17L 12s

Todo: complete table populate scale tree with entries

17L 12s is a 2/1-equivalent (octave-equivalent) moment of symmetry scale containing 17 large steps and 12 small steps, repeating every octave. 17L 12s is a great-grandchild scale of 5L 2s, expanding it by 22 tones. Generators that produce this scale range from 703.4 ¢ to 705.9 ¢, or from 494.1 ¢ to 496.6 ¢.

↖ 16L 11s	↑ 17L 11s	18L 11s ↗
← 16L 12s	17L 12s	18L 12s →
↙ 16L 13s	↓ 17L 13s	18L 13s ↘

Scale structure
Step pattern	LLsLsLLsLsLLsLsLsLLsLsLLsLsLs sLsLsLLsLsLLsLsLsLLsLsLLsLsLL
Equave	2/1 (1200.0 ¢)
Period	2/1 (1200.0 ¢)
Generator size
Bright	17\29 to 10\17 (703.4 ¢ to 705.9 ¢)
Dark	7\17 to 12\29 (494.1 ¢ to 496.6 ¢)
TAMNAMS information
Related to	5L 2s (diatonic)
With tunings	5:2 to 3:1 (quasihard)
Related MOS scales
Parent	12L 5s
Sister	12L 17s
Daughters	29L 17s, 17L 29s
Neutralized	5L 24s
2-Flought	46L 12s, 17L 41s
Equal tunings
Equalized (L:s = 1:1)	17\29 (703.4 ¢)
Supersoft (L:s = 4:3)	61\104 (703.8 ¢)
Soft (L:s = 3:2)	44\75 (704.0 ¢)
Semisoft (L:s = 5:3)	71\121 (704.1 ¢)
Basic (L:s = 2:1)	27\46 (704.3 ¢)
Semihard (L:s = 5:2)	64\109 (704.6 ¢)
Hard (L:s = 3:1)	37\63 (704.8 ¢)
Superhard (L:s = 4:1)	47\80 (705.0 ¢)
Collapsed (L:s = 1:0)	10\17 (705.9 ¢)
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This mos, belonging to the leapday temperament, is generated by taking a chain of 29 fifths tempered 1.49 to 3.93 ¢ sharp. That is to say, its region includes all linear combinations of 17edo and 29edo and divides at 80edo into Margo Schulter's gentle region extending down to 29edo and the noble region^{[idiosyncratic term]} extending up to 17edo.

