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:
- The perfect fourth and fifth in 19-ET are less close a match to the just intervals than they are in 31-ET. In 19-ET, these intervals are off by 7.22 cents, whereas in 31-ET they are off by 5.19 cents. Although the difference between the two matches is slight, it falls in a particular sensitive range, such that 31-ET tends to be outside the perceptual limits of an untrained ear, whereas in 19-ET, the intervals tend to fall within this limit. What this means is that fourths and fifths will sound slightly out-of-tune to a substantially broader audience in 19-ET than in 31-ET.
- The matches to the septimal tritones in 31-ET are nearly exact, whereas, although 19-ET distinguishes between the greater and lesser septimal tritones, the matches to both intervals are poor, off by 14.09 cents. Although this difference makes the two intervals easier to distinguish by ear in 19-ET, it makes their harmonic function and relationship to consonances involving the 7th harmonic much harder to hear or use.
- 19-ET does not distinguish between the septimal minor third and septimal whole tones, instead dividing the perfect fourth in half. The match to the septimal minor third is out-of-tune, and the match to the septimal whole tone is so out-of-tune as to be almost unusable in this function. 31-ET, by contrast, matches both intervals very closely. Since these intervals are unfamiliar to most people's ears, having them be out-of-tune to the harmonic series becomes even more problematic.
- 19-ET has a narrow whole tone, matching the minor tone (10:9) more closely than the major tone (9:8). 31-ET is closer to being equal, but matches the major tone more closely. Having a narrow whole tone is disadvantageous for two reasons: first, the more narrow the whole tone is, the less familiar it will be to people used to 12-ET (which has a wide whole tone, matching the major tone very closely). Second, since the major tone is a stronger and more fundamental harmonic interval, it is more useful to have a good match to this tone than to the minor tone.
- 19-ET does not match any intervals including the 11th harmonic. 31-ET closely matches and distinguishes between nearly all of them. The result is that harmonies involving the 11th harmonic are available in 31-ET, whereas they are not available in 19-ET.
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.