19L 5s

↖ 18L 4s	↑ 19L 4s	20L 4s ↗
← 18L 5s	19L 5s	20L 5s →
↙ 18L 6s	↓ 19L 6s	20L 6s ↘

┌╥╥╥╥┬╥╥╥╥┬╥╥╥╥┬╥╥╥╥┬╥╥╥┬┐
│║║║║│║║║║│║║║║│║║║║│║║║││
││││││││││││││││││││││││││
└┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┘

Scale structure

Step pattern

LLLLsLLLLsLLLLsLLLLsLLLs
sLLLsLLLLsLLLLsLLLLsLLLL

Equave

2/1 (1200.0 ¢)

Period

2/1 (1200.0 ¢)

Generator size

Bright

5\24 to 4\19 (250.0 ¢ to 252.6 ¢)

Dark

15\19 to 19\24 (947.4 ¢ to 950.0 ¢)

TAMNAMS information

Related to

5L 4s (semiquartal)

With tunings

3:1 to 4:1 (parahard)

Related MOS scales

Equal tunings

Equalized (L:s = 1:1)

5\24 (250.0 ¢)

Supersoft (L:s = 4:3)

19\91 (250.5 ¢)

14\67 (250.7 ¢)

23\110 (250.9 ¢)

9\43 (251.2 ¢)

22\105 (251.4 ¢)

13\62 (251.6 ¢)

Superhard (L:s = 4:1)

17\81 (251.9 ¢)

Collapsed (L:s = 1:0)

4\19 (252.6 ¢)

19L 5s is a 2/1-equivalent (octave-equivalent) moment of symmetry scale containing 19 large steps and 5 small steps, repeating every octave. 19L 5s is a great-grandchild scale of 5L 4s, expanding it by 15 tones. Generators that produce this scale range from 250 ¢ to 252.6 ¢, or from 947.4 ¢ to 950 ¢.

Scale properties

This article uses TAMNAMS conventions for the names of this scale's intervals and scale degrees. The use of 1-indexed ordinal names is reserved for interval regions.

