User:Overthink/13-limit interval flavors: Difference between revisions

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== The flavors of intervals ==
== The flavors of intervals ==
We first look at the pythagorean intervals:
{| class="wikitable"
{| class="wikitable"
|+Pythagorean (wa)
|+Pythagorean (wa)
Line 122: Line 123:
|P8
|P8
|wa 8ve
|wa 8ve
|}
{| class="wikitable"
We then look at intervals of 5:
|+Classical (yo, gu)
!Cents
!Ratio
!FJS Name
!Color name
|-
|21.506
|81/80
|P1<sub>5</sub>
|gu 1sn
|-
|111.731
|16/15
|m2<sub>5</sub>
|gu 2nd
|-
|182.404
|10/9
|M2<sup>5</sup>
|yo 2nd
|-
|315.641
|6/5
|m3<sub>5</sub>
|gu 3rd
|-
|386.314
|5/4
|M3<sup>5</sup>
|yo 3rd
|-
|519.551
|27/20
|P4<sub>5</sub>
|gu 4th
|-
|590.224
|45/32
|A4<sup>5</sup>
|yo 4th
|-
|609.776
|64/45
|d5<sub>5</sub>
|gu 5th
|-
|680.449
|40/27
|P5<sup>5</sup>
|yo 5th
|-
|813.686
|8/5
|m6<sub>5</sub>
|gu 6th
|-
|884.359
|5/3
|M6<sup>5</sup>
|yo 6th
|-
|1017.596
|9/5
|m7<sub>5</sub>
|gu 7th
|-
|1088.269
|15/8
|M7<sup>5</sup>
|yo 7th
|-
|1178.494
|160/81
|P8<sup>5</sup>
|yo 8ve
|}
|}

Revision as of 23:49, 24 September 2025

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

We first look at the pythagorean 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
We then look at intervals of 5:
Classical (yo, gu)
Cents Ratio FJS Name Color name
21.506 81/80 P15 gu 1sn
111.731 16/15 m25 gu 2nd
182.404 10/9 M25 yo 2nd
315.641 6/5 m35 gu 3rd
386.314 5/4 M35 yo 3rd
519.551 27/20 P45 gu 4th
590.224 45/32 A45 yo 4th
609.776 64/45 d55 gu 5th
680.449 40/27 P55 yo 5th
813.686 8/5 m65 gu 6th
884.359 5/3 M65 yo 6th
1017.596 9/5 m75 gu 7th
1088.269 15/8 M75 yo 7th
1178.494 160/81 P85 yo 8ve
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