User:Overthink/13-limit interval flavors
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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.
| 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
| 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 |