Intervals

Intervals of 19L 5s
Intervals			Steps subtended	Range in cents
Generic	Specific	Abbrev.	Steps subtended	Range in cents
0-mosstep	Perfect 0-mosstep	P0ms	0	0.0 ¢
1-mosstep	Minor 1-mosstep	m1ms	s	0.0 ¢ to 50.0 ¢
1-mosstep	Major 1-mosstep	M1ms	L	50.0 ¢ to 63.2 ¢
2-mosstep	Minor 2-mosstep	m2ms	L + s	63.2 ¢ to 100.0 ¢
2-mosstep	Major 2-mosstep	M2ms	2L	100.0 ¢ to 126.3 ¢
3-mosstep	Minor 3-mosstep	m3ms	2L + s	126.3 ¢ to 150.0 ¢
3-mosstep	Major 3-mosstep	M3ms	3L	150.0 ¢ to 189.5 ¢
4-mosstep	Minor 4-mosstep	m4ms	3L + s	189.5 ¢ to 200.0 ¢
4-mosstep	Major 4-mosstep	M4ms	4L	200.0 ¢ to 252.6 ¢
5-mosstep	Diminished 5-mosstep	d5ms	3L + 2s	189.5 ¢ to 250.0 ¢
5-mosstep	Perfect 5-mosstep	P5ms	4L + s	250.0 ¢ to 252.6 ¢
6-mosstep	Minor 6-mosstep	m6ms	4L + 2s	252.6 ¢ to 300.0 ¢
6-mosstep	Major 6-mosstep	M6ms	5L + s	300.0 ¢ to 315.8 ¢
7-mosstep	Minor 7-mosstep	m7ms	5L + 2s	315.8 ¢ to 350.0 ¢
7-mosstep	Major 7-mosstep	M7ms	6L + s	350.0 ¢ to 378.9 ¢
8-mosstep	Minor 8-mosstep	m8ms	6L + 2s	378.9 ¢ to 400.0 ¢
8-mosstep	Major 8-mosstep	M8ms	7L + s	400.0 ¢ to 442.1 ¢
9-mosstep	Minor 9-mosstep	m9ms	7L + 2s	442.1 ¢ to 450.0 ¢
9-mosstep	Major 9-mosstep	M9ms	8L + s	450.0 ¢ to 505.3 ¢
10-mosstep	Minor 10-mosstep	m10ms	7L + 3s	442.1 ¢ to 500.0 ¢
10-mosstep	Major 10-mosstep	M10ms	8L + 2s	500.0 ¢ to 505.3 ¢
11-mosstep	Minor 11-mosstep	m11ms	8L + 3s	505.3 ¢ to 550.0 ¢
11-mosstep	Major 11-mosstep	M11ms	9L + 2s	550.0 ¢ to 568.4 ¢
12-mosstep	Minor 12-mosstep	m12ms	9L + 3s	568.4 ¢ to 600.0 ¢
12-mosstep	Major 12-mosstep	M12ms	10L + 2s	600.0 ¢ to 631.6 ¢
13-mosstep	Minor 13-mosstep	m13ms	10L + 3s	631.6 ¢ to 650.0 ¢
13-mosstep	Major 13-mosstep	M13ms	11L + 2s	650.0 ¢ to 694.7 ¢
14-mosstep	Minor 14-mosstep	m14ms	11L + 3s	694.7 ¢ to 700.0 ¢
14-mosstep	Major 14-mosstep	M14ms	12L + 2s	700.0 ¢ to 757.9 ¢
15-mosstep	Minor 15-mosstep	m15ms	11L + 4s	694.7 ¢ to 750.0 ¢
15-mosstep	Major 15-mosstep	M15ms	12L + 3s	750.0 ¢ to 757.9 ¢
16-mosstep	Minor 16-mosstep	m16ms	12L + 4s	757.9 ¢ to 800.0 ¢
16-mosstep	Major 16-mosstep	M16ms	13L + 3s	800.0 ¢ to 821.1 ¢
17-mosstep	Minor 17-mosstep	m17ms	13L + 4s	821.1 ¢ to 850.0 ¢
17-mosstep	Major 17-mosstep	M17ms	14L + 3s	850.0 ¢ to 884.2 ¢
18-mosstep	Minor 18-mosstep	m18ms	14L + 4s	884.2 ¢ to 900.0 ¢
18-mosstep	Major 18-mosstep	M18ms	15L + 3s	900.0 ¢ to 947.4 ¢
19-mosstep	Perfect 19-mosstep	P19ms	15L + 4s	947.4 ¢ to 950.0 ¢
19-mosstep	Augmented 19-mosstep	A19ms	16L + 3s	950.0 ¢ to 1010.5 ¢
20-mosstep	Minor 20-mosstep	m20ms	15L + 5s	947.4 ¢ to 1000.0 ¢
20-mosstep	Major 20-mosstep	M20ms	16L + 4s	1000.0 ¢ to 1010.5 ¢
21-mosstep	Minor 21-mosstep	m21ms	16L + 5s	1010.5 ¢ to 1050.0 ¢
21-mosstep	Major 21-mosstep	M21ms	17L + 4s	1050.0 ¢ to 1073.7 ¢
22-mosstep	Minor 22-mosstep	m22ms	17L + 5s	1073.7 ¢ to 1100.0 ¢
22-mosstep	Major 22-mosstep	M22ms	18L + 4s	1100.0 ¢ to 1136.8 ¢
23-mosstep	Minor 23-mosstep	m23ms	18L + 5s	1136.8 ¢ to 1150.0 ¢
23-mosstep	Major 23-mosstep	M23ms	19L + 4s	1150.0 ¢ to 1200.0 ¢
24-mosstep	Perfect 24-mosstep	P24ms	19L + 5s	1200.0 ¢

