17L 2s

↖ 16L 1s	↑ 17L 1s	18L 1s ↗
← 16L 2s	17L 2s	18L 2s →
↙ 16L 3s	↓ 17L 3s	18L 3s ↘

┌╥╥╥╥╥╥╥╥╥┬╥╥╥╥╥╥╥╥┬┐
│║║║║║║║║║│║║║║║║║║││
│││││││││││││││││││││
└┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┘

Scale structure

Step pattern

LLLLLLLLLsLLLLLLLLs
sLLLLLLLLsLLLLLLLLL

Equave

2/1 (1200.0 ¢)

Period

2/1 (1200.0 ¢)

Generator size

Bright

10\19 to 9\17 (631.6 ¢ to 635.3 ¢)

Dark

8\17 to 9\19 (564.7 ¢ to 568.4 ¢)

TAMNAMS information

Related to

2L 7s (balzano)

With tunings

5:1 to 6:1

Related MOS scales

Equal tunings

Equalized (L:s = 1:1)

10\19 (631.6 ¢)

Supersoft (L:s = 4:3)

39\74 (632.4 ¢)

29\55 (632.7 ¢)

48\91 (633.0 ¢)

19\36 (633.3 ¢)

47\89 (633.7 ¢)

28\53 (634.0 ¢)

Superhard (L:s = 4:1)

37\70 (634.3 ¢)

Collapsed (L:s = 1:0)

9\17 (635.3 ¢)

17L 2s is a 2/1-equivalent (octave-equivalent) moment of symmetry scale containing 17 large steps and 2 small steps, repeating every octave. 17L 2s is related to 2L 7s, expanding it by 10 tones. Generators that produce this scale range from 631.6 ¢ to 635.3 ¢, or from 564.7 ¢ to 568.4 ¢. From a regular temperament theory perspective, this scale is notable for corresponding to the mega chromatic scale of the Alphatricot family temperaments. Three bright generators can be interpreted to stack to 3/1, but unfortunately, the generator of 17L 2s itself does not have a very convenient rational representation, since the simple ratio 23/16 is off-scale flat, as is (just barely) the compound ratio 36/25, while the prime-over-compound ratio 13/9 is off-scale sharp. Using very high prime harmonics/subharmonics, we can make the interpretations of ~62/43 (bright generator) or ~43/31 (dark generator); the aforementioned Alphatricot family uses the highly compound ~59049/40960 as a generator; and probably the best rational that falls within the scale is ~75/52, three of which differ from 3/1 by the 0.2-cent comma of 140625/140608, the catasma.

A pitfall of the use of compound harmonics and subharmonics in a generator is that they multiply the effect of shifts in mapping of their respective primes with scale hardness — for instance, ~59049/40960 only maps correctly within a narrow step ratio range close to 10:3, while ~36/25 fails to map correctly even for several EDOs close to the soft end of the scale's tuning spectrum (as does the simpler but flatter ~23/16); the even simpler ~13/9 (off-scale sharp) is likewise affected. Using such generators outside of a narrow subset of the EDOs supporting the scale depends upon direct approximation of a compound harmonic and/or subharmonic such as 9 or 25. This is awkward when one also needs to use a component harmonic as specified in the patent vals of the EDOs, thus requiring the use of nonstandard conditional subgroup temperaments such as 2.3♯.3♭.5 and 2.3.5♯.5♭ (or 2.3.9.5 and 2.3.5.25), with provision of a rule specifying when to use the direct approximation as opposed to the patent val mapping.

