17L 7s

↖ 16L 6s	↑ 17L 6s	18L 6s ↗
← 16L 7s	17L 7s	18L 7s →
↙ 16L 8s	↓ 17L 8s	18L 8s ↘

Scale structure
Step pattern	LLLsLLsLLLsLLsLLLsLLsLLs sLLsLLsLLLsLLsLLLsLLsLLL
Equave	2/1 (1200.0 ¢)
Period	2/1 (1200.0 ¢)
Generator size
Bright	7\24 to 5\17 (350.0 ¢ to 352.9 ¢)
Dark	12\17 to 17\24 (847.1 ¢ to 850.0 ¢)
TAMNAMS information
Related to	7L 3s (dicoid)
With tunings	2:1 to 3:1 (hypohard)
Related MOS scales
Parent	7L 10s
Sister	7L 17s
Daughters	24L 17s, 17L 24s
Neutralized	10L 14s
2-Flought	41L 7s, 17L 31s
Equal tunings
Equalized (L:s = 1:1)	7\24 (350.0 ¢)
Supersoft (L:s = 4:3)	26\89 (350.6 ¢)
Soft (L:s = 3:2)	19\65 (350.8 ¢)
Semisoft (L:s = 5:3)	31\106 (350.9 ¢)
Basic (L:s = 2:1)	12\41 (351.2 ¢)
Semihard (L:s = 5:2)	29\99 (351.5 ¢)
Hard (L:s = 3:1)	17\58 (351.7 ¢)
Superhard (L:s = 4:1)	22\75 (352.0 ¢)
Collapsed (L:s = 1:0)	5\17 (352.9 ¢)
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17L 7s is a 2/1-equivalent (octave-equivalent) moment of symmetry scale containing 17 large steps and 7 small steps, repeating every octave. 17L 7s is a grandchild scale of 7L 3s, expanding it by 14 tones. Generators that produce this scale range from 350 ¢ to 352.9 ¢, or from 847.1 ¢ to 850 ¢.

