11L 3s: Difference between revisions

From Xenharmonic Wiki
Jump to navigation Jump to search
← Older edit
VisualWikitext
Ganaram inukshuk (talk | contribs)
autopatrolled
4,810 edits
Mos intro
No edit summary
 
(6 intermediate revisions by 3 users not shown)
Line 8: Line 8:
| Pattern = LLLLsLLLLsLLLs
| Pattern = LLLLsLLLLsLLLs
}}
}}
{{MOS intro|Other Names=the Ketradektriatoh scale}}
{{MOS intro|Other Names=}}


The '''11L 3s''' [[MOS scale]] was named the "Ketradektriatoh scale" by [[Osmiorisbendi‎]]
== 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.


This is a type of scale which denotes the use of a scale placed between [[11edo]] and [[14edo]].
== Modes ==
{{MOS modes}}


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).
== Intervals ==
{{MOS intervals}}


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:
{{MOS tuning spectrum}}
{| 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
{{todo|expand}}
|-
|
|
|
|
|
|
|
| 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]]

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"