Generator chain

Generator chain of 19L 5s
Bright gens	Scale degree	Abbrev.
42	Augmented 18-mosdegree	A18md
41	Augmented 13-mosdegree	A13md
40	Augmented 8-mosdegree	A8md
39	Augmented 3-mosdegree	A3md
38	Augmented 22-mosdegree	A22md
37	Augmented 17-mosdegree	A17md
36	Augmented 12-mosdegree	A12md
35	Augmented 7-mosdegree	A7md
34	Augmented 2-mosdegree	A2md
33	Augmented 21-mosdegree	A21md
32	Augmented 16-mosdegree	A16md
31	Augmented 11-mosdegree	A11md
30	Augmented 6-mosdegree	A6md
29	Augmented 1-mosdegree	A1md
28	Augmented 20-mosdegree	A20md
27	Augmented 15-mosdegree	A15md
26	Augmented 10-mosdegree	A10md
25	Augmented 5-mosdegree	A5md
24	Augmented 0-mosdegree	A0md
23	Augmented 19-mosdegree	A19md
22	Major 14-mosdegree	M14md
21	Major 9-mosdegree	M9md
20	Major 4-mosdegree	M4md
19	Major 23-mosdegree	M23md
18	Major 18-mosdegree	M18md
17	Major 13-mosdegree	M13md
16	Major 8-mosdegree	M8md
15	Major 3-mosdegree	M3md
14	Major 22-mosdegree	M22md
13	Major 17-mosdegree	M17md
12	Major 12-mosdegree	M12md
11	Major 7-mosdegree	M7md
10	Major 2-mosdegree	M2md
9	Major 21-mosdegree	M21md
8	Major 16-mosdegree	M16md
7	Major 11-mosdegree	M11md
6	Major 6-mosdegree	M6md
5	Major 1-mosdegree	M1md
4	Major 20-mosdegree	M20md
3	Major 15-mosdegree	M15md
2	Major 10-mosdegree	M10md
1	Perfect 5-mosdegree	P5md
0	Perfect 0-mosdegree Perfect 24-mosdegree	P0md P24md
−1	Perfect 19-mosdegree	P19md
−2	Minor 14-mosdegree	m14md
−3	Minor 9-mosdegree	m9md
−4	Minor 4-mosdegree	m4md
−5	Minor 23-mosdegree	m23md
−6	Minor 18-mosdegree	m18md
−7	Minor 13-mosdegree	m13md
−8	Minor 8-mosdegree	m8md
−9	Minor 3-mosdegree	m3md
−10	Minor 22-mosdegree	m22md
−11	Minor 17-mosdegree	m17md
−12	Minor 12-mosdegree	m12md
−13	Minor 7-mosdegree	m7md
−14	Minor 2-mosdegree	m2md
−15	Minor 21-mosdegree	m21md
−16	Minor 16-mosdegree	m16md
−17	Minor 11-mosdegree	m11md
−18	Minor 6-mosdegree	m6md
−19	Minor 1-mosdegree	m1md
−20	Minor 20-mosdegree	m20md
−21	Minor 15-mosdegree	m15md
−22	Minor 10-mosdegree	m10md
−23	Diminished 5-mosdegree	d5md
−24	Diminished 24-mosdegree	d24md
−25	Diminished 19-mosdegree	d19md
−26	Diminished 14-mosdegree	d14md
−27	Diminished 9-mosdegree	d9md
−28	Diminished 4-mosdegree	d4md
−29	Diminished 23-mosdegree	d23md
−30	Diminished 18-mosdegree	d18md
−31	Diminished 13-mosdegree	d13md
−32	Diminished 8-mosdegree	d8md
−33	Diminished 3-mosdegree	d3md
−34	Diminished 22-mosdegree	d22md
−35	Diminished 17-mosdegree	d17md
−36	Diminished 12-mosdegree	d12md
−37	Diminished 7-mosdegree	d7md
−38	Diminished 2-mosdegree	d2md
−39	Diminished 21-mosdegree	d21md
−40	Diminished 16-mosdegree	d16md
−41	Diminished 11-mosdegree	d11md
−42	Diminished 6-mosdegree	d6md