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 17L 7s

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 50.0 ¢
	Major 1-mosstep	M1ms	L	50.0 ¢ to 70.6 ¢
2-mosstep	Minor 2-mosstep	m2ms	L + s	70.6 ¢ to 100.0 ¢
	Major 2-mosstep	M2ms	2L	100.0 ¢ to 141.2 ¢
3-mosstep	Minor 3-mosstep	m3ms	2L + s	141.2 ¢ to 150.0 ¢
	Major 3-mosstep	M3ms	3L	150.0 ¢ to 211.8 ¢
4-mosstep	Minor 4-mosstep	m4ms	2L + 2s	141.2 ¢ to 200.0 ¢
	Major 4-mosstep	M4ms	3L + s	200.0 ¢ to 211.8 ¢
5-mosstep	Minor 5-mosstep	m5ms	3L + 2s	211.8 ¢ to 250.0 ¢
	Major 5-mosstep	M5ms	4L + s	250.0 ¢ to 282.4 ¢
6-mosstep	Minor 6-mosstep	m6ms	4L + 2s	282.4 ¢ to 300.0 ¢
	Major 6-mosstep	M6ms	5L + s	300.0 ¢ to 352.9 ¢
7-mosstep	Diminished 7-mosstep	d7ms	4L + 3s	282.4 ¢ to 350.0 ¢
	Perfect 7-mosstep	P7ms	5L + 2s	350.0 ¢ to 352.9 ¢
8-mosstep	Minor 8-mosstep	m8ms	5L + 3s	352.9 ¢ to 400.0 ¢
	Major 8-mosstep	M8ms	6L + 2s	400.0 ¢ to 423.5 ¢
9-mosstep	Minor 9-mosstep	m9ms	6L + 3s	423.5 ¢ to 450.0 ¢
	Major 9-mosstep	M9ms	7L + 2s	450.0 ¢ to 494.1 ¢
10-mosstep	Minor 10-mosstep	m10ms	7L + 3s	494.1 ¢ to 500.0 ¢
	Major 10-mosstep	M10ms	8L + 2s	500.0 ¢ to 564.7 ¢
11-mosstep	Minor 11-mosstep	m11ms	7L + 4s	494.1 ¢ to 550.0 ¢
	Major 11-mosstep	M11ms	8L + 3s	550.0 ¢ to 564.7 ¢
12-mosstep	Minor 12-mosstep	m12ms	8L + 4s	564.7 ¢ to 600.0 ¢
	Major 12-mosstep	M12ms	9L + 3s	600.0 ¢ to 635.3 ¢
13-mosstep	Minor 13-mosstep	m13ms	9L + 4s	635.3 ¢ to 650.0 ¢
	Major 13-mosstep	M13ms	10L + 3s	650.0 ¢ to 705.9 ¢
14-mosstep	Minor 14-mosstep	m14ms	9L + 5s	635.3 ¢ to 700.0 ¢
	Major 14-mosstep	M14ms	10L + 4s	700.0 ¢ to 705.9 ¢
15-mosstep	Minor 15-mosstep	m15ms	10L + 5s	705.9 ¢ to 750.0 ¢
	Major 15-mosstep	M15ms	11L + 4s	750.0 ¢ to 776.5 ¢
16-mosstep	Minor 16-mosstep	m16ms	11L + 5s	776.5 ¢ to 800.0 ¢
	Major 16-mosstep	M16ms	12L + 4s	800.0 ¢ to 847.1 ¢
17-mosstep	Perfect 17-mosstep	P17ms	12L + 5s	847.1 ¢ to 850.0 ¢
	Augmented 17-mosstep	A17ms	13L + 4s	850.0 ¢ to 917.6 ¢
18-mosstep	Minor 18-mosstep	m18ms	12L + 6s	847.1 ¢ to 900.0 ¢
	Major 18-mosstep	M18ms	13L + 5s	900.0 ¢ to 917.6 ¢
19-mosstep	Minor 19-mosstep	m19ms	13L + 6s	917.6 ¢ to 950.0 ¢
	Major 19-mosstep	M19ms	14L + 5s	950.0 ¢ to 988.2 ¢
20-mosstep	Minor 20-mosstep	m20ms	14L + 6s	988.2 ¢ to 1000.0 ¢
	Major 20-mosstep	M20ms	15L + 5s	1000.0 ¢ to 1058.8 ¢
21-mosstep	Minor 21-mosstep	m21ms	14L + 7s	988.2 ¢ to 1050.0 ¢
	Major 21-mosstep	M21ms	15L + 6s	1050.0 ¢ to 1058.8 ¢
22-mosstep	Minor 22-mosstep	m22ms	15L + 7s	1058.8 ¢ to 1100.0 ¢
	Major 22-mosstep	M22ms	16L + 6s	1100.0 ¢ to 1129.4 ¢
23-mosstep	Minor 23-mosstep	m23ms	16L + 7s	1129.4 ¢ to 1150.0 ¢
	Major 23-mosstep	M23ms	17L + 6s	1150.0 ¢ to 1200.0 ¢
24-mosstep	Perfect 24-mosstep	P24ms	17L + 7s	1200.0 ¢

