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)
Required step ratio range	4:1 to 1:0 (ultrahard)
Related MOS scales
Parent	5L 12s
Sister	17L 5s
Daughters	22L 5s 5L 22s
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	Rotational 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

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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