7L 2s (5/2-equivalent)

↖ 6L 1s⟨5/2⟩	↑ 7L 1s⟨5/2⟩	8L 1s⟨5/2⟩ ↗
← 6L 2s⟨5/2⟩	7L 2s (5/2-equivalent)	8L 2s⟨5/2⟩ →
↙ 6L 3s⟨5/2⟩	↓ 7L 3s⟨5/2⟩	8L 3s⟨5/2⟩ ↘

Scale structure
Step pattern	LLLLsLLLs sLLLsLLLL
Equave	5/2 (1586.3 ¢)
Period	5/2 (1586.3 ¢)
Generator size(ed5/2)
Bright	5\9 to 4\7 (881.3 ¢ to 906.5 ¢)
Dark	3\7 to 4\9 (679.8 ¢ to 705.0 ¢)
Related MOS scales
Parent	2L 5s⟨5/2⟩
Sister	2L 7s⟨5/2⟩
Daughters	9L 7s⟨5/2⟩, 7L 9s⟨5/2⟩
Neutralized	5L 4s⟨5/2⟩
2-Flought	16L 2s⟨5/2⟩, 7L 11s⟨5/2⟩
Equal tunings(ed5/2)
Equalized (L:s = 1:1)	5\9 (881.3 ¢)
Supersoft (L:s = 4:3)	19\34 (886.5 ¢)
Soft (L:s = 3:2)	14\25 (888.3 ¢)
Semisoft (L:s = 5:3)	23\41 (889.9 ¢)
Basic (L:s = 2:1)	9\16 (892.3 ¢)
Semihard (L:s = 5:2)	22\39 (894.8 ¢)
Hard (L:s = 3:1)	13\23 (896.6 ¢)
Superhard (L:s = 4:1)	17\30 (898.9 ¢)
Collapsed (L:s = 1:0)	4\7 (906.5 ¢)
View • Talk • Edit

7L 2s⟨5/2⟩ is a 5/2-equivalent (non-octave) moment of symmetry scale containing 7 large steps and 2 small steps, repeating every interval of 5/2 (1586.3 ¢). Generators that produce this scale range from 881.3 ¢ to 906.5 ¢, or from 679.8 ¢ to 705 ¢. It is significant due to being generated by fifths, like diatonic, and also having a similar structure to diatonic. With a tempered period, 19edo makes for a good tuning.

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 7L 2s⟨5/2⟩

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 176.3 ¢
	Major 1-mosstep	M1ms	L	176.3 ¢ to 226.6 ¢
2-mosstep	Minor 2-mosstep	m2ms	L + s	226.6 ¢ to 352.5 ¢
	Major 2-mosstep	M2ms	2L	352.5 ¢ to 453.2 ¢
3-mosstep	Minor 3-mosstep	m3ms	2L + s	453.2 ¢ to 528.8 ¢
	Major 3-mosstep	M3ms	3L	528.8 ¢ to 679.8 ¢
4-mosstep	Perfect 4-mosstep	P4ms	3L + s	679.8 ¢ to 705.0 ¢
	Augmented 4-mosstep	A4ms	4L	705.0 ¢ to 906.5 ¢
5-mosstep	Diminished 5-mosstep	d5ms	3L + 2s	679.8 ¢ to 881.3 ¢
	Perfect 5-mosstep	P5ms	4L + s	881.3 ¢ to 906.5 ¢
6-mosstep	Minor 6-mosstep	m6ms	4L + 2s	906.5 ¢ to 1057.5 ¢
	Major 6-mosstep	M6ms	5L + s	1057.5 ¢ to 1133.1 ¢
7-mosstep	Minor 7-mosstep	m7ms	5L + 2s	1133.1 ¢ to 1233.8 ¢
	Major 7-mosstep	M7ms	6L + s	1233.8 ¢ to 1359.7 ¢
8-mosstep	Minor 8-mosstep	m8ms	6L + 2s	1359.7 ¢ to 1410.1 ¢
	Major 8-mosstep	M8ms	7L + s	1410.1 ¢ to 1586.3 ¢
9-mosstep	Perfect 9-mosstep	P9ms	7L + 2s	1586.3 ¢

