9L 8s

↖ 8L 7s	↑ 9L 7s	10L 7s ↗
← 8L 8s	9L 8s	10L 8s →
↙ 8L 9s	↓ 9L 9s	10L 9s ↘

┌╥╥┬╥┬╥┬╥┬╥┬╥┬╥┬╥┬┐ │║║│║│║│║│║│║│║│║││ │││││││││││││││││││ └┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┘
Scale structure
Step pattern	LLsLsLsLsLsLsLsLs sLsLsLsLsLsLsLsLL
Equave	2/1 (1200.0¢)
Period	2/1 (1200.0¢)
Generator size
Bright	15\17 to 8\9 (1058.8¢ to 1066.7¢)
Dark	1\9 to 2\17 (133.3¢ to 141.2¢)
TAMNAMS information
Descends from	8L 1s
Ancestor's step ratio range	1:1 to 2:1 (soft-of-basic)
Related MOS scales
Parent	8L 1s
Sister	8L 9s
Daughters	17L 9s, 9L 17s
Neutralized	1L 16s
2-Flought	26L 8s, 9L 25s
Equal tunings
Equalized (L:s = 1:1)	15\17 (1058.8¢)
Supersoft (L:s = 4:3)	53\60 (1060.0¢)
Soft (L:s = 3:2)	38\43 (1060.5¢)
Semisoft (L:s = 5:3)	61\69 (1060.9¢)
Basic (L:s = 2:1)	23\26 (1061.5¢)
Semihard (L:s = 5:2)	54\61 (1062.3¢)
Hard (L:s = 3:1)	31\35 (1062.9¢)
Superhard (L:s = 4:1)	39\44 (1063.6¢)
Collapsed (L:s = 1:0)	8\9 (1066.7¢)

9L 8s is a 2/1-equivalent (octave-equivalent) moment of symmetry scale containing 9 large steps and 8 small steps, repeating every octave. 9L 8s is a child scale of 8L 1s, expanding it by 8 tones. Generators that produce this scale range from 1058.8¢ to 1066.7¢, or from 133.3¢ to 141.2¢.

Modes

Modes of 9L 8s

UDP	Cyclic order	Step pattern
16|0	1	LLsLsLsLsLsLsLsLs
15|1	16	LsLLsLsLsLsLsLsLs
14|2	14	LsLsLLsLsLsLsLsLs
13|3	12	LsLsLsLLsLsLsLsLs
12|4	10	LsLsLsLsLLsLsLsLs
11|5	8	LsLsLsLsLsLLsLsLs
10|6	6	LsLsLsLsLsLsLLsLs
9|7	4	LsLsLsLsLsLsLsLLs
8|8	2	LsLsLsLsLsLsLsLsL
7|9	17	sLLsLsLsLsLsLsLsL
6|10	15	sLsLLsLsLsLsLsLsL
5|11	13	sLsLsLLsLsLsLsLsL
4|12	11	sLsLsLsLLsLsLsLsL
3|13	9	sLsLsLsLsLLsLsLsL
2|14	7	sLsLsLsLsLsLLsLsL
1|15	5	sLsLsLsLsLsLsLLsL
0|16	3	sLsLsLsLsLsLsLsLL

