11L 3s

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↖ 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 ¢)
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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 ¢.

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 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

The table below shows an extension of edos which supports the Ketradektriatoh scale, with respect to the principal generator and their results for each L/s sizes:

4\11 436.364 109.091 0
29\80 435 105 15
25\69 434.783 104.348 17.391
21\58 434.483 103.448 20.69
17\47 434.043 102.128 25.532
30\83 433.735 101.208 28.916
73\202 433.663 100.990 29.703 Since here are the optimal range Lufsur mode (?)
43\119 433.613 100.840 30.252
433.459 100.377 31.95
13\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\61 432.787 98.361 39.344
9\25 432 96 48 Boundary of propriety;

generators smaller than this are proper

431.417 94.25 54.4155
23\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\39 430.769 92.308 61.538
47\131 430.534 91.603 64.122
80\223 430.493 91.480 64.575 Until here are the optimal range Fuslur mode (?)
33\92 430.435 91.304 65.217
19\53 430.189 90.566 67.925
24\67 429.851 89.552 71.642
29\81 429.63 88.889 74.074
34\95 429.474 88.421 75.7895
5\14 428.571 85.714 85.714

As an EDO subset

EDO Subset Special properties
25 2 2 2 1 2 2 2 2 1 2 2 2 2 1 Middle range
36 3 3 3 1 3 3 3 3 1 3 3 3 3 1 Lusfur range
39 3 3 3 2 3 3 3 3 2 3 3 3 3 2 Fuslur range
47 4 4 4 1 4 4 4 4 1 4 4 4 4 1
50 4 4 4 2 4 4 4 4 2 4 4 4 4 2
53 4 4 4 3 4 4 4 4 3 4 4 4 4 3
58 5 5 5 1 5 5 5 5 1 5 5 5 5 1
61 5 5 5 2 5 5 5 5 2 5 5 5 5 2 Split-φ
64 5 5 5 3 5 5 5 5 3 5 5 5 5 3 φ
67 5 5 5 4 5 5 5 5 4 5 5 5 5 4
69 6 6 6 1 6 6 6 6 1 6 6 6 6 1
81 6 6 6 5 6 6 6 6 5 6 6 6 6 5
80 7 7 7 1 7 7 7 7 1 7 7 7 7 1
83 7 7 7 2 7 7 7 7 2 7 7 7 7 2
86 7 7 7 3 7 7 7 7 3 7 7 7 7 3
89 7 7 7 4 7 7 7 7 4 7 7 7 7 4
92 7 7 7 5 7 7 7 7 5 7 7 7 7 5
95 7 7 7 6 7 7 7 7 6 7 7 7 7 6
91 8 8 8 1 8 8 8 8 1 8 8 8 8 1
97 8 8 8 3 8 8 8 8 3 8 8 8 8 3 Split-φ
103 8 8 8 5 8 8 8 8 5 8 8 8 8 5 φ
109 8 8 8 7 8 8 8 8 7 8 8 8 8 7
102 9 9 9 1 9 9 9 9 1 9 9 9 9 1
105 9 9 9 2 9 9 9 9 2 9 9 9 9 2
111 9 9 9 4 9 9 9 9 4 9 9 9 9 4
114 9 9 9 5 9 9 9 9 5 9 9 9 9 5
120 9 9 9 7 9 9 9 9 7 9 9 9 9 7
123 9 9 9 8 9 9 9 9 8 9 9 9 9 8
113 10 10 10 1 10 10 10 10 1 10 10 10 10 1
119 10 10 10 3 10 10 10 10 3 10 10 10 10 3
131 10 10 10 7 10 10 10 10 7 10 10 10 10 7
137 10 10 10 9 10 10 10 10 9 10 10 10 10 9
124 11 11 11 1 11 11 11 11 1 11 11 11 11 1
127 11 11 11 2 11 11 11 11 2 11 11 11 11 2
130 11 11 11 3 11 11 11 11 3 11 11 11 11 3
133 11 11 11 4 11 11 11 11 4 11 11 11 11 4
136 11 11 11 5 11 11 11 11 5 11 11 11 11 5
