User:MisterShafXen/3L 14s

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↙ 2L 15s	↓ 3L 15s	4L 15s ↘

Scale structure
Step pattern	LssssLsssssLsssss sssssLsssssLssssL
Equave	2/1 (1200.0 ¢)
Period	2/1 (1200.0 ¢)
Generator size
Bright	11\17 to 2\3 (776.5 ¢ to 800.0 ¢)
Dark	1\3 to 6\17 (400.0 ¢ to 423.5 ¢)
TAMNAMS information
Related to	3L 5s (checkertonic)
With tunings	4:1 to 1:0 (ultrahard)
Related MOS scales
Parent	3L 11s
Sister	14L 3s
Daughters	17L 3s, 3L 17s
Neutralized	6L 11s
2-Flought	20L 14s, 3L 31s
Equal tunings
Equalized (L:s = 1:1)	11\17 (776.5 ¢)
Supersoft (L:s = 4:3)	35\54 (777.8 ¢)
Soft (L:s = 3:2)	24\37 (778.4 ¢)
Semisoft (L:s = 5:3)	37\57 (778.9 ¢)
Basic (L:s = 2:1)	13\20 (780.0 ¢)
Semihard (L:s = 5:2)	28\43 (781.4 ¢)
Hard (L:s = 3:1)	15\23 (782.6 ¢)
Superhard (L:s = 4:1)	17\26 (784.6 ¢)
Collapsed (L:s = 1:0)	2\3 (800.0 ¢)
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3L 14s is a 2/1-equivalent (octave-equivalent) moment of symmetry scale containing 3 large steps and 14 small steps, repeating every octave. 3L 14s is a great-grandchild scale of 3L 5s, expanding it by 9 tones. Generators that produce this scale range from 776.5 ¢ to 800 ¢, or from 400 ¢ to 423.5 ¢.

Scale properties

Intervals of 3L 14s

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 70.6 ¢
	Major 1-mosstep	M1ms	L	70.6 ¢ to 400.0 ¢
2-mosstep	Minor 2-mosstep	m2ms	2s	0.0 ¢ to 141.2 ¢
	Major 2-mosstep	M2ms	L + s	141.2 ¢ to 400.0 ¢
3-mosstep	Minor 3-mosstep	m3ms	3s	0.0 ¢ to 211.8 ¢
	Major 3-mosstep	M3ms	L + 2s	211.8 ¢ to 400.0 ¢
4-mosstep	Minor 4-mosstep	m4ms	4s	0.0 ¢ to 282.4 ¢
	Major 4-mosstep	M4ms	L + 3s	282.4 ¢ to 400.0 ¢
5-mosstep	Minor 5-mosstep	m5ms	5s	0.0 ¢ to 352.9 ¢
	Major 5-mosstep	M5ms	L + 4s	352.9 ¢ to 400.0 ¢
6-mosstep	Perfect 6-mosstep	P6ms	L + 5s	400.0 ¢ to 423.5 ¢
	Augmented 6-mosstep	A6ms	2L + 4s	423.5 ¢ to 800.0 ¢
7-mosstep	Minor 7-mosstep	m7ms	L + 6s	400.0 ¢ to 494.1 ¢
	Major 7-mosstep	M7ms	2L + 5s	494.1 ¢ to 800.0 ¢
8-mosstep	Minor 8-mosstep	m8ms	L + 7s	400.0 ¢ to 564.7 ¢
	Major 8-mosstep	M8ms	2L + 6s	564.7 ¢ to 800.0 ¢
9-mosstep	Minor 9-mosstep	m9ms	L + 8s	400.0 ¢ to 635.3 ¢
	Major 9-mosstep	M9ms	2L + 7s	635.3 ¢ to 800.0 ¢
10-mosstep	Minor 10-mosstep	m10ms	L + 9s	400.0 ¢ to 705.9 ¢
	Major 10-mosstep	M10ms	2L + 8s	705.9 ¢ to 800.0 ¢
11-mosstep	Diminished 11-mosstep	d11ms	L + 10s	400.0 ¢ to 776.5 ¢
	Perfect 11-mosstep	P11ms	2L + 9s	776.5 ¢ to 800.0 ¢
12-mosstep	Minor 12-mosstep	m12ms	2L + 10s	800.0 ¢ to 847.1 ¢
	Major 12-mosstep	M12ms	3L + 9s	847.1 ¢ to 1200.0 ¢
13-mosstep	Minor 13-mosstep	m13ms	2L + 11s	800.0 ¢ to 917.6 ¢
	Major 13-mosstep	M13ms	3L + 10s	917.6 ¢ to 1200.0 ¢
14-mosstep	Minor 14-mosstep	m14ms	2L + 12s	800.0 ¢ to 988.2 ¢
	Major 14-mosstep	M14ms	3L + 11s	988.2 ¢ to 1200.0 ¢
15-mosstep	Minor 15-mosstep	m15ms	2L + 13s	800.0 ¢ to 1058.8 ¢
	Major 15-mosstep	M15ms	3L + 12s	1058.8 ¢ to 1200.0 ¢
16-mosstep	Minor 16-mosstep	m16ms	2L + 14s	800.0 ¢ to 1129.4 ¢
	Major 16-mosstep	M16ms	3L + 13s	1129.4 ¢ to 1200.0 ¢
17-mosstep	Perfect 17-mosstep	P17ms	3L + 14s	1200.0 ¢

