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| '''Trithagorean''' or '''freivaldthree''' is a [[just intonation]], [[tritave]]-repeating [[nonoctave]] scale invented by [[Jake Freivald]] in 2011. It has 13 unequal tones per tritave.
| | #redirect [[Trithagorean]] |
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| == Freivald's description ==
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| "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.
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| In [[cents]], that's this:
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| 0.000 unison, perfect prime
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| 133.238 large limma, BP small semitone
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| 266.475 two (large limma, BP small semitone)
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| 399.713
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| 617.884
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| 751.121
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| 884.359 major sixth, BP sixth
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| 1017.596 just minor seventh, BP seventh
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| 1150.834 octave - maximal diesis
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| 1284.071
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| 1502.242
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| 1635.480
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| 1768.717 classic augmented eleventh, BP twelfth
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| 1901.955 perfect 12th"
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| == Scala file ==
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| <pre>
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| ! freivaldthree.scl
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| !
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| JI tritave repeating scale, similar to ennon13
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| ! Mode of the 13-note tritave MOS of ennealimmal
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| 13
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| !
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| 27/25
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| 729/625
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| 19683/15625
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| 3125/2187
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| 125/81
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| 5/3
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| 9/5
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| 243/125
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| 6561/3125
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| 15625/6561
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| 625/243
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| 25/9
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| 3/1
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| </pre>
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| As (3, 5) monzos:
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| |3 -2>
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| |6 -4>
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| |9 -6>
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| |5 -7>
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| |3 -4>
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| |-1 1>
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| |2 -1>
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| |5 -3>
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| |8 -5>
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| |-6 8>
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| |-5 6>
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| |-2 2>
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| |1 0>
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| == Music ==
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| ; [[Jake Freivald]]
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| * [https://soundcloud.com/jdfreivald/three-days-apart Three Days Apart]
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| [[Category:13-tone scales]]
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| [[Category:Just intonation scales]] | | [[Category:Just intonation scales]] |
| [[Category:Tritave]]
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| [[Category:MOS scales]]
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| [[Category:Ennealimmal]]
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| [[Category:Pages with Scala files]]
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| {{todo|intro}}
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