4L 17s

↖ 3L 16s	↑ 4L 16s	5L 16s ↗
← 3L 17s	4L 17s	5L 17s →
↙ 3L 18s	↓ 4L 18s	5L 18s ↘

┌╥┬┬┬┬╥┬┬┬┬╥┬┬┬┬╥┬┬┬┬┬┐ │║││││║││││║││││║││││││ │││││││││││││││││││││││ └┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┘
Scale structure
Step pattern	LssssLssssLssssLsssss sssssLssssLssssLssssL
Equave	2/1 (1200.0¢)
Period	2/1 (1200.0¢)
Generator size
Bright	5\21 to 1\4 (285.7¢ to 300.0¢)
Dark	3\4 to 16\21 (900.0¢ to 914.3¢)
TAMNAMS information
Descends from	4L 5s (gramitonic)
Ancestor's step ratio range	4:1 to 1:0 (ultrahard)
Related MOS scales
Parent	4L 13s
Sister	17L 4s
Daughters	21L 4s, 4L 21s
Neutralized	8L 13s
2-Flought	25L 17s, 4L 38s
Equal tunings
Equalized (L:s = 1:1)	5\21 (285.7¢)
Supersoft (L:s = 4:3)	16\67 (286.6¢)
Soft (L:s = 3:2)	11\46 (287.0¢)
Semisoft (L:s = 5:3)	17\71 (287.3¢)
Basic (L:s = 2:1)	6\25 (288.0¢)
Semihard (L:s = 5:2)	13\54 (288.9¢)
Hard (L:s = 3:1)	7\29 (289.7¢)
Superhard (L:s = 4:1)	8\33 (290.9¢)
Collapsed (L:s = 1:0)	1\4 (300.0¢)

4L 17s is a 2/1-equivalent (octave-equivalent) moment of symmetry scale containing 4 large steps and 17 small steps, repeating every octave. 4L 17s is a great-grandchild scale of 4L 5s, expanding it by 12 tones. Generators that produce this scale range from 285.7¢ to 300¢, or from 900¢ to 914.3¢.

Modes

Modes of 4L 17s

UDP	Cyclic order	Step pattern
20|0	1	LssssLssssLssssLsssss
19|1	6	LssssLssssLsssssLssss
18|2	11	LssssLsssssLssssLssss
17|3	16	LsssssLssssLssssLssss
16|4	21	sLssssLssssLssssLssss
15|5	5	sLssssLssssLsssssLsss
14|6	10	sLssssLsssssLssssLsss
13|7	15	sLsssssLssssLssssLsss
12|8	20	ssLssssLssssLssssLsss
11|9	4	ssLssssLssssLsssssLss
10|10	9	ssLssssLsssssLssssLss
9|11	14	ssLsssssLssssLssssLss
8|12	19	sssLssssLssssLssssLss
7|13	3	sssLssssLssssLsssssLs
6|14	8	sssLssssLsssssLssssLs
5|15	13	sssLsssssLssssLssssLs
4|16	18	ssssLssssLssssLssssLs
3|17	2	ssssLssssLssssLsssssL
2|18	7	ssssLssssLsssssLssssL
1|19	12	ssssLsssssLssssLssssL
0|20	17	sssssLssssLssssLssssL

