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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
| Collapsed = 4
| Pattern = LLLLsLLLLsLLLs
}}
{{MOS intro|Other Names=}}


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.
== Name ==
Vector Graphics proposes '''ketradekic''' as a name for this scale, based on the name "Ketradektriatoh scale" proposed by [[Osmiorisbendi‎]], adapted to fit scale naming conventions.


<u>'''ED2s that contains this scale:'''</u>
== Modes ==
{{MOS modes}}


'''2 2 2 1 2 2 2 2 1 2 2 2 2 1: [[25edo|25]] (Middle range)'''
== Intervals ==
{{MOS intervals}}


'''3 3 3 1 3 3 3 3 1 3 3 3 3 1: [[36edo|36]] (Lufsur range)'''
== Scale tree ==
{{MOS tuning spectrum}}


'''3 3 3 2 3 3 3 3 2 3 3 3 3 2: [[39edo|39]] (Fuslur range)'''
{{todo|expand}}


4 4 4 1 4 4 4 4 1 4 4 4 4 1: [[47edo|47]]
[[Category:14-tone scales]]
 
4 4 4 2 4 4 4 4 2 4 4 4 4 2: [[50edo|50]]
 
4 4 4 3 4 4 4 4 3 4 4 4 4 3: [[53edo|53]]
 
5 5 5 1 5 5 5 5 1 5 5 5 5 1: [[58edo|58]]
 
'''5 5 5 2 5 5 5 5 2 5 5 5 5 2: [[61edo|61]] Split-φ'''
 
'''5 5 5 3 5 5 5 5 3 5 5 5 5 3: [[64edo|64]]''' '''φ'''
 
5 5 5 4 5 5 5 5 4 5 5 5 5 4: [[67edo|67]]
 
6 6 6 1 6 6 6 6 1 6 6 6 6 1: [[69edo|69]]
 
6 6 6 5 6 6 6 6 5 6 6 6 6 5: [[81edo|81]]
 
7 7 7 1 7 7 7 7 1 7 7 7 7 1: [[80edo|80]]
 
7 7 7 2 7 7 7 7 2 7 7 7 7 2: [[83edo|83]]
 
7 7 7 3 7 7 7 7 3 7 7 7 7 3: [[86edo|86]]
 
7 7 7 4 7 7 7 7 4 7 7 7 7 4: [[89edo|89]]
 
7 7 7 5 7 7 7 7 5 7 7 7 7 5: [[92edo|92]]
 
7 7 7 6 7 7 7 7 6 7 7 7 7 6: [[95edo|95]]
 
8 8 8 1 8 8 8 8 1 8 8 8 8 1: [[91edo|91]]
 
'''8 8 8 3 8 8 8 8 3 8 8 8 8 3: [[97edo|97]] Split-φ'''
 
'''8 8 8 5 8 8 8 8 5 8 8 8 8 5: [[103edo|103]]''' '''φ'''
 
8 8 8 7 8 8 8 8 7 8 8 8 8 7: [[109edo|109]]
 
9 9 9 1 9 9 9 9 1 9 9 9 9 1: [[102edo|102]]
 
9 9 9 2 9 9 9 9 2 9 9 9 9 2: [[105edo|105]]
 
9 9 9 4 9 9 9 9 4 9 9 9 9 4: [[111edo|111]]
 
9 9 9 5 9 9 9 9 5 9 9 9 9 5: [[114edo|114]]
 
9 9 9 7 9 9 9 9 7 9 9 9 9 7: [[120edo|120]]
 
9 9 9 8 9 9 9 9 8 9 9 9 9 8: [[123edo|123]]
 
10 10 10 1 10 10 10 10 1 10 10 10 10 1:[[113edo|113]]
 
10 10 10 3 10 10 10 10 3 10 10 10 10 3: [[119edo|119]]
 
10 10 10 7 10 10 10 10 7 10 10 10 10 7: [[131edo|131]]
 
10 10 10 9 10 10 10 10 9 10 10 10 10 9: [[137edo|137]]
 
11 11 11 '''<span style="color: #006209;">1</span>''' 11 11 11 11 '''<span style="color: #006209;">1</span>''' 11 11 11 11 '''<span style="color: #006209;">1</span>''': [[124edo|124]]
 
11 11 11 2 11 11 11 11 2 11 11 11 11 2: [[127edo|127]]
 
11 11 11 3 11 11 11 11 3 11 11 11 11 3: [[130edo|130]]
 
11 11 11 4 11 11 11 11 4 11 11 11 11 4: [[133edo|133]]
 
11 11 11 5 11 11 11 11 5 11 11 11 11 5: [[136edo|136]]
 
11 11 11 6 11 11 11 11 6 11 11 11 11 6: [[139edo|139]]
 