Generator chain

Generator chain of 17L 7s

Bright gens	Scale degree	Abbrev.
40	Augmented 16-mosdegree	A16md
39	Augmented 9-mosdegree	A9md
38	Augmented 2-mosdegree	A2md
37	Augmented 19-mosdegree	A19md
36	Augmented 12-mosdegree	A12md
35	Augmented 5-mosdegree	A5md
34	Augmented 22-mosdegree	A22md
33	Augmented 15-mosdegree	A15md
32	Augmented 8-mosdegree	A8md
31	Augmented 1-mosdegree	A1md
30	Augmented 18-mosdegree	A18md
29	Augmented 11-mosdegree	A11md
28	Augmented 4-mosdegree	A4md
27	Augmented 21-mosdegree	A21md
26	Augmented 14-mosdegree	A14md
25	Augmented 7-mosdegree	A7md
24	Augmented 0-mosdegree	A0md
23	Augmented 17-mosdegree	A17md
22	Major 10-mosdegree	M10md
21	Major 3-mosdegree	M3md
20	Major 20-mosdegree	M20md
19	Major 13-mosdegree	M13md
18	Major 6-mosdegree	M6md
17	Major 23-mosdegree	M23md
16	Major 16-mosdegree	M16md
15	Major 9-mosdegree	M9md
14	Major 2-mosdegree	M2md
13	Major 19-mosdegree	M19md
12	Major 12-mosdegree	M12md
11	Major 5-mosdegree	M5md
10	Major 22-mosdegree	M22md
9	Major 15-mosdegree	M15md
8	Major 8-mosdegree	M8md
7	Major 1-mosdegree	M1md
6	Major 18-mosdegree	M18md
5	Major 11-mosdegree	M11md
4	Major 4-mosdegree	M4md
3	Major 21-mosdegree	M21md
2	Major 14-mosdegree	M14md
1	Perfect 7-mosdegree	P7md
0	Perfect 0-mosdegree Perfect 24-mosdegree	P0md P24md
−1	Perfect 17-mosdegree	P17md
−2	Minor 10-mosdegree	m10md
−3	Minor 3-mosdegree	m3md
−4	Minor 20-mosdegree	m20md
−5	Minor 13-mosdegree	m13md
−6	Minor 6-mosdegree	m6md
−7	Minor 23-mosdegree	m23md
−8	Minor 16-mosdegree	m16md
−9	Minor 9-mosdegree	m9md
−10	Minor 2-mosdegree	m2md
−11	Minor 19-mosdegree	m19md
−12	Minor 12-mosdegree	m12md
−13	Minor 5-mosdegree	m5md
−14	Minor 22-mosdegree	m22md
−15	Minor 15-mosdegree	m15md
−16	Minor 8-mosdegree	m8md
−17	Minor 1-mosdegree	m1md
−18	Minor 18-mosdegree	m18md
−19	Minor 11-mosdegree	m11md
−20	Minor 4-mosdegree	m4md
−21	Minor 21-mosdegree	m21md
−22	Minor 14-mosdegree	m14md
−23	Diminished 7-mosdegree	d7md
−24	Diminished 24-mosdegree	d24md
−25	Diminished 17-mosdegree	d17md
−26	Diminished 10-mosdegree	d10md
−27	Diminished 3-mosdegree	d3md
−28	Diminished 20-mosdegree	d20md
−29	Diminished 13-mosdegree	d13md
−30	Diminished 6-mosdegree	d6md
−31	Diminished 23-mosdegree	d23md
−32	Diminished 16-mosdegree	d16md
−33	Diminished 9-mosdegree	d9md
−34	Diminished 2-mosdegree	d2md
−35	Diminished 19-mosdegree	d19md
−36	Diminished 12-mosdegree	d12md
−37	Diminished 5-mosdegree	d5md
−38	Diminished 22-mosdegree	d22md
−39	Diminished 15-mosdegree	d15md
−40	Diminished 8-mosdegree	d8md

