5L 17s

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

Scale structure
Step pattern	LsssLsssLssssLsssLssss ssssLsssLssssLsssLsssL
Equave	2/1 (1200.0 ¢)
Period	2/1 (1200.0 ¢)
Generator size
Bright	13\22 to 3\5 (709.1 ¢ to 720.0 ¢)
Dark	2\5 to 9\22 (480.0 ¢ to 490.9 ¢)
TAMNAMS information
Related to	5L 2s (diatonic)
With tunings	4:1 to 1:0 (ultrahard)
Related MOS scales
Parent	5L 12s
Sister	17L 5s
Daughters	22L 5s, 5L 22s
Neutralized	10L 12s
2-Flought	27L 17s, 5L 39s
Equal tunings
Equalized (L:s = 1:1)	13\22 (709.1 ¢)
Supersoft (L:s = 4:3)	42\71 (709.9 ¢)
Soft (L:s = 3:2)	29\49 (710.2 ¢)
Semisoft (L:s = 5:3)	45\76 (710.5 ¢)
Basic (L:s = 2:1)	16\27 (711.1 ¢)
Semihard (L:s = 5:2)	35\59 (711.9 ¢)
Hard (L:s = 3:1)	19\32 (712.5 ¢)
Superhard (L:s = 4:1)	22\37 (713.5 ¢)
Collapsed (L:s = 1:0)	3\5 (720.0 ¢)
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5L 17s is a 2/1-equivalent (octave-equivalent) moment of symmetry scale containing 5 large steps and 17 small steps, repeating every octave. 5L 17s is a great-grandchild scale of 5L 2s, expanding it by 15 tones. Generators that produce this scale range from 709.1 ¢ to 720 ¢, or from 480 ¢ to 490.9 ¢.

This scale corresponds to the 22-note MOS of superpyth temperament, and any proper tuning of this scale makes for a reasonable tuning of superpyth. This scale is also present in quasiultra and ultrapyth, though these tunings are improper unlike superpyth.