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 2s
Intervals			Steps subtended	Range in cents
Generic	Specific	Abbrev.	Steps subtended	Range in cents
0-mosstep	Perfect 0-mosstep	P0ms	0	0.0 ¢
1-mosstep	Minor 1-mosstep	m1ms	s	0.0 ¢ to 63.2 ¢
1-mosstep	Major 1-mosstep	M1ms	L	63.2 ¢ to 70.6 ¢
2-mosstep	Minor 2-mosstep	m2ms	L + s	70.6 ¢ to 126.3 ¢
2-mosstep	Major 2-mosstep	M2ms	2L	126.3 ¢ to 141.2 ¢
3-mosstep	Minor 3-mosstep	m3ms	2L + s	141.2 ¢ to 189.5 ¢
3-mosstep	Major 3-mosstep	M3ms	3L	189.5 ¢ to 211.8 ¢
4-mosstep	Minor 4-mosstep	m4ms	3L + s	211.8 ¢ to 252.6 ¢
4-mosstep	Major 4-mosstep	M4ms	4L	252.6 ¢ to 282.4 ¢
5-mosstep	Minor 5-mosstep	m5ms	4L + s	282.4 ¢ to 315.8 ¢
5-mosstep	Major 5-mosstep	M5ms	5L	315.8 ¢ to 352.9 ¢
6-mosstep	Minor 6-mosstep	m6ms	5L + s	352.9 ¢ to 378.9 ¢
6-mosstep	Major 6-mosstep	M6ms	6L	378.9 ¢ to 423.5 ¢
7-mosstep	Minor 7-mosstep	m7ms	6L + s	423.5 ¢ to 442.1 ¢
7-mosstep	Major 7-mosstep	M7ms	7L	442.1 ¢ to 494.1 ¢
8-mosstep	Minor 8-mosstep	m8ms	7L + s	494.1 ¢ to 505.3 ¢
8-mosstep	Major 8-mosstep	M8ms	8L	505.3 ¢ to 564.7 ¢
9-mosstep	Perfect 9-mosstep	P9ms	8L + s	564.7 ¢ to 568.4 ¢
9-mosstep	Augmented 9-mosstep	A9ms	9L	568.4 ¢ to 635.3 ¢
10-mosstep	Diminished 10-mosstep	d10ms	8L + 2s	564.7 ¢ to 631.6 ¢
10-mosstep	Perfect 10-mosstep	P10ms	9L + s	631.6 ¢ to 635.3 ¢
11-mosstep	Minor 11-mosstep	m11ms	9L + 2s	635.3 ¢ to 694.7 ¢
11-mosstep	Major 11-mosstep	M11ms	10L + s	694.7 ¢ to 705.9 ¢
12-mosstep	Minor 12-mosstep	m12ms	10L + 2s	705.9 ¢ to 757.9 ¢
12-mosstep	Major 12-mosstep	M12ms	11L + s	757.9 ¢ to 776.5 ¢
13-mosstep	Minor 13-mosstep	m13ms	11L + 2s	776.5 ¢ to 821.1 ¢
13-mosstep	Major 13-mosstep	M13ms	12L + s	821.1 ¢ to 847.1 ¢
14-mosstep	Minor 14-mosstep	m14ms	12L + 2s	847.1 ¢ to 884.2 ¢
14-mosstep	Major 14-mosstep	M14ms	13L + s	884.2 ¢ to 917.6 ¢
15-mosstep	Minor 15-mosstep	m15ms	13L + 2s	917.6 ¢ to 947.4 ¢
15-mosstep	Major 15-mosstep	M15ms	14L + s	947.4 ¢ to 988.2 ¢
16-mosstep	Minor 16-mosstep	m16ms	14L + 2s	988.2 ¢ to 1010.5 ¢
16-mosstep	Major 16-mosstep	M16ms	15L + s	1010.5 ¢ to 1058.8 ¢
17-mosstep	Minor 17-mosstep	m17ms	15L + 2s	1058.8 ¢ to 1073.7 ¢
17-mosstep	Major 17-mosstep	M17ms	16L + s	1073.7 ¢ to 1129.4 ¢
18-mosstep	Minor 18-mosstep	m18ms	16L + 2s	1129.4 ¢ to 1136.8 ¢
18-mosstep	Major 18-mosstep	M18ms	17L + s	1136.8 ¢ to 1200.0 ¢
19-mosstep	Perfect 19-mosstep	P19ms	17L + 2s	1200.0 ¢

