9L 1s

9L 1s, named sinatonic in TAMNAMS, is a 2/1-equivalent (octave-equivalent) moment of symmetry scale containing 9 large steps and 1 small step, repeating every octave. Generators that produce this scale range from 120 ¢ to 133.3 ¢, or from 1066.7 ¢ to 1080 ¢. Scales of this form are always proper because there is only one small step. It appears as the albitonic scale in temperaments such as Negri and Twothirdtonic.

← 8L 1s	9L 1s	10L 1s →
↙ 8L 2s	↓ 9L 2s	10L 2s ↘

Scale structure
Step pattern	LLLLLLLLLs sLLLLLLLLL
Equave	2/1 (1200.0 ¢)
Period	2/1 (1200.0 ¢)
Generator size
Bright	1\10 to 1\9 (120.0 ¢ to 133.3 ¢)
Dark	8\9 to 9\10 (1066.7 ¢ to 1080.0 ¢)
TAMNAMS information
Name	sinatonic
Prefix	sina-
Abbrev.	si
Related MOS scales
Parent	1L 8s
Sister	1L 9s
Daughters	10L 9s, 9L 10s
Neutralized	8L 2s
2-Flought	19L 1s, 9L 11s
Equal tunings
Equalized (L:s = 1:1)	1\10 (120.0 ¢)
Supersoft (L:s = 4:3)	4\39 (123.1 ¢)
Soft (L:s = 3:2)	3\29 (124.1 ¢)
Semisoft (L:s = 5:3)	5\48 (125.0 ¢)
Basic (L:s = 2:1)	2\19 (126.3 ¢)
Semihard (L:s = 5:2)	5\47 (127.7 ¢)
Hard (L:s = 3:1)	3\28 (128.6 ¢)
Superhard (L:s = 4:1)	4\37 (129.7 ¢)
Collapsed (L:s = 1:0)	1\9 (133.3 ¢)
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Names

The TAMNAMS system calls this scale pattern sinatonic after sinaic, a proposed interval category name for 14/13-like intervals that generate the scale. Graham Breed's MOS naming calls this the "Grumpy" decatonic scale.

Scale properties

This article uses TAMNAMS conventions for the names of this scale's intervals and scale degrees. The use of 1-indexed ordinal names is reserved for interval regions.

Intervals

Intervals of 9L 1s

Intervals			Steps subtended	Range in cents
Generic	Specific	Abbrev.
0-sinastep	Perfect 0-sinastep	P0sis	0	0.0 ¢
1-sinastep	Diminished 1-sinastep	d1sis	s	0.0 ¢ to 120.0 ¢
	Perfect 1-sinastep	P1sis	L	120.0 ¢ to 133.3 ¢
2-sinastep	Minor 2-sinastep	m2sis	L + s	133.3 ¢ to 240.0 ¢
	Major 2-sinastep	M2sis	2L	240.0 ¢ to 266.7 ¢
3-sinastep	Minor 3-sinastep	m3sis	2L + s	266.7 ¢ to 360.0 ¢
	Major 3-sinastep	M3sis	3L	360.0 ¢ to 400.0 ¢
4-sinastep	Minor 4-sinastep	m4sis	3L + s	400.0 ¢ to 480.0 ¢
	Major 4-sinastep	M4sis	4L	480.0 ¢ to 533.3 ¢
5-sinastep	Minor 5-sinastep	m5sis	4L + s	533.3 ¢ to 600.0 ¢
	Major 5-sinastep	M5sis	5L	600.0 ¢ to 666.7 ¢
6-sinastep	Minor 6-sinastep	m6sis	5L + s	666.7 ¢ to 720.0 ¢
	Major 6-sinastep	M6sis	6L	720.0 ¢ to 800.0 ¢
7-sinastep	Minor 7-sinastep	m7sis	6L + s	800.0 ¢ to 840.0 ¢
	Major 7-sinastep	M7sis	7L	840.0 ¢ to 933.3 ¢
8-sinastep	Minor 8-sinastep	m8sis	7L + s	933.3 ¢ to 960.0 ¢
	Major 8-sinastep	M8sis	8L	960.0 ¢ to 1066.7 ¢
9-sinastep	Perfect 9-sinastep	P9sis	8L + s	1066.7 ¢ to 1080.0 ¢
	Augmented 9-sinastep	A9sis	9L	1080.0 ¢ to 1200.0 ¢
10-sinastep	Perfect 10-sinastep	P10sis	9L + s	1200.0 ¢

