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=<span style="color: #800061; font-size: 103%;">The Ketradektriatoh Scale</span>=
{{Infobox MOS
| Other names = Ketradektriatoh
| Periods = 1
| nLargeSteps = 11
| nSmallSteps = 3
| Equalized = 5
| Paucitonic = 4
| Pattern = LLLLsLLLLsLLLs
}}
The '''11L 3s''' [[MOS scale]] was named the "Ketradektriatoh scale" by [[Osmiorisbendi‎]].


This is a type of scale which denotes the use of a scale placed between [[11edo|11]] and [[14edo|14]] ED2's, employing a ratio generator between 41/32 ~ 9/7 (being [[25edo|25-ED2]] the middle size of the Ketradektriatoh spectrum, in the 2;1 relation), resulting in a variant of tetradecatonic scale comforms by this scheme: LLLsLLLLsLLLLs.
This is a type of scale which denotes the use of a scale placed between [[11edo]] and [[14edo]], employing a ratio generator between 41/32 ~ 9/7 ([[25edo]] being the middle size of the Ketradektriatoh spectrum, in the 2:1 relation), resulting in a variant of tetradecatonic scale which conforms by this scheme: LLLLsLLLLsLLLs.
 
<u>'''ED2s that contains this scale:'''</u>


== Edos that contains this scale ==
'''2 2 2 1 2 2 2 2 1 2 2 2 2 1: [[25edo|25]] (Middle range)'''
'''2 2 2 1 2 2 2 2 1 2 2 2 2 1: [[25edo|25]] (Middle range)'''


Line 197: Line 205:
17 17 17 16 17 17 17 17 16 17 17 17 17 16: [[235edo|235]]
17 17 17 16 17 17 17 17 16 17 17 17 17 16: [[235edo|235]]


The next table below shows an extension of ED2s which supports the Ketradektriatoh scale, with respect to the principal generator and their results for each L/s sizes:
== Scale tree ==
 
The next 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:
{| class="wikitable"
{| class="wikitable"
|-
|-
| | 4\[[11edo|11]]
| 4\[[11edo|11]]
| |  
|  
| |  
|  
| |  
|  
| |  
|  
| |  
|  
| |  
|  
| | 436.364
| 436.364
| | 109.091
| 109.091
| | 0
| 0
| style="text-align:center;" |  
| style="text-align:center;" |  
|-
|-
| |  
|  
| |  
|  
| |  
|  
| |  
|  
| |  
|  
| |  
|  
| | 29\[[80edo|80]]
| 29\[[80edo|80]]
| | 435
| 435
| | 105
| 105
| | 15
| 15
| |  
|  
|-
|-
| |  
|  
| |  
|  
| |  
|  
| |  
|  
| |  
|  
| | 25\[[69edo|69]]
| 25\[[69edo|69]]
| |  
|  
| | 434.783
| 434.783
| | 104.348
| 104.348
| | 17.391
| 17.391
| |  
|  
|-
|-
| |  
|  
| |  
|  
| |  
|  
| |  
|  
| | 21\[[58edo|58]]
| 21\[[58edo|58]]
| |  
|  
| |  
|  
| | 434.483
| 434.483
| | 103.448
| 103.448
| | 20.69
| 20.69
| |  
|  
|-
|-
| |  
|  
| |  
|  
| |  
|  
| | 17\[[47edo|47]]
| 17\[[47edo|47]]
| |  
|  
| |  
|  
| |  
|  
| | 434.043
| 434.043
| | 102.128
| 102.128
| | 25.532
| 25.532
| |  
|  
|-
|-
| |  
|  
| |  
|  
| |  
|  
| |  
|  
| | 30\[[83edo|83]]
| 30\[[83edo|83]]
| |  
|  
| |  
|  
| | 433.735
| 433.735
| | 101.208
| 101.208
| | 28.916
| 28.916
| |  
|  
|-
|-
| |  
|  
| |  
|  
| |  
|  
| |  
|  
| |  
|  
| |  
|  
| | 73\[[202edo|202]]
| 73\[[202edo|202]]
| | 433.663
| 433.663
| | 100.990
| 100.990
| | 29.703
| 29.703
| | Since here are the optimal range Lufsur mode (?)
| Since here are the optimal range Lufsur mode (?)
|-
|-
| |  
|  
| |  
|  
| |  
|  
| |  
|  
| |  
|  
| | 43\[[119edo|119]]
| 43\[[119edo|119]]
| |  
|  
| | 433.613
| 433.613
| | 100.840
| 100.840
| | 30.252
| 30.252
| |  
|  
|-
|-
| |  
|  
| |  
|  
| |  
|  
| |  
|  
| |  
|  
| |  
|  
| |  
|  
| | 433.459
| 433.459
| | 100.377
| 100.377
| | 31.95
| 31.95
| |  
|  
|-
|-
| |  
|  
| |  
|  
| | 13\[[36edo|36]]
| 13\[[36edo|36]]
| |  
|  
| |  
|  
| |  
|  
| |  
|  
| | 433.333
| 433.333
| | 100
| 100
| | 33.333
| 33.333
| |  
|  
|-
|-
| |  
|  
| |  
|  
| |  
|  
| |  
|  
| |  
|  
| |  
|  
| |  
|  
| | 433.048
| 433.048
| | 99.144
| 99.144
| | 36.473
| 36.473
| |  
|  
|-
|-
| |  
|  
| |  
|  
| |  
|  
| |  
|  
| | 35\97
| 35\97
| |  
|  
| |  
|  
| | 432.99
| 432.99
| | 98.969
| 98.969
| | 37.113
| 37.113
| |  
|  
|-
|-
| |  
|  
| |  
|  
| |  
|  
| |  
|  
| |  
|  
| |  
|  
| |  
|  
| | 432.933
| 432.933
| | 98.799
| 98.799
| | 37.738
| 37.738
| |  
|  
|-
|-
| |  
|  
| |  
|  
| |  
|  
| | 22\[[61edo|61]]
| 22\[[61edo|61]]
| |  
|  
| |  
|  
| |  
|  
| | 432.787
| 432.787
| | 98.361
| 98.361
| | 39.344
| 39.344
| |  
|  
|-
|-
| |  
|  
| | 9\[[25edo|25]]
| 9\[[25edo|25]]
| |  
|  
| |  
|  
| |  
|  
| |  
|  
| |  
|  
| | 432
| 432
| | 96
| 96
| | 48
| 48
| style="text-align:center;" | Boundary of propriety;
| style="text-align:center;" | Boundary of propriety;