Generator chain

Generator chain of 17L 2s
Bright gens	Scale degree	Abbrev.
35	Augmented 8-mosdegree	A8md
34	Augmented 17-mosdegree	A17md
33	Augmented 7-mosdegree	A7md
32	Augmented 16-mosdegree	A16md
31	Augmented 6-mosdegree	A6md
30	Augmented 15-mosdegree	A15md
29	Augmented 5-mosdegree	A5md
28	Augmented 14-mosdegree	A14md
27	Augmented 4-mosdegree	A4md
26	Augmented 13-mosdegree	A13md
25	Augmented 3-mosdegree	A3md
24	Augmented 12-mosdegree	A12md
23	Augmented 2-mosdegree	A2md
22	Augmented 11-mosdegree	A11md
21	Augmented 1-mosdegree	A1md
20	Augmented 10-mosdegree	A10md
19	Augmented 0-mosdegree	A0md
18	Augmented 9-mosdegree	A9md
17	Major 18-mosdegree	M18md
16	Major 8-mosdegree	M8md
15	Major 17-mosdegree	M17md
14	Major 7-mosdegree	M7md
13	Major 16-mosdegree	M16md
12	Major 6-mosdegree	M6md
11	Major 15-mosdegree	M15md
10	Major 5-mosdegree	M5md
9	Major 14-mosdegree	M14md
8	Major 4-mosdegree	M4md
7	Major 13-mosdegree	M13md
6	Major 3-mosdegree	M3md
5	Major 12-mosdegree	M12md
4	Major 2-mosdegree	M2md
3	Major 11-mosdegree	M11md
2	Major 1-mosdegree	M1md
1	Perfect 10-mosdegree	P10md
0	Perfect 0-mosdegree Perfect 19-mosdegree	P0md P19md
−1	Perfect 9-mosdegree	P9md
−2	Minor 18-mosdegree	m18md
−3	Minor 8-mosdegree	m8md
−4	Minor 17-mosdegree	m17md
−5	Minor 7-mosdegree	m7md
−6	Minor 16-mosdegree	m16md
−7	Minor 6-mosdegree	m6md
−8	Minor 15-mosdegree	m15md
−9	Minor 5-mosdegree	m5md
−10	Minor 14-mosdegree	m14md
−11	Minor 4-mosdegree	m4md
−12	Minor 13-mosdegree	m13md
−13	Minor 3-mosdegree	m3md
−14	Minor 12-mosdegree	m12md
−15	Minor 2-mosdegree	m2md
−16	Minor 11-mosdegree	m11md
−17	Minor 1-mosdegree	m1md
−18	Diminished 10-mosdegree	d10md
−19	Diminished 19-mosdegree	d19md
−20	Diminished 9-mosdegree	d9md
−21	Diminished 18-mosdegree	d18md
−22	Diminished 8-mosdegree	d8md
−23	Diminished 17-mosdegree	d17md
−24	Diminished 7-mosdegree	d7md
−25	Diminished 16-mosdegree	d16md
−26	Diminished 6-mosdegree	d6md
−27	Diminished 15-mosdegree	d15md
−28	Diminished 5-mosdegree	d5md
−29	Diminished 14-mosdegree	d14md
−30	Diminished 4-mosdegree	d4md
−31	Diminished 13-mosdegree	d13md
−32	Diminished 3-mosdegree	d3md
−33	Diminished 12-mosdegree	d12md
−34	Diminished 2-mosdegree	d2md
−35	Diminished 11-mosdegree	d11md

