11L 3s

↖ 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

Equal tunings

Equalized (L:s = 1:1)

5\14 (428.6 ¢)

Supersoft (L:s = 4:3)

19\53 (430.2 ¢)

14\39 (430.8 ¢)

23\64 (431.2 ¢)

9\25 (432.0 ¢)

22\61 (432.8 ¢)

13\36 (433.3 ¢)

Superhard (L:s = 4:1)

17\47 (434.0 ¢)

Collapsed (L:s = 1:0)

4\11 (436.4 ¢)

11L 3s, also called the Ketradektriatoh scale, 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

11L 3s

Scale tree

As an EDO subset

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