4L 19s

↖ 3L 18s	↑ 4L 18s	5L 18s ↗
← 3L 19s	4L 19s	5L 19s →
↙ 3L 20s	↓ 4L 20s	5L 20s ↘

┌╥┬┬┬┬╥┬┬┬┬┬╥┬┬┬┬┬╥┬┬┬┬┬┐ │║││││║│││││║│││││║││││││ │││││││││││││││││││││││││ └┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┘
Scale structure
Step pattern	LssssLsssssLsssssLsssss sssssLsssssLsssssLssssL
Equave	2/1 (1200.0¢)
Period	2/1 (1200.0¢)
Generator size
Bright	17\23 to 3\4 (887.0¢ to 900.0¢)
Dark	1\4 to 6\23 (300.0¢ to 313.0¢)
TAMNAMS information
Descends from	4L 3s (smitonic)
Ancestor's step ratio range	5:1 to 1:0
Related MOS scales
Parent	4L 15s
Sister	19L 4s
Daughters	23L 4s, 4L 23s
Neutralized	8L 15s
2-Flought	27L 19s, 4L 42s
Equal tunings
Equalized (L:s = 1:1)	17\23 (887.0¢)
Supersoft (L:s = 4:3)	54\73 (887.7¢)
Soft (L:s = 3:2)	37\50 (888.0¢)
Semisoft (L:s = 5:3)	57\77 (888.3¢)
Basic (L:s = 2:1)	20\27 (888.9¢)
Semihard (L:s = 5:2)	43\58 (889.7¢)
Hard (L:s = 3:1)	23\31 (890.3¢)
Superhard (L:s = 4:1)	26\35 (891.4¢)
Collapsed (L:s = 1:0)	3\4 (900.0¢)

4L 19s is a 2/1-equivalent (octave-equivalent) moment of symmetry scale containing 4 large steps and 19 small steps, repeating every octave. 4L 19s is related to 4L 3s, expanding it by 16 tones. Generators that produce this scale range from 887¢ to 900¢, or from 300¢ to 313¢.

Modes

Modes of 4L 19s

UDP	Cyclic order	Step pattern
22|0	1	LssssLsssssLsssssLsssss
21|1	18	LsssssLssssLsssssLsssss
20|2	12	LsssssLsssssLssssLsssss
19|3	6	LsssssLsssssLsssssLssss
18|4	23	sLssssLsssssLsssssLssss
17|5	17	sLsssssLssssLsssssLssss
16|6	11	sLsssssLsssssLssssLssss
15|7	5	sLsssssLsssssLsssssLsss
14|8	22	ssLssssLsssssLsssssLsss
13|9	16	ssLsssssLssssLsssssLsss
12|10	10	ssLsssssLsssssLssssLsss
11|11	4	ssLsssssLsssssLsssssLss
10|12	21	sssLssssLsssssLsssssLss
9|13	15	sssLsssssLssssLsssssLss
8|14	9	sssLsssssLsssssLssssLss
7|15	3	sssLsssssLsssssLsssssLs
6|16	20	ssssLssssLsssssLsssssLs
5|17	14	ssssLsssssLssssLsssssLs
4|18	8	ssssLsssssLsssssLssssLs
3|19	2	ssssLsssssLsssssLsssssL
2|20	19	sssssLssssLsssssLsssssL
1|21	13	sssssLsssssLssssLsssssL
0|22	7	sssssLsssssLsssssLssssL