11 11 11 7 11 11 11 11 7 11 11 11 11 7: [[142edo|142]]
 
11 11 11 8 11 11 11 11 8 11 11 11 11 8: [[145edo|145]]
 
11 11 11 9 11 11 11 11 9 11 11 11 11 9 :[[148edo|148]]
 
11 11 11 10 11 11 11 11 10 11 11 11 11 10: [[151edo|151]]
 
12 12 12 1 12 12 12 12 1 12 12 12 12 1: [[135edo|135]]
 
12 12 12 5 12 12 12 12 5 12 12 12 12 5: [[147edo|147]]
 
12 12 12 7 12 12 12 12 7 12 12 12 12 7: [[153edo|153]]
 
12 12 12 11 12 12 12 12 11 12 12 12 12 11: [[165edo|165]]
 
13 13 13 1 13 13 13 13 1 13 13 13 13 1: [[146edo|146]]
 
13 13 13 2 13 13 13 13 2 13 13 13 13 2: [[149edo|149]]
 
13 13 13 3 13 13 13 13 3 13 13 13 13 3: [[152edo|152]]
 
13 13 13 4 13 13 13 13 4 13 13 13 13 4: [[155edo|155]]
 
'''13 13 13 5 13 13 13 13 5 13 13 13 13 5: [[158edo|158]] Split-φ'''
 
13 13 13 6 13 13 13 13 6 13 13 13 13 6: [[161edo|161]]
 
13 13 13 7 13 13 13 13 7 13 13 13 13 7: [[164edo|164]]
 
'''13 13 13 8 13 13 13 13 8 13 13 13 13 8: [[167edo|167]]''' '''φ'''
 
13 13 13 9 13 13 13 13 9 13 13 13 13 9: [[170edo|170]]
 
13 13 13 10 13 13 13 13 10 13 13 13 13 10: [[173edo|173]]
 
13 13 13 11 13 13 13 13 11 13 13 13 13 11: [[176edo|176]]
 
13 13 13 12 13 13 13 13 12 13 13 13 13 12: [[179edo|179]]
 
14 14 14 1 14 14 14 14 1 14 14 14 14 1: [[157edo|157]]
 
14 14 14 3 14 14 14 14 3 14 14 14 14 3: [[163edo|163]]
 
14 14 14 5 14 14 14 14 5 14 14 14 14 5: [[169edo|169]]
 
14 14 14 9 14 14 14 14 9 14 14 14 14 9: [[181edo|181]]
 
14 14 14 11 14 14 14 14 11 14 14 14 14 11: [[187edo|187]]
 
14 14 14 13 14 14 14 14 13 14 14 14 14 13: [[193edo|193]]
 
15 15 15 1 15 15 15 15 1 15 15 15 15 1: [[168edo|168]]
 
15 15 15 2 15 15 15 15 2 15 15 15 15 2: [[171edo|171]]
 
15 15 15 4 15 15 15 15 4 15 15 15 15 4: [[177edo|177]]
 
15 15 15 7 15 15 15 15 7 15 15 15 15 7: [[186edo|186]]
 
15 15 15 8 15 15 15 15 8 15 15 15 15 8: [[189edo|189]]
 
15 15 15 11 15 15 15 15 11 15 15 15 15 11: [[198edo|198]]
 
15 15 15 13 15 15 15 15 13 15 15 15 15 13: [[204edo|204]]
 
15 15 15 14 15 15 15 15 14 15 15 15 15 14: [[207edo|207]]
 
16 16 16 1 16 16 16 16 1 16 16 16 16 1: [[179edo|179]]
 
16 16 16 3 16 16 16 16 3 16 16 16 16 3: [[185edo|185]]
 
16 16 16 5 16 16 16 16 5 16 16 16 16 5: [[191edo|191]]
 
16 16 16 7 16 16 16 16 7 16 16 16 16 7: [[197edo|197]]
 
16 16 16 9 16 16 16 16 9 16 16 16 16 9: [[203edo|203]]
 
16 16 16 11 16 16 16 16 11 16 16 16 16 11: [[209edo|209]]
 
16 16 16 13 16 16 16 16 13 16 16 16 16 13: [[215edo|215]]
 
16 16 16 15 16 16 16 16 15 16 16 16 16 15: [[221edo|221]]
 
17 17 17 1 17 17 17 17 1 17 17 17 17 1: [[190edo|190]]
 
17 17 17 2 17 17 17 17 2 17 17 17 17 2: [[193edo|193]]
 
17 17 17 3 17 17 17 17 3 17 17 17 17 3: [[196edo|196]]
 
17 17 17 4 17 17 17 17 4 17 17 17 17 4: [[199edo|199]]
 
'''17 17 17 5 17 17 17 17 5 17 17 17 17 5: [[202edo|202]] (Top limit for Lufsur range)'''
 
