User:MisterShafXen/17L 34s

17L 34s is a 2/1-equivalent (octave-equivalent) moment of symmetry scale containing 17 large steps and 34 small steps, with a period of 1 large step and 2 small steps that repeats every 70.6 ¢, or 17 times every octave. 17L 34s is a child scale of 17L 17s, expanding it by 17 tones. Generators that produce this scale range from 47.1 ¢ to 70.6 ¢, or from 0 ¢ to 23.5 ¢.

↖ 16L 33s	↑ 17L 33s	18L 33s ↗
← 16L 34s	17L 34s	18L 34s →
↙ 16L 35s	↓ 17L 35s	18L 35s ↘

Scale structure
Step pattern	...51 steps...
Equave	2/1 (1200.0 ¢)
Period	1\17 (70.6 ¢)
Generator size
Bright	2\51 to 1\17 (47.1 ¢ to 70.6 ¢)
Dark	0\17 to 1\51 (0.0 ¢ to 23.5 ¢)
TAMNAMS information
Related to	17L 17s
With tunings	2:1 to 1:0 (hard-of-basic)
Related MOS scales
Parent	17L 17s
Sister	34L 17s
Daughters	51L 17s, 17L 51s
Neutralized	34L 17s
2-Flought	68L 34s, 17L 85s
Equal tunings
Equalized (L:s = 1:1)	2\51 (47.1 ¢)
Supersoft (L:s = 4:3)	7\170 (49.4 ¢)
Soft (L:s = 3:2)	5\119 (50.4 ¢)
Semisoft (L:s = 5:3)	8\187 (51.3 ¢)
Basic (L:s = 2:1)	3\68 (52.9 ¢)
Semihard (L:s = 5:2)	7\153 (54.9 ¢)
Hard (L:s = 3:1)	4\85 (56.5 ¢)
Superhard (L:s = 4:1)	5\102 (58.8 ¢)
Collapsed (L:s = 1:0)	1\17 (70.6 ¢)
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Scale properties

