7L 16s

↖ 6L 15s	↑ 7L 15s	8L 15s ↗
← 6L 16s	7L 16s	8L 16s →
↙ 6L 17s	↓ 7L 17s	8L 17s ↘

┌╥┬┬╥┬┬╥┬┬╥┬┬┬╥┬┬╥┬┬╥┬┬┬┐ │║││║││║││║│││║││║││║││││ │││││││││││││││││││││││││ └┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┘
Scale structure
Step pattern	LssLssLssLsssLssLssLsss sssLssLssLsssLssLssLssL
Equave	2/1 (1200.0¢)
Period	2/1 (1200.0¢)
Generator size
Bright	13\23 to 4\7 (678.3¢ to 685.7¢)
Dark	3\7 to 10\23 (514.3¢ to 521.7¢)
TAMNAMS information
Descends from	7L 2s (armotonic)
Ancestor's step ratio range	3:1 to 1:0 (hard)
Related MOS scales
Parent	7L 9s
Sister	16L 7s
Daughters	23L 7s, 7L 23s
Neutralized	14L 9s
2-Flought	30L 16s, 7L 39s
Equal tunings
Equalized (L:s = 1:1)	13\23 (678.3¢)
Supersoft (L:s = 4:3)	43\76 (678.9¢)
Soft (L:s = 3:2)	30\53 (679.2¢)
Semisoft (L:s = 5:3)	47\83 (679.5¢)
Basic (L:s = 2:1)	17\30 (680.0¢)
Semihard (L:s = 5:2)	38\67 (680.6¢)
Hard (L:s = 3:1)	21\37 (681.1¢)
Superhard (L:s = 4:1)	25\44 (681.8¢)
Collapsed (L:s = 1:0)	4\7 (685.7¢)

7L 16s is a 2/1-equivalent (octave-equivalent) moment of symmetry scale containing 7 large steps and 16 small steps, repeating every octave. 7L 16s is a grandchild scale of 7L 2s, expanding it by 14 tones. Generators that produce this scale range from 678.3¢ to 685.7¢, or from 514.3¢ to 521.7¢.

Modes

Modes of 7L 16s

UDP	Cyclic Order	Step Pattern
22|0	1	LssLssLssLsssLssLssLsss
21|1	14	LssLssLsssLssLssLssLsss
20|2	4	LssLssLsssLssLssLsssLss
19|3	17	LssLsssLssLssLssLsssLss
18|4	7	LssLsssLssLssLsssLssLss
17|5	20	LsssLssLssLssLsssLssLss
16|6	10	LsssLssLssLsssLssLssLss
15|7	23	sLssLssLssLsssLssLssLss
14|8	13	sLssLssLsssLssLssLssLss
13|9	3	sLssLssLsssLssLssLsssLs
12|10	16	sLssLsssLssLssLssLsssLs
11|11	6	sLssLsssLssLssLsssLssLs
10|12	19	sLsssLssLssLssLsssLssLs
9|13	9	sLsssLssLssLsssLssLssLs
8|14	22	ssLssLssLssLsssLssLssLs
7|15	12	ssLssLssLsssLssLssLssLs
6|16	2	ssLssLssLsssLssLssLsssL
5|17	15	ssLssLsssLssLssLssLsssL
4|18	5	ssLssLsssLssLssLsssLssL
3|19	18	ssLsssLssLssLssLsssLssL
2|20	8	ssLsssLssLssLsssLssLssL
1|21	21	sssLssLssLssLsssLssLssL
0|22	11	sssLssLssLsssLssLssLssL

Scale tree

Scale Tree and Tuning Spectrum of 7L 16s

Generator(edo)						Cents		Step Ratio		Comments
						Bright	Dark	L:s	Hardness
13\23						678.261	521.739	1:1	1.000	Equalized 7L 16s
					69\122	678.689	521.311	6:5	1.200
				56\99		678.788	521.212	5:4	1.250
					99\175	678.857	521.143	9:7	1.286
			43\76			678.947	521.053	4:3	1.333	Supersoft 7L 16s
					116\205	679.024	520.976	11:8	1.375
				73\129		679.070	520.930	7:5	1.400
					103\182	679.121	520.879	10:7	1.429
		30\53				679.245	520.755	3:2	1.500	Soft 7L 16s
					107\189	679.365	520.635	11:7	1.571
				77\136		679.412	520.588	8:5	1.600
					124\219	679.452	520.548	13:8	1.625
			47\83			679.518	520.482	5:3	1.667	Semisoft 7L 16s
					111\196	679.592	520.408	12:7	1.714
				64\113		679.646	520.354	7:4	1.750
					81\143	679.720	520.280	9:5	1.800
	17\30					680.000	520.000	2:1	2.000	Basic 7L 16s Scales with tunings softer than this are proper
					72\127	680.315	519.685	9:4	2.250
				55\97		680.412	519.588	7:3	2.333
					93\164	680.488	519.512	12:5	2.400
			38\67			680.597	519.403	5:2	2.500	Semihard 7L 16s
					97\171	680.702	519.298	13:5	2.600
				59\104		680.769	519.231	8:3	2.667
					80\141	680.851	519.149	11:4	2.750
		21\37				681.081	518.919	3:1	3.000	Hard 7L 16s
					67\118	681.356	518.644	10:3	3.333
				46\81		681.481	518.519	7:2	3.500
					71\125	681.600	518.400	11:3	3.667
			25\44			681.818	518.182	4:1	4.000	Superhard 7L 16s
					54\95	682.105	517.895	9:2	4.500
				29\51		682.353	517.647	5:1	5.000
					33\58	682.759	517.241	6:1	6.000
4\7						685.714	514.286	1:0	→ ∞	Collapsed 7L 16s