9L 1s

← 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 ¢)

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.

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.

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 ¢

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

Todo: complete table , add examples Populate scale tree