User:Overthink/13-limit interval flavors: Difference between revisions
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{{Editable user page|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. | 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. | ||
{| class="wikitable" | {| class="wikitable" | ||
| Line 124: | Line 125: | ||
|wa 8ve | |wa 8ve | ||
|} | |} | ||
We then look at intervals of 5: | |||
{| class="wikitable" | {| class="wikitable" | ||
|+Classical (yo, gu) | |+Classical (yo, gu) | ||
!Cents | !Cents | ||
| Line 202: | 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. | |||
'''Drafts below this line''' | |||
From what I see here it seems like I should add A1 and possibly also A5 to the tables. | |||
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: (104/81,) 52/27*, 13/9, 13/12, 13/8, 39/32, 117/64, 351/256, 1053/1024, (3159/2048) | |||
Flavor /13: (81/52,) 27/26*, 18/13, 24/13, 16/13, 64/39, 128/117, 512/351, 2048/1053, (4096/3159) | |||
Flavor 7/5: (<- Marvelous 45/28,) 15/14*, 7/5, 21/20, 63/40, 189/160, 567/320, 1701/1280, 5103/2560, ... | |||
Flavor 5/7: (<- Marvelous 56/45,) 28/15*, 10/7, 40/21, 80/63, 320/189, 640/567, 2560/1701, 5120/5103, ... | |||
Flavor 11/5: (176/135,) 88/45, 22/15, 11/10, 33/20, 99/80, 297/160, 891/640, (2673/2560, ...) | |||
Flavor 13/5: 208/135, 52/45, 26/15, 13/10, 39/20, 117/80 | |||
Flavor 11/7: | |||