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 5L 17s

Intervals			Steps subtended	Range in cents
Generic	Specific	Abbrev.
0-mosstep	Perfect 0-mosstep	P0ms	0	0.0 ¢
1-mosstep	Minor 1-mosstep	m1ms	s	0.0 ¢ to 54.5 ¢
	Major 1-mosstep	M1ms	L	54.5 ¢ to 240.0 ¢
2-mosstep	Minor 2-mosstep	m2ms	2s	0.0 ¢ to 109.1 ¢
	Major 2-mosstep	M2ms	L + s	109.1 ¢ to 240.0 ¢
3-mosstep	Minor 3-mosstep	m3ms	3s	0.0 ¢ to 163.6 ¢
	Major 3-mosstep	M3ms	L + 2s	163.6 ¢ to 240.0 ¢
4-mosstep	Minor 4-mosstep	m4ms	4s	0.0 ¢ to 218.2 ¢
	Major 4-mosstep	M4ms	L + 3s	218.2 ¢ to 240.0 ¢
5-mosstep	Minor 5-mosstep	m5ms	L + 4s	240.0 ¢ to 272.7 ¢
	Major 5-mosstep	M5ms	2L + 3s	272.7 ¢ to 480.0 ¢
6-mosstep	Minor 6-mosstep	m6ms	L + 5s	240.0 ¢ to 327.3 ¢
	Major 6-mosstep	M6ms	2L + 4s	327.3 ¢ to 480.0 ¢
7-mosstep	Minor 7-mosstep	m7ms	L + 6s	240.0 ¢ to 381.8 ¢
	Major 7-mosstep	M7ms	2L + 5s	381.8 ¢ to 480.0 ¢
8-mosstep	Minor 8-mosstep	m8ms	L + 7s	240.0 ¢ to 436.4 ¢
	Major 8-mosstep	M8ms	2L + 6s	436.4 ¢ to 480.0 ¢
9-mosstep	Perfect 9-mosstep	P9ms	2L + 7s	480.0 ¢ to 490.9 ¢
	Augmented 9-mosstep	A9ms	3L + 6s	490.9 ¢ to 720.0 ¢
10-mosstep	Minor 10-mosstep	m10ms	2L + 8s	480.0 ¢ to 545.5 ¢
	Major 10-mosstep	M10ms	3L + 7s	545.5 ¢ to 720.0 ¢
11-mosstep	Minor 11-mosstep	m11ms	2L + 9s	480.0 ¢ to 600.0 ¢
	Major 11-mosstep	M11ms	3L + 8s	600.0 ¢ to 720.0 ¢
12-mosstep	Minor 12-mosstep	m12ms	2L + 10s	480.0 ¢ to 654.5 ¢
	Major 12-mosstep	M12ms	3L + 9s	654.5 ¢ to 720.0 ¢
13-mosstep	Diminished 13-mosstep	d13ms	2L + 11s	480.0 ¢ to 709.1 ¢
	Perfect 13-mosstep	P13ms	3L + 10s	709.1 ¢ to 720.0 ¢
14-mosstep	Minor 14-mosstep	m14ms	3L + 11s	720.0 ¢ to 763.6 ¢
	Major 14-mosstep	M14ms	4L + 10s	763.6 ¢ to 960.0 ¢
15-mosstep	Minor 15-mosstep	m15ms	3L + 12s	720.0 ¢ to 818.2 ¢
	Major 15-mosstep	M15ms	4L + 11s	818.2 ¢ to 960.0 ¢
16-mosstep	Minor 16-mosstep	m16ms	3L + 13s	720.0 ¢ to 872.7 ¢
	Major 16-mosstep	M16ms	4L + 12s	872.7 ¢ to 960.0 ¢
17-mosstep	Minor 17-mosstep	m17ms	3L + 14s	720.0 ¢ to 927.3 ¢
	Major 17-mosstep	M17ms	4L + 13s	927.3 ¢ to 960.0 ¢
18-mosstep	Minor 18-mosstep	m18ms	4L + 14s	960.0 ¢ to 981.8 ¢
	Major 18-mosstep	M18ms	5L + 13s	981.8 ¢ to 1200.0 ¢
19-mosstep	Minor 19-mosstep	m19ms	4L + 15s	960.0 ¢ to 1036.4 ¢
	Major 19-mosstep	M19ms	5L + 14s	1036.4 ¢ to 1200.0 ¢
20-mosstep	Minor 20-mosstep	m20ms	4L + 16s	960.0 ¢ to 1090.9 ¢
	Major 20-mosstep	M20ms	5L + 15s	1090.9 ¢ to 1200.0 ¢
21-mosstep	Minor 21-mosstep	m21ms	4L + 17s	960.0 ¢ to 1145.5 ¢
	Major 21-mosstep	M21ms	5L + 16s	1145.5 ¢ to 1200.0 ¢
22-mosstep	Perfect 22-mosstep	P22ms	5L + 17s	1200.0 ¢

