|
|
| (3 intermediate revisions by the same user not shown) |
| Line 1: |
Line 1: |
| '''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]] |
|
| |
|
| == 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 ==
| |
| <pre>
| |
| ! 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
| |
| </pre>
| |
|
| |
| 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]]
| |
| * [https://soundcloud.com/jdfreivald/three-days-apart Three Days Apart]
| |
|
| |
| [[Category:13-tone scales]]
| |
| [[Category:Just intonation scales]] | | [[Category:Just intonation scales]] |
| [[Category:Tritave]]
| |
| [[Category:MOS scales]]
| |
| [[Category:Ennealimmal]]
| |
| [[Category:Pages with Scala files]]
| |
| {{todo|intro}}
| |