Modes

Scale degrees of the modes of 17L 7s

UDP	Cyclic order	Step pattern	Scale degree (mosdegree)
			0	1	2	3	4	5	6	7	8	9	10	11	12	13	14	15	16	17	18	19	20	21	22	23	24
23|0	1	LLLsLLsLLLsLLsLLLsLLsLLs	Perf.	Maj.	Maj.	Maj.	Maj.	Maj.	Maj.	Perf.	Maj.	Maj.	Maj.	Maj.	Maj.	Maj.	Maj.	Maj.	Maj.	Aug.	Maj.	Maj.	Maj.	Maj.	Maj.	Maj.	Perf.
22|1	8	LLLsLLsLLLsLLsLLsLLLsLLs	Perf.	Maj.	Maj.	Maj.	Maj.	Maj.	Maj.	Perf.	Maj.	Maj.	Maj.	Maj.	Maj.	Maj.	Maj.	Maj.	Maj.	Perf.	Maj.	Maj.	Maj.	Maj.	Maj.	Maj.	Perf.
21|2	15	LLLsLLsLLsLLLsLLsLLLsLLs	Perf.	Maj.	Maj.	Maj.	Maj.	Maj.	Maj.	Perf.	Maj.	Maj.	Min.	Maj.	Maj.	Maj.	Maj.	Maj.	Maj.	Perf.	Maj.	Maj.	Maj.	Maj.	Maj.	Maj.	Perf.
20|3	22	LLsLLLsLLsLLLsLLsLLLsLLs	Perf.	Maj.	Maj.	Min.	Maj.	Maj.	Maj.	Perf.	Maj.	Maj.	Min.	Maj.	Maj.	Maj.	Maj.	Maj.	Maj.	Perf.	Maj.	Maj.	Maj.	Maj.	Maj.	Maj.	Perf.
19|4	5	LLsLLLsLLsLLLsLLsLLsLLLs	Perf.	Maj.	Maj.	Min.	Maj.	Maj.	Maj.	Perf.	Maj.	Maj.	Min.	Maj.	Maj.	Maj.	Maj.	Maj.	Maj.	Perf.	Maj.	Maj.	Min.	Maj.	Maj.	Maj.	Perf.
18|5	12	LLsLLLsLLsLLsLLLsLLsLLLs	Perf.	Maj.	Maj.	Min.	Maj.	Maj.	Maj.	Perf.	Maj.	Maj.	Min.	Maj.	Maj.	Min.	Maj.	Maj.	Maj.	Perf.	Maj.	Maj.	Min.	Maj.	Maj.	Maj.	Perf.
17|6	19	LLsLLsLLLsLLsLLLsLLsLLLs	Perf.	Maj.	Maj.	Min.	Maj.	Maj.	Min.	Perf.	Maj.	Maj.	Min.	Maj.	Maj.	Min.	Maj.	Maj.	Maj.	Perf.	Maj.	Maj.	Min.	Maj.	Maj.	Maj.	Perf.
16|7	2	LLsLLsLLLsLLsLLLsLLsLLsL	Perf.	Maj.	Maj.	Min.	Maj.	Maj.	Min.	Perf.	Maj.	Maj.	Min.	Maj.	Maj.	Min.	Maj.	Maj.	Maj.	Perf.	Maj.	Maj.	Min.	Maj.	Maj.	Min.	Perf.
15|8	9	LLsLLsLLLsLLsLLsLLLsLLsL	Perf.	Maj.	Maj.	Min.	Maj.	Maj.	Min.	Perf.	Maj.	Maj.	Min.	Maj.	Maj.	Min.	Maj.	Maj.	Min.	Perf.	Maj.	Maj.	Min.	Maj.	Maj.	Min.	Perf.
14|9	16	LLsLLsLLsLLLsLLsLLLsLLsL	Perf.	Maj.	Maj.	Min.	Maj.	Maj.	Min.	Perf.	Maj.	Min.	Min.	Maj.	Maj.	Min.	Maj.	Maj.	Min.	Perf.	Maj.	Maj.	Min.	Maj.	Maj.	Min.	Perf.
13|10	23	LsLLLsLLsLLLsLLsLLLsLLsL	Perf.	Maj.	Min.	Min.	Maj.	Maj.	Min.	Perf.	Maj.	Min.	Min.	Maj.	Maj.	Min.	Maj.	Maj.	Min.	Perf.	Maj.	Maj.	Min.	Maj.	Maj.	Min.	Perf.
12|11	6	LsLLLsLLsLLLsLLsLLsLLLsL	Perf.	Maj.	Min.	Min.	Maj.	Maj.	Min.	Perf.	Maj.	Min.	Min.	Maj.	Maj.	Min.	Maj.	Maj.	Min.	Perf.	Maj.	Min.	Min.	Maj.	Maj.	Min.	Perf.
11|12	13	LsLLLsLLsLLsLLLsLLsLLLsL	Perf.	Maj.	Min.	Min.	Maj.	Maj.	Min.	Perf.	Maj.	Min.	Min.	Maj.	Min.	Min.	Maj.	Maj.	Min.	Perf.	Maj.	Min.	Min.	Maj.	Maj.	Min.	Perf.
10|13	20	LsLLsLLLsLLsLLLsLLsLLLsL	Perf.	Maj.	Min.	Min.	Maj.	Min.	Min.	Perf.	Maj.	Min.	Min.	Maj.	Min.	Min.	Maj.	Maj.	Min.	Perf.	Maj.	Min.	Min.	Maj.	Maj.	Min.	Perf.
9|14	3	LsLLsLLLsLLsLLLsLLsLLsLL	Perf.	Maj.	Min.	Min.	Maj.	Min.	Min.	Perf.	Maj.	Min.	Min.	Maj.	Min.	Min.	Maj.	Maj.	Min.	Perf.	Maj.	Min.	Min.	Maj.	Min.	Min.	Perf.
8|15	10	LsLLsLLLsLLsLLsLLLsLLsLL	Perf.	Maj.	Min.	Min.	Maj.	Min.	Min.	Perf.	Maj.	Min.	Min.	Maj.	Min.	Min.	Maj.	Min.	Min.	Perf.	Maj.	Min.	Min.	Maj.	Min.	Min.	Perf.
7|16	17	LsLLsLLsLLLsLLsLLLsLLsLL	Perf.	Maj.	Min.	Min.	Maj.	Min.	Min.	Perf.	Min.	Min.	Min.	Maj.	Min.	Min.	Maj.	Min.	Min.	Perf.	Maj.	Min.	Min.	Maj.	Min.	Min.	Perf.
6|17	24	sLLLsLLsLLLsLLsLLLsLLsLL	Perf.	Min.	Min.	Min.	Maj.	Min.	Min.	Perf.	Min.	Min.	Min.	Maj.	Min.	Min.	Maj.	Min.	Min.	Perf.	Maj.	Min.	Min.	Maj.	Min.	Min.	Perf.
5|18	7	sLLLsLLsLLLsLLsLLsLLLsLL	Perf.	Min.	Min.	Min.	Maj.	Min.	Min.	Perf.	Min.	Min.	Min.	Maj.	Min.	Min.	Maj.	Min.	Min.	Perf.	Min.	Min.	Min.	Maj.	Min.	Min.	Perf.
4|19	14	sLLLsLLsLLsLLLsLLsLLLsLL	Perf.	Min.	Min.	Min.	Maj.	Min.	Min.	Perf.	Min.	Min.	Min.	Min.	Min.	Min.	Maj.	Min.	Min.	Perf.	Min.	Min.	Min.	Maj.	Min.	Min.	Perf.
3|20	21	sLLsLLLsLLsLLLsLLsLLLsLL	Perf.	Min.	Min.	Min.	Min.	Min.	Min.	Perf.	Min.	Min.	Min.	Min.	Min.	Min.	Maj.	Min.	Min.	Perf.	Min.	Min.	Min.	Maj.	Min.	Min.	Perf.
2|21	4	sLLsLLLsLLsLLLsLLsLLsLLL	Perf.	Min.	Min.	Min.	Min.	Min.	Min.	Perf.	Min.	Min.	Min.	Min.	Min.	Min.	Maj.	Min.	Min.	Perf.	Min.	Min.	Min.	Min.	Min.	Min.	Perf.
1|22	11	sLLsLLLsLLsLLsLLLsLLsLLL	Perf.	Min.	Min.	Min.	Min.	Min.	Min.	Perf.	Min.	Min.	Min.	Min.	Min.	Min.	Min.	Min.	Min.	Perf.	Min.	Min.	Min.	Min.	Min.	Min.	Perf.
0|23	18	sLLsLLsLLLsLLsLLLsLLsLLL	Perf.	Min.	Min.	Min.	Min.	Min.	Min.	Dim.	Min.	Min.	Min.	Min.	Min.	Min.	Min.	Min.	Min.	Perf.	Min.	Min.	Min.	Min.	Min.	Min.	Perf.

