sounds out-of-tune, especially with intervals involving the 7th harmonic, but even fifths are detectably more out-of-tune than in 31-ET. The only intervals better matched in 19-ET are the minor third (which is nearly perfect in 19-ET) and septimal major third...however, both of these intervals are within less than 10 cents of their just intervals in 31-ET, so this advantage of 19-ET over 31-ET is slight.

31-ET can do everything that 19-ET can do, but it can do a lot more things, and generally does most things better. The price to be paid is in the increased complexity and smaller interval size of 31-ET, and a slight sacrifice in the intonation of minor thirds and septimal major thirds. On a personal note, having composed some music in 19-ET, I found the poor intonation of intervals and lack of distinction between septimal minor thirds and septimal whole tones to be the main deal-breaker with this tuning, which ultimately drove me to explore 31-ET.