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
Related to	4L 3s (smitonic)
With tunings	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 ¢)
View • Talk • Edit

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

4L 19s is generated by the 27&31 temperament, which unites 27edo and 31edo, both zeta edos by some metrics, and also 58edo, another unusually accurate tuning.

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