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 12s

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 41.4 ¢
	Major 1-mosstep	M1ms	L	41.4 ¢ to 70.6 ¢
2-mosstep	Minor 2-mosstep	m2ms	L + s	70.6 ¢ to 82.8 ¢
	Major 2-mosstep	M2ms	2L	82.8 ¢ to 141.2 ¢
3-mosstep	Minor 3-mosstep	m3ms	L + 2s	70.6 ¢ to 124.1 ¢
	Major 3-mosstep	M3ms	2L + s	124.1 ¢ to 141.2 ¢
4-mosstep	Minor 4-mosstep	m4ms	2L + 2s	141.2 ¢ to 165.5 ¢
	Major 4-mosstep	M4ms	3L + s	165.5 ¢ to 211.8 ¢
5-mosstep	Minor 5-mosstep	m5ms	2L + 3s	141.2 ¢ to 206.9 ¢
	Major 5-mosstep	M5ms	3L + 2s	206.9 ¢ to 211.8 ¢
6-mosstep	Minor 6-mosstep	m6ms	3L + 3s	211.8 ¢ to 248.3 ¢
	Major 6-mosstep	M6ms	4L + 2s	248.3 ¢ to 282.4 ¢
7-mosstep	Minor 7-mosstep	m7ms	4L + 3s	282.4 ¢ to 289.7 ¢
	Major 7-mosstep	M7ms	5L + 2s	289.7 ¢ to 352.9 ¢
8-mosstep	Minor 8-mosstep	m8ms	4L + 4s	282.4 ¢ to 331.0 ¢
	Major 8-mosstep	M8ms	5L + 3s	331.0 ¢ to 352.9 ¢
9-mosstep	Minor 9-mosstep	m9ms	5L + 4s	352.9 ¢ to 372.4 ¢
	Major 9-mosstep	M9ms	6L + 3s	372.4 ¢ to 423.5 ¢
10-mosstep	Minor 10-mosstep	m10ms	5L + 5s	352.9 ¢ to 413.8 ¢
	Major 10-mosstep	M10ms	6L + 4s	413.8 ¢ to 423.5 ¢
11-mosstep	Minor 11-mosstep	m11ms	6L + 5s	423.5 ¢ to 455.2 ¢
	Major 11-mosstep	M11ms	7L + 4s	455.2 ¢ to 494.1 ¢
12-mosstep	Perfect 12-mosstep	P12ms	7L + 5s	494.1 ¢ to 496.6 ¢
	Augmented 12-mosstep	A12ms	8L + 4s	496.6 ¢ to 564.7 ¢
13-mosstep	Minor 13-mosstep	m13ms	7L + 6s	494.1 ¢ to 537.9 ¢
	Major 13-mosstep	M13ms	8L + 5s	537.9 ¢ to 564.7 ¢
14-mosstep	Minor 14-mosstep	m14ms	8L + 6s	564.7 ¢ to 579.3 ¢
	Major 14-mosstep	M14ms	9L + 5s	579.3 ¢ to 635.3 ¢
15-mosstep	Minor 15-mosstep	m15ms	8L + 7s	564.7 ¢ to 620.7 ¢
	Major 15-mosstep	M15ms	9L + 6s	620.7 ¢ to 635.3 ¢
16-mosstep	Minor 16-mosstep	m16ms	9L + 7s	635.3 ¢ to 662.1 ¢
	Major 16-mosstep	M16ms	10L + 6s	662.1 ¢ to 705.9 ¢
17-mosstep	Diminished 17-mosstep	d17ms	9L + 8s	635.3 ¢ to 703.4 ¢
	Perfect 17-mosstep	P17ms	10L + 7s	703.4 ¢ to 705.9 ¢
18-mosstep	Minor 18-mosstep	m18ms	10L + 8s	705.9 ¢ to 744.8 ¢
	Major 18-mosstep	M18ms	11L + 7s	744.8 ¢ to 776.5 ¢
19-mosstep	Minor 19-mosstep	m19ms	11L + 8s	776.5 ¢ to 786.2 ¢
	Major 19-mosstep	M19ms	12L + 7s	786.2 ¢ to 847.1 ¢
20-mosstep	Minor 20-mosstep	m20ms	11L + 9s	776.5 ¢ to 827.6 ¢
	Major 20-mosstep	M20ms	12L + 8s	827.6 ¢ to 847.1 ¢
21-mosstep	Minor 21-mosstep	m21ms	12L + 9s	847.1 ¢ to 869.0 ¢
	Major 21-mosstep	M21ms	13L + 8s	869.0 ¢ to 917.6 ¢
22-mosstep	Minor 22-mosstep	m22ms	12L + 10s	847.1 ¢ to 910.3 ¢
	Major 22-mosstep	M22ms	13L + 9s	910.3 ¢ to 917.6 ¢
23-mosstep	Minor 23-mosstep	m23ms	13L + 10s	917.6 ¢ to 951.7 ¢
	Major 23-mosstep	M23ms	14L + 9s	951.7 ¢ to 988.2 ¢
24-mosstep	Minor 24-mosstep	m24ms	14L + 10s	988.2 ¢ to 993.1 ¢
	Major 24-mosstep	M24ms	15L + 9s	993.1 ¢ to 1058.8 ¢
25-mosstep	Minor 25-mosstep	m25ms	14L + 11s	988.2 ¢ to 1034.5 ¢
	Major 25-mosstep	M25ms	15L + 10s	1034.5 ¢ to 1058.8 ¢
26-mosstep	Minor 26-mosstep	m26ms	15L + 11s	1058.8 ¢ to 1075.9 ¢
	Major 26-mosstep	M26ms	16L + 10s	1075.9 ¢ to 1129.4 ¢
27-mosstep	Minor 27-mosstep	m27ms	15L + 12s	1058.8 ¢ to 1117.2 ¢
	Major 27-mosstep	M27ms	16L + 11s	1117.2 ¢ to 1129.4 ¢
28-mosstep	Minor 28-mosstep	m28ms	16L + 12s	1129.4 ¢ to 1158.6 ¢
	Major 28-mosstep	M28ms	17L + 11s	1158.6 ¢ to 1200.0 ¢
29-mosstep	Perfect 29-mosstep	P29ms	17L + 12s	1200.0 ¢

