17L 1s

← 16L 1s	17L 1s	18L 1s →
↙ 16L 2s	↓ 17L 2s	18L 2s ↘

┌╥╥╥╥╥╥╥╥╥╥╥╥╥╥╥╥╥┬┐ │║║║║║║║║║║║║║║║║║││ ││││││││││││││││││││ └┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┘
Scale structure
Step pattern	LLLLLLLLLLLLLLLLLs sLLLLLLLLLLLLLLLLL
Equave	2/1 (1200.0¢)
Period	2/1 (1200.0¢)
Generator size
Bright	1\18 to 1\17 (66.7¢ to 70.6¢)
Dark	16\17 to 17\18 (1129.4¢ to 1133.3¢)
TAMNAMS information
Descends from	1L 9s (antisinatonic)
Ancestor's step ratio range	8:1 to 9:1
Related MOS scales
Parent	1L 16s
Sister	1L 17s
Daughters	18L 17s, 17L 18s
Neutralized	16L 2s
2-Flought	35L 1s, 17L 19s
Equal tunings
Equalized (L:s = 1:1)	1\18 (66.7¢)
Supersoft (L:s = 4:3)	4\71 (67.6¢)
Soft (L:s = 3:2)	3\53 (67.9¢)
Semisoft (L:s = 5:3)	5\88 (68.2¢)
Basic (L:s = 2:1)	2\35 (68.6¢)
Semihard (L:s = 5:2)	5\87 (69.0¢)
Hard (L:s = 3:1)	3\52 (69.2¢)
Superhard (L:s = 4:1)	4\69 (69.6¢)
Collapsed (L:s = 1:0)	1\17 (70.6¢)

17L 1s is a 2/1-equivalent (octave-equivalent) moment of symmetry scale containing 17 large steps and 1 small step, repeating every octave. 17L 1s is related to 1L 9s, expanding it by 8 tones. Generators that produce this scale range from 66.7¢ to 70.6¢, or from 1129.4¢ to 1133.3¢. Scales of this form are always proper because there is only one small step.

Modes

Modes of 17L 1s

UDP	Cyclic order	Step pattern
17|0	1	LLLLLLLLLLLLLLLLLs
16|1	2	LLLLLLLLLLLLLLLLsL
15|2	3	LLLLLLLLLLLLLLLsLL
14|3	4	LLLLLLLLLLLLLLsLLL
13|4	5	LLLLLLLLLLLLLsLLLL
12|5	6	LLLLLLLLLLLLsLLLLL
11|6	7	LLLLLLLLLLLsLLLLLL
10|7	8	LLLLLLLLLLsLLLLLLL
9|8	9	LLLLLLLLLsLLLLLLLL
8|9	10	LLLLLLLLsLLLLLLLLL
7|10	11	LLLLLLLsLLLLLLLLLL
6|11	12	LLLLLLsLLLLLLLLLLL
5|12	13	LLLLLsLLLLLLLLLLLL
4|13	14	LLLLsLLLLLLLLLLLLL
3|14	15	LLLsLLLLLLLLLLLLLL
2|15	16	LLsLLLLLLLLLLLLLLL
1|16	17	LsLLLLLLLLLLLLLLLL
0|17	18	sLLLLLLLLLLLLLLLLL

