1L 9s

1L 9s, named antisinatonic in TAMNAMS, is a 2/1-equivalent (octave-equivalent) moment of symmetry scale containing 1 large step and 9 small steps, repeating every octave. Generators that produce this scale range from 1080 ¢ to 1200 ¢, or from 0 ¢ to 120 ¢. This MOS is also called the "Happy" decatonic scale in Graham Breed's naming system. It is the simplest MOS which may be used as a complete version of Miracle temperament, which is also its harmonic entropy minimum.

	↑ 1L 8s	2L 8s ↗
	1L 9s	2L 9s →
	↓ 1L 10s	2L 10s ↘

Scale structure
Step pattern	Lsssssssss sssssssssL
Equave	2/1 (1200.0 ¢)
Period	2/1 (1200.0 ¢)
Generator size
Bright	9\10 to 1\1 (1080.0 ¢ to 1200.0 ¢)
Dark	0\1 to 1\10 (0.0 ¢ to 120.0 ¢)
TAMNAMS information
Name	antisinatonic
Prefix	asina-
Abbrev.	asi
Related MOS scales
Parent	1L 8s
Sister	9L 1s
Daughters	10L 1s, 1L 10s
Neutralized	2L 8s
2-Flought	11L 9s, 1L 19s
Equal tunings
Equalized (L:s = 1:1)	9\10 (1080.0 ¢)
Supersoft (L:s = 4:3)	28\31 (1083.9 ¢)
Soft (L:s = 3:2)	19\21 (1085.7 ¢)
Semisoft (L:s = 5:3)	29\32 (1087.5 ¢)
Basic (L:s = 2:1)	10\11 (1090.9 ¢)
Semihard (L:s = 5:2)	21\23 (1095.7 ¢)
Hard (L:s = 3:1)	11\12 (1100.0 ¢)
Superhard (L:s = 4:1)	12\13 (1107.7 ¢)
Collapsed (L:s = 1:0)	1\1 (1200.0 ¢)
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Modes

• 9|0 Lsssssssss
• 8|1 sLssssssss
• 7|2 ssLsssssss
• 6|3 sssLssssss
• 5|4 ssssLsssss
• 4|5 sssssLssss
• 3|6 ssssssLsss
• 2|7 sssssssLss
• 1|8 ssssssssLs
• 0|9 sssssssssL

Scale tree

Generator ranges:

• Chroma-positive generator: 1080 cents (9\10) to 1200 cents (1\1)
• Chroma-negative generator: 0 cents (0\1) to 120 cents (1\10)

Small step (chroma-negative generator)						Cents	L	s	L/s	Comments
1\10						120.000	1	1	1.000
					5\51	117.647	6	5	1.200
				4\41		117.073	5	4	1.250
					7\72	116.667	9	7	1.286	Miracle
			3\31			116.129	4	3	1.333
					8\83	115.663	11	8	1.375
				5\52		115.385	7	5	1.400
					7\73	115.068	10	7	1.429
		2\21				114.286	3	2	1.500
					7\74	113.514	11	7	1.571
				5\53		113.208	8	5	1.600
					8\85	112.941	13	8	1.625	Golden misneb (113.0153¢)
			3\32			112.500	5	3	1.667
					7\75	112.000	12	7	1.714
				4\43		111.628	7	4	1.750
					5\54	111.111	9	5	1.800
	1\11					109.091	2	1	2.000	Basic 1L 9s (small steps larger than this are proper)
					4\45	106.667	9	4	2.250
				3\34		105.882	7	3	2.333
					5\57	105.263	12	5	2.400
			2\23			104.348	5	2	2.500
					5\58	103.448	13	5	2.600	Golden ripple (103.2877¢)
				3\35		102.857	8	3	2.667
					4\47	102.128	11	4	2.750
		1\12				100.000	3	1	3.000	Ripple
					3\37	97.297	10	3	3.333	Passion
				2\25		96.000	7	2	3.500
					3\38	94.737	11	3	3.667
			1\13			92.308	4	1	4.000
					2\27	88.889	9	2	4.500
				1\14		85.714	5	1	5.000
					1\15	80.000	6	1	6.000	Valentine
0\1						0.000	1	0	→ inf