1L 11s

	↑ 1L 10s	2L 10s ↗
	1L 11s	2L 11s →
	↓ 1L 12s	2L 12s ↘

┌╥┬┬┬┬┬┬┬┬┬┬┬┐ │║││││││││││││ ││││││││││││││ └┴┴┴┴┴┴┴┴┴┴┴┴┘
Scale structure
Step pattern	Lsssssssssss sssssssssssL
Equave	2/1 (1200.0 ¢)
Period	2/1 (1200.0 ¢)
Generator size
Bright	11\12 to 1\1 (1100.0 ¢ to 1200.0 ¢)
Dark	0\1 to 1\12 (0.0 ¢ to 100.0 ¢)
TAMNAMS information
Related to	1L 9s (antisinatonic)
With tunings	3:1 to 1:0 (hard)
Related MOS scales
Parent	1L 10s
Sister	11L 1s
Daughters	12L 1s, 1L 12s
Neutralized	2L 10s
2-Flought	13L 11s, 1L 23s
Equal tunings
Equalized (L:s = 1:1)	11\12 (1100.0 ¢)
Supersoft (L:s = 4:3)	34\37 (1102.7 ¢)
Soft (L:s = 3:2)	23\25 (1104.0 ¢)
Semisoft (L:s = 5:3)	35\38 (1105.3 ¢)
Basic (L:s = 2:1)	12\13 (1107.7 ¢)
Semihard (L:s = 5:2)	25\27 (1111.1 ¢)
Hard (L:s = 3:1)	13\14 (1114.3 ¢)
Superhard (L:s = 4:1)	14\15 (1120.0 ¢)
Collapsed (L:s = 1:0)	1\1 (1200.0 ¢)

1L 11s is the MOS pattern Lsssssssssss with small steps ranging from 0\1 (0¢) to 1\12 (one step of 12edo = 100¢).

This MOS, also called the "happy dodecatonic", is not a complete scale for any "interesting" temperament ― the simplest absolute harmonic entropy minimum for it is where +7 generators equals a meantone fifth, and even there it implies a val with warts for 3 and (for the most part) 5. Perhaps the only use for it is to extend it to 13 tones, i.e. to make it into a different MOS.

Modes

• 11|0 Lsssssssssss
• 10|1 sLssssssssss
• 9|2 ssLsssssssss
• 8|3 sssLssssssss
• 7|4 ssssLsssssss
• 6|5 sssssLssssss
• 5|6 ssssssLsssss
• 4|7 sssssssLssss
• 3|8 ssssssssLsss
• 2|9 sssssssssLss
• 1|10 ssssssssssLs
• 0|11 sssssssssssL

Scale tree

Generator ranges:

• Chroma-positive generator: 1100 cents (11\12) to 1200 cents (1\1)
• Chroma-negative generator: 0 cents (0\1) to 100 cents (1\12)

