9L 2s

9L 2s is a 2/1-equivalent (octave-equivalent) moment of symmetry scale containing 9 large steps and 2 small steps, repeating every octave. 9L 2s is a child scale of 2L 7s, expanding it by 2 tones. Generators that produce this scale range from 654.5 ¢ to 666.7 ¢, or from 533.3 ¢ to 545.5 ¢.

↖ 8L 1s	↑ 9L 1s	10L 1s ↗
← 8L 2s	9L 2s	10L 2s →
↙ 8L 3s	↓ 9L 3s	10L 3s ↘

Scale structure
Step pattern	LLLLLsLLLLs sLLLLsLLLLL
Equave	2/1 (1200.0 ¢)
Period	2/1 (1200.0 ¢)
Generator size
Bright	6\11 to 5\9 (654.5 ¢ to 666.7 ¢)
Dark	4\9 to 5\11 (533.3 ¢ to 545.5 ¢)
TAMNAMS information
Related to	2L 7s (balzano)
With tunings	1:1 to 2:1 (soft-of-basic)
Related MOS scales
Parent	2L 7s
Sister	2L 9s
Daughters	11L 9s, 9L 11s
Neutralized	7L 4s
2-Flought	20L 2s, 9L 13s
Equal tunings
Equalized (L:s = 1:1)	6\11 (654.5 ¢)
Supersoft (L:s = 4:3)	23\42 (657.1 ¢)
Soft (L:s = 3:2)	17\31 (658.1 ¢)
Semisoft (L:s = 5:3)	28\51 (658.8 ¢)
Basic (L:s = 2:1)	11\20 (660.0 ¢)
Semihard (L:s = 5:2)	27\49 (661.2 ¢)
Hard (L:s = 3:1)	16\29 (662.1 ¢)
Superhard (L:s = 4:1)	21\38 (663.2 ¢)
Collapsed (L:s = 1:0)	5\9 (666.7 ¢)
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It represents temperaments like Avila (narrow generator) and Casablanca (wide). CompactStar has suggested the names ultradiatonic and superarmotonic by analogy to 7L 2s's name of superdiatonic, while Ganaram Inukshuk has suggested villatonic as a reference to the aforementioned Avila and Casablanca.

Modes

Modes of 9L 2s

UDP	Cyclic order	Step pattern
10|0	1	LLLLLsLLLLs
9|1	7	LLLLsLLLLLs
8|2	2	LLLLsLLLLsL
7|3	8	LLLsLLLLLsL
6|4	3	LLLsLLLLsLL
5|5	9	LLsLLLLLsLL
4|6	4	LLsLLLLsLLL
3|7	10	LsLLLLLsLLL
2|8	5	LsLLLLsLLLL
1|9	11	sLLLLLsLLLL
0|10	6	sLLLLsLLLLL

Proposed Names

• 10|0 LLLLLsLLLLs "Ultralydian"
• 9|1 LLLLsLLLLLs "Ultraionian"
• 8|2 LLLLsLLLLsL "Ultramixolydian"
• 7|3 LLLsLLLLLsL "Ultracorinthian"
• 6|4 LLLsLLLLsLL "Ultraolympian"
• 5|5 LLsLLLLLsLL "Ultralycian"
• 4|6 LLsLLLLsLLL "Ultrapisidian"
• 3|7 LsLLLLLsLLL "Ultradorian"
• 2|8 LsLLLLsLLLL "Ultraaeolian"
• 1|9 sLLLLLsLLLL "Ultraphrygian"
• 0|10 sLLLLsLLLLL "Ultralocrian"

Mode degrees

Scale degrees of the modes of 9L 2s

UDP	Cyclic order	Step pattern	Scale degree (mosdegree)
			0	1	2	3	4	5	6	7	8	9	10	11
10|0	1	LLLLLsLLLLs	Perf.	Maj.	Maj.	Maj.	Maj.	Aug.	Perf.	Maj.	Maj.	Maj.	Maj.	Perf.
9|1	7	LLLLsLLLLLs	Perf.	Maj.	Maj.	Maj.	Maj.	Perf.	Perf.	Maj.	Maj.	Maj.	Maj.	Perf.
8|2	2	LLLLsLLLLsL	Perf.	Maj.	Maj.	Maj.	Maj.	Perf.	Perf.	Maj.	Maj.	Maj.	Min.	Perf.
7|3	8	LLLsLLLLLsL	Perf.	Maj.	Maj.	Maj.	Min.	Perf.	Perf.	Maj.	Maj.	Maj.	Min.	Perf.
6|4	3	LLLsLLLLsLL	Perf.	Maj.	Maj.	Maj.	Min.	Perf.	Perf.	Maj.	Maj.	Min.	Min.	Perf.
5|5	9	LLsLLLLLsLL	Perf.	Maj.	Maj.	Min.	Min.	Perf.	Perf.	Maj.	Maj.	Min.	Min.	Perf.
4|6	4	LLsLLLLsLLL	Perf.	Maj.	Maj.	Min.	Min.	Perf.	Perf.	Maj.	Min.	Min.	Min.	Perf.
3|7	10	LsLLLLLsLLL	Perf.	Maj.	Min.	Min.	Min.	Perf.	Perf.	Maj.	Min.	Min.	Min.	Perf.
2|8	5	LsLLLLsLLLL	Perf.	Maj.	Min.	Min.	Min.	Perf.	Perf.	Min.	Min.	Min.	Min.	Perf.
1|9	11	sLLLLLsLLLL	Perf.	Min.	Min.	Min.	Min.	Perf.	Perf.	Min.	Min.	Min.	Min.	Perf.
0|10	6	sLLLLsLLLLL	Perf.	Min.	Min.	Min.	Min.	Perf.	Dim.	Min.	Min.	Min.	Min.	Perf.

