User:Overthink/13-limit interval flavors

From Xenharmonic Wiki
Revision as of 23:35, 24 September 2025 by Overthink (talk | contribs)
Jump to navigation Jump to search

In this article, we will cover the various flavors of 13-limit intervals. We consider intervals that differ by a pythagorean interval to have the same flavor. The flavor of an interval depends on the primes higher than 3 in its prime factorization.

13-limit flavors
D\N 1/3/9 5 7 11 13
1/3/9 1/1 (wa) 5/4 (yo) 7/4 (zo) 11/8 (ilo) 13/8 (tho)
5 8/5 (gu) 1/1 7/5 (zogu) 11/10 (logu) 13/10 (thogu)
7 8/7 (ru) 10/7 (yoru) 1/1 11/7 (loru) 13/7 (thoru)
11 16/11 (lu) 20/11 (yolu) 14/11 (zolu) 1/1 13/11 (tholu)
13 16/13 (thu) 20/13 (yothu) 14/13 (zothu) 22/13 (lothu) 1/1

The flavors of intervals

Pythagorean (wa)
Cents Ratio FJS Name Color name
0.000 1/1 P1 wa 1sn
90.225 256/243 m2 sawa 2nd
203.910 9/8 M2 wa 2nd
294.135 32/27 m3 wa 3rd
407.820 81/64 M3 lawa 3rd
498.045 4/3 P4 wa 4th
588.270 1024/729 d5 sawa 5th
611.730 729/512 A4 lawa 4th
701.955 3/2 P5 wa 5th
792.180 128/81 m6 sawa 6th
905.865 27/16 M6 wa 6th
996.090 16/9 m7 wa 7th
1109.775 243/128 M7 lawa 7th
1200.000 2/1 P8 wa 8ve