17L 5s

↖16L 4s	↑17L 4s	18L 4s↗
←16L 5s	17L 5s	18L 5s→
↙16L 6s	↓17L 6s	18L 6s↘

┌╥╥╥╥┬╥╥╥┬╥╥╥╥┬╥╥╥┬╥╥╥┬┐ │║║║║│║║║│║║║║│║║║│║║║││ ││││││││││││││││││││││││ └┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┘
Scale structure
Step pattern	LLLLsLLLsLLLLsLLLsLLLs sLLLsLLLsLLLLsLLLsLLLL
Equave	2/1 (1200.0¢)
Period	2/1 (1200.0¢)
Generator size
Bright	9\22 to 7\17 (490.9¢ to 494.1¢)
Dark	10\17 to 13\22 (705.9¢ to 709.1¢)
TAMNAMS information
Descends from	5L 2s (diatonic)
Required step ratio range	3:1 to 4:1 (parahard)
Related MOS scales
Parent	5L 12s
Sister	5L 17s
Daughters	22L 17s 17L 22s
Equal tunings
Equalized (L:s = 1:1)	9\22 (490.9¢)
Supersoft (L:s = 4:3)	34\83 (491.6¢)
Soft (L:s = 3:2)	25\61 (491.8¢)
Semisoft (L:s = 5:3)	41\100 (492.0¢)
Basic (L:s = 2:1)	16\39 (492.3¢)
Semihard (L:s = 5:2)	39\95 (492.6¢)
Hard (L:s = 3:1)	23\56 (492.9¢)
Superhard (L:s = 4:1)	30\73 (493.2¢)
Collapsed (L:s = 1:0)	7\17 (494.1¢)

17L 5s is a 2/1-equivalent (octave-equivalent) moment of symmetry scale containing 17 large steps and 5 small steps, repeating every octave. 17L 5s is a great-grandchild scale of 5L 2s, expanding it by 15 tones. Generators that produce this scale range from 490.9¢ to 494.1¢, or from 705.9¢ to 709.1¢.

This scale is the parent of another MOS scale that exhibits the fractal-like acoustic effects for which Archagall temperament is named- however, this scale also has tuning areas that don't support these effects.

Modes

Modes of 17L 5s

UDP	Rotational order	Step pattern
21|0	1	LLLLsLLLsLLLLsLLLsLLLs
20|1	10	LLLLsLLLsLLLsLLLLsLLLs
19|2	19	LLLsLLLLsLLLsLLLLsLLLs
18|3	6	LLLsLLLLsLLLsLLLsLLLLs
17|4	15	LLLsLLLsLLLLsLLLsLLLLs
16|5	2	LLLsLLLsLLLLsLLLsLLLsL
15|6	11	LLLsLLLsLLLsLLLLsLLLsL
14|7	20	LLsLLLLsLLLsLLLLsLLLsL
13|8	7	LLsLLLLsLLLsLLLsLLLLsL
12|9	16	LLsLLLsLLLLsLLLsLLLLsL
11|10	3	LLsLLLsLLLLsLLLsLLLsLL
10|11	12	LLsLLLsLLLsLLLLsLLLsLL
9|12	21	LsLLLLsLLLsLLLLsLLLsLL
8|13	8	LsLLLLsLLLsLLLsLLLLsLL
7|14	17	LsLLLsLLLLsLLLsLLLLsLL
6|15	4	LsLLLsLLLLsLLLsLLLsLLL
5|16	13	LsLLLsLLLsLLLLsLLLsLLL
4|17	22	sLLLLsLLLsLLLLsLLLsLLL
3|18	9	sLLLLsLLLsLLLsLLLLsLLL
2|19	18	sLLLsLLLLsLLLsLLLLsLLL
1|20	5	sLLLsLLLLsLLLsLLLsLLLL
0|21	14	sLLLsLLLsLLLLsLLLsLLLL

Scale tree

Scale tree and tuning spectrum of 17L 5s

Generator(edo)						Cents		Step ratio		Comments
						Bright	Dark	L:s	Hardness
9\22						490.909	709.091	1:1	1.000	Equalized 17L 5s
					52\127	491.339	708.661	6:5	1.200
				43\105		491.429	708.571	5:4	1.250
					77\188	491.489	708.511	9:7	1.286
			34\83			491.566	708.434	4:3	1.333	Supersoft 17L 5s
					93\227	491.630	708.370	11:8	1.375
				59\144		491.667	708.333	7:5	1.400
					84\205	491.707	708.293	10:7	1.429
		25\61				491.803	708.197	3:2	1.500	Soft 17L 5s
					91\222	491.892	708.108	11:7	1.571
				66\161		491.925	708.075	8:5	1.600
					107\261	491.954	708.046	13:8	1.625
			41\100			492.000	708.000	5:3	1.667	Semisoft 17L 5s
					98\239	492.050	707.950	12:7	1.714
				57\139		492.086	707.914	7:4	1.750
					73\178	492.135	707.865	9:5	1.800
	16\39					492.308	707.692	2:1	2.000	Basic 17L 5s Scales with tunings softer than this are proper
					71\173	492.486	707.514	9:4	2.250
				55\134		492.537	707.463	7:3	2.333
					94\229	492.576	707.424	12:5	2.400
			39\95			492.632	707.368	5:2	2.500	Semihard 17L 5s
					101\246	492.683	707.317	13:5	2.600
				62\151		492.715	707.285	8:3	2.667
					85\207	492.754	707.246	11:4	2.750
		23\56				492.857	707.143	3:1	3.000	Hard 17L 5s
					76\185	492.973	707.027	10:3	3.333
				53\129		493.023	706.977	7:2	3.500
					83\202	493.069	706.931	11:3	3.667
			30\73			493.151	706.849	4:1	4.000	Superhard 17L 5s Archagall
					67\163	493.252	706.748	9:2	4.500
				37\90		493.333	706.667	5:1	5.000
					44\107	493.458	706.542	6:1	6.000
7\17						494.118	705.882	1:0	→ ∞	Collapsed 17L 5s