'''17 17 17 6 17 17 17 17 6 17 17 17 17 6: [[205edo|205]]'''
 
'''17 17 17 7 17 17 17 17 7 17 17 17 17 7: [[208edo|208]]'''
 
'''17 17 17 8 17 17 17 17 8 17 17 17 17 8: [[211edo|211]]'''
 
'''17 17 17 9 17 17 17 17 9 17 17 17 17 9: [[214edo|214]]'''
 
'''17 17 17 10 17 17 17 17 10 17 17 17 17 10: [[217edo|217]]'''
 
'''17 17 17 11 17 17 17 17 11 17 17 17 17 11: [[220edo|220]]'''
 
'''17 17 17 12 17 17 17 17 12 17 17 17 17 12: [[223edo|223]] (Top limit for Fuslur range)'''
 
17 17 17 13 17 17 17 17 13 17 17 17 17 13: [[226edo|226]]
 
17 17 17 14 17 17 17 17 14 17 17 17 17 14: [[229edo|229]]
 
17 17 17 15 17 17 17 17 15 17 17 17 17 15: [[232edo|232]]
 
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:
 
{| 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;" |
|}

Latest revision as of 06:29, 18 June 2025

↖ 10L 2s ↑ 11L 2s 12L 2s ↗
← 10L 3s 11L 3s 12L 3s →
↙ 10L 4s ↓ 11L 4s 12L 4s ↘ 
┌╥╥╥╥┬╥╥╥╥┬╥╥╥┬┐
│║║║║│║║║║│║║║││
││││││││││││││││
└┴┴┴┴┴┴┴┴┴┴┴┴┴┴┘
Scale structure
Step pattern LLLLsLLLLsLLLs
sLLLsLLLLsLLLL
Equave 2/1 (1200.0 ¢)
Period 2/1 (1200.0 ¢)
Generator size
Bright 5\14 to 4\11 (428.6 ¢ to 436.4 ¢)
Dark 7\11 to 9\14 (763.6 ¢ to 771.4 ¢)
TAMNAMS information
Related to 3L 5s (checkertonic)
With tunings 2:1 to 3:1 (hypohard)
Related MOS scales
Parent 3L 8s
Sister 3L 11s
Daughters 14L 11s, 11L 14s
Neutralized 8L 6s
2-Flought 25L 3s, 11L 17s
Equal tunings
Equalized (L:s = 1:1) 5\14 (428.6 ¢)
Supersoft (L:s = 4:3) 19\53 (430.2 ¢)
Soft (L:s = 3:2) 14\39 (430.8 ¢)
Semisoft (L:s = 5:3) 23\64 (431.2 ¢)
Basic (L:s = 2:1) 9\25 (432.0 ¢)
Semihard (L:s = 5:2) 22\61 (432.8 ¢)
Hard (L:s = 3:1) 13\36 (433.3 ¢)
Superhard (L:s = 4:1) 17\47 (434.0 ¢)
Collapsed (L:s = 1:0) 4\11 (436.4 ¢)

11L 3s is a 2/1-equivalent (octave-equivalent) moment of symmetry scale containing 11 large steps and 3 small steps, repeating every octave. 11L 3s is a grandchild scale of 3L 5s, expanding it by 6 tones. Generators that produce this scale range from 428.6 ¢ to 436.4 ¢, or from 763.6 ¢ to 771.4 ¢.

Name

Vector Graphics proposes ketradekic as a name for this scale, based on the name "Ketradektriatoh scale" proposed by Osmiorisbendi‎, adapted to fit scale naming conventions.

Modes

Modes of 11L 3s
UDP Cyclic
order		 Step
pattern
13|0 1 LLLLsLLLLsLLLs
12|1 6 LLLLsLLLsLLLLs
11|2 11 LLLsLLLLsLLLLs
10|3 2 LLLsLLLLsLLLsL
9|4 7 LLLsLLLsLLLLsL
8|5 12 LLsLLLLsLLLLsL
7|6 3 LLsLLLLsLLLsLL
6|7 8 LLsLLLsLLLLsLL
5|8 13 LsLLLLsLLLLsLL
4|9 4 LsLLLLsLLLsLLL
3|10 9 LsLLLsLLLLsLLL
2|11 14 sLLLLsLLLLsLLL
1|12 5 sLLLLsLLLsLLLL
0|13 10 sLLLsLLLLsLLLL