Comparison of various tunings

Tuning	A0	m1	M1	m2	M2	m3	M3	m4	M4	m5	M5	P6	A6	m7	M7	m8	M8	m9	M9	m10	M10	d11	P11	m12	M12	m13	M13	m14	M14	m15	M15	m16	M16	d17
1:1 (17edo)	0¢	71¢	71¢	141¢	141¢	212¢	212¢	282¢	282¢	353¢	353¢	424¢	424¢	494¢	494¢	565¢	565¢	635¢	635¢	706¢	706¢	776¢	776¢	847¢	847¢	918¢	918¢	988¢	988¢	1059¢	1059¢	1121¢	1121¢	1200¢
2:1 (20edo)	60¢	60¢	120¢	120¢	180¢	180¢	240¢	240¢	300¢	300¢	360¢	420¢	480¢	480¢	540¢	540¢	600¢	600¢	660¢	660¢	720¢	720¢	780¢	840¢	900¢	900¢	960¢	960¢	1020¢	1020¢	1080¢	1080¢	1140¢	1140¢
3:1 (23edo)	104¢	52¢	157¢	104¢	209¢	157¢	261¢	209¢	313¢	261¢	365¢	417¢	522¢	470¢	574¢	522¢	626¢	574¢	678¢	626¢	730¢	678¢	783¢	835¢	939¢	887¢	991¢	939¢	1043¢	991¢	1096¢	1043¢	1148¢	1096¢
4:1 (26edo)	138¢	46¢	185¢	92¢	231¢	138¢	277¢	185¢	323¢	231¢	369¢	415¢	554¢	462¢	600¢	508¢	646¢	554¢	692¢	600¢	738¢	646¢	785¢	831¢	969¢	877¢	1015¢	923¢	1062¢	969¢	1108¢	1015¢	1154¢	1062¢
1:0 (3edo)	400¢	0¢	400¢	0¢	400¢	0¢	400¢	0¢	400¢	0¢	400¢	400¢	800¢	400¢	800¢	400¢	800¢	400¢	800¢	400¢	800¢	400¢	800¢	800¢	1200¢	800¢	1200¢	800¢	1200¢	800¢	1200¢	800¢	1200¢	800¢

