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11L 3s: Difference between revisions

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Replaced scale tree, removed edo table since scale tree displays edos already; removed "lufsur" and "fuslur" as it was never made clear what they meant, pending further investigation
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{{todo|cleanup|inline=1|text=Replace scale tree and populate with entries, rework intro}}
{{Infobox MOS
{{Infobox MOS
| Other names = Ketradektriatoh
| Other names = Ketradektriatoh
Line 10: Line 9:
}}
}}
{{MOS intro|Other Names=the Ketradektriatoh scale}}
{{MOS intro|Other Names=the Ketradektriatoh scale}}
The '''11L 3s''' [[MOS scale]] was named the "Ketradektriatoh scale" by [[Osmiorisbendi‎]]
This scale was named the "Ketradektriatoh scale" by [[Osmiorisbendi‎]].
 
This is a type of scale which denotes the use of a scale placed between [[11edo]] and [[14edo]].
 
It employs a ratio generator between [[41/32]] and [[9/7]] ([[25edo]] being the middle size of the Ketradektriatoh spectrum, in the 2:1 relation).
 
This results in a variant of tetradecatonic scale which conforms by this scheme: LLLLsLLLLsLLLs.
== Scale tree ==
== Scale tree ==
The table below shows an extension of [[edo]]s which supports the Ketradektriatoh scale, with respect to the principal generator and their results for each L/s sizes:
{{Scale tree}}
{| class="wikitable"
|-
| 4\[[11edo|11]]
|
|
|
|
|
|
| 436.364
| 109.091
| 0
| style="text-align:center;" |
|-
|
|
|
|
|
|
| 29\[[80edo|80]]
| 435
| 105
| 15
|
|-
|
|
|
|
|
| 25\[[69edo|69]]
|
| 434.783
| 104.348
| 17.391
|
|-
|
|
|
|
| 21\[[58edo|58]]
|
|
| 434.483
| 103.448
| 20.69
|
|-
|
|
|
| 17\[[47edo|47]]
|
|
|
| 434.043
| 102.128
| 25.532
|
|-
|
|
|
|
| 30\[[83edo|83]]
|
|
| 433.735
| 101.208
| 28.916
|
|-
|
|
|
|
|
|
| 73\[[202edo|202]]
| 433.663
| 100.990
| 29.703
| Since here are the optimal range Lufsur mode (?)
|-
|
|
|
|
|
| 43\[[119edo|119]]
|
| 433.613
| 100.840
| 30.252
|
|-
|
|
|
|
|
|
|
| 433.459
| 100.377
| 31.95
|
|-
|
|
| 13\[[36edo|36]]
|
|
|
|
| 433.333
| 100
| 33.333
|
|-
|
|
|
|
|
|
|
| 433.048
| 99.144
| 36.473
|
|-
|
|
|
|
| 35\97
|
|
| 432.99
| 98.969
| 37.113
|
|-
|
|
|
|
|
|
|
| 432.933
| 98.799
| 37.738
|
|-
|
|
|
| 22\[[61edo|61]]
|
|
|
| 432.787
| 98.361
| 39.344
|
|-
|
| 9\[[25edo|25]]
|
|
|
|
|
| 432
| 96
| 48
| style="text-align:center;" | Boundary of propriety;
 
generators smaller than this are proper
|-
|
|
|
|
|
|
|
| 431.417
| 94.25
| 54.4155
|
|-
|
|
|
| 23\[[64edo|64]]
|
|
|
| 431.25
| 93.75
| 56.25
|
|-
|
|
|
|
|
|
|
| 431.1185
| 93.355
| 57.697
|
|-
|
|
|
|
| 37\103
|
|
| 431.068
| 93.204
| 58.25
|
|-
|
|
|
|
|
|
|
| 430.984
| 92.952
| 58.175
|
|-
|
|
| 14\[[39edo|39]]
|
|
|
|
| 430.769
| 92.308
| 61.538
|
|-
|
|
|
|
|
| 47\[[131edo|131]]
|
| 430.534
| 91.603
| 64.122
|
|-
|
|
|
|
|
|
| 80\[[223edo|223]]
| 430.493
| 91.480
| 64.575
| Until here are the optimal range Fuslur mode (?)