Intervals

Intervals of 4L 19s

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 52.2¢
	Major 1-mosstep	M1ms	L	52.2¢ to 300.0¢
2-mosstep	Minor 2-mosstep	m2ms	2s	0.0¢ to 104.3¢
	Major 2-mosstep	M2ms	L + s	104.3¢ to 300.0¢
3-mosstep	Minor 3-mosstep	m3ms	3s	0.0¢ to 156.5¢
	Major 3-mosstep	M3ms	L + 2s	156.5¢ to 300.0¢
4-mosstep	Minor 4-mosstep	m4ms	4s	0.0¢ to 208.7¢
	Major 4-mosstep	M4ms	L + 3s	208.7¢ to 300.0¢
5-mosstep	Minor 5-mosstep	m5ms	5s	0.0¢ to 260.9¢
	Major 5-mosstep	M5ms	L + 4s	260.9¢ to 300.0¢
6-mosstep	Perfect 6-mosstep	P6ms	L + 5s	300.0¢ to 313.0¢
	Augmented 6-mosstep	A6ms	2L + 4s	313.0¢ to 600.0¢
7-mosstep	Minor 7-mosstep	m7ms	L + 6s	300.0¢ to 365.2¢
	Major 7-mosstep	M7ms	2L + 5s	365.2¢ to 600.0¢
8-mosstep	Minor 8-mosstep	m8ms	L + 7s	300.0¢ to 417.4¢
	Major 8-mosstep	M8ms	2L + 6s	417.4¢ to 600.0¢
9-mosstep	Minor 9-mosstep	m9ms	L + 8s	300.0¢ to 469.6¢
	Major 9-mosstep	M9ms	2L + 7s	469.6¢ to 600.0¢
10-mosstep	Minor 10-mosstep	m10ms	L + 9s	300.0¢ to 521.7¢
	Major 10-mosstep	M10ms	2L + 8s	521.7¢ to 600.0¢
11-mosstep	Minor 11-mosstep	m11ms	L + 10s	300.0¢ to 573.9¢
	Major 11-mosstep	M11ms	2L + 9s	573.9¢ to 600.0¢
12-mosstep	Minor 12-mosstep	m12ms	2L + 10s	600.0¢ to 626.1¢
	Major 12-mosstep	M12ms	3L + 9s	626.1¢ to 900.0¢
13-mosstep	Minor 13-mosstep	m13ms	2L + 11s	600.0¢ to 678.3¢
	Major 13-mosstep	M13ms	3L + 10s	678.3¢ to 900.0¢
14-mosstep	Minor 14-mosstep	m14ms	2L + 12s	600.0¢ to 730.4¢
	Major 14-mosstep	M14ms	3L + 11s	730.4¢ to 900.0¢
15-mosstep	Minor 15-mosstep	m15ms	2L + 13s	600.0¢ to 782.6¢
	Major 15-mosstep	M15ms	3L + 12s	782.6¢ to 900.0¢
16-mosstep	Minor 16-mosstep	m16ms	2L + 14s	600.0¢ to 834.8¢
	Major 16-mosstep	M16ms	3L + 13s	834.8¢ to 900.0¢
17-mosstep	Diminished 17-mosstep	d17ms	2L + 15s	600.0¢ to 887.0¢
	Perfect 17-mosstep	P17ms	3L + 14s	887.0¢ to 900.0¢
18-mosstep	Minor 18-mosstep	m18ms	3L + 15s	900.0¢ to 939.1¢
	Major 18-mosstep	M18ms	4L + 14s	939.1¢ to 1200.0¢
19-mosstep	Minor 19-mosstep	m19ms	3L + 16s	900.0¢ to 991.3¢
	Major 19-mosstep	M19ms	4L + 15s	991.3¢ to 1200.0¢
20-mosstep	Minor 20-mosstep	m20ms	3L + 17s	900.0¢ to 1043.5¢
	Major 20-mosstep	M20ms	4L + 16s	1043.5¢ to 1200.0¢
21-mosstep	Minor 21-mosstep	m21ms	3L + 18s	900.0¢ to 1095.7¢
	Major 21-mosstep	M21ms	4L + 17s	1095.7¢ to 1200.0¢
22-mosstep	Minor 22-mosstep	m22ms	3L + 19s	900.0¢ to 1147.8¢
	Major 22-mosstep	M22ms	4L + 18s	1147.8¢ to 1200.0¢
23-mosstep	Perfect 23-mosstep	P23ms	4L + 19s	1200.0¢

Scale tree

Scale Tree and Tuning Spectrum of 4L 19s

Generator(edo)						Cents		Step ratio		Comments
						Bright	Dark	L:s	Hardness
17\23						886.957	313.043	1:1	1.000	Equalized 4L 19s
					88\119	887.395	312.605	6:5	1.200
				71\96		887.500	312.500	5:4	1.250
					125\169	887.574	312.426	9:7	1.286
			54\73			887.671	312.329	4:3	1.333	Supersoft 4L 19s
					145\196	887.755	312.245	11:8	1.375
				91\123		887.805	312.195	7:5	1.400
					128\173	887.861	312.139	10:7	1.429
		37\50				888.000	312.000	3:2	1.500	Soft 4L 19s
					131\177	888.136	311.864	11:7	1.571
				94\127		888.189	311.811	8:5	1.600
					151\204	888.235	311.765	13:8	1.625
			57\77			888.312	311.688	5:3	1.667	Semisoft 4L 19s
					134\181	888.398	311.602	12:7	1.714
				77\104		888.462	311.538	7:4	1.750
					97\131	888.550	311.450	9:5	1.800
	20\27					888.889	311.111	2:1	2.000	Basic 4L 19s Scales with tunings softer than this are proper
					83\112	889.286	310.714	9:4	2.250
				63\85		889.412	310.588	7:3	2.333
					106\143	889.510	310.490	12:5	2.400
			43\58			889.655	310.345	5:2	2.500	Semihard 4L 19s
					109\147	889.796	310.204	13:5	2.600
				66\89		889.888	310.112	8:3	2.667
					89\120	890.000	310.000	11:4	2.750
		23\31				890.323	309.677	3:1	3.000	Hard 4L 19s
					72\97	890.722	309.278	10:3	3.333
				49\66		890.909	309.091	7:2	3.500
					75\101	891.089	308.911	11:3	3.667
			26\35			891.429	308.571	4:1	4.000	Superhard 4L 19s
					55\74	891.892	308.108	9:2	4.500
				29\39		892.308	307.692	5:1	5.000
					32\43	893.023	306.977	6:1	6.000
3\4						900.000	300.000	1:0	→ ∞	Collapsed 4L 19s

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