Intervals

Intervals of 17L 1s

Intervals			Steps subtended	Range in cents
Generic	Specific	Abbrev.
0-mosstep	Perfect 0-mosstep	P0ms	0	0.0¢
1-mosstep	Diminished 1-mosstep	d1ms	s	0.0¢ to 66.7¢
	Perfect 1-mosstep	P1ms	L	66.7¢ to 70.6¢
2-mosstep	Minor 2-mosstep	m2ms	L + s	70.6¢ to 133.3¢
	Major 2-mosstep	M2ms	2L	133.3¢ to 141.2¢
3-mosstep	Minor 3-mosstep	m3ms	2L + s	141.2¢ to 200.0¢
	Major 3-mosstep	M3ms	3L	200.0¢ to 211.8¢
4-mosstep	Minor 4-mosstep	m4ms	3L + s	211.8¢ to 266.7¢
	Major 4-mosstep	M4ms	4L	266.7¢ to 282.4¢
5-mosstep	Minor 5-mosstep	m5ms	4L + s	282.4¢ to 333.3¢
	Major 5-mosstep	M5ms	5L	333.3¢ to 352.9¢
6-mosstep	Minor 6-mosstep	m6ms	5L + s	352.9¢ to 400.0¢
	Major 6-mosstep	M6ms	6L	400.0¢ to 423.5¢
7-mosstep	Minor 7-mosstep	m7ms	6L + s	423.5¢ to 466.7¢
	Major 7-mosstep	M7ms	7L	466.7¢ to 494.1¢
8-mosstep	Minor 8-mosstep	m8ms	7L + s	494.1¢ to 533.3¢
	Major 8-mosstep	M8ms	8L	533.3¢ to 564.7¢
9-mosstep	Minor 9-mosstep	m9ms	8L + s	564.7¢ to 600.0¢
	Major 9-mosstep	M9ms	9L	600.0¢ to 635.3¢
10-mosstep	Minor 10-mosstep	m10ms	9L + s	635.3¢ to 666.7¢
	Major 10-mosstep	M10ms	10L	666.7¢ to 705.9¢
11-mosstep	Minor 11-mosstep	m11ms	10L + s	705.9¢ to 733.3¢
	Major 11-mosstep	M11ms	11L	733.3¢ to 776.5¢
12-mosstep	Minor 12-mosstep	m12ms	11L + s	776.5¢ to 800.0¢
	Major 12-mosstep	M12ms	12L	800.0¢ to 847.1¢
13-mosstep	Minor 13-mosstep	m13ms	12L + s	847.1¢ to 866.7¢
	Major 13-mosstep	M13ms	13L	866.7¢ to 917.6¢
14-mosstep	Minor 14-mosstep	m14ms	13L + s	917.6¢ to 933.3¢
	Major 14-mosstep	M14ms	14L	933.3¢ to 988.2¢
15-mosstep	Minor 15-mosstep	m15ms	14L + s	988.2¢ to 1000.0¢
	Major 15-mosstep	M15ms	15L	1000.0¢ to 1058.8¢
16-mosstep	Minor 16-mosstep	m16ms	15L + s	1058.8¢ to 1066.7¢
	Major 16-mosstep	M16ms	16L	1066.7¢ to 1129.4¢
17-mosstep	Perfect 17-mosstep	P17ms	16L + s	1129.4¢ to 1133.3¢
	Augmented 17-mosstep	A17ms	17L	1133.3¢ to 1200.0¢
18-mosstep	Perfect 18-mosstep	P18ms	17L + s	1200.0¢

Scale tree

Scale Tree and Tuning Spectrum of 17L 1s

Generator(edo)						Cents		Step ratio		Comments(always proper)
						Bright	Dark	L:s	Hardness
1\18						66.667	1133.333	1:1	1.000	Equalized 17L 1s
					6\107	67.290	1132.710	6:5	1.200
				5\89		67.416	1132.584	5:4	1.250
					9\160	67.500	1132.500	9:7	1.286
			4\71			67.606	1132.394	4:3	1.333	Supersoft 17L 1s
					11\195	67.692	1132.308	11:8	1.375
				7\124		67.742	1132.258	7:5	1.400
					10\177	67.797	1132.203	10:7	1.429
		3\53				67.925	1132.075	3:2	1.500	Soft 17L 1s
					11\194	68.041	1131.959	11:7	1.571
				8\141		68.085	1131.915	8:5	1.600
					13\229	68.122	1131.878	13:8	1.625
			5\88			68.182	1131.818	5:3	1.667	Semisoft 17L 1s
					12\211	68.246	1131.754	12:7	1.714
				7\123		68.293	1131.707	7:4	1.750
					9\158	68.354	1131.646	9:5	1.800
	2\35					68.571	1131.429	2:1	2.000	Basic 17L 1s
					9\157	68.790	1131.210	9:4	2.250
				7\122		68.852	1131.148	7:3	2.333
					12\209	68.900	1131.100	12:5	2.400
			5\87			68.966	1131.034	5:2	2.500	Semihard 17L 1s
					13\226	69.027	1130.973	13:5	2.600
				8\139		69.065	1130.935	8:3	2.667
					11\191	69.110	1130.890	11:4	2.750
		3\52				69.231	1130.769	3:1	3.000	Hard 17L 1s
					10\173	69.364	1130.636	10:3	3.333
				7\121		69.421	1130.579	7:2	3.500
					11\190	69.474	1130.526	11:3	3.667
			4\69			69.565	1130.435	4:1	4.000	Superhard 17L 1s
					9\155	69.677	1130.323	9:2	4.500
				5\86		69.767	1130.233	5:1	5.000
					6\103	69.903	1130.097	6:1	6.000
1\17						70.588	1129.412	1:0	→ ∞	Collapsed 17L 1s

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