|-
|
|
|
|
| 33\[[92edo|92]]
|
|
| 430.435
| 91.304
| 65.217
|
|-
|
|
|
| 19\[[53edo|53]]
|
|
|
| 430.189
| 90.566
| 67.925
|
|-
|
|
|
|
| 24\[[67edo|67]]
|
|
| 429.851
| 89.552
| 71.642
|
|-
|
|
|
|
|
| 29\[[81edo|81]]
|
| 429.63
| 88.889
| 74.074
|
|-
|
|
|
|
|
|
| 34\[[95edo|95]]
| 429.474
| 88.421
| 75.7895
|
|-
| 5\[[14edo|14]]
|
|
|
|
|
|
| 428.571
| 85.714
| 85.714
| style="text-align:center;" |
|}
 
== As an EDO subset ==
{| class="wikitable sortable"
|EDO
|Subset
|Special properties
|-
|[[25edo|25]]
|2 2 2 1 2 2 2 2 1 2 2 2 2 1
|Middle range
|-
|[[36edo|36]]
|3 3 3 1 3 3 3 3 1 3 3 3 3 1
|Lusfur range
|-
|[[39edo|39]]
|3 3 3 2 3 3 3 3 2 3 3 3 3 2
|Fuslur range
|-
|[[47edo|47]]
|4 4 4 1 4 4 4 4 1 4 4 4 4 1
|
|-
|[[50edo|50]]
|4 4 4 2 4 4 4 4 2 4 4 4 4 2
|
|-
|[[53edo|53]]
|4 4 4 3 4 4 4 4 3 4 4 4 4 3
|
|-
|[[58edo|58]]
|5 5 5 1 5 5 5 5 1 5 5 5 5 1
|
|-
|[[61edo|61]]
|5 5 5 2 5 5 5 5 2 5 5 5 5 2
|Split-φ
|-
|[[64edo|64]]
|5 5 5 3 5 5 5 5 3 5 5 5 5 3
|φ
|-
|[[67edo|67]]
|5 5 5 4 5 5 5 5 4 5 5 5 5 4
|
|-
|[[69edo|69]]
|6 6 6 1 6 6 6 6 1 6 6 6 6 1
|
|-
|[[81edo|81]]
|6 6 6 5 6 6 6 6 5 6 6 6 6 5
|
|-
|[[80edo|80]]
|7 7 7 1 7 7 7 7 1 7 7 7 7 1
|
|-
|[[83-limit|83]]
|7 7 7 2 7 7 7 7 2 7 7 7 7 2
|
|-
|[[86edo|86]]
|7 7 7 3 7 7 7 7 3 7 7 7 7 3
|
|-
|[[89edo|89]]
|7 7 7 4 7 7 7 7 4 7 7 7 7 4
|
|-
|[[92edo|92]]
|7 7 7 5 7 7 7 7 5 7 7 7 7 5
|
|-
|[[95edo|95]]
|7 7 7 6 7 7 7 7 6 7 7 7 7 6
|
|-
|[[91edo|91]]
|8 8 8 1 8 8 8 8 1 8 8 8 8 1
|
|-
|[[97edo|97]]
|8 8 8 3 8 8 8 8 3 8 8 8 8 3
|Split-φ
|-
|[[103edo|103]]
|8 8 8 5 8 8 8 8 5 8 8 8 8 5
|φ
|-
|[[109edo|109]]
|8 8 8 7 8 8 8 8 7 8 8 8 8 7
|
|-
|[[102edo|102]]
|9 9 9 1 9 9 9 9 1 9 9 9 9 1
|
|-
|[[105edo|105]]
|9 9 9 2 9 9 9 9 2 9 9 9 9 2
|
|-
|[[111edo|111]]
|9 9 9 4 9 9 9 9 4 9 9 9 9 4
|
|-
|[[114edo|114]]
|9 9 9 5 9 9 9 9 5 9 9 9 9 5
|
|-
|[[120edo|120]]
|9 9 9 7 9 9 9 9 7 9 9 9 9 7
|
|-
|[[123edo|123]]
|9 9 9 8 9 9 9 9 8 9 9 9 9 8
|
|-
|[[113edo|113]]
|10 10 10 1 10 10 10 10 1 10 10 10 10 1
|
|-
|[[119edo|119]]
|10 10 10 3 10 10 10 10 3 10 10 10 10 3
|
|-
|[[131edo|131]]
|10 10 10 7 10 10 10 10 7 10 10 10 10 7
|