Intervals of 17L 34s

Intervals			Steps subtended	Range in cents
Generic	Specific	Abbrev.
0-mosstep	Perfect 0-mosstep	P0ms	0	0.0 ¢
1-mosstep	Perfect 1-mosstep	P1ms	s	0.0 ¢ to 23.5 ¢
	Augmented 1-mosstep	A1ms	L	23.5 ¢ to 70.6 ¢
2-mosstep	Diminished 2-mosstep	d2ms	2s	0.0 ¢ to 47.1 ¢
	Perfect 2-mosstep	P2ms	L + s	47.1 ¢ to 70.6 ¢
3-mosstep	Perfect 3-mosstep	P3ms	L + 2s	70.6 ¢
4-mosstep	Perfect 4-mosstep	P4ms	L + 3s	70.6 ¢ to 94.1 ¢
	Augmented 4-mosstep	A4ms	2L + 2s	94.1 ¢ to 141.2 ¢
5-mosstep	Diminished 5-mosstep	d5ms	L + 4s	70.6 ¢ to 117.6 ¢
	Perfect 5-mosstep	P5ms	2L + 3s	117.6 ¢ to 141.2 ¢
6-mosstep	Perfect 6-mosstep	P6ms	2L + 4s	141.2 ¢
7-mosstep	Perfect 7-mosstep	P7ms	2L + 5s	141.2 ¢ to 164.7 ¢
	Augmented 7-mosstep	A7ms	3L + 4s	164.7 ¢ to 211.8 ¢
8-mosstep	Diminished 8-mosstep	d8ms	2L + 6s	141.2 ¢ to 188.2 ¢
	Perfect 8-mosstep	P8ms	3L + 5s	188.2 ¢ to 211.8 ¢
9-mosstep	Perfect 9-mosstep	P9ms	3L + 6s	211.8 ¢
10-mosstep	Perfect 10-mosstep	P10ms	3L + 7s	211.8 ¢ to 235.3 ¢
	Augmented 10-mosstep	A10ms	4L + 6s	235.3 ¢ to 282.4 ¢
11-mosstep	Diminished 11-mosstep	d11ms	3L + 8s	211.8 ¢ to 258.8 ¢
	Perfect 11-mosstep	P11ms	4L + 7s	258.8 ¢ to 282.4 ¢
12-mosstep	Perfect 12-mosstep	P12ms	4L + 8s	282.4 ¢
13-mosstep	Perfect 13-mosstep	P13ms	4L + 9s	282.4 ¢ to 305.9 ¢
	Augmented 13-mosstep	A13ms	5L + 8s	305.9 ¢ to 352.9 ¢
14-mosstep	Diminished 14-mosstep	d14ms	4L + 10s	282.4 ¢ to 329.4 ¢
	Perfect 14-mosstep	P14ms	5L + 9s	329.4 ¢ to 352.9 ¢
15-mosstep	Perfect 15-mosstep	P15ms	5L + 10s	352.9 ¢
16-mosstep	Perfect 16-mosstep	P16ms	5L + 11s	352.9 ¢ to 376.5 ¢
	Augmented 16-mosstep	A16ms	6L + 10s	376.5 ¢ to 423.5 ¢
17-mosstep	Diminished 17-mosstep	d17ms	5L + 12s	352.9 ¢ to 400.0 ¢
	Perfect 17-mosstep	P17ms	6L + 11s	400.0 ¢ to 423.5 ¢
18-mosstep	Perfect 18-mosstep	P18ms	6L + 12s	423.5 ¢
19-mosstep	Perfect 19-mosstep	P19ms	6L + 13s	423.5 ¢ to 447.1 ¢
	Augmented 19-mosstep	A19ms	7L + 12s	447.1 ¢ to 494.1 ¢
20-mosstep	Diminished 20-mosstep	d20ms	6L + 14s	423.5 ¢ to 470.6 ¢
	Perfect 20-mosstep	P20ms	7L + 13s	470.6 ¢ to 494.1 ¢
21-mosstep	Perfect 21-mosstep	P21ms	7L + 14s	494.1 ¢
22-mosstep	Perfect 22-mosstep	P22ms	7L + 15s	494.1 ¢ to 517.6 ¢
	Augmented 22-mosstep	A22ms	8L + 14s	517.6 ¢ to 564.7 ¢
23-mosstep	Diminished 23-mosstep	d23ms	7L + 16s	494.1 ¢ to 541.2 ¢
	Perfect 23-mosstep	P23ms	8L + 15s	541.2 ¢ to 564.7 ¢
24-mosstep	Perfect 24-mosstep	P24ms	8L + 16s	564.7 ¢
25-mosstep	Perfect 25-mosstep	P25ms	8L + 17s	564.7 ¢ to 588.2 ¢
	Augmented 25-mosstep	A25ms	9L + 16s	588.2 ¢ to 635.3 ¢
26-mosstep	Diminished 26-mosstep	d26ms	8L + 18s	564.7 ¢ to 611.8 ¢
