3L 17s

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

Scale structure
Step pattern	LsssssLssssssLssssss ssssssLssssssLsssssL
Equave	2/1 (1200.0 ¢)
Period	2/1 (1200.0 ¢)
Generator size
Bright	13\20 to 2\3 (780.0 ¢ to 800.0 ¢)
Dark	1\3 to 7\20 (400.0 ¢ to 420.0 ¢)
TAMNAMS information
Related to	3L 5s (checkertonic)
With tunings	5:1 to 1:0
Related MOS scales
Parent	3L 14s
Sister	17L 3s
Daughters	20L 3s, 3L 20s
Neutralized	6L 14s
2-Flought	23L 17s, 3L 37s
Equal tunings
Equalized (L:s = 1:1)	13\20 (780.0 ¢)
Supersoft (L:s = 4:3)	41\63 (781.0 ¢)
Soft (L:s = 3:2)	28\43 (781.4 ¢)
Semisoft (L:s = 5:3)	43\66 (781.8 ¢)
Basic (L:s = 2:1)	15\23 (782.6 ¢)
Semihard (L:s = 5:2)	32\49 (783.7 ¢)
Hard (L:s = 3:1)	17\26 (784.6 ¢)
Superhard (L:s = 4:1)	19\29 (786.2 ¢)
Collapsed (L:s = 1:0)	2\3 (800.0 ¢)
View • Talk • Edit

3L 17s is a 2/1-equivalent (octave-equivalent) moment of symmetry scale containing 3 large steps and 17 small steps, repeating every octave. 3L 17s is related to 3L 5s, expanding it by 12 tones. Generators that produce this scale range from 780 ¢ to 800 ¢, or from 400 ¢ to 420 ¢.

This is the MOS which splits its small steps 6-6-5 between its large steps. Its most consonant generator is a 14/11 supermajor third, and its generator in general is a major third of no more than 7\20edo (420 cents).

Modes

Modes of 3L 17s

UDP	Cyclic order	Step pattern
19|0	1	LsssssLssssssLssssss
18|1	14	LssssssLsssssLssssss
17|2	7	LssssssLssssssLsssss
16|3	20	sLsssssLssssssLsssss
15|4	13	sLssssssLsssssLsssss
14|5	6	sLssssssLssssssLssss
13|6	19	ssLsssssLssssssLssss
12|7	12	ssLssssssLsssssLssss
11|8	5	ssLssssssLssssssLsss
10|9	18	sssLsssssLssssssLsss
9|10	11	sssLssssssLsssssLsss
8|11	4	sssLssssssLssssssLss
7|12	17	ssssLsssssLssssssLss
6|13	10	ssssLssssssLsssssLss
5|14	3	ssssLssssssLssssssLs
4|15	16	sssssLsssssLssssssLs
3|16	9	sssssLssssssLsssssLs
2|17	2	sssssLssssssLssssssL
1|18	15	ssssssLsssssLssssssL
0|19	8	ssssssLssssssLsssssL