|-
|[[137edo|137]]
|10 10 10 9 10 10 10 10 9 10 10 10 10 9
|
|-
|[[124edo|124]]
|11 11 11 1 11 11 11 11 1 11 11 11 11 1
|
|-
|[[127edo|127]]
|11 11 11 2 11 11 11 11 2 11 11 11 11 2
|
|-
|[[130edo|130]]
|11 11 11 3 11 11 11 11 3 11 11 11 11 3
|
|-
|[[133edo|133]]
|11 11 11 4 11 11 11 11 4 11 11 11 11 4
|
|-
|[[136edo|136]]
|11 11 11 5 11 11 11 11 5 11 11 11 11 5
|
|-
|[[139edo|139]]
|11 11 11 6 11 11 11 11 6 11 11 11 11 6
|
|-
|[[142edo|142]]
|11 11 11 7 11 11 11 11 7 11 11 11 11 7
|
|-
|[[145edo|145]]
|11 11 11 8 11 11 11 11 8 11 11 11 11 8
|
|-
|[[148edo|148]]
|11 11 11 9 11 11 11 11 9 11 11 11 11 9
|
|-
|[[151edo|151]]
|11 11 11 10 11 11 11 11 10 11 11 11 11 10
|
|-
|[[135edo|135]]
|12 12 12 1 12 12 12 12 1 12 12 12 12 1
|
|-
|[[147edo|147]]
|12 12 12 5 12 12 12 12 5 12 12 12 12 5
|
|-
|[[153edo|153]]
|12 12 12 7 12 12 12 12 7 12 12 12 12 7
|
|-
|[[165edo|165]]
|12 12 12 11 12 12 12 12 11 12 12 12 12 11
|
|-
|[[146edo|146]]
|13 13 13 1 13 13 13 13 1 13 13 13 13 1
|
|-
|[[149edo|149]]
|13 13 13 2 13 13 13 13 2 13 13 13 13 2
|
|-
|[[152edo|152]]
|13 13 13 3 13 13 13 13 3 13 13 13 13 3
|
|-
|[[155edo|155]]
|13 13 13 4 13 13 13 13 4 13 13 13 13 4
|
|-
|[[158edo|158]]
|13 13 13 5 13 13 13 13 5 13 13 13 13 5
|Split-φ
|-
|[[161edo|161]]
|13 13 13 6 13 13 13 13 6 13 13 13 13 6
|
|-
|[[164edo|164]]
|13 13 13 7 13 13 13 13 7 13 13 13 13 7
|
|-
|[[167edo|167]]
|13 13 13 8 13 13 13 13 8 13 13 13 13 8
|φ
|-
|[[170edo|170]]
|13 13 13 9 13 13 13 13 9 13 13 13 13 9
|
|-
|[[173edo|173]]
|13 13 13 10 13 13 13 13 10 13 13 13 13 10
|
|-
|[[176edo|176]]
|13 13 13 11 13 13 13 13 11 13 13 13 13 11
|
|-
|[[179edo|179]]
|13 13 13 12 13 13 13 13 12 13 13 13 13 12
|
|-
|[[157edo|157]]
|14 14 14 1 14 14 14 14 1 14 14 14 14 1
|
|-
|[[163edo|163]]
|14 14 14 3 14 14 14 14 3 14 14 14 14 3
|
|-
|[[169edo|169]]
|14 14 14 5 14 14 14 14 5 14 14 14 14 5
|
|-
|[[181edo|181]]
|14 14 14 9 14 14 14 14 9 14 14 14 14 9
|
|-
|[[187edo|187]]
|14 14 14 11 14 14 14 14 11 14 14 14 14 11
|
|-
|[[193edo|193]]
|14 14 14 13 14 14 14 14 13 14 14 14 14 13
|
|-
|[[168edo|168]]
|15 15 15 1 15 15 15 15 1 15 15 15 15 1
