11L 4s

↖ 10L 3s	↑ 11L 3s	12L 3s ↗
← 10L 4s	11L 4s	12L 4s →
↙ 10L 5s	↓ 11L 5s	12L 5s ↘

Scale structure
Step pattern	LLLsLLLsLLLsLLs sLLsLLLsLLLsLLL
Equave	2/1 (1200.0 ¢)
Period	2/1 (1200.0 ¢)
Generator size
Bright	4\15 to 3\11 (320.0 ¢ to 327.3 ¢)
Dark	8\11 to 11\15 (872.7 ¢ to 880.0 ¢)
TAMNAMS information
Related to	4L 3s (smitonic)
With tunings	2:1 to 3:1 (hypohard)
Related MOS scales
Parent	4L 7s
Sister	4L 11s
Daughters	15L 11s, 11L 15s
Neutralized	7L 8s
2-Flought	26L 4s, 11L 19s
Equal tunings
Equalized (L:s = 1:1)	4\15 (320.0 ¢)
Supersoft (L:s = 4:3)	15\56 (321.4 ¢)
Soft (L:s = 3:2)	11\41 (322.0 ¢)
Semisoft (L:s = 5:3)	18\67 (322.4 ¢)
Basic (L:s = 2:1)	7\26 (323.1 ¢)
Semihard (L:s = 5:2)	17\63 (323.8 ¢)
Hard (L:s = 3:1)	10\37 (324.3 ¢)
Superhard (L:s = 4:1)	13\48 (325.0 ¢)
Collapsed (L:s = 1:0)	3\11 (327.3 ¢)
View • Talk • Edit

11L 4s is a 2/1-equivalent (octave-equivalent) moment of symmetry scale containing 11 large steps and 4 small steps, repeating every octave. 11L 4s is a grandchild scale of 4L 3s, expanding it by 8 tones. Generators that produce this scale range from 320 ¢ to 327.3 ¢, or from 872.7 ¢ to 880 ¢. The bright generator represents a minor third slightly sharp of 6/5 (315.6¢), though this MOS is most reasonably interpreted in the 2.7.11 orgone temperament where it is identified as ~77/64. At its harmonic entropy minimum, the octave-reduced 7th harmonic (about 968¢) equals 3 of these generators.

Modes

Modes of 11L 4s

UDP	Cyclic order	Step pattern
14|0	1	LLLsLLLsLLLsLLs
13|1	5	LLLsLLLsLLsLLLs
12|2	9	LLLsLLsLLLsLLLs
11|3	13	LLsLLLsLLLsLLLs
10|4	2	LLsLLLsLLLsLLsL
9|5	6	LLsLLLsLLsLLLsL
8|6	10	LLsLLsLLLsLLLsL
7|7	14	LsLLLsLLLsLLLsL
6|8	3	LsLLLsLLLsLLsLL
5|9	7	LsLLLsLLsLLLsLL
4|10	11	LsLLsLLLsLLLsLL
3|11	15	sLLLsLLLsLLLsLL
2|12	4	sLLLsLLLsLLsLLL
1|13	8	sLLLsLLsLLLsLLL
0|14	12	sLLsLLLsLLLsLLL