Generator chain

Generator chain of 7L 2s⟨5/2⟩

Bright gens	Scale degree	Abbrev.
15	Augmented 3-mosdegree	A3md
14	Augmented 7-mosdegree	A7md
13	Augmented 2-mosdegree	A2md
12	Augmented 6-mosdegree	A6md
11	Augmented 1-mosdegree	A1md
10	Augmented 5-mosdegree	A5md
9	Augmented 0-mosdegree	A0md
8	Augmented 4-mosdegree	A4md
7	Major 8-mosdegree	M8md
6	Major 3-mosdegree	M3md
5	Major 7-mosdegree	M7md
4	Major 2-mosdegree	M2md
3	Major 6-mosdegree	M6md
2	Major 1-mosdegree	M1md
1	Perfect 5-mosdegree	P5md
0	Perfect 0-mosdegree Perfect 9-mosdegree	P0md P9md
−1	Perfect 4-mosdegree	P4md
−2	Minor 8-mosdegree	m8md
−3	Minor 3-mosdegree	m3md
−4	Minor 7-mosdegree	m7md
−5	Minor 2-mosdegree	m2md
−6	Minor 6-mosdegree	m6md
−7	Minor 1-mosdegree	m1md
−8	Diminished 5-mosdegree	d5md
−9	Diminished 9-mosdegree	d9md
−10	Diminished 4-mosdegree	d4md
−11	Diminished 8-mosdegree	d8md
−12	Diminished 3-mosdegree	d3md
−13	Diminished 7-mosdegree	d7md
−14	Diminished 2-mosdegree	d2md
−15	Diminished 6-mosdegree	d6md

Modes

Scale degrees of the modes of 7L 2s⟨5/2⟩

UDP	Cyclic order	Step pattern	Scale degree (mosdegree)
			0	1	2	3	4	5	6	7	8	9
8|0	1	LLLLsLLLs	Perf.	Maj.	Maj.	Maj.	Aug.	Perf.	Maj.	Maj.	Maj.	Perf.
7|1	6	LLLsLLLLs	Perf.	Maj.	Maj.	Maj.	Perf.	Perf.	Maj.	Maj.	Maj.	Perf.
6|2	2	LLLsLLLsL	Perf.	Maj.	Maj.	Maj.	Perf.	Perf.	Maj.	Maj.	Min.	Perf.
5|3	7	LLsLLLLsL	Perf.	Maj.	Maj.	Min.	Perf.	Perf.	Maj.	Maj.	Min.	Perf.
4|4	3	LLsLLLsLL	Perf.	Maj.	Maj.	Min.	Perf.	Perf.	Maj.	Min.	Min.	Perf.
3|5	8	LsLLLLsLL	Perf.	Maj.	Min.	Min.	Perf.	Perf.	Maj.	Min.	Min.	Perf.
2|6	4	LsLLLsLLL	Perf.	Maj.	Min.	Min.	Perf.	Perf.	Min.	Min.	Min.	Perf.
1|7	9	sLLLLsLLL	Perf.	Min.	Min.	Min.	Perf.	Perf.	Min.	Min.	Min.	Perf.
0|8	5	sLLLsLLLL	Perf.	Min.	Min.	Min.	Perf.	Dim.	Min.	Min.	Min.	Perf.

Scale tree

Scale tree and tuning spectrum of 7L 2s⟨5/2⟩

Generator(ed5/2)						Cents		Step ratio		Comments
						Bright	Dark	L:s	Hardness
5\9						881.285	705.028	1:1	1.000	Equalized 7L 2s⟨5/2⟩
					29\52	884.675	701.639	6:5	1.200
				24\43		885.384	700.929	5:4	1.250
					43\77	885.864	700.450	9:7	1.286
			19\34			886.469	699.844	4:3	1.333	Supersoft 7L 2s⟨5/2⟩
					52\93	886.971	699.343	11:8	1.375
				33\59		887.260	699.054	7:5	1.400
					47\84	887.580	698.733	10:7	1.429
		14\25				888.336	697.978	3:2	1.500	Soft 7L 2s⟨5/2⟩
					51\91	889.033	697.281	11:7	1.571
				37\66		889.297	697.017	8:5	1.600
					60\107	889.522	696.792	13:8	1.625
			23\41			889.883	696.430	5:3	1.667	Semisoft 7L 2s⟨5/2⟩
					55\98	890.278	696.036	12:7	1.714
				32\57		890.562	695.752	7:4	1.750
					41\73	890.943	695.370	9:5	1.800
	9\16					892.301	694.012	2:1	2.000	Basic 7L 2s⟨5/2⟩ Scales with tunings softer than this are proper
					40\71	893.698	692.616	9:4	2.250
				31\55		894.104	692.210	7:3	2.333
					53\94	894.411	691.903	12:5	2.400
			22\39			894.844	691.470	5:2	2.500	Semihard 7L 2s⟨5/2⟩
					57\101	895.246	691.067	13:5	2.600
				35\62		895.500	690.814	8:3	2.667
					48\85	895.801	690.513	11:4	2.750
		13\23				896.612	689.702	3:1	3.000	Hard 7L 2s⟨5/2⟩
					43\76	897.520	688.794	10:3	3.333
				30\53		897.913	688.400	7:2	3.500
					47\83	898.274	688.040	11:3	3.667
			17\30			898.911	687.403	4:1	4.000	Superhard 7L 2s⟨5/2⟩
					38\67	899.700	686.613	9:2	4.500
				21\37		900.340	685.973	5:1	5.000
					25\44	901.315	684.999	6:1	6.000
4\7						906.465	679.849	1:0	→ ∞	Collapsed 7L 2s⟨5/2⟩

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