Generator chain of 3L 14s

Bright gens	Scale degree	Abbrev.
19	Augmented 5-mosdegree	A5md
18	Augmented 11-mosdegree	A11md
17	Augmented 0-mosdegree	A0md
16	Augmented 6-mosdegree	A6md
15	Major 12-mosdegree	M12md
14	Major 1-mosdegree	M1md
13	Major 7-mosdegree	M7md
12	Major 13-mosdegree	M13md
11	Major 2-mosdegree	M2md
10	Major 8-mosdegree	M8md
9	Major 14-mosdegree	M14md
8	Major 3-mosdegree	M3md
7	Major 9-mosdegree	M9md
6	Major 15-mosdegree	M15md
5	Major 4-mosdegree	M4md
4	Major 10-mosdegree	M10md
3	Major 16-mosdegree	M16md
2	Major 5-mosdegree	M5md
1	Perfect 11-mosdegree	P11md
0	Perfect 0-mosdegree Perfect 17-mosdegree	P0md P17md
−1	Perfect 6-mosdegree	P6md
−2	Minor 12-mosdegree	m12md
−3	Minor 1-mosdegree	m1md
−4	Minor 7-mosdegree	m7md
−5	Minor 13-mosdegree	m13md
−6	Minor 2-mosdegree	m2md
−7	Minor 8-mosdegree	m8md
−8	Minor 14-mosdegree	m14md
−9	Minor 3-mosdegree	m3md
−10	Minor 9-mosdegree	m9md
−11	Minor 15-mosdegree	m15md
−12	Minor 4-mosdegree	m4md
−13	Minor 10-mosdegree	m10md
−14	Minor 16-mosdegree	m16md
−15	Minor 5-mosdegree	m5md
−16	Diminished 11-mosdegree	d11md
−17	Diminished 17-mosdegree	d17md
−18	Diminished 6-mosdegree	d6md
−19	Diminished 12-mosdegree	d12md

Modes of 3L 14s

UDP	Cyclic order	Step pattern
16|0	1	LssssLsssssLsssss
15|1	12	LsssssLssssLsssss
14|2	6	LsssssLsssssLssss
13|3	17	sLssssLsssssLssss
12|4	11	sLsssssLssssLssss
11|5	5	sLsssssLsssssLsss
10|6	16	ssLssssLsssssLsss
9|7	10	ssLsssssLssssLsss
8|8	4	ssLsssssLsssssLss
7|9	15	sssLssssLsssssLss
6|10	9	sssLsssssLssssLss
5|11	3	sssLsssssLsssssLs
4|12	14	ssssLssssLsssssLs
3|13	8	ssssLsssssLssssLs
2|14	2	ssssLsssssLsssssL
1|15	13	sssssLssssLsssssL
0|16	7	sssssLsssssLssssL

Scale tree

Scale tree and tuning spectrum of 3L 14s

Generator(edo)						Cents		Step ratio		Comments
						Bright	Dark	L:s	Hardness
11\17						776.471	423.529	1:1	1.000	Equalized 3L 14s
					57\88	777.273	422.727	6:5	1.200
				46\71		777.465	422.535	5:4	1.250
					81\125	777.600	422.400	9:7	1.286
			35\54			777.778	422.222	4:3	1.333	Supersoft 3L 14s
					94\145	777.931	422.069	11:8	1.375
				59\91		778.022	421.978	7:5	1.400
					83\128	778.125	421.875	10:7	1.429
		24\37				778.378	421.622	3:2	1.500	Soft 3L 14s
					85\131	778.626	421.374	11:7	1.571
				61\94		778.723	421.277	8:5	1.600
					98\151	778.808	421.192	13:8	1.625
			37\57			778.947	421.053	5:3	1.667	Semisoft 3L 14s
					87\134	779.104	420.896	12:7	1.714
				50\77		779.221	420.779	7:4	1.750
					63\97	779.381	420.619	9:5	1.800
	13\20					780.000	420.000	2:1	2.000	Basic 3L 14s Scales with tunings softer than this are proper
					54\83	780.723	419.277	9:4	2.250
				41\63		780.952	419.048	7:3	2.333
					69\106	781.132	418.868	12:5	2.400
			28\43			781.395	418.605	5:2	2.500	Semihard 3L 14s
					71\109	781.651	418.349	13:5	2.600
				43\66		781.818	418.182	8:3	2.667
					58\89	782.022	417.978	11:4	2.750
		15\23				782.609	417.391	3:1	3.000	Hard 3L 14s
					47\72	783.333	416.667	10:3	3.333
				32\49		783.673	416.327	7:2	3.500
					49\75	784.000	416.000	11:3	3.667
			17\26			784.615	415.385	4:1	4.000	Superhard 3L 14s
					36\55	785.455	414.545	9:2	4.500
				19\29		786.207	413.793	5:1	5.000
					21\32	787.500	412.500	6:1	6.000
2\3						800.000	400.000	1:0	→ ∞	Collapsed 3L 14s