Modes

Scale degrees of the modes of 19L 5s
UDP	Cyclic order	Step pattern	Scale degree (mosdegree)
UDP	Cyclic order	Step pattern	0	1	2	3	4	5	6	7	8	9	10	11	12	13	14	15	16	17	18	19	20	21	22	23	24
23\|0	1	LLLLsLLLLsLLLLsLLLLsLLLs	Perf.	Maj.	Maj.	Maj.	Maj.	Perf.	Maj.	Maj.	Maj.	Maj.	Maj.	Maj.	Maj.	Maj.	Maj.	Maj.	Maj.	Maj.	Maj.	Aug.	Maj.	Maj.	Maj.	Maj.	Perf.
22\|1	6	LLLLsLLLLsLLLLsLLLsLLLLs	Perf.	Maj.	Maj.	Maj.	Maj.	Perf.	Maj.	Maj.	Maj.	Maj.	Maj.	Maj.	Maj.	Maj.	Maj.	Maj.	Maj.	Maj.	Maj.	Perf.	Maj.	Maj.	Maj.	Maj.	Perf.
21\|2	11	LLLLsLLLLsLLLsLLLLsLLLLs	Perf.	Maj.	Maj.	Maj.	Maj.	Perf.	Maj.	Maj.	Maj.	Maj.	Maj.	Maj.	Maj.	Maj.	Min.	Maj.	Maj.	Maj.	Maj.	Perf.	Maj.	Maj.	Maj.	Maj.	Perf.
20\|3	16	LLLLsLLLsLLLLsLLLLsLLLLs	Perf.	Maj.	Maj.	Maj.	Maj.	Perf.	Maj.	Maj.	Maj.	Min.	Maj.	Maj.	Maj.	Maj.	Min.	Maj.	Maj.	Maj.	Maj.	Perf.	Maj.	Maj.	Maj.	Maj.	Perf.
19\|4	21	LLLsLLLLsLLLLsLLLLsLLLLs	Perf.	Maj.	Maj.	Maj.	Min.	Perf.	Maj.	Maj.	Maj.	Min.	Maj.	Maj.	Maj.	Maj.	Min.	Maj.	Maj.	Maj.	Maj.	Perf.	Maj.	Maj.	Maj.	Maj.	Perf.
18\|5	2	LLLsLLLLsLLLLsLLLLsLLLsL	Perf.	Maj.	Maj.	Maj.	Min.	Perf.	Maj.	Maj.	Maj.	Min.	Maj.	Maj.	Maj.	Maj.	Min.	Maj.	Maj.	Maj.	Maj.	Perf.	Maj.	Maj.	Maj.	Min.	Perf.
17\|6	7	LLLsLLLLsLLLLsLLLsLLLLsL	Perf.	Maj.	Maj.	Maj.	Min.	Perf.	Maj.	Maj.	Maj.	Min.	Maj.	Maj.	Maj.	Maj.	Min.	Maj.	Maj.	Maj.	Min.	Perf.	Maj.	Maj.	Maj.	Min.	Perf.
16\|7	12	LLLsLLLLsLLLsLLLLsLLLLsL	Perf.	Maj.	Maj.	Maj.	Min.	Perf.	Maj.	Maj.	Maj.	Min.	Maj.	Maj.	Maj.	Min.	Min.	Maj.	Maj.	Maj.	Min.	Perf.	Maj.	Maj.	Maj.	Min.	Perf.
15\|8	17	LLLsLLLsLLLLsLLLLsLLLLsL	Perf.	Maj.	Maj.	Maj.	Min.	Perf.	Maj.	Maj.	Min.	Min.	Maj.	Maj.	Maj.	Min.	Min.	Maj.	Maj.	Maj.	Min.	Perf.	Maj.	Maj.	Maj.	Min.	Perf.
14\|9	22	LLsLLLLsLLLLsLLLLsLLLLsL	Perf.	Maj.	Maj.	Min.	Min.	Perf.	Maj.	Maj.	Min.	Min.	Maj.	Maj.	Maj.	Min.	Min.	Maj.	Maj.	Maj.	Min.	Perf.	Maj.	Maj.	Maj.	Min.	Perf.
13\|10	3	LLsLLLLsLLLLsLLLLsLLLsLL	Perf.	Maj.	Maj.	Min.	Min.	Perf.	Maj.	Maj.	Min.	Min.	Maj.	Maj.	Maj.	Min.	Min.	Maj.	Maj.	Maj.	Min.	Perf.	Maj.	Maj.	Min.	Min.	Perf.
