11L 2s

↖ 10L 1s	↑ 11L 1s	12L 1s ↗
← 10L 2s	11L 2s	12L 2s →
↙ 10L 3s	↓ 11L 3s	12L 3s ↘

┌╥╥╥╥╥╥┬╥╥╥╥╥┬┐ │║║║║║║│║║║║║││ │││││││││││││││ └┴┴┴┴┴┴┴┴┴┴┴┴┴┘
Scale structure
Step pattern	LLLLLLsLLLLLs sLLLLLsLLLLLL
Equave	2/1 (1200.0 ¢)
Period	2/1 (1200.0 ¢)
Generator size
Bright	7\13 to 6\11 (646.2 ¢ to 654.5 ¢)
Dark	5\11 to 6\13 (545.5 ¢ to 553.8 ¢)
TAMNAMS information
Related to	2L 7s (balzano)
With tunings	2:1 to 3:1 (hypohard)
Related MOS scales
Parent	2L 9s
Sister	2L 11s
Daughters	13L 11s, 11L 13s
Neutralized	9L 4s
2-Flought	24L 2s, 11L 15s
Equal tunings
Equalized (L:s = 1:1)	7\13 (646.2 ¢)
Supersoft (L:s = 4:3)	27\50 (648.0 ¢)
Soft (L:s = 3:2)	20\37 (648.6 ¢)
Semisoft (L:s = 5:3)	33\61 (649.2 ¢)
Basic (L:s = 2:1)	13\24 (650.0 ¢)
Semihard (L:s = 5:2)	32\59 (650.8 ¢)
Hard (L:s = 3:1)	19\35 (651.4 ¢)
Superhard (L:s = 4:1)	25\46 (652.2 ¢)
Collapsed (L:s = 1:0)	6\11 (654.5 ¢)

11L 2s, also called hendecoid or Wyschnegradsky's diatonicized chromatic scale, is a 2/1-equivalent (octave-equivalent) moment of symmetry scale containing 11 large steps and 2 small steps, repeating every octave. 11L 2s is a grandchild scale of 2L 7s, expanding it by 4 tones. Generators that produce this scale range from 646.2 ¢ to 654.5 ¢, or from 545.5 ¢ to 553.8 ¢. This scale is most notable for being used by Ivan Wyschnegradsky, bearing the name diatonicized chromatic scale. Eliora has proposed the name hendecoid for its strong relationship to the number 11, as it's an 11+-limit scale and has generators that are close to 11/8. Frostburn has proposed the name p-enhar balzano, as a grandchild scale of 2L 7s.

From a regular temperament theory perspective, this scale is notable for corresponding to the mega chromatic scale of Heinz temperament. Its generator of 5\11 to 6\13 hits so close to 11/8 as to be able to be called nothing but that interval, making it an 11+-limit scale. If just 11/8 is used as generator, the step ratio is around 1.509.

Modes

Modes of 11L 2s

UDP	Cyclic order	Step pattern
12|0	1	LLLLLLsLLLLLs
11|1	8	LLLLLsLLLLLLs
10|2	2	LLLLLsLLLLLsL
9|3	9	LLLLsLLLLLLsL
8|4	3	LLLLsLLLLLsLL
7|5	10	LLLsLLLLLLsLL
6|6	4	LLLsLLLLLsLLL
5|7	11	LLsLLLLLLsLLL
4|8	5	LLsLLLLLsLLLL
3|9	12	LsLLLLLLsLLLL
2|10	6	LsLLLLLsLLLLL
1|11	13	sLLLLLLsLLLLL
0|12	7	sLLLLLsLLLLLL