Intervals

Intervals of 9L 8s

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 70.6¢
	Major 1-mosstep	M1ms	L	70.6¢ to 133.3¢
2-mosstep	Perfect 2-mosstep	P2ms	L + s	133.3¢ to 141.2¢
	Augmented 2-mosstep	A2ms	2L	141.2¢ to 266.7¢
3-mosstep	Minor 3-mosstep	m3ms	L + 2s	133.3¢ to 211.8¢
	Major 3-mosstep	M3ms	2L + s	211.8¢ to 266.7¢
4-mosstep	Minor 4-mosstep	m4ms	2L + 2s	266.7¢ to 282.4¢
	Major 4-mosstep	M4ms	3L + s	282.4¢ to 400.0¢
5-mosstep	Minor 5-mosstep	m5ms	2L + 3s	266.7¢ to 352.9¢
	Major 5-mosstep	M5ms	3L + 2s	352.9¢ to 400.0¢
6-mosstep	Minor 6-mosstep	m6ms	3L + 3s	400.0¢ to 423.5¢
	Major 6-mosstep	M6ms	4L + 2s	423.5¢ to 533.3¢
7-mosstep	Minor 7-mosstep	m7ms	3L + 4s	400.0¢ to 494.1¢
	Major 7-mosstep	M7ms	4L + 3s	494.1¢ to 533.3¢
8-mosstep	Minor 8-mosstep	m8ms	4L + 4s	533.3¢ to 564.7¢
	Major 8-mosstep	M8ms	5L + 3s	564.7¢ to 666.7¢
9-mosstep	Minor 9-mosstep	m9ms	4L + 5s	533.3¢ to 635.3¢
	Major 9-mosstep	M9ms	5L + 4s	635.3¢ to 666.7¢
10-mosstep	Minor 10-mosstep	m10ms	5L + 5s	666.7¢ to 705.9¢
	Major 10-mosstep	M10ms	6L + 4s	705.9¢ to 800.0¢
11-mosstep	Minor 11-mosstep	m11ms	5L + 6s	666.7¢ to 776.5¢
	Major 11-mosstep	M11ms	6L + 5s	776.5¢ to 800.0¢
12-mosstep	Minor 12-mosstep	m12ms	6L + 6s	800.0¢ to 847.1¢
	Major 12-mosstep	M12ms	7L + 5s	847.1¢ to 933.3¢
13-mosstep	Minor 13-mosstep	m13ms	6L + 7s	800.0¢ to 917.6¢
	Major 13-mosstep	M13ms	7L + 6s	917.6¢ to 933.3¢
14-mosstep	Minor 14-mosstep	m14ms	7L + 7s	933.3¢ to 988.2¢
	Major 14-mosstep	M14ms	8L + 6s	988.2¢ to 1066.7¢
15-mosstep	Diminished 15-mosstep	d15ms	7L + 8s	933.3¢ to 1058.8¢
	Perfect 15-mosstep	P15ms	8L + 7s	1058.8¢ to 1066.7¢
16-mosstep	Minor 16-mosstep	m16ms	8L + 8s	1066.7¢ to 1129.4¢
	Major 16-mosstep	M16ms	9L + 7s	1129.4¢ to 1200.0¢
17-mosstep	Perfect 17-mosstep	P17ms	9L + 8s	1200.0¢

Tuning spectrum

Todo: review Review entries from past page revision and enter them into the scale tree.

Scale Tree and Tuning Spectrum of 9L 8s

Generator(edo)						Cents		Step ratio		Comments
						Bright	Dark	L:s	Hardness
15\17						1058.824	141.176	1:1	1.000	Equalized 9L 8s
					83\94	1059.574	140.426	6:5	1.200
				68\77		1059.740	140.260	5:4	1.250
					121\137	1059.854	140.146	9:7	1.286
			53\60			1060.000	140.000	4:3	1.333	Supersoft 9L 8s
					144\163	1060.123	139.877	11:8	1.375
				91\103		1060.194	139.806	7:5	1.400
					129\146	1060.274	139.726	10:7	1.429
		38\43				1060.465	139.535	3:2	1.500	Soft 9L 8s
					137\155	1060.645	139.355	11:7	1.571
				99\112		1060.714	139.286	8:5	1.600
					160\181	1060.773	139.227	13:8	1.625
			61\69			1060.870	139.130	5:3	1.667	Semisoft 9L 8s
					145\164	1060.976	139.024	12:7	1.714
				84\95		1061.053	138.947	7:4	1.750
					107\121	1061.157	138.843	9:5	1.800
	23\26					1061.538	138.462	2:1	2.000	Basic 9L 8s Scales with tunings softer than this are proper
					100\113	1061.947	138.053	9:4	2.250
				77\87		1062.069	137.931	7:3	2.333
					131\148	1062.162	137.838	12:5	2.400
			54\61			1062.295	137.705	5:2	2.500	Semihard 9L 8s
					139\157	1062.420	137.580	13:5	2.600
				85\96		1062.500	137.500	8:3	2.667
					116\131	1062.595	137.405	11:4	2.750
		31\35				1062.857	137.143	3:1	3.000	Hard 9L 8s
					101\114	1063.158	136.842	10:3	3.333
				70\79		1063.291	136.709	7:2	3.500
					109\123	1063.415	136.585	11:3	3.667
			39\44			1063.636	136.364	4:1	4.000	Superhard 9L 8s
					86\97	1063.918	136.082	9:2	4.500
				47\53		1064.151	135.849	5:1	5.000
					55\62	1064.516	135.484	6:1	6.000
8\9						1066.667	133.333	1:0	→ ∞	Collapsed 9L 8s

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