Intervals

Intervals of 9L 2s

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 109.1 ¢
	Major 1-mosstep	M1ms	L	109.1 ¢ to 133.3 ¢
2-mosstep	Minor 2-mosstep	m2ms	L + s	133.3 ¢ to 218.2 ¢
	Major 2-mosstep	M2ms	2L	218.2 ¢ to 266.7 ¢
3-mosstep	Minor 3-mosstep	m3ms	2L + s	266.7 ¢ to 327.3 ¢
	Major 3-mosstep	M3ms	3L	327.3 ¢ to 400.0 ¢
4-mosstep	Minor 4-mosstep	m4ms	3L + s	400.0 ¢ to 436.4 ¢
	Major 4-mosstep	M4ms	4L	436.4 ¢ to 533.3 ¢
5-mosstep	Perfect 5-mosstep	P5ms	4L + s	533.3 ¢ to 545.5 ¢
	Augmented 5-mosstep	A5ms	5L	545.5 ¢ to 666.7 ¢
6-mosstep	Diminished 6-mosstep	d6ms	4L + 2s	533.3 ¢ to 654.5 ¢
	Perfect 6-mosstep	P6ms	5L + s	654.5 ¢ to 666.7 ¢
7-mosstep	Minor 7-mosstep	m7ms	5L + 2s	666.7 ¢ to 763.6 ¢
	Major 7-mosstep	M7ms	6L + s	763.6 ¢ to 800.0 ¢
8-mosstep	Minor 8-mosstep	m8ms	6L + 2s	800.0 ¢ to 872.7 ¢
	Major 8-mosstep	M8ms	7L + s	872.7 ¢ to 933.3 ¢
9-mosstep	Minor 9-mosstep	m9ms	7L + 2s	933.3 ¢ to 981.8 ¢
	Major 9-mosstep	M9ms	8L + s	981.8 ¢ to 1066.7 ¢
10-mosstep	Minor 10-mosstep	m10ms	8L + 2s	1066.7 ¢ to 1090.9 ¢
	Major 10-mosstep	M10ms	9L + s	1090.9 ¢ to 1200.0 ¢
11-mosstep	Perfect 11-mosstep	P11ms	9L + 2s	1200.0 ¢

Scale tree

Template: Scale tree is deprecated. Please use Template: MOS tuning spectrum instead. Details: Use of a single Comments parameter has become unmaintainable. Existing scale trees should be migrated to the new template, where comments are entered using a step ratio p/q as a parameter: {{MOS tuning spectrum | 3/2 = Example comment | 4/3 = Another example comment }} The parameters tuning and depth have been replaced with Scale Signature and Depth, respectively.

Scale tree and tuning spectrum of 9L 2s

Generator(edo)						Cents		Step ratio		Comments
						Bright	Dark	L:s	Hardness
6\11						654.545	545.455	1:1	1.000	Equalized 9L 2s
					35\64	656.250	543.750	6:5	1.200
				29\53		656.604	543.396	5:4	1.250
					52\95	656.842	543.158	9:7	1.286
			23\42			657.143	542.857	4:3	1.333	Supersoft 9L 2s
					63\115	657.391	542.609	11:8	1.375
				40\73		657.534	542.466	7:5	1.400
					57\104	657.692	542.308	10:7	1.429
		17\31				658.065	541.935	3:2	1.500	Soft 9L 2s
					62\113	658.407	541.593	11:7	1.571
				45\82		658.537	541.463	8:5	1.600
					73\133	658.647	541.353	13:8	1.625
			28\51			658.824	541.176	5:3	1.667	Semisoft 9L 2s
					67\122	659.016	540.984	12:7	1.714
				39\71		659.155	540.845	7:4	1.750
					50\91	659.341	540.659	9:5	1.800
	11\20					660.000	540.000	2:1	2.000	Basic 9L 2s Scales with tunings softer than this are proper
					49\89	660.674	539.326	9:4	2.250
				38\69		660.870	539.130	7:3	2.333
					65\118	661.017	538.983	12:5	2.400
			27\49			661.224	538.776	5:2	2.500	Semihard 9L 2s
					70\127	661.417	538.583	13:5	2.600
				43\78		661.538	538.462	8:3	2.667
					59\107	661.682	538.318	11:4	2.750
		16\29				662.069	537.931	3:1	3.000	Hard 9L 2s
					53\96	662.500	537.500	10:3	3.333
				37\67		662.687	537.313	7:2	3.500
					58\105	662.857	537.143	11:3	3.667
			21\38			663.158	536.842	4:1	4.000	Superhard 9L 2s
					47\85	663.529	536.471	9:2	4.500
				26\47		663.830	536.170	5:1	5.000
					31\56	664.286	535.714	6:1	6.000
5\9						666.667	533.333	1:0	→ ∞	Collapsed 9L 2s