Modes

Scale degrees of the modes of 17L 2s
UDP	Cyclic order	Step pattern	Scale degree (mosdegree)
UDP	Cyclic order	Step pattern	0	1	2	3	4	5	6	7	8	9	10	11	12	13	14	15	16	17	18	19
18\|0	1	LLLLLLLLLsLLLLLLLLs	Perf.	Maj.	Maj.	Maj.	Maj.	Maj.	Maj.	Maj.	Maj.	Aug.	Perf.	Maj.	Maj.	Maj.	Maj.	Maj.	Maj.	Maj.	Maj.	Perf.
17\|1	11	LLLLLLLLsLLLLLLLLLs	Perf.	Maj.	Maj.	Maj.	Maj.	Maj.	Maj.	Maj.	Maj.	Perf.	Perf.	Maj.	Maj.	Maj.	Maj.	Maj.	Maj.	Maj.	Maj.	Perf.
16\|2	2	LLLLLLLLsLLLLLLLLsL	Perf.	Maj.	Maj.	Maj.	Maj.	Maj.	Maj.	Maj.	Maj.	Perf.	Perf.	Maj.	Maj.	Maj.	Maj.	Maj.	Maj.	Maj.	Min.	Perf.
15\|3	12	LLLLLLLsLLLLLLLLLsL	Perf.	Maj.	Maj.	Maj.	Maj.	Maj.	Maj.	Maj.	Min.	Perf.	Perf.	Maj.	Maj.	Maj.	Maj.	Maj.	Maj.	Maj.	Min.	Perf.
14\|4	3	LLLLLLLsLLLLLLLLsLL	Perf.	Maj.	Maj.	Maj.	Maj.	Maj.	Maj.	Maj.	Min.	Perf.	Perf.	Maj.	Maj.	Maj.	Maj.	Maj.	Maj.	Min.	Min.	Perf.
13\|5	13	LLLLLLsLLLLLLLLLsLL	Perf.	Maj.	Maj.	Maj.	Maj.	Maj.	Maj.	Min.	Min.	Perf.	Perf.	Maj.	Maj.	Maj.	Maj.	Maj.	Maj.	Min.	Min.	Perf.
12\|6	4	LLLLLLsLLLLLLLLsLLL	Perf.	Maj.	Maj.	Maj.	Maj.	Maj.	Maj.	Min.	Min.	Perf.	Perf.	Maj.	Maj.	Maj.	Maj.	Maj.	Min.	Min.	Min.	Perf.
11\|7	14	LLLLLsLLLLLLLLLsLLL	Perf.	Maj.	Maj.	Maj.	Maj.	Maj.	Min.	Min.	Min.	Perf.	Perf.	Maj.	Maj.	Maj.	Maj.	Maj.	Min.	Min.	Min.	Perf.
10\|8	5	LLLLLsLLLLLLLLsLLLL	Perf.	Maj.	Maj.	Maj.	Maj.	Maj.	Min.	Min.	Min.	Perf.	Perf.	Maj.	Maj.	Maj.	Maj.	Min.	Min.	Min.	Min.	Perf.
9\|9	15	LLLLsLLLLLLLLLsLLLL	Perf.	Maj.	Maj.	Maj.	Maj.	Min.	Min.	Min.	Min.	Perf.	Perf.	Maj.	Maj.	Maj.	Maj.	Min.	Min.	Min.	Min.	Perf.
8\|10	6	LLLLsLLLLLLLLsLLLLL	Perf.	Maj.	Maj.	Maj.	Maj.	Min.	Min.	Min.	Min.	Perf.	Perf.	Maj.	Maj.	Maj.	Min.	Min.	Min.	Min.	Min.	Perf.
7\|11	16	LLLsLLLLLLLLLsLLLLL	Perf.	Maj.	Maj.	Maj.	Min.	Min.	Min.	Min.	Min.	Perf.	Perf.	Maj.	Maj.	Maj.	Min.	Min.	Min.	Min.	Min.	Perf.
6\|12	7	LLLsLLLLLLLLsLLLLLL	Perf.	Maj.	Maj.	Maj.	Min.	Min.	Min.	Min.	Min.	Perf.	Perf.	Maj.	Maj.	Min.	Min.	Min.	Min.	Min.	Min.	Perf.
5\|13	17	LLsLLLLLLLLLsLLLLLL	Perf.	Maj.	Maj.	Min.	Min.	Min.	Min.	Min.	Min.	Perf.	Perf.	Maj.	Maj.	Min.	Min.	Min.	Min.	Min.	Min.	Perf.
4\|14	8	LLsLLLLLLLLsLLLLLLL	Perf.	Maj.	Maj.	Min.	Min.	Min.	Min.	Min.	Min.	Perf.	Perf.	Maj.	Min.	Min.	Min.	Min.	Min.	Min.	Min.	Perf.
3\|15	18	LsLLLLLLLLLsLLLLLLL	Perf.	Maj.	Min.	Min.	Min.	Min.	Min.	Min.	Min.	Perf.	Perf.	Maj.	Min.	Min.	Min.	Min.	Min.	Min.	Min.	Perf.
2\|16	9	LsLLLLLLLLsLLLLLLLL	Perf.	Maj.	Min.	Min.	Min.	Min.	Min.	Min.	Min.	Perf.	Perf.	Min.	Min.	Min.	Min.	Min.	Min.	Min.	Min.	Perf.
1\|17	19	sLLLLLLLLLsLLLLLLLL	Perf.	Min.	Min.	Min.	Min.	Min.	Min.	Min.	Min.	Perf.	Perf.	Min.	Min.	Min.	Min.	Min.	Min.	Min.	Min.	Perf.
0\|18	10	sLLLLLLLLsLLLLLLLLL	Perf.	Min.	Min.	Min.	Min.	Min.	Min.	Min.	Min.	Perf.	Dim.	Min.	Min.	Min.	Min.	Min.	Min.	Min.	Min.	Perf.