139 11 11 11 6 11 11 11 11 6 11 11 11 11 6
142 11 11 11 7 11 11 11 11 7 11 11 11 11 7
145 11 11 11 8 11 11 11 11 8 11 11 11 11 8
148 11 11 11 9 11 11 11 11 9 11 11 11 11 9
151 11 11 11 10 11 11 11 11 10 11 11 11 11 10
135 12 12 12 1 12 12 12 12 1 12 12 12 12 1
147 12 12 12 5 12 12 12 12 5 12 12 12 12 5
153 12 12 12 7 12 12 12 12 7 12 12 12 12 7
165 12 12 12 11 12 12 12 12 11 12 12 12 12 11
146 13 13 13 1 13 13 13 13 1 13 13 13 13 1
149 13 13 13 2 13 13 13 13 2 13 13 13 13 2
152 13 13 13 3 13 13 13 13 3 13 13 13 13 3
155 13 13 13 4 13 13 13 13 4 13 13 13 13 4
158 13 13 13 5 13 13 13 13 5 13 13 13 13 5 Split-φ
161 13 13 13 6 13 13 13 13 6 13 13 13 13 6
164 13 13 13 7 13 13 13 13 7 13 13 13 13 7
167 13 13 13 8 13 13 13 13 8 13 13 13 13 8 φ
170 13 13 13 9 13 13 13 13 9 13 13 13 13 9
173 13 13 13 10 13 13 13 13 10 13 13 13 13 10
176 13 13 13 11 13 13 13 13 11 13 13 13 13 11
179 13 13 13 12 13 13 13 13 12 13 13 13 13 12
157 14 14 14 1 14 14 14 14 1 14 14 14 14 1
163 14 14 14 3 14 14 14 14 3 14 14 14 14 3
169 14 14 14 5 14 14 14 14 5 14 14 14 14 5
181 14 14 14 9 14 14 14 14 9 14 14 14 14 9
187 14 14 14 11 14 14 14 14 11 14 14 14 14 11
193 14 14 14 13 14 14 14 14 13 14 14 14 14 13
168 15 15 15 1 15 15 15 15 1 15 15 15 15 1
171 15 15 15 2 15 15 15 15 2 15 15 15 15 2
177 15 15 15 4 15 15 15 15 4 15 15 15 15 4
186 15 15 15 7 15 15 15 15 7 15 15 15 15 7
189 15 15 15 8 15 15 15 15 8 15 15 15 15 8
198 15 15 15 11 15 15 15 15 11 15 15 15 15 11
204 15 15 15 13 15 15 15 15 13 15 15 15 15 13
207 15 15 15 14 15 15 15 15 14 15 15 15 15 14
179 16 16 16 1 16 16 16 16 1 16 16 16 16 1
185 16 16 16 3 16 16 16 16 3 16 16 16 16 3
191 16 16 16 5 16 16 16 16 5 16 16 16 16 5
197 16 16 16 7 16 16 16 16 7 16 16 16 16 7
203 16 16 16 9 16 16 16 16 9 16 16 16 16 9
209 16 16 16 11 16 16 16 16 11 16 16 16 16 11
215 16 16 16 13 16 16 16 16 13 16 16 16 16 13
221 16 16 16 15 16 16 16 16 15 16 16 16 16 15
190 17 17 17 1 17 17 17 17 1 17 17 17 17 1
193 17 17 17 2 17 17 17 17 2 17 17 17 17 2
196 17 17 17 3 17 17 17 17 3 17 17 17 17 3
199 17 17 17 4 17 17 17 17 4 17 17 17 17 4
202 17 17 17 5 17 17 17 17 5 17 17 17 17 5 Top limit for Lusfur range
205 17 17 17 6 17 17 17 17 6 17 17 17 17 6
208 17 17 17 7 17 17 17 17 7 17 17 17 17 7
211 17 17 17 8 17 17 17 17 8 17 17 17 17 8
214 17 17 17 9 17 17 17 17 9 17 17 17 17 9
217 17 17 17 10 17 17 17 17 10 17 17 17 17 10
220 17 17 17 11 17 17 17 17 11 17 17 17 17 11
223 17 17 17 12 17 17 17 17 12 17 17 17 17 12 Top limit for Fuslur range
226 17 17 17 13 17 17 17 17 13 17 17 17 17 13
229 17 17 17 14 17 17 17 17 14 17 17 17 17 14
232 17 17 17 15 17 17 17 17 15 17 17 17 17 15
235 17 17 17 16 17 17 17 17 16 17 17 17 17 16
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