Intervals

Intervals of 3L 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 60.0 ¢
	Major 1-mosstep	M1ms	L	60.0 ¢ to 400.0 ¢
2-mosstep	Minor 2-mosstep	m2ms	2s	0.0 ¢ to 120.0 ¢
	Major 2-mosstep	M2ms	L + s	120.0 ¢ to 400.0 ¢
3-mosstep	Minor 3-mosstep	m3ms	3s	0.0 ¢ to 180.0 ¢
	Major 3-mosstep	M3ms	L + 2s	180.0 ¢ to 400.0 ¢
4-mosstep	Minor 4-mosstep	m4ms	4s	0.0 ¢ to 240.0 ¢
	Major 4-mosstep	M4ms	L + 3s	240.0 ¢ to 400.0 ¢
5-mosstep	Minor 5-mosstep	m5ms	5s	0.0 ¢ to 300.0 ¢
	Major 5-mosstep	M5ms	L + 4s	300.0 ¢ to 400.0 ¢
6-mosstep	Minor 6-mosstep	m6ms	6s	0.0 ¢ to 360.0 ¢
	Major 6-mosstep	M6ms	L + 5s	360.0 ¢ to 400.0 ¢
7-mosstep	Perfect 7-mosstep	P7ms	L + 6s	400.0 ¢ to 420.0 ¢
	Augmented 7-mosstep	A7ms	2L + 5s	420.0 ¢ to 800.0 ¢
8-mosstep	Minor 8-mosstep	m8ms	L + 7s	400.0 ¢ to 480.0 ¢
	Major 8-mosstep	M8ms	2L + 6s	480.0 ¢ to 800.0 ¢
9-mosstep	Minor 9-mosstep	m9ms	L + 8s	400.0 ¢ to 540.0 ¢
	Major 9-mosstep	M9ms	2L + 7s	540.0 ¢ to 800.0 ¢
10-mosstep	Minor 10-mosstep	m10ms	L + 9s	400.0 ¢ to 600.0 ¢
	Major 10-mosstep	M10ms	2L + 8s	600.0 ¢ to 800.0 ¢
11-mosstep	Minor 11-mosstep	m11ms	L + 10s	400.0 ¢ to 660.0 ¢
	Major 11-mosstep	M11ms	2L + 9s	660.0 ¢ to 800.0 ¢
12-mosstep	Minor 12-mosstep	m12ms	L + 11s	400.0 ¢ to 720.0 ¢
	Major 12-mosstep	M12ms	2L + 10s	720.0 ¢ to 800.0 ¢
13-mosstep	Diminished 13-mosstep	d13ms	L + 12s	400.0 ¢ to 780.0 ¢
	Perfect 13-mosstep	P13ms	2L + 11s	780.0 ¢ to 800.0 ¢
14-mosstep	Minor 14-mosstep	m14ms	2L + 12s	800.0 ¢ to 840.0 ¢
	Major 14-mosstep	M14ms	3L + 11s	840.0 ¢ to 1200.0 ¢
15-mosstep	Minor 15-mosstep	m15ms	2L + 13s	800.0 ¢ to 900.0 ¢
	Major 15-mosstep	M15ms	3L + 12s	900.0 ¢ to 1200.0 ¢
16-mosstep	Minor 16-mosstep	m16ms	2L + 14s	800.0 ¢ to 960.0 ¢
	Major 16-mosstep	M16ms	3L + 13s	960.0 ¢ to 1200.0 ¢
17-mosstep	Minor 17-mosstep	m17ms	2L + 15s	800.0 ¢ to 1020.0 ¢
	Major 17-mosstep	M17ms	3L + 14s	1020.0 ¢ to 1200.0 ¢
18-mosstep	Minor 18-mosstep	m18ms	2L + 16s	800.0 ¢ to 1080.0 ¢
	Major 18-mosstep	M18ms	3L + 15s	1080.0 ¢ to 1200.0 ¢
19-mosstep	Minor 19-mosstep	m19ms	2L + 17s	800.0 ¢ to 1140.0 ¢
	Major 19-mosstep	M19ms	3L + 16s	1140.0 ¢ to 1200.0 ¢
20-mosstep	Perfect 20-mosstep	P20ms	3L + 17s	1200.0 ¢

Scale tree

Template: Scale tree is deprecated. Please use Template: MOS tuning spectrum instead. Details: Use of a single Comments parameter has become unmaintainable. Existing scale trees should be migrated to the new template, where comments are entered using a step ratio p/q as a parameter: {{MOS tuning spectrum | 3/2 = Example comment | 4/3 = Another example comment }} The parameters tuning and depth have been replaced with Scale Signature and Depth, respectively.

Scale tree and tuning spectrum of 3L 17s

Generator(edo)						Cents		Step ratio		Comments
						Bright	Dark	L:s	Hardness
13\20						780.000	420.000	1:1	1.000	Equalized 3L 17s
					67\103	780.583	419.417	6:5	1.200
				54\83		780.723	419.277	5:4	1.250
					95\146	780.822	419.178	9:7	1.286
			41\63			780.952	419.048	4:3	1.333	Supersoft 3L 17s
					110\169	781.065	418.935	11:8	1.375
				69\106		781.132	418.868	7:5	1.400
					97\149	781.208	418.792	10:7	1.429
		28\43				781.395	418.605	3:2	1.500	Soft 3L 17s
					99\152	781.579	418.421	11:7	1.571
				71\109		781.651	418.349	8:5	1.600
					114\175	781.714	418.286	13:8	1.625
			43\66			781.818	418.182	5:3	1.667	Semisoft 3L 17s
					101\155	781.935	418.065	12:7	1.714
				58\89		782.022	417.978	7:4	1.750
					73\112	782.143	417.857	9:5	1.800
	15\23					782.609	417.391	2:1	2.000	Basic 3L 17s Scales with tunings softer than this are proper
					62\95	783.158	416.842	9:4	2.250
				47\72		783.333	416.667	7:3	2.333
					79\121	783.471	416.529	12:5	2.400
			32\49			783.673	416.327	5:2	2.500	Semihard 3L 17s
					81\124	783.871	416.129	13:5	2.600
				49\75		784.000	416.000	8:3	2.667
					66\101	784.158	415.842	11:4	2.750
		17\26				784.615	415.385	3:1	3.000	Hard 3L 17s
					53\81	785.185	414.815	10:3	3.333
				36\55		785.455	414.545	7:2	3.500
					55\84	785.714	414.286	11:3	3.667
			19\29			786.207	413.793	4:1	4.000	Superhard 3L 17s
					40\61	786.885	413.115	9:2	4.500
				21\32		787.500	412.500	5:1	5.000
					23\35	788.571	411.429	6:1	6.000
2\3						800.000	400.000	1:0	→ ∞	Collapsed 3L 17s