Intervals

Intervals of 11L 4s

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 80.0 ¢
	Major 1-mosstep	M1ms	L	80.0 ¢ to 109.1 ¢
2-mosstep	Minor 2-mosstep	m2ms	L + s	109.1 ¢ to 160.0 ¢
	Major 2-mosstep	M2ms	2L	160.0 ¢ to 218.2 ¢
3-mosstep	Minor 3-mosstep	m3ms	2L + s	218.2 ¢ to 240.0 ¢
	Major 3-mosstep	M3ms	3L	240.0 ¢ to 327.3 ¢
4-mosstep	Diminished 4-mosstep	d4ms	2L + 2s	218.2 ¢ to 320.0 ¢
	Perfect 4-mosstep	P4ms	3L + s	320.0 ¢ to 327.3 ¢
5-mosstep	Minor 5-mosstep	m5ms	3L + 2s	327.3 ¢ to 400.0 ¢
	Major 5-mosstep	M5ms	4L + s	400.0 ¢ to 436.4 ¢
6-mosstep	Minor 6-mosstep	m6ms	4L + 2s	436.4 ¢ to 480.0 ¢
	Major 6-mosstep	M6ms	5L + s	480.0 ¢ to 545.5 ¢
7-mosstep	Minor 7-mosstep	m7ms	5L + 2s	545.5 ¢ to 560.0 ¢
	Major 7-mosstep	M7ms	6L + s	560.0 ¢ to 654.5 ¢
8-mosstep	Minor 8-mosstep	m8ms	5L + 3s	545.5 ¢ to 640.0 ¢
	Major 8-mosstep	M8ms	6L + 2s	640.0 ¢ to 654.5 ¢
9-mosstep	Minor 9-mosstep	m9ms	6L + 3s	654.5 ¢ to 720.0 ¢
	Major 9-mosstep	M9ms	7L + 2s	720.0 ¢ to 763.6 ¢
10-mosstep	Minor 10-mosstep	m10ms	7L + 3s	763.6 ¢ to 800.0 ¢
	Major 10-mosstep	M10ms	8L + 2s	800.0 ¢ to 872.7 ¢
11-mosstep	Perfect 11-mosstep	P11ms	8L + 3s	872.7 ¢ to 880.0 ¢
	Augmented 11-mosstep	A11ms	9L + 2s	880.0 ¢ to 981.8 ¢
12-mosstep	Minor 12-mosstep	m12ms	8L + 4s	872.7 ¢ to 960.0 ¢
	Major 12-mosstep	M12ms	9L + 3s	960.0 ¢ to 981.8 ¢
13-mosstep	Minor 13-mosstep	m13ms	9L + 4s	981.8 ¢ to 1040.0 ¢
	Major 13-mosstep	M13ms	10L + 3s	1040.0 ¢ to 1090.9 ¢
14-mosstep	Minor 14-mosstep	m14ms	10L + 4s	1090.9 ¢ to 1120.0 ¢
	Major 14-mosstep	M14ms	11L + 3s	1120.0 ¢ to 1200.0 ¢
15-mosstep	Perfect 15-mosstep	P15ms	11L + 4s	1200.0 ¢

Scale tree

Scale tree and tuning spectrum of 11L 4s

Generator(edo)						Cents		Step ratio		Comments
						Bright	Dark	L:s	Hardness
4\15						320.000	880.000	1:1	1.000	Equalized 11L 4s
					23\86	320.930	879.070	6:5	1.200
				19\71		321.127	878.873	5:4	1.250
					34\127	321.260	878.740	9:7	1.286
			15\56			321.429	878.571	4:3	1.333	Supersoft 11L 4s
					41\153	321.569	878.431	11:8	1.375
				26\97		321.649	878.351	7:5	1.400
					37\138	321.739	878.261	10:7	1.429	Superkleismic
		11\41				321.951	878.049	3:2	1.500	Soft 11L 4s
					40\149	322.148	877.852	11:7	1.571
				29\108		322.222	877.778	8:5	1.600
					47\175	322.286	877.714	13:8	1.625	Golden superklesimic
			18\67			322.388	877.612	5:3	1.667	Semisoft 11L 4s
					43\160	322.500	877.500	12:7	1.714
				25\93		322.581	877.419	7:4	1.750
					32\119	322.689	877.311	9:5	1.800	Senator
	7\26					323.077	876.923	2:1	2.000	Basic 11L 4s Scales with tunings softer than this are proper
					31\115	323.478	876.522	9:4	2.250	Orgone
				24\89		323.596	876.404	7:3	2.333
					41\152	323.684	876.316	12:5	2.400
			17\63			323.810	876.190	5:2	2.500	Semihard 11L 4s Hyperkleismic
					44\163	323.926	876.074	13:5	2.600
				27\100		324.000	876.000	8:3	2.667
					37\137	324.088	875.912	11:4	2.750
		10\37				324.324	875.676	3:1	3.000	Hard 11L 4s
					33\122	324.590	875.410	10:3	3.333
				23\85		324.706	875.294	7:2	3.500
					36\133	324.812	875.188	11:3	3.667
			13\48			325.000	875.000	4:1	4.000	Superhard 11L 4s
					29\107	325.234	874.766	9:2	4.500
				16\59		325.424	874.576	5:1	5.000	Oregon
					19\70	325.714	874.286	6:1	6.000	Ork/Orca
3\11						327.273	872.727	1:0	→ ∞	Collapsed 11L 4s