Trithagorean

Trithagorean or freivaldthree is a just intonation, tritave-repeating nonoctave scale invented by Jake Freivald in 2011. It has 13 unequal tones per tritave.

Freivald's description

"

This was an experiment with something I jokingly call "trithagorean" -- a 3/1-repeating scale based on repeated stackings of perfect 5/3s and 9/5s. That can give you an MOS at 13 or 15 notes, but I only used about 10 of them. There are no octaves anywhere in this scale.

In cents, that's this:

• 0.000 unison, perfect prime
• 133.238 large limma, BP small semitone
• 266.475 two (large limma, BP small semitone)
• 399.713
• 617.884
• 751.121
• 884.359 major sixth, BP sixth
• 1017.596 just minor seventh, BP seventh
• 1150.834 octave - maximal diesis
• 1284.071
• 1502.242
• 1635.480
• 1768.717 classic augmented eleventh, BP twelfth
• 1901.955 perfect 12th

"

Scala file

! freivaldthree.scl
!
JI tritave repeating scale, similar to ennon13
! Mode of the 13-note tritave MOS of ennealimmal
13
!
27/25
729/625
19683/15625
3125/2187
125/81
5/3
9/5
243/125
6561/3125
15625/6561
625/243
25/9
3/1

As (3, 5) monzos: |3 -2> |6 -4> |9 -6> |5 -7> |3 -4> |-1 1> |2 -1> |5 -3> |8 -5> |-6 8> |-5 6> |-2 2> |1 0>

12-tone version

! trithagorean.scl
!
Jake Freivald's Trithagorean scale: Can be viewed as ennealimmal with period 3 and generator 5/3; -6 to 6 missing -3 (i.e., 243/125) to fit into 12 tones.
12
!
27/25
729/625
19683/15625
3125/2187
125/81
5/3
9/5
6561/3125
15625/6561
625/243
25/9
3/1

Music

Jake Freivald

• Three Days Apart (2011)