Intervals

Intervals of 11L 2s

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 92.3 ¢
	Major 1-mosstep	M1ms	L	92.3 ¢ to 109.1 ¢
2-mosstep	Minor 2-mosstep	m2ms	L + s	109.1 ¢ to 184.6 ¢
	Major 2-mosstep	M2ms	2L	184.6 ¢ to 218.2 ¢
3-mosstep	Minor 3-mosstep	m3ms	2L + s	218.2 ¢ to 276.9 ¢
	Major 3-mosstep	M3ms	3L	276.9 ¢ to 327.3 ¢
4-mosstep	Minor 4-mosstep	m4ms	3L + s	327.3 ¢ to 369.2 ¢
	Major 4-mosstep	M4ms	4L	369.2 ¢ to 436.4 ¢
5-mosstep	Minor 5-mosstep	m5ms	4L + s	436.4 ¢ to 461.5 ¢
	Major 5-mosstep	M5ms	5L	461.5 ¢ to 545.5 ¢
6-mosstep	Perfect 6-mosstep	P6ms	5L + s	545.5 ¢ to 553.8 ¢
	Augmented 6-mosstep	A6ms	6L	553.8 ¢ to 654.5 ¢
7-mosstep	Diminished 7-mosstep	d7ms	5L + 2s	545.5 ¢ to 646.2 ¢
	Perfect 7-mosstep	P7ms	6L + s	646.2 ¢ to 654.5 ¢
8-mosstep	Minor 8-mosstep	m8ms	6L + 2s	654.5 ¢ to 738.5 ¢
	Major 8-mosstep	M8ms	7L + s	738.5 ¢ to 763.6 ¢
9-mosstep	Minor 9-mosstep	m9ms	7L + 2s	763.6 ¢ to 830.8 ¢
	Major 9-mosstep	M9ms	8L + s	830.8 ¢ to 872.7 ¢
10-mosstep	Minor 10-mosstep	m10ms	8L + 2s	872.7 ¢ to 923.1 ¢
	Major 10-mosstep	M10ms	9L + s	923.1 ¢ to 981.8 ¢
11-mosstep	Minor 11-mosstep	m11ms	9L + 2s	981.8 ¢ to 1015.4 ¢
	Major 11-mosstep	M11ms	10L + s	1015.4 ¢ to 1090.9 ¢
12-mosstep	Minor 12-mosstep	m12ms	10L + 2s	1090.9 ¢ to 1107.7 ¢
	Major 12-mosstep	M12ms	11L + s	1107.7 ¢ to 1200.0 ¢
13-mosstep	Perfect 13-mosstep	P13ms	11L + 2s	1200.0 ¢

Scale tree

Scale tree and tuning spectrum of 11L 2s

Generator(edo)						Cents		Step ratio		Comments
						Bright	Dark	L:s	Hardness
7\13						646.154	553.846	1:1	1.000	Equalized 11L 2s
					41\76	647.368	552.632	6:5	1.200
				34\63		647.619	552.381	5:4	1.250
					61\113	647.788	552.212	9:7	1.286
			27\50			648.000	552.000	4:3	1.333	Supersoft 11L 2s
					74\137	648.175	551.825	11:8	1.375
				47\87		648.276	551.724	7:5	1.400	↕ Emka
					67\124	648.387	551.613	10:7	1.429
		20\37				648.649	551.351	3:2	1.500	Soft 11L 2s
					73\135	648.889	551.111	11:7	1.571
				53\98		648.980	551.020	8:5	1.600	↕ Freivald
					86\159	649.057	550.943	13:8	1.625
			33\61			649.180	550.820	5:3	1.667	Semisoft 11L 2s
					79\146	649.315	550.685	12:7	1.714
				46\85		649.412	550.588	7:4	1.750
					59\109	649.541	550.459	9:5	1.800
	13\24					650.000	550.000	2:1	2.000	Basic 11L 2s Scales with tunings softer than this are proper
					58\107	650.467	549.533	9:4	2.250
				45\83		650.602	549.398	7:3	2.333
					77\142	650.704	549.296	12:5	2.400
			32\59			650.847	549.153	5:2	2.500	Semihard 11L 2s
					83\153	650.980	549.020	13:5	2.600
				51\94		651.064	548.936	8:3	2.667
					70\129	651.163	548.837	11:4	2.750
		19\35				651.429	548.571	3:1	3.000	Hard 11L 2s
					63\116	651.724	548.276	10:3	3.333
				44\81		651.852	548.148	7:2	3.500
					69\127	651.969	548.031	11:3	3.667
			25\46			652.174	547.826	4:1	4.000	Superhard 11L 2s Heinz
					56\103	652.427	547.573	9:2	4.500
				31\57		652.632	547.368	5:1	5.000
					37\68	652.941	547.059	6:1	6.000
6\11						654.545	545.455	1:0	→ ∞	Collapsed 11L 2s