12edt

Division of the tritave (3/1) into 12 equal parts

12edt divides 3, the tritave, into 12 equal parts of 158.496 cents each, corresponding to 7.571 edo, and can be used as a generator chain for hemikleismic temperament. From a no-twos point of view, it tempers out 49/45 and 27/25 in the 7-limit, and 1331/1125 and 1331/1225 in the 11-limit.

Scala file

! C:\Cakewalk\scales\tritave-in-12.scl
!
3/1 in 12
12
!
158.49625
316.99250
475.48875
633.98500
792.48125
950.97750
1109.47375
1267.97000
1426.46625
1584.96250
1743.45875
3/1

Exactly analogous to meantone

In octave land, 12edo handles the 2.3.5 subgroup and 11edo handles the 2.7.11 subgroup - ie. meantone and orgone temperaments. In tritave land however, 13edt handles the 3.5.7 territory (Bohlen-Pierce) and 12edt handles the 2.3.5.13.17.19 -- AND! it is a multiple of 4edt which is the simplest BP equal temperament. Now, exactly analogous to meantone, in which (3/2)^4=5/1, here (17/9)^4=(19/10)^4=13/1, tempering out the 171/170, 85293/83521 and 130321/130000 commas. In fact, even the MOS pattern is the same for this higher limit meantone! Relish the sweet 9:13:17 and 20:27:38 chords.

Another example of a macrodiatonic scale is hyperpyth which is found in the fifth harmonic and is based on the 5:9:13:(17):(21) chord.

Compositions

Instant Gamelan by Carlo Serafini

Tritave in 12 by Chris Vaisvil