Scale tree

Scale tree and tuning spectrum of 17L 7s

Generator(edo)						Cents		Step ratio		Comments
						Bright	Dark	L:s	Hardness
7\24						350.000	850.000	1:1	1.000	Equalized 17L 7s
					40\137	350.365	849.635	6:5	1.200
				33\113		350.442	849.558	5:4	1.250
					59\202	350.495	849.505	9:7	1.286
			26\89			350.562	849.438	4:3	1.333	Supersoft 17L 7s
					71\243	350.617	849.383	11:8	1.375
				45\154		350.649	849.351	7:5	1.400
					64\219	350.685	849.315	10:7	1.429
		19\65				350.769	849.231	3:2	1.500	Soft 17L 7s
					69\236	350.847	849.153	11:7	1.571
				50\171		350.877	849.123	8:5	1.600
					81\277	350.903	849.097	13:8	1.625
			31\106			350.943	849.057	5:3	1.667	Semisoft 17L 7s
					74\253	350.988	849.012	12:7	1.714
				43\147		351.020	848.980	7:4	1.750
					55\188	351.064	848.936	9:5	1.800
	12\41					351.220	848.780	2:1	2.000	Basic 17L 7s Scales with tunings softer than this are proper
					53\181	351.381	848.619	9:4	2.250
				41\140		351.429	848.571	7:3	2.333
					70\239	351.464	848.536	12:5	2.400
			29\99			351.515	848.485	5:2	2.500	Semihard 17L 7s
					75\256	351.562	848.438	13:5	2.600
				46\157		351.592	848.408	8:3	2.667
					63\215	351.628	848.372	11:4	2.750
		17\58				351.724	848.276	3:1	3.000	Hard 17L 7s
					56\191	351.832	848.168	10:3	3.333
				39\133		351.880	848.120	7:2	3.500
					61\208	351.923	848.077	11:3	3.667
			22\75			352.000	848.000	4:1	4.000	Superhard 17L 7s
					49\167	352.096	847.904	9:2	4.500
				27\92		352.174	847.826	5:1	5.000
					32\109	352.294	847.706	6:1	6.000
5\17						352.941	847.059	1:0	→ ∞	Collapsed 17L 7s

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