1L 10s

Todo: review
Adopt scale tree template, review entries

	↑1L 9s	2L 9s↗
	1L 10s	2L 10s→
	↓1L 11s	2L 11s↘

┌╥┬┬┬┬┬┬┬┬┬┬┐ │║│││││││││││ │││││││││││││ └┴┴┴┴┴┴┴┴┴┴┴┘
Scale structure
Step pattern	Lssssssssss ssssssssssL
Equave	2/1 (1200.0¢)
Period	2/1 (1200.0¢)
Step size
Large	1\11 to 1\1 (109.1¢ to 1200.0¢)
Small	0\1 to 1\11 (0.0¢ to 109.1¢)
Generator size
Bright	10\11 to 1\1 (1090.9¢ to 1200.0¢)
Dark	0\1 to 1\11 (0.0¢ to 109.1¢)
TAMNAMS information
Descends from	1L 9s (antisinatonic)
Related MOS scales
Parent	1L 9s
Sister	10L 1s
Daughters	11L 1s 1L 11s
Equal tunings
Equalized (L:s = 1:1)	10\11 (1090.9¢)
Supersoft (L:s = 4:3)	31\34 (1094.1¢)
Soft (L:s = 3:2)	21\23 (1095.7¢)
Semisoft (L:s = 5:3)	32\35 (1097.1¢)
Basic (L:s = 2:1)	11\12 (1100.0¢)
Semihard (L:s = 5:2)	23\25 (1104.0¢)
Hard (L:s = 3:1)	12\13 (1107.7¢)
Superhard (L:s = 4:1)	13\14 (1114.3¢)
Collapsed (L:s = 1:0)	1\1 (1200.0¢)

1L 10s is a 2/1-equivalent (octave-equivalent) moment of symmetry scale containing 1 large step and 10 small steps, repeating every octave. 1L 10s is a child scale of 1L 9s, expanding it by 1 tones. Generators that produce this scale range from 1090.9¢ to 1200¢, or from 0¢ to 109.1¢.

This MOS achieves its simplest harmonic entropy minimum where two generators equal 9/8. The temperament which occupies this harmonic entropy minimum is called Ripple, but there are several lower (and more complex) harmonic entropy minima of note including (in descending order of generator height): Passion (6/5 = +3 generators), Octacot (3/2 = +8 generators), Nautilus (3/2 = -6 generators) and Valentine (7/4 = -3 generators).

Modes

• 10|0 Lssssssssss
• 9|1 sLsssssssss
• 8|2 ssLssssssss
• 7|3 sssLsssssss
• 6|4 ssssLssssss
• 5|5 sssssLsssss
• 4|6 ssssssLssss
• 3|7 sssssssLsss
• 2|8 ssssssssLss
• 1|9 sssssssssLs
• 0|10 ssssssssssL

Scale tree

Generator ranges:

• Chroma-positive generator: 1090.9091 cents (10\11) to 1200 cents (1\1)
• Chroma-negative generator: 0 cents (0\1) to 109.0909 cents (1\11)

Small step (chroma-negative generator)						Cents	L	s	L/s	Comments
1\11						109.091	1	1	1.000
					5\56	107.143	6	5	1.200
				4\45		106.667	5	4	1.250
					7\79	106.329	9	7	1.286
			3\34			105.882	4	3	1.333
					8\91	105.495	11	8	1.375
				5\57		105.263	7	5	1.400
					7\80	105.000	10	7	1.429	Septendesemi
		2\23				104.348	3	2	1.500
					7\81	103.704	11	7	1.571
				5\58		103.448	8	5	1.600
					8\93	103.226	13	8	1.625	Golden ripple (103.2877¢)
			3\35			102.857	5	3	1.667
					7\82	102.439	12	7	1.714
				4\47		102.128	7	4	1.750
					5\59	101.695	9	5	1.800
	1\12					100.000	2	1	2.000	Basic 1L 10s (small steps larger than this are proper)
					4\49	97.959	9	4	2.250
				3\37		97.297	7	3	2.333	Passion
					5\62	96.774	12	5	2.400
			2\25			96.000	5	2	2.500
					5\63	95.238	13	5	2.600	Unnamed golden tuning (95.102¢)
				3\38		94.737	8	3	2.667
					4\51	94.118	11	4	2.750
		1\13				92.308	3	1	3.000
					3\40	90.000	10	3	3.333
				2\27		88.889	7	2	3.500
					3\41	87.805	11	3	3.667	Octacot
			1\14			85.714	4	1	4.000
					2\29	82.759	9	2	4.500
				1\15		80.000	5	1	5.000	Valentine
					1\16	75.000	6	1	6.000
0\1						0.000	1	0	→ inf