Generator chain

Generator chain of 5L 17s

Bright gens	Scale degree	Abbrev.
26	Augmented 8-mosdegree	A8md
25	Augmented 17-mosdegree	A17md
24	Augmented 4-mosdegree	A4md
23	Augmented 13-mosdegree	A13md
22	Augmented 0-mosdegree	A0md
21	Augmented 9-mosdegree	A9md
20	Major 18-mosdegree	M18md
19	Major 5-mosdegree	M5md
18	Major 14-mosdegree	M14md
17	Major 1-mosdegree	M1md
16	Major 10-mosdegree	M10md
15	Major 19-mosdegree	M19md
14	Major 6-mosdegree	M6md
13	Major 15-mosdegree	M15md
12	Major 2-mosdegree	M2md
11	Major 11-mosdegree	M11md
10	Major 20-mosdegree	M20md
9	Major 7-mosdegree	M7md
8	Major 16-mosdegree	M16md
7	Major 3-mosdegree	M3md
6	Major 12-mosdegree	M12md
5	Major 21-mosdegree	M21md
4	Major 8-mosdegree	M8md
3	Major 17-mosdegree	M17md
2	Major 4-mosdegree	M4md
1	Perfect 13-mosdegree	P13md
0	Perfect 0-mosdegree Perfect 22-mosdegree	P0md P22md
−1	Perfect 9-mosdegree	P9md
−2	Minor 18-mosdegree	m18md
−3	Minor 5-mosdegree	m5md
−4	Minor 14-mosdegree	m14md
−5	Minor 1-mosdegree	m1md
−6	Minor 10-mosdegree	m10md
−7	Minor 19-mosdegree	m19md
−8	Minor 6-mosdegree	m6md
−9	Minor 15-mosdegree	m15md
−10	Minor 2-mosdegree	m2md
−11	Minor 11-mosdegree	m11md
−12	Minor 20-mosdegree	m20md
−13	Minor 7-mosdegree	m7md
−14	Minor 16-mosdegree	m16md
−15	Minor 3-mosdegree	m3md
−16	Minor 12-mosdegree	m12md
−17	Minor 21-mosdegree	m21md
−18	Minor 8-mosdegree	m8md
−19	Minor 17-mosdegree	m17md
−20	Minor 4-mosdegree	m4md
−21	Diminished 13-mosdegree	d13md
−22	Diminished 22-mosdegree	d22md
−23	Diminished 9-mosdegree	d9md
−24	Diminished 18-mosdegree	d18md
−25	Diminished 5-mosdegree	d5md
−26	Diminished 14-mosdegree	d14md

Scale tree

Scale tree and tuning spectrum of 5L 17s

Generator(edo)						Cents		Step ratio		Comments
						Bright	Dark	L:s	Hardness
13\22						709.091	490.909	1:1	1.000	Equalized 5L 17s
					68\115	709.565	490.435	6:5	1.200
				55\93		709.677	490.323	5:4	1.250
					97\164	709.756	490.244	9:7	1.286
			42\71			709.859	490.141	4:3	1.333	Supersoft 5L 17s
					113\191	709.948	490.052	11:8	1.375
				71\120		710.000	490.000	7:5	1.400
					100\169	710.059	489.941	10:7	1.429
		29\49				710.204	489.796	3:2	1.500	Soft 5L 17s
					103\174	710.345	489.655	11:7	1.571
				74\125		710.400	489.600	8:5	1.600
					119\201	710.448	489.552	13:8	1.625
			45\76			710.526	489.474	5:3	1.667	Semisoft 5L 17s
					106\179	710.615	489.385	12:7	1.714
				61\103		710.680	489.320	7:4	1.750
					77\130	710.769	489.231	9:5	1.800
	16\27					711.111	488.889	2:1	2.000	Basic 5L 17s Scales with tunings softer than this are proper
					67\113	711.504	488.496	9:4	2.250
				51\86		711.628	488.372	7:3	2.333
					86\145	711.724	488.276	12:5	2.400
			35\59			711.864	488.136	5:2	2.500	Semihard 5L 17s
					89\150	712.000	488.000	13:5	2.600
				54\91		712.088	487.912	8:3	2.667
					73\123	712.195	487.805	11:4	2.750
		19\32				712.500	487.500	3:1	3.000	Hard 5L 17s
					60\101	712.871	487.129	10:3	3.333
				41\69		713.043	486.957	7:2	3.500
					63\106	713.208	486.792	11:3	3.667
			22\37			713.514	486.486	4:1	4.000	Superhard 5L 17s
					47\79	713.924	486.076	9:2	4.500
				25\42		714.286	485.714	5:1	5.000
					28\47	714.894	485.106	6:1	6.000
3\5						720.000	480.000	1:0	→ ∞	Collapsed 5L 17s