17L 3s

↖ 16L 2s	↑ 17L 2s	18L 2s ↗
← 16L 3s	17L 3s	18L 3s →
↙ 16L 4s	↓ 17L 4s	18L 4s ↘

┌╥╥╥╥╥╥┬╥╥╥╥╥╥┬╥╥╥╥╥┬┐ │║║║║║║│║║║║║║│║║║║║││ ││││││││││││││││││││││ └┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┘
Scale structure
Step pattern	LLLLLLsLLLLLLsLLLLLs sLLLLLsLLLLLLsLLLLLL
Equave	2/1 (1200.0¢)
Period	2/1 (1200.0¢)
Generator size
Bright	7\20 to 6\17 (420.0¢ to 423.5¢)
Dark	11\17 to 13\20 (776.5¢ to 780.0¢)
TAMNAMS information
Descends from	3L 5s (checkertonic)
Ancestor's step ratio range	4:1 to 5:1
Related MOS scales
Parent	3L 14s
Sister	3L 17s
Daughters	20L 17s, 17L 20s
Neutralized	14L 6s
2-Flought	37L 3s, 17L 23s
Equal tunings
Equalized (L:s = 1:1)	7\20 (420.0¢)
Supersoft (L:s = 4:3)	27\77 (420.8¢)
Soft (L:s = 3:2)	20\57 (421.1¢)
Semisoft (L:s = 5:3)	33\94 (421.3¢)
Basic (L:s = 2:1)	13\37 (421.6¢)
Semihard (L:s = 5:2)	32\91 (422.0¢)
Hard (L:s = 3:1)	19\54 (422.2¢)
Superhard (L:s = 4:1)	25\71 (422.5¢)
Collapsed (L:s = 1:0)	6\17 (423.5¢)

17L 3s is a 2/1-equivalent (octave-equivalent) moment of symmetry scale containing 17 large steps and 3 small steps, repeating every octave. 17L 3s is related to 3L 5s, expanding it by 12 tones. Generators that produce this scale range from 420¢ to 423.5¢, or from 776.5¢ to 780¢.

Modes

Modes of 17L 3s

UDP	Cyclic order	Step pattern
19|0	1	LLLLLLsLLLLLLsLLLLLs
18|1	8	LLLLLLsLLLLLsLLLLLLs
17|2	15	LLLLLsLLLLLLsLLLLLLs
16|3	2	LLLLLsLLLLLLsLLLLLsL
15|4	9	LLLLLsLLLLLsLLLLLLsL
14|5	16	LLLLsLLLLLLsLLLLLLsL
13|6	3	LLLLsLLLLLLsLLLLLsLL
12|7	10	LLLLsLLLLLsLLLLLLsLL
11|8	17	LLLsLLLLLLsLLLLLLsLL
10|9	4	LLLsLLLLLLsLLLLLsLLL
9|10	11	LLLsLLLLLsLLLLLLsLLL
8|11	18	LLsLLLLLLsLLLLLLsLLL
7|12	5	LLsLLLLLLsLLLLLsLLLL
6|13	12	LLsLLLLLsLLLLLLsLLLL
5|14	19	LsLLLLLLsLLLLLLsLLLL
4|15	6	LsLLLLLLsLLLLLsLLLLL
3|16	13	LsLLLLLsLLLLLLsLLLLL
2|17	20	sLLLLLLsLLLLLLsLLLLL
1|18	7	sLLLLLLsLLLLLsLLLLLL
0|19	14	sLLLLLsLLLLLLsLLLLLL