12\|11	8	LLsLLLLsLLLLsLLLsLLLLsLL	Perf.	Maj.	Maj.	Min.	Min.	Perf.	Maj.	Maj.	Min.	Min.	Maj.	Maj.	Maj.	Min.	Min.	Maj.	Maj.	Min.	Min.	Perf.	Maj.	Maj.	Min.	Min.	Perf.
11\|12	13	LLsLLLLsLLLsLLLLsLLLLsLL	Perf.	Maj.	Maj.	Min.	Min.	Perf.	Maj.	Maj.	Min.	Min.	Maj.	Maj.	Min.	Min.	Min.	Maj.	Maj.	Min.	Min.	Perf.	Maj.	Maj.	Min.	Min.	Perf.
10\|13	18	LLsLLLsLLLLsLLLLsLLLLsLL	Perf.	Maj.	Maj.	Min.	Min.	Perf.	Maj.	Min.	Min.	Min.	Maj.	Maj.	Min.	Min.	Min.	Maj.	Maj.	Min.	Min.	Perf.	Maj.	Maj.	Min.	Min.	Perf.
9\|14	23	LsLLLLsLLLLsLLLLsLLLLsLL	Perf.	Maj.	Min.	Min.	Min.	Perf.	Maj.	Min.	Min.	Min.	Maj.	Maj.	Min.	Min.	Min.	Maj.	Maj.	Min.	Min.	Perf.	Maj.	Maj.	Min.	Min.	Perf.
8\|15	4	LsLLLLsLLLLsLLLLsLLLsLLL	Perf.	Maj.	Min.	Min.	Min.	Perf.	Maj.	Min.	Min.	Min.	Maj.	Maj.	Min.	Min.	Min.	Maj.	Maj.	Min.	Min.	Perf.	Maj.	Min.	Min.	Min.	Perf.
7\|16	9	LsLLLLsLLLLsLLLsLLLLsLLL	Perf.	Maj.	Min.	Min.	Min.	Perf.	Maj.	Min.	Min.	Min.	Maj.	Maj.	Min.	Min.	Min.	Maj.	Min.	Min.	Min.	Perf.	Maj.	Min.	Min.	Min.	Perf.
6\|17	14	LsLLLLsLLLsLLLLsLLLLsLLL	Perf.	Maj.	Min.	Min.	Min.	Perf.	Maj.	Min.	Min.	Min.	Maj.	Min.	Min.	Min.	Min.	Maj.	Min.	Min.	Min.	Perf.	Maj.	Min.	Min.	Min.	Perf.
5\|18	19	LsLLLsLLLLsLLLLsLLLLsLLL	Perf.	Maj.	Min.	Min.	Min.	Perf.	Min.	Min.	Min.	Min.	Maj.	Min.	Min.	Min.	Min.	Maj.	Min.	Min.	Min.	Perf.	Maj.	Min.	Min.	Min.	Perf.
4\|19	24	sLLLLsLLLLsLLLLsLLLLsLLL	Perf.	Min.	Min.	Min.	Min.	Perf.	Min.	Min.	Min.	Min.	Maj.	Min.	Min.	Min.	Min.	Maj.	Min.	Min.	Min.	Perf.	Maj.	Min.	Min.	Min.	Perf.
3\|20	5	sLLLLsLLLLsLLLLsLLLsLLLL	Perf.	Min.	Min.	Min.	Min.	Perf.	Min.	Min.	Min.	Min.	Maj.	Min.	Min.	Min.	Min.	Maj.	Min.	Min.	Min.	Perf.	Min.	Min.	Min.	Min.	Perf.
2\|21	10	sLLLLsLLLLsLLLsLLLLsLLLL	Perf.	Min.	Min.	Min.	Min.	Perf.	Min.	Min.	Min.	Min.	Maj.	Min.	Min.	Min.	Min.	Min.	Min.	Min.	Min.	Perf.	Min.	Min.	Min.	Min.	Perf.
1\|22	15	sLLLLsLLLsLLLLsLLLLsLLLL	Perf.	Min.	Min.	Min.	Min.	Perf.	Min.	Min.	Min.	Min.	Min.	Min.	Min.	Min.	Min.	Min.	Min.	Min.	Min.	Perf.	Min.	Min.	Min.	Min.	Perf.
0\|23	20	sLLLsLLLLsLLLLsLLLLsLLLL	Perf.	Min.	Min.	Min.	Min.	Dim.	Min.	Min.	Min.	Min.	Min.	Min.	Min.	Min.	Min.	Min.	Min.	Min.	Min.	Perf.	Min.	Min.	Min.	Min.	Perf.

