13edo scales: Difference between revisions

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==Nonatonic (4L 5s)==

Generated by 3\13, the 276.9-cent minor third approximating [[13/11]], this scale sounds a little like the octatonic scale in 12edo with an extra small step inserted. Two of these make an 11/8 and three make a 13/8, making this scale very good for 4:11:13 triads. (In terms of regular temperament theory, this makes 13edo a tuning for the [[Color notation|bithotrilu]] temperament that tempers out the bithotrilu comma 1352/1331 = {{monzo|3 0 0 0 -3 2}}, aka "lovecraft temperament".) [[17edo]] also supports bithotrilu temperament and thus has a similar 4L 5s scale, generated by the 4\17 minor third. ~~[[Orwell|~~Similar scales]] also exist in 22edo and 31edo with flatter generators, but they won't approximate the 13th harmonic.

Generated by 3\13, the 276.9-cent minor third approximating [[13/11]], this scale sounds a little like the octatonic scale in 12edo with an extra small step inserted. Two of these make an 11/8 and three make a 13/8, making this scale very good for 4:11:13 triads. (In terms of regular temperament theory, this makes 13edo a tuning for the [[Color notation|bithotrilu]] temperament that tempers out the bithotrilu comma 1352/1331 = {{monzo|3 0 0 0 -3 2}}, aka "lovecraft temperament".) [[17edo]] also supports bithotrilu temperament and thus has a similar 4L 5s scale, generated by the 4\17 minor third. Similar scales also exist in 22edo and 31edo with flatter generators, but they use a [[Orwell|different temperament]] and won't approximate the 13th harmonic.

The brightest mode is 0-2-3-5-6-8-9-11-12-13. The triad 4:11:13 occurs on degrees 1, 2, 3, 5, 7 and 9; these can be extended to either 4:10:11:13:17, 4:9:11:13:21, or 4:5:9:11:13 depending on what degree you're on. Since you get 21/16 as the minor version of 11/8, you also get two 8:13:17:21's with the same interval classes, on degrees 6 and 8. Degree 4 has a 4:5:11.

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 ==Nonatonic (4L 5s)==
-Generated by 3\13, the 276.9-cent minor third approximating [[13/11]], this scale sounds a little like the octatonic scale in 12edo with an extra small step inserted. Two of these make an 11/8 and three make a 13/8, making this scale very good for 4:11:13 triads. (In terms of regular temperament theory, this makes 13edo a tuning for the [[Color notation|bithotrilu]] temperament that tempers out the bithotrilu comma 1352/1331 = {{monzo|3 0 0 0 -3 2}}, aka "lovecraft temperament".) [[17edo]] also supports bithotrilu temperament and thus has a similar 4L 5s scale, generated by the 4\17 minor third. [[Orwell|Similar scales]] also exist in 22edo and 31edo with flatter generators, but they won't approximate the 13th harmonic.
+Generated by 3\13, the 276.9-cent minor third approximating [[13/11]], this scale sounds a little like the octatonic scale in 12edo with an extra small step inserted. Two of these make an 11/8 and three make a 13/8, making this scale very good for 4:11:13 triads. (In terms of regular temperament theory, this makes 13edo a tuning for the [[Color notation|bithotrilu]] temperament that tempers out the bithotrilu comma 1352/1331 = {{monzo|3 0 0 0 -3 2}}, aka "lovecraft temperament".) [[17edo]] also supports bithotrilu temperament and thus has a similar 4L 5s scale, generated by the 4\17 minor third. Similar scales also exist in 22edo and 31edo with flatter generators, but they use a [[Orwell|different temperament]] and won't approximate the 13th harmonic.
 The brightest mode is 0-2-3-5-6-8-9-11-12-13. The triad 4:11:13 occurs on degrees 1, 2, 3, 5, 7 and 9; these can be extended to either 4:10:11:13:17, 4:9:11:13:21, or 4:5:9:11:13 depending on what degree you're on. Since you get 21/16 as the minor version of 11/8, you also get two 8:13:17:21's with the same interval classes, on degrees 6 and 8. Degree 4 has a 4:5:11.