5L 17s

↖ 4L 16s	↑ 5L 16s	6L 16s ↗
← 4L 17s	5L 17s	6L 17s →
↙ 4L 18s	↓ 5L 18s	6L 18s ↘

┌╥┬┬┬╥┬┬┬╥┬┬┬┬╥┬┬┬╥┬┬┬┬┐ │║│││║│││║││││║│││║│││││ ││││││││││││││││││││││││ └┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┘
Scale structure
Step pattern	LsssLsssLssssLsssLssss ssssLsssLssssLsssLsssL
Equave	2/1 (1200.0¢)
Period	2/1 (1200.0¢)
Generator size
Bright	13\22 to 3\5 (709.1¢ to 720.0¢)
Dark	2\5 to 9\22 (480.0¢ to 490.9¢)
TAMNAMS information
Descends from	5L 2s (diatonic)
Ancestor's step ratio range	4:1 to 1:0 (ultrahard)
Related MOS scales
Parent	5L 12s
Sister	17L 5s
Daughters	22L 5s, 5L 22s
Neutralized	10L 12s
2-Flought	27L 17s, 5L 39s
Equal tunings
Equalized (L:s = 1:1)	13\22 (709.1¢)
Supersoft (L:s = 4:3)	42\71 (709.9¢)
Soft (L:s = 3:2)	29\49 (710.2¢)
Semisoft (L:s = 5:3)	45\76 (710.5¢)
Basic (L:s = 2:1)	16\27 (711.1¢)
Semihard (L:s = 5:2)	35\59 (711.9¢)
Hard (L:s = 3:1)	19\32 (712.5¢)
Superhard (L:s = 4:1)	22\37 (713.5¢)
Collapsed (L:s = 1:0)	3\5 (720.0¢)

5L 17s is a 2/1-equivalent (octave-equivalent) moment of symmetry scale containing 5 large steps and 17 small steps, repeating every octave. 5L 17s is a great-grandchild scale of 5L 2s, expanding it by 15 tones. Generators that produce this scale range from 709.1¢ to 720¢, or from 480¢ to 490.9¢.

Modes

Modes of 5L 17s

UDP	Cyclic order	Step pattern
21|0	1	LsssLsssLssssLsssLssss
20|1	14	LsssLssssLsssLsssLssss
19|2	5	LsssLssssLsssLssssLsss
18|3	18	LssssLsssLsssLssssLsss
17|4	9	LssssLsssLssssLsssLsss
16|5	22	sLsssLsssLssssLsssLsss
15|6	13	sLsssLssssLsssLsssLsss
14|7	4	sLsssLssssLsssLssssLss
13|8	17	sLssssLsssLsssLssssLss
12|9	8	sLssssLsssLssssLsssLss
11|10	21	ssLsssLsssLssssLsssLss
10|11	12	ssLsssLssssLsssLsssLss
9|12	3	ssLsssLssssLsssLssssLs
8|13	16	ssLssssLsssLsssLssssLs
7|14	7	ssLssssLsssLssssLsssLs
6|15	20	sssLsssLsssLssssLsssLs
5|16	11	sssLsssLssssLsssLsssLs
4|17	2	sssLsssLssssLsssLssssL
3|18	15	sssLssssLsssLsssLssssL
2|19	6	sssLssssLsssLssssLsssL
1|20	19	ssssLsssLsssLssssLsssL
0|21	10	ssssLsssLssssLsssLsssL