generators smaller than this are proper
generators smaller than this are proper
|-
|-
| |  
|  
| |  
|  
| |  
|  
| |  
|  
| |  
|  
| |  
|  
| |  
|  
| | 431.417
| 431.417
| | 94.25
| 94.25
| | 54.4155
| 54.4155
| |  
|  
|-
|-
| |  
|  
| |  
|  
| |  
|  
| | 23\[[64edo|64]]
| 23\[[64edo|64]]
| |  
|  
| |  
|  
| |  
|  
| | 431.25
| 431.25
| | 93.75
| 93.75
| | 56.25
| 56.25
| |  
|  
|-
|-
| |  
|  
| |  
|  
| |  
|  
| |  
|  
| |  
|  
| |  
|  
| |  
|  
| | 431.1185
| 431.1185
| | 93.355
| 93.355
| | 57.697
| 57.697
| |  
|  
|-
|-
| |  
|  
| |  
|  
| |  
|  
| |  
|  
| | 37\103
| 37\103
| |  
|  
| |  
|  
| | 431.068
| 431.068
| | 93.204
| 93.204
| | 58.25
| 58.25
| |  
|  
|-
|-
| |  
|  
| |  
|  
| |  
|  
| |  
|  
| |  
|  
| |  
|  
| |  
|  
| | 430.984
| 430.984
| | 92.952
| 92.952
| | 58.175
| 58.175
| |  
|  
|-
|-
| |  
|  
| |  
|  
| | 14\[[39edo|39]]
| 14\[[39edo|39]]
| |  
|  
| |  
|  
| |  
|  
| |  
|  
| | 430.769
| 430.769
| | 92.308
| 92.308
| | 61.538
| 61.538
| |  
|  
|-
|-
| |  
|  
| |  
|  
| |  
|  
| |  
|  
| |  
|  
| | 47\[[131edo|131]]
| 47\[[131edo|131]]
| |  
|  
| | 430.534
| 430.534
| | 91.603
| 91.603
| | 64.122
| 64.122
| |  
|  
|-
|-
| |  
|  
| |  
|  
| |  
|  
| |  
|  
| |  
|  
| |  
|  
| | 80\[[223edo|223]]
| 80\[[223edo|223]]
| | 430.493
| 430.493
| | 91.480
| 91.480
| | 64.575
| 64.575
| | Until here are the optimal range Fuslur mode (?)
| Until here are the optimal range Fuslur mode (?)
|-
|-
| |  
|  
| |  
|  
| |  
|  
| |  
|  
| | 33\[[92edo|92]]
| 33\[[92edo|92]]
| |  
|  
| |  
|  
| | 430.435
| 430.435
| | 91.304
| 91.304
| | 65.217
| 65.217
| |  
|  
|-
|-
| |  
|  
| |  
|  
| |  
|  
| | 19\[[53edo|53]]
| 19\[[53edo|53]]
| |  
|  
| |  
|  
| |  
|  
| | 430.189
| 430.189
| | 90.566
| 90.566
| | 67.925
| 67.925
| |  
|  
|-
|-
| |  
|  
| |  
|  
| |  
|  
| |  
|  
| | 24\[[67edo|67]]
| 24\[[67edo|67]]
| |  
|  
| |  
|  
| | 429.851
| 429.851
| | 89.552
| 89.552
| | 71.642
| 71.642
| |  
|  
|-
|-
| |  
|  
| |  
|  
| |  
|  
| |  
|  
| |  
|  
| | 29\[[81edo|81]]
| 29\[[81edo|81]]
| |  
|  
| | 429.63
| 429.63
| | 88.889
| 88.889
| | 74.074
| 74.074
| |  
|  
|-
|-
| |  
|  
| |  
|  
| |  
|  
| |  
|  
| |  
|  
| |  
|  
| | 34\[[95edo|95]]
| 34\[[95edo|95]]
| | 429.474
| 429.474
| | 88.421
| 88.421
| | 75.7895
| 75.7895
| |  
|  
|-
|-
| | 5\[[14edo|14]]
| 5\[[14edo|14]]
| |  
|  
| |  
|  
| |  
|  
| |  
|  
| |  
|  
| |  
|  
| | 428.571
| 428.571
| | 85.714
| 85.714
| | 85.714
| 85.714
| style="text-align:center;" |  
| style="text-align:center;" |  
|}
|}
{{todo|cleanup}}
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