Generator chain

Generator chain of 9L 1s

Bright gens	Scale degree	Abbrev.
18	Augmented 8-sinadegree	A8sid
17	Augmented 7-sinadegree	A7sid
16	Augmented 6-sinadegree	A6sid
15	Augmented 5-sinadegree	A5sid
14	Augmented 4-sinadegree	A4sid
13	Augmented 3-sinadegree	A3sid
12	Augmented 2-sinadegree	A2sid
11	Augmented 1-sinadegree	A1sid
10	Augmented 0-sinadegree	A0sid
9	Augmented 9-sinadegree	A9sid
8	Major 8-sinadegree	M8sid
7	Major 7-sinadegree	M7sid
6	Major 6-sinadegree	M6sid
5	Major 5-sinadegree	M5sid
4	Major 4-sinadegree	M4sid
3	Major 3-sinadegree	M3sid
2	Major 2-sinadegree	M2sid
1	Perfect 1-sinadegree	P1sid
0	Perfect 0-sinadegree Perfect 10-sinadegree	P0sid P10sid
−1	Perfect 9-sinadegree	P9sid
−2	Minor 8-sinadegree	m8sid
−3	Minor 7-sinadegree	m7sid
−4	Minor 6-sinadegree	m6sid
−5	Minor 5-sinadegree	m5sid
−6	Minor 4-sinadegree	m4sid
−7	Minor 3-sinadegree	m3sid
−8	Minor 2-sinadegree	m2sid
−9	Diminished 1-sinadegree	d1sid
−10	Diminished 10-sinadegree	d10sid
−11	Diminished 9-sinadegree	d9sid
−12	Diminished 8-sinadegree	d8sid
−13	Diminished 7-sinadegree	d7sid
−14	Diminished 6-sinadegree	d6sid
−15	Diminished 5-sinadegree	d5sid
−16	Diminished 4-sinadegree	d4sid
−17	Diminished 3-sinadegree	d3sid
−18	Diminished 2-sinadegree	d2sid

Modes

Scale degrees of the modes of 9L 1s

UDP	Cyclic order	Step pattern	Scale degree (sinadegree)
			0	1	2	3	4	5	6	7	8	9	10
9|0	1	LLLLLLLLLs	Perf.	Perf.	Maj.	Maj.	Maj.	Maj.	Maj.	Maj.	Maj.	Aug.	Perf.
8|1	2	LLLLLLLLsL	Perf.	Perf.	Maj.	Maj.	Maj.	Maj.	Maj.	Maj.	Maj.	Perf.	Perf.
7|2	3	LLLLLLLsLL	Perf.	Perf.	Maj.	Maj.	Maj.	Maj.	Maj.	Maj.	Min.	Perf.	Perf.
6|3	4	LLLLLLsLLL	Perf.	Perf.	Maj.	Maj.	Maj.	Maj.	Maj.	Min.	Min.	Perf.	Perf.
5|4	5	LLLLLsLLLL	Perf.	Perf.	Maj.	Maj.	Maj.	Maj.	Min.	Min.	Min.	Perf.	Perf.
4|5	6	LLLLsLLLLL	Perf.	Perf.	Maj.	Maj.	Maj.	Min.	Min.	Min.	Min.	Perf.	Perf.
3|6	7	LLLsLLLLLL	Perf.	Perf.	Maj.	Maj.	Min.	Min.	Min.	Min.	Min.	Perf.	Perf.
2|7	8	LLsLLLLLLL	Perf.	Perf.	Maj.	Min.	Min.	Min.	Min.	Min.	Min.	Perf.	Perf.
1|8	9	LsLLLLLLLL	Perf.	Perf.	Min.	Min.	Min.	Min.	Min.	Min.	Min.	Perf.	Perf.
0|9	10	sLLLLLLLLL	Perf.	Dim.	Min.	Min.	Min.	Min.	Min.	Min.	Min.	Perf.	Perf.

Scale tree

Scale tree and tuning spectrum of 9L 1s

Generator(edo)						Cents		Step ratio		Comments(always proper)
						Bright	Dark	L:s	Hardness
1\10						120.000	1080.000	1:1	1.000	Equalized 9L 1s
					6\59	122.034	1077.966	6:5	1.200
				5\49		122.449	1077.551	5:4	1.250
					9\88	122.727	1077.273	9:7	1.286
			4\39			123.077	1076.923	4:3	1.333	Supersoft 9L 1s
					11\107	123.364	1076.636	11:8	1.375
				7\68		123.529	1076.471	7:5	1.400
					10\97	123.711	1076.289	10:7	1.429
		3\29				124.138	1075.862	3:2	1.500	Soft 9L 1s
					11\106	124.528	1075.472	11:7	1.571
				8\77		124.675	1075.325	8:5	1.600
					13\125	124.800	1075.200	13:8	1.625
			5\48			125.000	1075.000	5:3	1.667	Semisoft 9L 1s
					12\115	125.217	1074.783	12:7	1.714
				7\67		125.373	1074.627	7:4	1.750
					9\86	125.581	1074.419	9:5	1.800
	2\19					126.316	1073.684	2:1	2.000	Basic 9L 1s
					9\85	127.059	1072.941	9:4	2.250
				7\66		127.273	1072.727	7:3	2.333
					12\113	127.434	1072.566	12:5	2.400
			5\47			127.660	1072.340	5:2	2.500	Semihard 9L 1s
					13\122	127.869	1072.131	13:5	2.600
				8\75		128.000	1072.000	8:3	2.667
					11\103	128.155	1071.845	11:4	2.750
		3\28				128.571	1071.429	3:1	3.000	Hard 9L 1s
					10\93	129.032	1070.968	10:3	3.333
				7\65		129.231	1070.769	7:2	3.500
					11\102	129.412	1070.588	11:3	3.667
			4\37			129.730	1070.270	4:1	4.000	Superhard 9L 1s
					9\83	130.120	1069.880	9:2	4.500
				5\46		130.435	1069.565	5:1	5.000
					6\55	130.909	1069.091	6:1	6.000
1\9						133.333	1066.667	1:0	→ ∞	Collapsed 9L 1s

Todo: complete table, add examples, improve synopsis Populate scale tree