Freivaldthree: Difference between revisions
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== Freivald's description == | == 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. | " | ||
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: | In [[cents]], that's this: | ||
0.000 unison, perfect prime | * 0.000 unison, perfect prime | ||
133.238 large limma, BP small semitone | * 133.238 large limma, BP small semitone | ||
266.475 two (large limma, BP small semitone) | * 266.475 two (large limma, BP small semitone) | ||
399.713 | * 399.713 | ||
617.884 | * 617.884 | ||
751.121 | * 751.121 | ||
884.359 major sixth, BP sixth | * 884.359 major sixth, BP sixth | ||
1017.596 just minor seventh, BP seventh | * 1017.596 just minor seventh, BP seventh | ||
1150.834 octave - maximal diesis | * 1150.834 octave - maximal diesis | ||
1284.071 | * 1284.071 | ||
1502.242 | * 1502.242 | ||
1635.480 | * 1635.480 | ||
1768.717 classic augmented eleventh, BP twelfth | * 1768.717 classic augmented eleventh, BP twelfth | ||
1901.955 perfect 12th" | * 1901.955 perfect 12th | ||
" | |||
== Scala file == | == Scala file == | ||
Revision as of 01:42, 27 September 2025
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>