Freivaldthree

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>

Music

Jake Freivald

• Three Days Apart