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

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|wa 8ve
|wa 8ve
|}
|}
We then look at intervals of 5:
{| class="wikitable"
{| class="wikitable"
We then look at intervals of 5:
|+Classical (yo, gu)
|+Classical (yo, gu)
!Cents
!Cents
Line 203: Line 203:
|yo 8ve
|yo 8ve
|}
|}
And intervals of 7.
{| class="wikitable"
|+Septimal (zo, ru)
!Cents
!Ratio
!FJS Name
!Color name
|-
|27.264
|64/63
|P1<sub>7</sub>
|ru 1sn
|-
|62.961
|28/27
|m2<sup>7</sup>
|zo 2nd
|-
|231.174
|8/7
|M2<sub>7</sub>
|ru 2nd
|-
|266.871
|7/6
|m3<sup>7</sup>
|zo 3rd
|-
|435.084
|9/7
|M3<sub>7</sub>
|ru 3rd
|-
|470.781
|21/16
|P4<sup>7</sup>
|zo 4th
|-
|561.006
|112/81
|d5<sup>7</sup>
|zo 5th
|-
|638.994
|81/56
|A4<sub>7</sub>
|ru 4th
|-
|729.219
|32/21
|P5<sub>7</sub>
|yo 5th
|-
|764.916
|14/9
|m6<sup>7</sup>
|gu 6th
|-
|933.129
|12/7
|M6<sub>7</sub>
|yo 6th
|-
|968.826
|7/4
|m7<sup>7</sup>
|gu 7th
|-
|1137.039
|27/14
|M7<sub>7</sub>
|yo 7th
|-
|1172.736
|63/32
|P8<sup>7</sup>
|yo 8ve
|}
== Draft section ==
Content in this section includes ideas and constructions that are not yet complete. This section will remain until the page is completed.
Flavor 11: 352/243, 88/81, 44/27, 11/9, 11/6, 11/8, 33/32, (99/64, 297/256, 891/512, 2673/2048)
Flavor /11: 243/176, 81/44, 27/22, 18/11, 12/11, 16/11, 64/33, (128/99, ...)
Flavor 13:

Revision as of 04:30, 25 September 2025

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Author comments: Please complete interval tables for flavors of 7, 11, 13, 7/5, 11/5, 11/7, 13/5, 13/7, and 13/11, with all perfect, major, and minor intervals, as well as A4 and d5. Note that the flavors of 7/5 and 5/7 should be placed in the same table.

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

And intervals of 7.

Septimal (zo, ru)
Cents Ratio FJS Name Color name
27.264 64/63 P17 ru 1sn
62.961 28/27 m27 zo 2nd
231.174 8/7 M27 ru 2nd
266.871 7/6 m37 zo 3rd
435.084 9/7 M37 ru 3rd
470.781 21/16 P47 zo 4th
561.006 112/81 d57 zo 5th
638.994 81/56 A47 ru 4th
729.219 32/21 P57 yo 5th
764.916 14/9 m67 gu 6th
933.129 12/7 M67 yo 6th
968.826 7/4 m77 gu 7th
1137.039 27/14 M77 yo 7th
1172.736 63/32 P87 yo 8ve

Draft section

Content in this section includes ideas and constructions that are not yet complete. This section will remain until the page is completed.

Flavor 11: 352/243, 88/81, 44/27, 11/9, 11/6, 11/8, 33/32, (99/64, 297/256, 891/512, 2673/2048)

Flavor /11: 243/176, 81/44, 27/22, 18/11, 12/11, 16/11, 64/33, (128/99, ...)

Flavor 13:

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