|
|-
|[[171edo|171]]
|15 15 15 2 15 15 15 15 2 15 15 15 15 2
|
|-
|[[177edo|177]]
|15 15 15 4 15 15 15 15 4 15 15 15 15 4
|
|-
|[[186edo|186]]
|15 15 15 7 15 15 15 15 7 15 15 15 15 7
|
|-
|[[189edo|189]]
|15 15 15 8 15 15 15 15 8 15 15 15 15 8
|
|-
|[[198edo|198]]
|15 15 15 11 15 15 15 15 11 15 15 15 15 11
|
|-
|[[204edo|204]]
|15 15 15 13 15 15 15 15 13 15 15 15 15 13
|
|-
|[[207edo|207]]
|15 15 15 14 15 15 15 15 14 15 15 15 15 14
|
|-
|[[179edo|179]]
|16 16 16 1 16 16 16 16 1 16 16 16 16 1
|
|-
|[[185edo|185]]
|16 16 16 3 16 16 16 16 3 16 16 16 16 3
|
|-
|[[191edo|191]]
|16 16 16 5 16 16 16 16 5 16 16 16 16 5
|
|-
|[[197edo|197]]
|16 16 16 7 16 16 16 16 7 16 16 16 16 7
|
|-
|[[203edo|203]]
|16 16 16 9 16 16 16 16 9 16 16 16 16 9
|
|-
|[[209edo|209]]
|16 16 16 11 16 16 16 16 11 16 16 16 16 11
|
|-
|[[215edo|215]]
|16 16 16 13 16 16 16 16 13 16 16 16 16 13
|
|-
|[[221edo|221]]
|16 16 16 15 16 16 16 16 15 16 16 16 16 15
|
|-
|[[190edo|190]]
|17 17 17 1 17 17 17 17 1 17 17 17 17 1
|
|-
|[[193edo|193]]
|17 17 17 2 17 17 17 17 2 17 17 17 17 2
|
|-
|[[196edo|196]]
|17 17 17 3 17 17 17 17 3 17 17 17 17 3
|
|-
|[[199edo|199]]
|17 17 17 4 17 17 17 17 4 17 17 17 17 4
|
|-
|[[202edo|202]]
|17 17 17 5 17 17 17 17 5 17 17 17 17 5
|Top limit for Lusfur range
|-
|[[205edo|205]]
|17 17 17 6 17 17 17 17 6 17 17 17 17 6
|
|-
|[[208edo|208]]
|17 17 17 7 17 17 17 17 7 17 17 17 17 7
|
|-
|[[211edo|211]]
|17 17 17 8 17 17 17 17 8 17 17 17 17 8
|
|-
|[[214edo|214]]
|17 17 17 9 17 17 17 17 9 17 17 17 17 9
|
|-
|[[217edo|217]]
|17 17 17 10 17 17 17 17 10 17 17 17 17 10
|
|-
|[[220edo|220]]
|17 17 17 11 17 17 17 17 11 17 17 17 17 11
|
|-
|[[223edo|223]]
|17 17 17 12 17 17 17 17 12 17 17 17 17 12
|Top limit for Fuslur range
|-
|[[226edo|226]]
|17 17 17 13 17 17 17 17 13 17 17 17 17 13
|
|-
|[[229edo|229]]
|17 17 17 14 17 17 17 17 14 17 17 17 17 14
|
|-
|[[232edo|232]]
|17 17 17 15 17 17 17 17 15 17 17 17 17 15
|
|-
|[[235edo|235]]
|17 17 17 16 17 17 17 17 16 17 17 17 17 16
|
|}
[[Category:14-tone scales]]
[[Category:14-tone scales]]
Retrieved from "https://en.xen.wiki/w/11L_3s"