Intervals

Intervals of 4L 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 57.1¢
	Major 1-mosstep	M1ms	L	57.1¢ to 300.0¢
2-mosstep	Minor 2-mosstep	m2ms	2s	0.0¢ to 114.3¢
	Major 2-mosstep	M2ms	L + s	114.3¢ to 300.0¢
3-mosstep	Minor 3-mosstep	m3ms	3s	0.0¢ to 171.4¢
	Major 3-mosstep	M3ms	L + 2s	171.4¢ to 300.0¢
4-mosstep	Minor 4-mosstep	m4ms	4s	0.0¢ to 228.6¢
	Major 4-mosstep	M4ms	L + 3s	228.6¢ to 300.0¢
5-mosstep	Diminished 5-mosstep	d5ms	5s	0.0¢ to 285.7¢
	Perfect 5-mosstep	P5ms	L + 4s	285.7¢ to 300.0¢
6-mosstep	Minor 6-mosstep	m6ms	L + 5s	300.0¢ to 342.9¢
	Major 6-mosstep	M6ms	2L + 4s	342.9¢ to 600.0¢
7-mosstep	Minor 7-mosstep	m7ms	L + 6s	300.0¢ to 400.0¢
	Major 7-mosstep	M7ms	2L + 5s	400.0¢ to 600.0¢
8-mosstep	Minor 8-mosstep	m8ms	L + 7s	300.0¢ to 457.1¢
	Major 8-mosstep	M8ms	2L + 6s	457.1¢ to 600.0¢
9-mosstep	Minor 9-mosstep	m9ms	L + 8s	300.0¢ to 514.3¢
	Major 9-mosstep	M9ms	2L + 7s	514.3¢ to 600.0¢
10-mosstep	Minor 10-mosstep	m10ms	L + 9s	300.0¢ to 571.4¢
	Major 10-mosstep	M10ms	2L + 8s	571.4¢ to 600.0¢
11-mosstep	Minor 11-mosstep	m11ms	2L + 9s	600.0¢ to 628.6¢
	Major 11-mosstep	M11ms	3L + 8s	628.6¢ to 900.0¢
12-mosstep	Minor 12-mosstep	m12ms	2L + 10s	600.0¢ to 685.7¢
	Major 12-mosstep	M12ms	3L + 9s	685.7¢ to 900.0¢
13-mosstep	Minor 13-mosstep	m13ms	2L + 11s	600.0¢ to 742.9¢
	Major 13-mosstep	M13ms	3L + 10s	742.9¢ to 900.0¢
14-mosstep	Minor 14-mosstep	m14ms	2L + 12s	600.0¢ to 800.0¢
	Major 14-mosstep	M14ms	3L + 11s	800.0¢ to 900.0¢
15-mosstep	Minor 15-mosstep	m15ms	2L + 13s	600.0¢ to 857.1¢
	Major 15-mosstep	M15ms	3L + 12s	857.1¢ to 900.0¢
16-mosstep	Perfect 16-mosstep	P16ms	3L + 13s	900.0¢ to 914.3¢
	Augmented 16-mosstep	A16ms	4L + 12s	914.3¢ to 1200.0¢
17-mosstep	Minor 17-mosstep	m17ms	3L + 14s	900.0¢ to 971.4¢
	Major 17-mosstep	M17ms	4L + 13s	971.4¢ to 1200.0¢
18-mosstep	Minor 18-mosstep	m18ms	3L + 15s	900.0¢ to 1028.6¢
	Major 18-mosstep	M18ms	4L + 14s	1028.6¢ to 1200.0¢
19-mosstep	Minor 19-mosstep	m19ms	3L + 16s	900.0¢ to 1085.7¢
	Major 19-mosstep	M19ms	4L + 15s	1085.7¢ to 1200.0¢
20-mosstep	Minor 20-mosstep	m20ms	3L + 17s	900.0¢ to 1142.9¢
	Major 20-mosstep	M20ms	4L + 16s	1142.9¢ to 1200.0¢
21-mosstep	Perfect 21-mosstep	P21ms	4L + 17s	1200.0¢

Scale tree

Scale Tree and Tuning Spectrum of 4L 17s

Generator(edo)						Cents		Step ratio		Comments
						Bright	Dark	L:s	Hardness
5\21						285.714	914.286	1:1	1.000	Equalized 4L 17s
					26\109	286.239	913.761	6:5	1.200
				21\88		286.364	913.636	5:4	1.250
					37\155	286.452	913.548	9:7	1.286
			16\67			286.567	913.433	4:3	1.333	Supersoft 4L 17s
					43\180	286.667	913.333	11:8	1.375
				27\113		286.726	913.274	7:5	1.400
					38\159	286.792	913.208	10:7	1.429
		11\46				286.957	913.043	3:2	1.500	Soft 4L 17s
					39\163	287.117	912.883	11:7	1.571
				28\117		287.179	912.821	8:5	1.600
					45\188	287.234	912.766	13:8	1.625
			17\71			287.324	912.676	5:3	1.667	Semisoft 4L 17s
					40\167	287.425	912.575	12:7	1.714
				23\96		287.500	912.500	7:4	1.750
					29\121	287.603	912.397	9:5	1.800
	6\25					288.000	912.000	2:1	2.000	Basic 4L 17s Scales with tunings softer than this are proper
					25\104	288.462	911.538	9:4	2.250
				19\79		288.608	911.392	7:3	2.333
					32\133	288.722	911.278	12:5	2.400
			13\54			288.889	911.111	5:2	2.500	Semihard 4L 17s
					33\137	289.051	910.949	13:5	2.600
				20\83		289.157	910.843	8:3	2.667
					27\112	289.286	910.714	11:4	2.750
		7\29				289.655	910.345	3:1	3.000	Hard 4L 17s
					22\91	290.110	909.890	10:3	3.333
				15\62		290.323	909.677	7:2	3.500
					23\95	290.526	909.474	11:3	3.667
			8\33			290.909	909.091	4:1	4.000	Superhard 4L 17s
					17\70	291.429	908.571	9:2	4.500
				9\37		291.892	908.108	5:1	5.000
					10\41	292.683	907.317	6:1	6.000
1\4						300.000	900.000	1:0	→ ∞	Collapsed 4L 17s

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