Trithagorean: Difference between revisions

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-! trithagorean.scl
+'''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 ==
+<pre>
+! freivaldthree.scl
 !
+JI tritave repeating scale, similar to ennon13
+! Mode of the 13-note tritave MOS of ennealimmal
+!
+/25
+/625
+/15625
+/2187
+/81
+/3
+/5
+/125
+/3125
+/6561
+/243
+/9
+/1
+</pre>
-[[Jake_Freivald|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.
+As (3, 5) monzos:
+|3 -2&gt;
+|6 -4&gt;
+|9 -6&gt;
+|5 -7&gt;
+|3 -4&gt;
+|-1 1&gt;
+|2 -1&gt;
+|5 -3&gt;
+|8 -5&gt;
+|-6 8&gt;
+|-5 6&gt;
+|-2 2&gt;
+|1 0&gt;
+=== 12-tone version ===
+<pre>
+! 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.
 !
 /25
 /625
 /15625
 /2187
 /81
 /3
 /5
 /3125
 /6561
 /243
+/9
+/1
+</pre>
-/9
+== Music ==
+; [[Jake Freivald]]
+* [https://soundcloud.com/jdfreivald/three-days-apart ''Three Days Apart''] (2011)
-/1
+[[Category:13-tone scales]]
-[[Category:12-tone]]
+[[Category:Just intonation scales]]
-[[Category:ji]]
+[[Category:Tritave]]
-[[Category:just]]
+[[Category:MOS scales]]
-[[Category:scale]]
+[[Category:Ennealimmal]]
 [[Category:Pages with Scala files]]
 [[Category:trithagorean]]