Generator chain

Generator chain of 17L 12s

Bright gens	Scale degree	Abbrev.
45	Augmented 11-mosdegree	A11md
44	Augmented 23-mosdegree	A23md
43	Augmented 6-mosdegree	A6md
42	Augmented 18-mosdegree	A18md
41	Augmented 1-mosdegree	A1md
40	Augmented 13-mosdegree	A13md
39	Augmented 25-mosdegree	A25md
38	Augmented 8-mosdegree	A8md
37	Augmented 20-mosdegree	A20md
36	Augmented 3-mosdegree	A3md
35	Augmented 15-mosdegree	A15md
34	Augmented 27-mosdegree	A27md
33	Augmented 10-mosdegree	A10md
32	Augmented 22-mosdegree	A22md
31	Augmented 5-mosdegree	A5md
30	Augmented 17-mosdegree	A17md
29	Augmented 0-mosdegree	A0md
28	Augmented 12-mosdegree	A12md
27	Major 24-mosdegree	M24md
26	Major 7-mosdegree	M7md
25	Major 19-mosdegree	M19md
24	Major 2-mosdegree	M2md
23	Major 14-mosdegree	M14md
22	Major 26-mosdegree	M26md
21	Major 9-mosdegree	M9md
20	Major 21-mosdegree	M21md
19	Major 4-mosdegree	M4md
18	Major 16-mosdegree	M16md
17	Major 28-mosdegree	M28md
16	Major 11-mosdegree	M11md
15	Major 23-mosdegree	M23md
14	Major 6-mosdegree	M6md
13	Major 18-mosdegree	M18md
12	Major 1-mosdegree	M1md
11	Major 13-mosdegree	M13md
10	Major 25-mosdegree	M25md
9	Major 8-mosdegree	M8md
8	Major 20-mosdegree	M20md
7	Major 3-mosdegree	M3md
6	Major 15-mosdegree	M15md
5	Major 27-mosdegree	M27md
4	Major 10-mosdegree	M10md
3	Major 22-mosdegree	M22md
2	Major 5-mosdegree	M5md
1	Perfect 17-mosdegree	P17md
0	Perfect 0-mosdegree Perfect 29-mosdegree	P0md P29md
−1	Perfect 12-mosdegree	P12md
−2	Minor 24-mosdegree	m24md
−3	Minor 7-mosdegree	m7md
−4	Minor 19-mosdegree	m19md
−5	Minor 2-mosdegree	m2md
−6	Minor 14-mosdegree	m14md
−7	Minor 26-mosdegree	m26md
−8	Minor 9-mosdegree	m9md
−9	Minor 21-mosdegree	m21md
−10	Minor 4-mosdegree	m4md
−11	Minor 16-mosdegree	m16md
−12	Minor 28-mosdegree	m28md
−13	Minor 11-mosdegree	m11md
−14	Minor 23-mosdegree	m23md
−15	Minor 6-mosdegree	m6md
−16	Minor 18-mosdegree	m18md
−17	Minor 1-mosdegree	m1md
−18	Minor 13-mosdegree	m13md
−19	Minor 25-mosdegree	m25md
−20	Minor 8-mosdegree	m8md
−21	Minor 20-mosdegree	m20md
−22	Minor 3-mosdegree	m3md
−23	Minor 15-mosdegree	m15md
−24	Minor 27-mosdegree	m27md
−25	Minor 10-mosdegree	m10md
−26	Minor 22-mosdegree	m22md
−27	Minor 5-mosdegree	m5md
−28	Diminished 17-mosdegree	d17md
−29	Diminished 29-mosdegree	d29md
−30	Diminished 12-mosdegree	d12md
−31	Diminished 24-mosdegree	d24md
−32	Diminished 7-mosdegree	d7md
−33	Diminished 19-mosdegree	d19md
−34	Diminished 2-mosdegree	d2md
−35	Diminished 14-mosdegree	d14md
−36	Diminished 26-mosdegree	d26md
−37	Diminished 9-mosdegree	d9md
−38	Diminished 21-mosdegree	d21md
−39	Diminished 4-mosdegree	d4md
−40	Diminished 16-mosdegree	d16md
−41	Diminished 28-mosdegree	d28md
−42	Diminished 11-mosdegree	d11md
−43	Diminished 23-mosdegree	d23md
−44	Diminished 6-mosdegree	d6md
−45	Diminished 18-mosdegree	d18md

Scale tree

Scale tree and tuning spectrum of 17L 12s

Generator(edo)						Cents		Step ratio		Comments
						Bright	Dark	L:s	Hardness
17\29						703.448	496.552	1:1	1.000	Equalized 17L 12s
					95\162	703.704	496.296	6:5	1.200
				78\133		703.759	496.241	5:4	1.250
					139\237	703.797	496.203	9:7	1.286
			61\104			703.846	496.154	4:3	1.333	Supersoft 17L 12s
					166\283	703.887	496.113	11:8	1.375
				105\179		703.911	496.089	7:5	1.400
					149\254	703.937	496.063	10:7	1.429
		44\75				704.000	496.000	3:2	1.500	Soft 17L 12s
					159\271	704.059	495.941	11:7	1.571
				115\196		704.082	495.918	8:5	1.600
					186\317	704.101	495.899	13:8	1.625	Golden neogothic (704.096 ¢)
			71\121			704.132	495.868	5:3	1.667	Semisoft 17L 12s
					169\288	704.167	495.833	12:7	1.714
				98\167		704.192	495.808	7:4	1.750	Polypyth
					125\213	704.225	495.775	9:5	1.800
	27\46					704.348	495.652	2:1	2.000	Basic 17L 12s Scales with tunings softer than this are proper
					118\201	704.478	495.522	9:4	2.250
				91\155		704.516	495.484	7:3	2.333
					155\264	704.545	495.455	12:5	2.400
			64\109			704.587	495.413	5:2	2.500	Semihard 17L 12s Leapweek
					165\281	704.626	495.374	13:5	2.600
				101\172		704.651	495.349	8:3	2.667
					138\235	704.681	495.319	11:4	2.750
		37\63				704.762	495.238	3:1	3.000	Hard 17L 12s Leapfrog
					121\206	704.854	495.146	10:3	3.333
				84\143		704.895	495.105	7:2	3.500
					131\223	704.933	495.067	11:3	3.667
			47\80			705.000	495.000	4:1	4.000	Superhard 17L 12s
					104\177	705.085	494.915	9:2	4.500
				57\97		705.155	494.845	5:1	5.000
					67\114	705.263	494.737	6:1	6.000
10\17						705.882	494.118	1:0	→ ∞	Collapsed 17L 12s