Intervals

Intervals of 11L 3s
Intervals Steps
subtended 		Range in cents
Generic Specific Abbrev.
0-mosstep Perfect 0-mosstep P0ms 0 0.0 ¢
1-mosstep Minor 1-mosstep m1ms s 0.0 ¢ to 85.7 ¢
Major 1-mosstep M1ms L 85.7 ¢ to 109.1 ¢
2-mosstep Minor 2-mosstep m2ms L + s 109.1 ¢ to 171.4 ¢
Major 2-mosstep M2ms 2L 171.4 ¢ to 218.2 ¢
3-mosstep Minor 3-mosstep m3ms 2L + s 218.2 ¢ to 257.1 ¢
Major 3-mosstep M3ms 3L 257.1 ¢ to 327.3 ¢
4-mosstep Minor 4-mosstep m4ms 3L + s 327.3 ¢ to 342.9 ¢
Major 4-mosstep M4ms 4L 342.9 ¢ to 436.4 ¢
5-mosstep Diminished 5-mosstep d5ms 3L + 2s 327.3 ¢ to 428.6 ¢
Perfect 5-mosstep P5ms 4L + s 428.6 ¢ to 436.4 ¢
6-mosstep Minor 6-mosstep m6ms 4L + 2s 436.4 ¢ to 514.3 ¢
Major 6-mosstep M6ms 5L + s 514.3 ¢ to 545.5 ¢
7-mosstep Minor 7-mosstep m7ms 5L + 2s 545.5 ¢ to 600.0 ¢
Major 7-mosstep M7ms 6L + s 600.0 ¢ to 654.5 ¢
8-mosstep Minor 8-mosstep m8ms 6L + 2s 654.5 ¢ to 685.7 ¢
Major 8-mosstep M8ms 7L + s 685.7 ¢ to 763.6 ¢
9-mosstep Perfect 9-mosstep P9ms 7L + 2s 763.6 ¢ to 771.4 ¢
Augmented 9-mosstep A9ms 8L + s 771.4 ¢ to 872.7 ¢
10-mosstep Minor 10-mosstep m10ms 7L + 3s 763.6 ¢ to 857.1 ¢
Major 10-mosstep M10ms 8L + 2s 857.1 ¢ to 872.7 ¢
11-mosstep Minor 11-mosstep m11ms 8L + 3s 872.7 ¢ to 942.9 ¢
Major 11-mosstep M11ms 9L + 2s 942.9 ¢ to 981.8 ¢
12-mosstep Minor 12-mosstep m12ms 9L + 3s 981.8 ¢ to 1028.6 ¢
Major 12-mosstep M12ms 10L + 2s 1028.6 ¢ to 1090.9 ¢
13-mosstep Minor 13-mosstep m13ms 10L + 3s 1090.9 ¢ to 1114.3 ¢
Major 13-mosstep M13ms 11L + 2s 1114.3 ¢ to 1200.0 ¢
14-mosstep Perfect 14-mosstep P14ms 11L + 3s 1200.0 ¢

Scale tree

Scale tree and tuning spectrum of 11L 3s
Generator(edo) Cents Step ratio Comments
Bright Dark L:s Hardness
5\14 428.571 771.429 1:1 1.000 Equalized 11L 3s
29\81 429.630 770.370 6:5 1.200
24\67 429.851 770.149 5:4 1.250
43\120 430.000 770.000 9:7 1.286
19\53 430.189 769.811 4:3 1.333 Supersoft 11L 3s
52\145 430.345 769.655 11:8 1.375
33\92 430.435 769.565 7:5 1.400
47\131 430.534 769.466 10:7 1.429
14\39 430.769 769.231 3:2 1.500 Soft 11L 3s
51\142 430.986 769.014 11:7 1.571
37\103 431.068 768.932 8:5 1.600
60\167 431.138 768.862 13:8 1.625
23\64 431.250 768.750 5:3 1.667 Semisoft 11L 3s
55\153 431.373 768.627 12:7 1.714
32\89 431.461 768.539 7:4 1.750
41\114 431.579 768.421 9:5 1.800
9\25 432.000 768.000 2:1 2.000 Basic 11L 3s
Scales with tunings softer than this are proper
40\111 432.432 767.568 9:4 2.250
31\86 432.558 767.442 7:3 2.333
53\147 432.653 767.347 12:5 2.400
22\61 432.787 767.213 5:2 2.500 Semihard 11L 3s
57\158 432.911 767.089 13:5 2.600
35\97 432.990 767.010 8:3 2.667
48\133 433.083 766.917 11:4 2.750
13\36 433.333 766.667 3:1 3.000 Hard 11L 3s
43\119 433.613 766.387 10:3 3.333
30\83 433.735 766.265 7:2 3.500
47\130 433.846 766.154 11:3 3.667
17\47 434.043 765.957 4:1 4.000 Superhard 11L 3s
38\105 434.286 765.714 9:2 4.500
21\58 434.483 765.517 5:1 5.000
25\69 434.783 765.217 6:1 6.000
4\11 436.364 763.636 1:0 → ∞ Collapsed 11L 3s
Retrieved from "https://en.xen.wiki/index.php?title=11L_3s&oldid=199902"