Intervals

Intervals of 17L 3s

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 60.0¢
	Major 1-mosstep	M1ms	L	60.0¢ to 70.6¢
2-mosstep	Minor 2-mosstep	m2ms	L + s	70.6¢ to 120.0¢
	Major 2-mosstep	M2ms	2L	120.0¢ to 141.2¢
3-mosstep	Minor 3-mosstep	m3ms	2L + s	141.2¢ to 180.0¢
	Major 3-mosstep	M3ms	3L	180.0¢ to 211.8¢
4-mosstep	Minor 4-mosstep	m4ms	3L + s	211.8¢ to 240.0¢
	Major 4-mosstep	M4ms	4L	240.0¢ to 282.4¢
5-mosstep	Minor 5-mosstep	m5ms	4L + s	282.4¢ to 300.0¢
	Major 5-mosstep	M5ms	5L	300.0¢ to 352.9¢
6-mosstep	Minor 6-mosstep	m6ms	5L + s	352.9¢ to 360.0¢
	Major 6-mosstep	M6ms	6L	360.0¢ to 423.5¢
7-mosstep	Diminished 7-mosstep	d7ms	5L + 2s	352.9¢ to 420.0¢
	Perfect 7-mosstep	P7ms	6L + s	420.0¢ to 423.5¢
8-mosstep	Minor 8-mosstep	m8ms	6L + 2s	423.5¢ to 480.0¢
	Major 8-mosstep	M8ms	7L + s	480.0¢ to 494.1¢
9-mosstep	Minor 9-mosstep	m9ms	7L + 2s	494.1¢ to 540.0¢
	Major 9-mosstep	M9ms	8L + s	540.0¢ to 564.7¢
10-mosstep	Minor 10-mosstep	m10ms	8L + 2s	564.7¢ to 600.0¢
	Major 10-mosstep	M10ms	9L + s	600.0¢ to 635.3¢
11-mosstep	Minor 11-mosstep	m11ms	9L + 2s	635.3¢ to 660.0¢
	Major 11-mosstep	M11ms	10L + s	660.0¢ to 705.9¢
12-mosstep	Minor 12-mosstep	m12ms	10L + 2s	705.9¢ to 720.0¢
	Major 12-mosstep	M12ms	11L + s	720.0¢ to 776.5¢
13-mosstep	Perfect 13-mosstep	P13ms	11L + 2s	776.5¢ to 780.0¢
	Augmented 13-mosstep	A13ms	12L + s	780.0¢ to 847.1¢
14-mosstep	Minor 14-mosstep	m14ms	11L + 3s	776.5¢ to 840.0¢
	Major 14-mosstep	M14ms	12L + 2s	840.0¢ to 847.1¢
15-mosstep	Minor 15-mosstep	m15ms	12L + 3s	847.1¢ to 900.0¢
	Major 15-mosstep	M15ms	13L + 2s	900.0¢ to 917.6¢
16-mosstep	Minor 16-mosstep	m16ms	13L + 3s	917.6¢ to 960.0¢
	Major 16-mosstep	M16ms	14L + 2s	960.0¢ to 988.2¢
17-mosstep	Minor 17-mosstep	m17ms	14L + 3s	988.2¢ to 1020.0¢
	Major 17-mosstep	M17ms	15L + 2s	1020.0¢ to 1058.8¢
18-mosstep	Minor 18-mosstep	m18ms	15L + 3s	1058.8¢ to 1080.0¢
	Major 18-mosstep	M18ms	16L + 2s	1080.0¢ to 1129.4¢
19-mosstep	Minor 19-mosstep	m19ms	16L + 3s	1129.4¢ to 1140.0¢
	Major 19-mosstep	M19ms	17L + 2s	1140.0¢ to 1200.0¢
20-mosstep	Perfect 20-mosstep	P20ms	17L + 3s	1200.0¢

Scale tree

Scale Tree and Tuning Spectrum of 17L 3s

Generator(edo)						Cents		Step ratio		Comments
						Bright	Dark	L:s	Hardness
7\20						420.000	780.000	1:1	1.000	Equalized 17L 3s
					41\117	420.513	779.487	6:5	1.200
				34\97		420.619	779.381	5:4	1.250
					61\174	420.690	779.310	9:7	1.286
			27\77			420.779	779.221	4:3	1.333	Supersoft 17L 3s
					74\211	420.853	779.147	11:8	1.375
				47\134		420.896	779.104	7:5	1.400
					67\191	420.942	779.058	10:7	1.429
		20\57				421.053	778.947	3:2	1.500	Soft 17L 3s
					73\208	421.154	778.846	11:7	1.571
				53\151		421.192	778.808	8:5	1.600
					86\245	421.224	778.776	13:8	1.625
			33\94			421.277	778.723	5:3	1.667	Semisoft 17L 3s
					79\225	421.333	778.667	12:7	1.714
				46\131		421.374	778.626	7:4	1.750
					59\168	421.429	778.571	9:5	1.800
	13\37					421.622	778.378	2:1	2.000	Basic 17L 3s Scales with tunings softer than this are proper
					58\165	421.818	778.182	9:4	2.250
				45\128		421.875	778.125	7:3	2.333
					77\219	421.918	778.082	12:5	2.400
			32\91			421.978	778.022	5:2	2.500	Semihard 17L 3s
					83\236	422.034	777.966	13:5	2.600
				51\145		422.069	777.931	8:3	2.667
					70\199	422.111	777.889	11:4	2.750
		19\54				422.222	777.778	3:1	3.000	Hard 17L 3s
					63\179	422.346	777.654	10:3	3.333
				44\125		422.400	777.600	7:2	3.500
					69\196	422.449	777.551	11:3	3.667
			25\71			422.535	777.465	4:1	4.000	Superhard 17L 3s
					56\159	422.642	777.358	9:2	4.500
				31\88		422.727	777.273	5:1	5.000
					37\105	422.857	777.143	6:1	6.000
6\17						423.529	776.471	1:0	→ ∞	Collapsed 17L 3s

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