Scale tree

Scale tree and tuning spectrum of 17L 2s
Generator^(edo)							Cents		Step ratio		Comments
Generator^(edo)							Bright	Dark	L:s	Hardness	Comments
10\19							631.579	568.421	1:1	1.000	Equalized 17L 2s
						69\131	632.061	567.939	7:6	1.167
					59\112		632.143	567.857	6:5	1.200
						108\205	632.195	567.805	11:9	1.222
				49\93			632.258	567.742	5:4	1.250	Pycnic
						137\260	632.308	567.692	14:11	1.273
					88\167		632.335	567.665	9:7	1.286
						127\241	632.365	567.635	13:10	1.300
			39\74				632.432	567.568	4:3	1.333	Supersoft 17L 2s Liese (as 74d)
						146\277	632.491	567.509	15:11	1.364
					107\203		632.512	567.488	11:8	1.375
						175\332	632.530	567.470	18:13	1.385
				68\129			632.558	567.442	7:5	1.400
						165\313	632.588	567.412	17:12	1.417
					97\184		632.609	567.391	10:7	1.429
						126\239	632.636	567.364	13:9	1.444
		29\55					632.727	567.273	3:2	1.500	Soft 17L 2s
						135\256	632.812	567.188	14:9	1.556
					106\201		632.836	567.164	11:7	1.571
						183\347	632.853	567.147	19:12	1.583
				77\146			632.877	567.123	8:5	1.600
						202\383	632.898	567.102	21:13	1.615
					125\237		632.911	567.089	13:8	1.625
						173\328	632.927	567.073	18:11	1.636
			48\91				632.967	567.033	5:3	1.667	Semisoft 17L 2s Liesel (as 91ceef)
						163\309	633.010	566.990	17:10	1.700
					115\218		633.028	566.972	12:7	1.714
						182\345	633.043	566.957	19:11	1.727
				67\127			633.071	566.929	7:4	1.750
						153\290	633.103	566.897	16:9	1.778
					86\163		633.129	566.871	9:5	1.800
						105\199	633.166	566.834	11:6	1.833
	19\36						633.333	566.667	2:1	2.000	Basic 17L 2s Scales with tunings softer than this are proper
						104\197	633.503	566.497	11:5	2.200
					85\161		633.540	566.460	9:4	2.250
						151\286	633.566	566.434	16:7	2.286
				66\125			633.600	566.400	7:3	2.333
						179\339	633.628	566.372	19:8	2.375
					113\214		633.645	566.355	12:5	2.400
						160\303	633.663	566.337	17:7	2.429
			47\89				633.708	566.292	5:2	2.500	Semihard 17L 2s
						169\320	633.750	566.250	18:7	2.571
					122\231		633.766	566.234	13:5	2.600
						197\373	633.780	566.220	21:8	2.625
				75\142			633.803	566.197	8:3	2.667
						178\337	633.828	566.172	19:7	2.714
					103\195		633.846	566.154	11:4	2.750
						131\248	633.871	566.129	14:5	2.800
		28\53					633.962	566.038	3:1	3.000	Hard 17L 2s
						121\229	634.061	565.939	13:4	3.250	Alphatricot/Alphatrident
					93\176		634.091	565.909	10:3	3.333
						158\299	634.114	565.886	17:5	3.400
				65\123			634.146	565.854	7:2	3.500
						167\316	634.177	565.823	18:5	3.600
					102\193		634.197	565.803	11:3	3.667
						139\263	634.221	565.779	15:4	3.750
			37\70				634.286	565.714	4:1	4.000	Superhard 17L 2s
						120\227	634.361	565.639	13:3	4.333
					83\157		634.395	565.605	9:2	4.500
						129\244	634.426	565.574	14:3	4.667
				46\87			634.483	565.517	5:1	5.000
						101\191	634.555	565.445	11:2	5.500
					55\104		634.615	565.385	6:1	6.000
						64\121	634.711	565.289	7:1	7.000
9\17							635.294	564.706	1:0	→ ∞	Collapsed 17L 2s

This page is a stub. You can help the Xenharmonic Wiki by expanding it.

17L 2s

Contents

Scale properties

Intervals

Generator chain

Modes

Scale tree

Navigation menu

17L 2s

Scale properties

Intervals

Generator chain

Modes

Scale tree

Navigation menu

Search