3L 16s

↖ 2L 15s	↑ 3L 15s	4L 15s ↗
← 2L 16s	3L 16s	4L 16s →
↙ 2L 17s	↓ 3L 17s	4L 17s ↘

Scale structure
Step pattern	LsssssLsssssLssssss ssssssLsssssLsssssL
Equave	2/1 (1200.0 ¢)
Period	2/1 (1200.0 ¢)
Generator size
Bright	6\19 to 1\3 (378.9 ¢ to 400.0 ¢)
Dark	2\3 to 13\19 (800.0 ¢ to 821.1 ¢)
TAMNAMS information
Related to	3L 7s (sephiroid)
With tunings	4:1 to 1:0 (ultrahard)
Related MOS scales
Parent	3L 13s
Sister	16L 3s
Daughters	19L 3s, 3L 19s
Neutralized	6L 13s
2-Flought	22L 16s, 3L 35s
Equal tunings
Equalized (L:s = 1:1)	6\19 (378.9 ¢)
Supersoft (L:s = 4:3)	19\60 (380.0 ¢)
Soft (L:s = 3:2)	13\41 (380.5 ¢)
Semisoft (L:s = 5:3)	20\63 (381.0 ¢)
Basic (L:s = 2:1)	7\22 (381.8 ¢)
Semihard (L:s = 5:2)	15\47 (383.0 ¢)
Hard (L:s = 3:1)	8\25 (384.0 ¢)
Superhard (L:s = 4:1)	9\28 (385.7 ¢)
Collapsed (L:s = 1:0)	1\3 (400.0 ¢)
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3L 16s occupies the spectrum from 19edo (L = s) to 3edo (s = 0).

This MOS divides its small steps 5-5-6 between its large steps. Its generator is a small major third no less than 6/19 octave (378.947 cents). Around +5g = 3, magic appears. Going higher, würschmidt appears where the generator is exactly 5/4.

Modes

• 18|0 LsssssLsssssLssssss
• 17|1 LsssssLssssssLsssss
• 16|2 LssssssLsssssLsssss
• 15|3 sLsssssLsssssLsssss
• 14|4 sLsssssLssssssLssss
• 13|5 sLssssssLsssssLssss
• 12|6 ssLsssssLsssssLssss
• 11|7 ssLsssssLssssssLsss
• 10|8 ssLssssssLsssssLsss
• 9|9 sssLsssssLsssssLsss
• 8|10 sssLsssssLssssssLss
• 7|11 sssLssssssLsssssLss
• 6|12 ssssLsssssLsssssLss
• 5|13 ssssLsssssLssssssLs
• 4|14 ssssLssssssLsssssLs
• 3|15 sssssLsssssLsssssLs
• 2|16 sssssLsssssLssssssL
• 1|17 sssssLssssssLsssssL
• 0|18 ssssssLsssssLsssssL

Scales tree

Generator ranges:

• Bright generator: 378.9474 cents (6\19) to 400 cents (1\3)
• Dark generator: 800 cents (2\3) to 821.0526 cents (13\19)

Bright generator						Cents	L	s	L/s	Comments
6\19						378.947	1	1	1.000
					31\98	379.592	6	5	1.200
				25\79		379.747	5	4	1.250
					44\139	379.856	9	7	1.286
			19\60			380.000	4	3	1.333
					51\161	380.124	11	8	1.375	Witchcraft
				32\101		380.198	7	5	1.400
					45\142	380.282	10	7	1.429
		13\41				380.488	3	2	1.500	Magic is around here
					46\145	380.690	11	7	1.571
				33\104		380.769	8	5	1.600
					53\167	380.838	13	8	1.625	Necromancy Golden magic (380.8191¢)
			20\63			380.952	5	3	1.667
					47\148	381.081	12	7	1.714
				27\85		381.176	7	4	1.750
					34\107	381.308	9	5	1.800
	7\22					381.818	2	1	2.000	Basic 3L 16s (Generators smaller than this are proper)
					29\91	382.418	9	4	2.250
				22\69		382.609	7	3	2.333	Marveltri
					37\116	382.759	12	5	2.400	Marveltri
			15\47			382.979	5	2	2.500	Marveltri
					38\119	383.193	13	5	2.600	Unnamed golden tuning (383.2314¢)
				23\72		383.333	8	3	2.667
					31\97	383.505	11	4	2.750
		8\25				384.000	3	1	3.000
					25\78	384.615	10	3	3.333
				17\53		384.906	7	2	3.500
					26\81	385.185	11	3	3.667
			9\28			385.714	4	1	4.000
					19\59	386.441	9	2	4.500	Sulis
				10\31		387.097	5	1	5.000	Grendel/Würschmidt
					11\34	388.235	6	1	6.000
1\3						400.000	1	0	→ inf