Endless Lack of Music

Fine work. You’ve overcome of the biggest drawbacks of a 12-note tuning like this — namely, you’ve avoided having it sound like out-of-tune conventional Western tuning.

You might consider some additive JI tunings: 25 notes of the 5/4 in the 2/1, also 17 note Pythagorean and 29 note Pythagorean.

To get 25 5/4s in the octave using Scala, do (from memory here):

Pyth
25
2/1

5/4

Essentially, you use the PYTHAGOREAN command to generate a scale with 25 notes and an octave of 2/1 but a fifth of 5/4.

Likewise, to produce 17 note Pythagorean you do

Pyth
17
2/1

Ditto 29 note Pythagorean:

Pyth
29
2/1

(I think, I’m doing this from memory. Check to details of the SCALA PYTHAGOREAN command to make sure.)

Each of these additive tunings is a 2-interval scale. That is, it has only 2 types of intervals — akin o the conventional Western tuning, which has only two types of intervals, the whole tone and the semitone. Divisive tunings typically have 3 intervals. For instance, the typical divisive 12 note 5-limit JI tuning has three intervals: the 9/8 whole tone and two different flavors of semitone, the 16/15 semitone and the 25/24 semitone. This makes it more awkward to deal with than a 2-interval tuning.

There are only 7 different 2-interval Pythagorean tunings, as you know: 5-note Py, 7 note, 17-note, 29-note, 41-note and 53-note. This latter is audibly indistinguishable from 53 equal.

One of the big disadvantages of the usual unimaginative JI tunings touted by clueless forums like the Alternative Wanking List on yahoo remains the fact that they always use the same basic basic intervals. So you get a 3/2 and a 5/4 and a 9/8 and their inversions and only the fine details of the intervals in between those intervals differ. So when you play music in these typical unimaginative JI tunings, it sounds pretty much like 12 equal: same perfect fifth, very similar major third, very similar minor third, audibly indistinguishable minor second and major second, and so on. Going to all the trouble of doing microtonality with a retunable softsynth just do you can wind up sounding the same intervals and triads as in conventional music seems pointless.

The key, of course, involves breaking out of the narrow mindset that identifies the 3/2 or 5/4 or 6/5 as the only possible perfect fifth or major third or minor third. In their crucial 1926 article “Variability of Judgments on Musical Interval,” J. Exp. Psych., Vol. 9, 1926m Moran and Pratt found that the range of musically recognizable perfect fifths ran all the way from 680 cents to 720 cents. The range of musically recognizable and functional major thirds and minor thirds were similarly wide.

Since this accords well with ethnomusicological findings about the prevalence of 7 equal and 5 equal tunings worldwide (7 equal has a p 5th of 685 cents, 5 equal has a p 5th of 720 cents) and since Moran & Pratt’s 1926 research has been confirmed by subsequent researchers (most notable “Perception of Musical Interval Tuning” by Donald E. Hall and Joan Taylor Hess, Music Perception, Vol. 2, No. 2, 1984, pp. 166-195), it makes good sense to abandon the ideological fixation on JI perfect fifths as 3/2 and JI major thirds as 5/4 and JI minor thirds as 6/5, etc.

The psychoacoustic range of musically functional perfect fifths runs from 680 cents to 720 cents, so by using a JI perfect fifth of, say, 710 cents or 690 cents or what-have-you, you’ll generate a quite different-sounding JI tuning with lots of freshness. It won’t sound like the same-old same-old.

Another strategy for avoiding the tired old sounds-like-conventional-Western-music-but-more-bland feature of unimaginative 5-limit JI is to throw away the conventional octave. 19 3/2 in the 5/1 or 22 11/8s in the 3/1 offer entirely new types of JI additive tunings. Divisive tunings can easily be generated as well by choosing a larger interval likethe 3/1 and successively subdividing it, rather than by starting with the 2/1 and chopping it up into the 3/2 and then the 5/4 and so on.

Tell you what, that is a hell of a piece. Sounds kinda spooky and calm at the same time. Tater likes when them chords ring out like good barbershop.