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
Descends from	5L 4s (semiquartal)
Related MOS scales
Parent	5L 14s
Sister	5L 19s
Daughters	24L 19s 19L 24s
Equal tunings
Equalized (L:s = 1:1)	5\24 (250.0¢)
Supersoft (L:s = 4:3)	19\91 (250.5¢)
Soft (L:s = 3:2)	14\67 (250.7¢)
Semisoft (L:s = 5:3)	23\110 (250.9¢)
Basic (L:s = 2:1)	9\43 (251.2¢)
Semihard (L:s = 5:2)	22\105 (251.4¢)
Hard (L:s = 3:1)	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¢.

Modes

Modes of 19L 5s

UDP	Rotational order	Step pattern
23|0	1	LLLLsLLLLsLLLLsLLLLsLLLs
22|1	6	LLLLsLLLLsLLLLsLLLsLLLLs
21|2	11	LLLLsLLLLsLLLsLLLLsLLLLs
20|3	16	LLLLsLLLsLLLLsLLLLsLLLLs
19|4	21	LLLsLLLLsLLLLsLLLLsLLLLs
18|5	2	LLLsLLLLsLLLLsLLLLsLLLsL
17|6	7	LLLsLLLLsLLLLsLLLsLLLLsL
16|7	12	LLLsLLLLsLLLsLLLLsLLLLsL
15|8	17	LLLsLLLsLLLLsLLLLsLLLLsL
14|9	22	LLsLLLLsLLLLsLLLLsLLLLsL
13|10	3	LLsLLLLsLLLLsLLLLsLLLsLL
12|11	8	LLsLLLLsLLLLsLLLsLLLLsLL
11|12	13	LLsLLLLsLLLsLLLLsLLLLsLL
10|13	18	LLsLLLsLLLLsLLLLsLLLLsLL
9|14	23	LsLLLLsLLLLsLLLLsLLLLsLL
8|15	4	LsLLLLsLLLLsLLLLsLLLsLLL
7|16	9	LsLLLLsLLLLsLLLsLLLLsLLL
6|17	14	LsLLLLsLLLsLLLLsLLLLsLLL
5|18	19	LsLLLsLLLLsLLLLsLLLLsLLL
4|19	24	sLLLLsLLLLsLLLLsLLLLsLLL
3|20	5	sLLLLsLLLLsLLLLsLLLsLLLL
2|21	10	sLLLLsLLLLsLLLsLLLLsLLLL
1|22	15	sLLLLsLLLsLLLLsLLLLsLLLL
0|23	20	sLLLsLLLLsLLLLsLLLLsLLLL

Scale tree

Scale tree and tuning spectrum of 19L 5s

Generator (in steps of edo)						Cents		Step ratio		Comments
						Bright	Dark	L:s	Hardness
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

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