Small step (chroma-negative generator)								Cents	L	s	L/s	Comments
1\12								100.000	1	1	1.000
							7\85	98.824	8	7	1.143	Passionate/pash
						6\73		98.630	7	6	1.167	Passionate
							11\134	98.507	13	11	1.182
					5\61			98.361	6	5	1.200
							14\171	98.246	17	14	1.214
						9\110		98.182	11	9	1.222
							13\159	98.113	16	13	1.231
				4\49				97.959	5	4	1.250	Passion
							15\184	97.826	19	15	1.267
						11\135		97.778	14	11	1.273
							18\221	97.738	23	18	1.278
					7\86			97.674	9	7	1.286
							17\209	97.608	22	17	1.294
						10\123		97.561	13	10	1.300
							13\160	97.500	17	13	1.308
			3\37					97.297	4	3	1.333
							14\173	97.110	19	14	1.357
						11\136		97.059	15	11	1.364
							19\235	97.021	26	19	1.368
					8\99			96.970	11	8	1.375
							21\260	96.923	29	21	1.381
						13\161		96.894	18	13	1.385
							18\223	96.861	25	18	1.389
				5\62				96.774	7	5	1.400
							17\211	96.682	24	17	1.412
						12\149		96.644	17	12	1.417
							19\236	96.610	27	19	1.421
					7\87			96.552	10	7	1.429
							16\199	96.482	23	16	1.438
						9\112		96.429	13	9	1.444
							11\137	96.35	16	11	1.455
		2\25						96.000	3	2	1.500
							11\138	95.652	17	11	1.545
						9\113		95.575	14	9	1.556
							16\201	95.522	25	16	1.563
					7\88			95.455	11	7	1.571
							19\239	95.397	30	19	1.579
						12\151		95.364	19	12	1.583
							17\214	95.327	27	17	1.588
				5\63				95.238	8	5	1.600
							18\227	95.154	29	18	1.611
						13\164		95.122	21	13	1.615
							21\265	95.094	34	21	1.619	Unnamed golden tuning (95.1020¢)
					8\101			95.050	13	8	1.625
							19\240	95.000	31	19	1.632
						11\139		94.964	18	11	1.636
							14\177	94.915	23	14	1.643
			3\38					94.737	5	3	1.667
							13\165	94.545	22	13	1.692
						10\127		94.488	17	10	1.700
							17\216	94.444	29	17	1.706
					7\89			94.382	12	7	1.714
							18\229	94.323	31	18	1.722
						11\140		94.286	19	11	1.727
							15\191	94.241	26	15	1.733
				4\51				94.118	7	4	1.750
							13\166	93.976	23	13	1.769
						9\115		93.913	16	9	1.778
							14\179	93.855	25	14	1.786
					5\64			93.750	9	5	1.800
							11\141	93.617	20	11	1.818
						6\77		93.506	11	6	1.833
							7\90	93.333	13	7	1.857
	1\13							92.308	2	1	2.000	Basic 1L 11s (small steps larger than this are proper)
							6\79	91.139	13	6	2.167
						5\66		90.909	11	5	2.200
							9\119	90.756	20	9	2.222
					4\53			90.566	9	4	2.250
							11\146	90.411	25	11	2.273
						7\93		90.323	16	7	2.286
							10\133	90.226	23	10	2.300
				3\40				90.000	7	3	2.333
							11\147	89.796	26	11	2.364
						8\107		89.720	19	8	2.375
							13\174	89.655	31	13	2.385
					5\67			89.552	12	5	2.400
							12\161	89.441	29	12	2.417
						7\94		89.362	17	7	2.429
							9\121	89.256	22	9	2.444	Slithy
			2\27					88.889	5	2	2.500
							9\122	88.525	23	9	2.556
						7\95		88.421	18	7	2.571
							12\163	88.344	31	12	2.583
					5\68			88.235	13	5	2.600
							13\177	88.136	34	13	2.615	Golden octacot (88.1184¢)
						8\109		88.073	21	8	2.625	Octacot
							11\150	88.000	29	11	2.636	Octacot
				3\41				87.805	8	3	2.667
							10\137	87.591	27	10	2.700
						7\96		87.500	19	7	2.714
							11\151	87.417	30	11	2.727
					4\55			87.273	11	4	2.750
							9\124	87.097	25	9	2.777
						5\69		86.957	14	5	2.800
							6\83	86.747	17	6	2.833
		1\14						85.714	3	1	3.000
							5\71	84.507	16	5	3.200
						4\57		84.211	13	4	3.250
							7\100	84.000	23	7	3.286
					3\43			83.721	10	3	3.333
							8\115	83.478	27	8	3.375
						5\72		83.333	17	5	3.400	Marvolo
							7\101	83.168	24	7	3.429
				2\29				82.759	7	2	3.500
							7\102	82.353	25	7	3.571
						5\73		82.192	18	5	3.600
							8\117	82.051	29	8	3.625
					3\44			81.818	11	3	3.667
							7\103	81.553	26	7	3.714
						4\59		81.356	15	4	3.750
							5\74	81.081	19	5	3.800
			1\15					80.000	4	1	4.000
							4\61	78.689	17	4	4.250
						3\46		78.261	13	3	4.333
							5\77	77.922	22	5	4.400	Valentine
					2\31			77.419	9	2	4.500
							5\78	76.923	23	5	4.600
						3\47		76.596	14	3	4.667
							4\63	76.190	19	4	4.750
				1\16				75.000	5	1	5.000
							3\49	73.469	16	3	5.333
						2\33		72.727	11	2	5.500
							3\50	72.000	17	3	5.667
					1\17			70.588	6	1	6.000
							2\35	68.571	13	2	6.500
						1\18		66.667	7	1	7.000
							1\19	63.158	8	1	8.000	Unicorn
0\1								0.000	1	0	→ inf