Scale tree

Scale tree and tuning spectrum of 19L 5s
Generator^(edo)						Cents		Step ratio		Comments
Generator^(edo)						Bright	Dark	L:s	Hardness	Comments
5\24						250.000	950.000	1:1	1.000	Equalized 19L 5s
					29\139	250.360	949.640	6:5	1.200
				24\115		250.435	949.565	5:4	1.250
					43\206	250.485	949.515	9:7	1.286
			19\91			250.549	949.451	4:3	1.333	Supersoft 19L 5s
					52\249	250.602	949.398	11:8	1.375
				33\158		250.633	949.367	7:5	1.400
					47\225	250.667	949.333	10:7	1.429
		14\67				250.746	949.254	3:2	1.500	Soft 19L 5s
					51\244	250.820	949.180	11:7	1.571
				37\177		250.847	949.153	8:5	1.600
					60\287	250.871	949.129	13:8	1.625
			23\110			250.909	949.091	5:3	1.667	Semisoft 19L 5s
					55\263	250.951	949.049	12:7	1.714
				32\153		250.980	949.020	7:4	1.750
					41\196	251.020	948.980	9:5	1.800
	9\43					251.163	948.837	2:1	2.000	Basic 19L 5s Scales with tunings softer than this are proper
					40\191	251.309	948.691	9:4	2.250
				31\148		251.351	948.649	7:3	2.333
					53\253	251.383	948.617	12:5	2.400
			22\105			251.429	948.571	5:2	2.500	Semihard 19L 5s
					57\272	251.471	948.529	13:5	2.600
				35\167		251.497	948.503	8:3	2.667
					48\229	251.528	948.472	11:4	2.750
		13\62				251.613	948.387	3:1	3.000	Hard 19L 5s
					43\205	251.707	948.293	10:3	3.333
				30\143		251.748	948.252	7:2	3.500
					47\224	251.786	948.214	11:3	3.667
			17\81			251.852	948.148	4:1	4.000	Superhard 19L 5s
					38\181	251.934	948.066	9:2	4.500
				21\100		252.000	948.000	5:1	5.000
					25\119	252.101	947.899	6:1	6.000
4\19						252.632	947.368	1:0	→ ∞	Collapsed 19L 5s

This page is a stub. You can help the Xenharmonic Wiki by expanding it.

19L 5s

Contents

Scale properties

Intervals

Generator chain

Modes

Scale tree

Navigation menu

19L 5s

Scale properties

Intervals

Generator chain

Modes

Scale tree

Navigation menu

Search