	Perfect 26-mosstep	P26ms	9L + 17s	611.8 ¢ to 635.3 ¢
27-mosstep	Perfect 27-mosstep	P27ms	9L + 18s	635.3 ¢
28-mosstep	Perfect 28-mosstep	P28ms	9L + 19s	635.3 ¢ to 658.8 ¢
	Augmented 28-mosstep	A28ms	10L + 18s	658.8 ¢ to 705.9 ¢
29-mosstep	Diminished 29-mosstep	d29ms	9L + 20s	635.3 ¢ to 682.4 ¢
	Perfect 29-mosstep	P29ms	10L + 19s	682.4 ¢ to 705.9 ¢
30-mosstep	Perfect 30-mosstep	P30ms	10L + 20s	705.9 ¢
31-mosstep	Perfect 31-mosstep	P31ms	10L + 21s	705.9 ¢ to 729.4 ¢
	Augmented 31-mosstep	A31ms	11L + 20s	729.4 ¢ to 776.5 ¢
32-mosstep	Diminished 32-mosstep	d32ms	10L + 22s	705.9 ¢ to 752.9 ¢
	Perfect 32-mosstep	P32ms	11L + 21s	752.9 ¢ to 776.5 ¢
33-mosstep	Perfect 33-mosstep	P33ms	11L + 22s	776.5 ¢
34-mosstep	Perfect 34-mosstep	P34ms	11L + 23s	776.5 ¢ to 800.0 ¢
	Augmented 34-mosstep	A34ms	12L + 22s	800.0 ¢ to 847.1 ¢
35-mosstep	Diminished 35-mosstep	d35ms	11L + 24s	776.5 ¢ to 823.5 ¢
	Perfect 35-mosstep	P35ms	12L + 23s	823.5 ¢ to 847.1 ¢
36-mosstep	Perfect 36-mosstep	P36ms	12L + 24s	847.1 ¢
37-mosstep	Perfect 37-mosstep	P37ms	12L + 25s	847.1 ¢ to 870.6 ¢
	Augmented 37-mosstep	A37ms	13L + 24s	870.6 ¢ to 917.6 ¢
38-mosstep	Diminished 38-mosstep	d38ms	12L + 26s	847.1 ¢ to 894.1 ¢
	Perfect 38-mosstep	P38ms	13L + 25s	894.1 ¢ to 917.6 ¢
39-mosstep	Perfect 39-mosstep	P39ms	13L + 26s	917.6 ¢
40-mosstep	Perfect 40-mosstep	P40ms	13L + 27s	917.6 ¢ to 941.2 ¢
	Augmented 40-mosstep	A40ms	14L + 26s	941.2 ¢ to 988.2 ¢
41-mosstep	Diminished 41-mosstep	d41ms	13L + 28s	917.6 ¢ to 964.7 ¢
	Perfect 41-mosstep	P41ms	14L + 27s	964.7 ¢ to 988.2 ¢
42-mosstep	Perfect 42-mosstep	P42ms	14L + 28s	988.2 ¢
43-mosstep	Perfect 43-mosstep	P43ms	14L + 29s	988.2 ¢ to 1011.8 ¢
	Augmented 43-mosstep	A43ms	15L + 28s	1011.8 ¢ to 1058.8 ¢
44-mosstep	Diminished 44-mosstep	d44ms	14L + 30s	988.2 ¢ to 1035.3 ¢
	Perfect 44-mosstep	P44ms	15L + 29s	1035.3 ¢ to 1058.8 ¢
45-mosstep	Perfect 45-mosstep	P45ms	15L + 30s	1058.8 ¢
46-mosstep	Perfect 46-mosstep	P46ms	15L + 31s	1058.8 ¢ to 1082.4 ¢
	Augmented 46-mosstep	A46ms	16L + 30s	1082.4 ¢ to 1129.4 ¢
47-mosstep	Diminished 47-mosstep	d47ms	15L + 32s	1058.8 ¢ to 1105.9 ¢
	Perfect 47-mosstep	P47ms	16L + 31s	1105.9 ¢ to 1129.4 ¢
48-mosstep	Perfect 48-mosstep	P48ms	16L + 32s	1129.4 ¢
49-mosstep	Perfect 49-mosstep	P49ms	16L + 33s	1129.4 ¢ to 1152.9 ¢
	Augmented 49-mosstep	A49ms	17L + 32s	1152.9 ¢ to 1200.0 ¢
50-mosstep	Diminished 50-mosstep	d50ms	16L + 34s	1129.4 ¢ to 1176.5 ¢
	Perfect 50-mosstep	P50ms	17L + 33s	1176.5 ¢ to 1200.0 ¢
51-mosstep	Perfect 51-mosstep	P51ms	17L + 34s	1200.0 ¢