Intervals

Intervals of 5L 17s

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 54.5¢
	Major 1-mosstep	M1ms	L	54.5¢ to 240.0¢
2-mosstep	Minor 2-mosstep	m2ms	2s	0.0¢ to 109.1¢
	Major 2-mosstep	M2ms	L + s	109.1¢ to 240.0¢
3-mosstep	Minor 3-mosstep	m3ms	3s	0.0¢ to 163.6¢
	Major 3-mosstep	M3ms	L + 2s	163.6¢ to 240.0¢
4-mosstep	Minor 4-mosstep	m4ms	4s	0.0¢ to 218.2¢
	Major 4-mosstep	M4ms	L + 3s	218.2¢ to 240.0¢
5-mosstep	Minor 5-mosstep	m5ms	L + 4s	240.0¢ to 272.7¢
	Major 5-mosstep	M5ms	2L + 3s	272.7¢ to 480.0¢
6-mosstep	Minor 6-mosstep	m6ms	L + 5s	240.0¢ to 327.3¢
	Major 6-mosstep	M6ms	2L + 4s	327.3¢ to 480.0¢
7-mosstep	Minor 7-mosstep	m7ms	L + 6s	240.0¢ to 381.8¢
	Major 7-mosstep	M7ms	2L + 5s	381.8¢ to 480.0¢
8-mosstep	Minor 8-mosstep	m8ms	L + 7s	240.0¢ to 436.4¢
	Major 8-mosstep	M8ms	2L + 6s	436.4¢ to 480.0¢
9-mosstep	Perfect 9-mosstep	P9ms	2L + 7s	480.0¢ to 490.9¢
	Augmented 9-mosstep	A9ms	3L + 6s	490.9¢ to 720.0¢
10-mosstep	Minor 10-mosstep	m10ms	2L + 8s	480.0¢ to 545.5¢
	Major 10-mosstep	M10ms	3L + 7s	545.5¢ to 720.0¢
11-mosstep	Minor 11-mosstep	m11ms	2L + 9s	480.0¢ to 600.0¢
	Major 11-mosstep	M11ms	3L + 8s	600.0¢ to 720.0¢
12-mosstep	Minor 12-mosstep	m12ms	2L + 10s	480.0¢ to 654.5¢
	Major 12-mosstep	M12ms	3L + 9s	654.5¢ to 720.0¢
13-mosstep	Diminished 13-mosstep	d13ms	2L + 11s	480.0¢ to 709.1¢
	Perfect 13-mosstep	P13ms	3L + 10s	709.1¢ to 720.0¢
14-mosstep	Minor 14-mosstep	m14ms	3L + 11s	720.0¢ to 763.6¢
	Major 14-mosstep	M14ms	4L + 10s	763.6¢ to 960.0¢
15-mosstep	Minor 15-mosstep	m15ms	3L + 12s	720.0¢ to 818.2¢
	Major 15-mosstep	M15ms	4L + 11s	818.2¢ to 960.0¢
16-mosstep	Minor 16-mosstep	m16ms	3L + 13s	720.0¢ to 872.7¢
	Major 16-mosstep	M16ms	4L + 12s	872.7¢ to 960.0¢
17-mosstep	Minor 17-mosstep	m17ms	3L + 14s	720.0¢ to 927.3¢
	Major 17-mosstep	M17ms	4L + 13s	927.3¢ to 960.0¢
18-mosstep	Minor 18-mosstep	m18ms	4L + 14s	960.0¢ to 981.8¢
	Major 18-mosstep	M18ms	5L + 13s	981.8¢ to 1200.0¢
19-mosstep	Minor 19-mosstep	m19ms	4L + 15s	960.0¢ to 1036.4¢
	Major 19-mosstep	M19ms	5L + 14s	1036.4¢ to 1200.0¢
20-mosstep	Minor 20-mosstep	m20ms	4L + 16s	960.0¢ to 1090.9¢
	Major 20-mosstep	M20ms	5L + 15s	1090.9¢ to 1200.0¢
21-mosstep	Minor 21-mosstep	m21ms	4L + 17s	960.0¢ to 1145.5¢
	Major 21-mosstep	M21ms	5L + 16s	1145.5¢ to 1200.0¢
22-mosstep	Perfect 22-mosstep	P22ms	5L + 17s	1200.0¢

Scale tree

Scale Tree and Tuning Spectrum of 5L 17s

Generator(edo)						Cents		Step ratio		Comments
						Bright	Dark	L:s	Hardness
13\22						709.091	490.909	1:1	1.000	Equalized 5L 17s
					68\115	709.565	490.435	6:5	1.200
				55\93		709.677	490.323	5:4	1.250
					97\164	709.756	490.244	9:7	1.286
			42\71			709.859	490.141	4:3	1.333	Supersoft 5L 17s
					113\191	709.948	490.052	11:8	1.375
				71\120		710.000	490.000	7:5	1.400
					100\169	710.059	489.941	10:7	1.429
		29\49				710.204	489.796	3:2	1.500	Soft 5L 17s
					103\174	710.345	489.655	11:7	1.571
				74\125		710.400	489.600	8:5	1.600
					119\201	710.448	489.552	13:8	1.625
			45\76			710.526	489.474	5:3	1.667	Semisoft 5L 17s
					106\179	710.615	489.385	12:7	1.714
				61\103		710.680	489.320	7:4	1.750
					77\130	710.769	489.231	9:5	1.800
	16\27					711.111	488.889	2:1	2.000	Basic 5L 17s Scales with tunings softer than this are proper
					67\113	711.504	488.496	9:4	2.250
				51\86		711.628	488.372	7:3	2.333
					86\145	711.724	488.276	12:5	2.400
			35\59			711.864	488.136	5:2	2.500	Semihard 5L 17s
					89\150	712.000	488.000	13:5	2.600
				54\91		712.088	487.912	8:3	2.667
					73\123	712.195	487.805	11:4	2.750
		19\32				712.500	487.500	3:1	3.000	Hard 5L 17s
					60\101	712.871	487.129	10:3	3.333
				41\69		713.043	486.957	7:2	3.500
					63\106	713.208	486.792	11:3	3.667
			22\37			713.514	486.486	4:1	4.000	Superhard 5L 17s
					47\79	713.924	486.076	9:2	4.500
				25\42		714.286	485.714	5:1	5.000
					28\47	714.894	485.106	6:1	6.000
3\5						720.000	480.000	1:0	→ ∞	Collapsed 5L 17s

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