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

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Created page with "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. {| class="wikitable" |+13-limit flavors !D\N !1/3/9 !5 !7 !11 !13 |- |1/3/9 |1/1 | | | | |- |5 | |1/1 |7/5 |11/10 |13/10 |- |7 | | |1/1 | | |- |11 | | | |1/1 | |- |13 | | | | |1/1 |}"
 
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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.
{{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.
{| class="wikitable"
{| class="wikitable"
|+13-limit flavors
|+13-limit flavors
Line 9: Line 10:
!13
!13
|-
|-
|1/3/9
!1/3/9
|[[1/1]]
|[[1/1]] (wa)
|
|[[5/4]] (yo)
|
|[[7/4]] (zo)
|
|[[11/8]] (ilo)
|
|[[13/8]] (tho)
|-
|-
|5
!5
|
|[[8/5]] (gu)
|1/1
|1/1
|[[7/5]]
|[[7/5]] (zogu)
|[[11/10]]
|[[11/10]] (logu)
|13/10
|[[13/10]] (thogu)
|-
|-
|7
!7
|
|[[8/7]] (ru)
|
|[[10/7]] (yoru)
|1/1
|1/1
|
|[[11/7]] (loru)
|
|[[13/7]] (thoru)
|-
|-
|11
!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
|1/1
|
|}
 
== The flavors of intervals ==
We first look at the pythagorean intervals:
{| class="wikitable"
|+Pythagorean (wa)
!Cents
!Ratio
!FJS Name
!Color name
|-
|-
|13
|0.000
|
|
|
|
|1/1
|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:
{| class="wikitable"
|+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
|}
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:
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