Generator chain of 17L 34s

Bright gens	Scale degree	Abbrev.	Scale degree	Abbrev.	Scale degree	Abbrev.	Scale degree	Abbrev.	Scale degree	Abbrev.	Scale degree	Abbrev.	Scale degree	Abbrev.	Scale degree	Abbrev.	Scale degree	Abbrev.	Scale degree	Abbrev.	Scale degree	Abbrev.	Scale degree	Abbrev.	Scale degree	Abbrev.	Scale degree	Abbrev.	Scale degree	Abbrev.	Scale degree	Abbrev.	Scale degree	Abbrev.
3	Augmented 0-mosdegree	A0md	Augmented 3-mosdegree	A3md	Augmented 6-mosdegree	A6md	Augmented 9-mosdegree	A9md	Augmented 12-mosdegree	A12md	Augmented 15-mosdegree	A15md	Augmented 18-mosdegree	A18md	Augmented 21-mosdegree	A21md	Augmented 24-mosdegree	A24md	Augmented 27-mosdegree	A27md	Augmented 30-mosdegree	A30md	Augmented 33-mosdegree	A33md	Augmented 36-mosdegree	A36md	Augmented 39-mosdegree	A39md	Augmented 42-mosdegree	A42md	Augmented 45-mosdegree	A45md	Augmented 48-mosdegree	A48md
2	Augmented 1-mosdegree	A1md	Augmented 4-mosdegree	A4md	Augmented 7-mosdegree	A7md	Augmented 10-mosdegree	A10md	Augmented 13-mosdegree	A13md	Augmented 16-mosdegree	A16md	Augmented 19-mosdegree	A19md	Augmented 22-mosdegree	A22md	Augmented 25-mosdegree	A25md	Augmented 28-mosdegree	A28md	Augmented 31-mosdegree	A31md	Augmented 34-mosdegree	A34md	Augmented 37-mosdegree	A37md	Augmented 40-mosdegree	A40md	Augmented 43-mosdegree	A43md	Augmented 46-mosdegree	A46md	Augmented 49-mosdegree	A49md
1	Perfect 2-mosdegree	P2md	Perfect 5-mosdegree	P5md	Perfect 8-mosdegree	P8md	Perfect 11-mosdegree	P11md	Perfect 14-mosdegree	P14md	Perfect 17-mosdegree	P17md	Perfect 20-mosdegree	P20md	Perfect 23-mosdegree	P23md	Perfect 26-mosdegree	P26md	Perfect 29-mosdegree	P29md	Perfect 32-mosdegree	P32md	Perfect 35-mosdegree	P35md	Perfect 38-mosdegree	P38md	Perfect 41-mosdegree	P41md	Perfect 44-mosdegree	P44md	Perfect 47-mosdegree	P47md	Perfect 50-mosdegree	P50md
0	Perfect 0-mosdegree Perfect 3-mosdegree	P0md P3md	Perfect 3-mosdegree Perfect 6-mosdegree	P3md P6md	Perfect 6-mosdegree Perfect 9-mosdegree	P6md P9md	Perfect 9-mosdegree Perfect 12-mosdegree	P9md P12md	Perfect 12-mosdegree Perfect 15-mosdegree	P12md P15md	Perfect 15-mosdegree Perfect 18-mosdegree	P15md P18md	Perfect 18-mosdegree Perfect 21-mosdegree	P18md P21md	Perfect 21-mosdegree Perfect 24-mosdegree	P21md P24md	Perfect 24-mosdegree Perfect 27-mosdegree	P24md P27md	Perfect 27-mosdegree Perfect 30-mosdegree	P27md P30md	Perfect 30-mosdegree Perfect 33-mosdegree	P30md P33md	Perfect 33-mosdegree Perfect 36-mosdegree	P33md P36md	Perfect 36-mosdegree Perfect 39-mosdegree	P36md P39md	Perfect 39-mosdegree Perfect 42-mosdegree	P39md P42md	Perfect 42-mosdegree Perfect 45-mosdegree	P42md P45md	Perfect 45-mosdegree Perfect 48-mosdegree	P45md P48md	Perfect 48-mosdegree Perfect 51-mosdegree	P48md P51md
−1	Perfect 1-mosdegree	P1md	Perfect 4-mosdegree	P4md	Perfect 7-mosdegree	P7md	Perfect 10-mosdegree	P10md	Perfect 13-mosdegree	P13md	Perfect 16-mosdegree	P16md	Perfect 19-mosdegree	P19md	Perfect 22-mosdegree	P22md	Perfect 25-mosdegree	P25md	Perfect 28-mosdegree	P28md	Perfect 31-mosdegree	P31md	Perfect 34-mosdegree	P34md	Perfect 37-mosdegree	P37md	Perfect 40-mosdegree	P40md	Perfect 43-mosdegree	P43md	Perfect 46-mosdegree	P46md	Perfect 49-mosdegree	P49md
−2	Diminished 2-mosdegree	d2md	Diminished 5-mosdegree	d5md	Diminished 8-mosdegree	d8md	Diminished 11-mosdegree	d11md	Diminished 14-mosdegree	d14md	Diminished 17-mosdegree	d17md	Diminished 20-mosdegree	d20md	Diminished 23-mosdegree	d23md	Diminished 26-mosdegree	d26md	Diminished 29-mosdegree	d29md	Diminished 32-mosdegree	d32md	Diminished 35-mosdegree	d35md	Diminished 38-mosdegree	d38md	Diminished 41-mosdegree	d41md	Diminished 44-mosdegree	d44md	Diminished 47-mosdegree	d47md	Diminished 50-mosdegree	d50md
−3	Diminished 3-mosdegree	d3md	Diminished 6-mosdegree	d6md	Diminished 9-mosdegree	d9md	Diminished 12-mosdegree	d12md	Diminished 15-mosdegree	d15md	Diminished 18-mosdegree	d18md	Diminished 21-mosdegree	d21md	Diminished 24-mosdegree	d24md	Diminished 27-mosdegree	d27md	Diminished 30-mosdegree	d30md	Diminished 33-mosdegree	d33md	Diminished 36-mosdegree	d36md	Diminished 39-mosdegree	d39md	Diminished 42-mosdegree	d42md	Diminished 45-mosdegree	d45md	Diminished 48-mosdegree	d48md	Diminished 51-mosdegree	d51md

Modes of 17L 34s

UDP	Cyclic order	Step pattern
34|0(17)	1	LssLssLssLssLssLssLssLssLssLssLssLssLssLssLssLssLss
17|17(17)	3	sLssLssLssLssLssLssLssLssLssLssLssLssLssLssLssLssLs
0|34(17)	2	ssLssLssLssLssLssLssLssLssLssLssLssLssLssLssLssLssL

Scale tree

Scale tree and tuning spectrum of 17L 34s

Generator(edo)						Cents		Step ratio		Comments
						Bright	Dark	L:s	Hardness
2\51						47.059	23.529	1:1	1.000	Equalized 17L 34s
					11\272	48.529	22.059	6:5	1.200
				9\221		48.869	21.719	5:4	1.250
					16\391	49.105	21.483	9:7	1.286
			7\170			49.412	21.176	4:3	1.333	Supersoft 17L 34s
					19\459	49.673	20.915	11:8	1.375
				12\289		49.827	20.761	7:5	1.400
					17\408	50.000	20.588	10:7	1.429
		5\119				50.420	20.168	3:2	1.500	Soft 17L 34s
					18\425	50.824	19.765	11:7	1.571
				13\306		50.980	19.608	8:5	1.600
					21\493	51.116	19.473	13:8	1.625
			8\187			51.337	19.251	5:3	1.667	Semisoft 17L 34s
					19\442	51.584	19.005	12:7	1.714
				11\255		51.765	18.824	7:4	1.750
					14\323	52.012	18.576	9:5	1.800
	3\68					52.941	17.647	2:1	2.000	Basic 17L 34s Scales with tunings softer than this are proper
					13\289	53.979	16.609	9:4	2.250
				10\221		54.299	16.290	7:3	2.333
					17\374	54.545	16.043	12:5	2.400
			7\153			54.902	15.686	5:2	2.500	Semihard 17L 34s
					18\391	55.243	15.345	13:5	2.600
				11\238		55.462	15.126	8:3	2.667
					15\323	55.728	14.861	11:4	2.750
		4\85				56.471	14.118	3:1	3.000	Hard 17L 34s
					13\272	57.353	13.235	10:3	3.333
				9\187		57.754	12.834	7:2	3.500
					14\289	58.131	12.457	11:3	3.667
			5\102			58.824	11.765	4:1	4.000	Superhard 17L 34s
					11\221	59.729	10.860	9:2	4.500
				6\119		60.504	10.084	5:1	5.000
					7\136	61.765	8.824	6:1	6.000
1\17						70.588	0.000	1:0	→ ∞	Collapsed 17L 34s