3L 7s (3/1-equivalent)

↖ 2L 6s⟨3/1⟩	↑ 3L 6s⟨3/1⟩	4L 6s⟨3/1⟩ ↗
← 2L 7s⟨3/1⟩	3L 7s (3/1-equivalent)	4L 7s⟨3/1⟩ →
↙ 2L 8s⟨3/1⟩	↓ 3L 8s⟨3/1⟩	4L 8s⟨3/1⟩ ↘

Scale structure
Step pattern	LssLssLsss sssLssLssL
Equave	3/1 (1902.0 ¢)
Period	3/1 (1902.0 ¢)
Generator size(edt)
Bright	3\10 to 1\3 (570.6 ¢ to 634.0 ¢)
Dark	2\3 to 7\10 (1268.0 ¢ to 1331.4 ¢)
Related MOS scales
Parent	3L 4s⟨3/1⟩
Sister	7L 3s⟨3/1⟩
Daughters	10L 3s⟨3/1⟩, 3L 10s⟨3/1⟩
Neutralized	6L 4s⟨3/1⟩
2-Flought	13L 7s⟨3/1⟩, 3L 17s⟨3/1⟩
Equal tunings(edt)
Equalized (L:s = 1:1)	3\10 (570.6 ¢)
Supersoft (L:s = 4:3)	10\33 (576.4 ¢)
Soft (L:s = 3:2)	7\23 (578.9 ¢)
Semisoft (L:s = 5:3)	11\36 (581.2 ¢)
Basic (L:s = 2:1)	4\13 (585.2 ¢)
Semihard (L:s = 5:2)	9\29 (590.3 ¢)
Hard (L:s = 3:1)	5\16 (594.4 ¢)
Superhard (L:s = 4:1)	6\19 (600.6 ¢)
Collapsed (L:s = 1:0)	1\3 (634.0 ¢)
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3L 7s⟨3/1⟩ is a 3/1-equivalent (tritave-equivalent) moment of symmetry scale containing 3 large steps and 7 small steps, repeating every interval of 3/1 (1902.0 ¢). Generators that produce this scale range from 570.6 ¢ to 634 ¢, or from 1268 ¢ to 1331.4 ¢.

It is the decatonic scale of the 7/5-generated Canopus temperament, one of the most notable no-twos temperaments after Bohlen-Pierce-Stearns. Basic 3L 7s⟨3/1⟩ is in 13edt (Bohlen-Pierce).

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.

{{p = 8/3, g = 2/1MOS data}}

Scale tree

Scale tree and tuning spectrum of 3L 7s⟨3/1⟩

Generator(edt)						Cents		Step ratio		Comments
						Bright	Dark	L:s	Hardness
3\10						570.587	1331.369	1:1	1.000	Equalized 3L 7s⟨3/1⟩
					16\53	574.175	1327.780	6:5	1.200
				13\43		575.010	1326.945	5:4	1.250
					23\76	575.592	1326.363	9:7	1.286
			10\33			576.350	1325.605	4:3	1.333	Supersoft 3L 7s⟨3/1⟩
					27\89	576.998	1324.957	11:8	1.375
				17\56		577.379	1324.576	7:5	1.400
					24\79	577.809	1324.146	10:7	1.429
		7\23				578.856	1323.099	3:2	1.500	Soft 3L 7s⟨3/1⟩
					25\82	579.864	1322.091	11:7	1.571
				18\59		580.257	1321.698	8:5	1.600
					29\95	580.597	1321.358	13:8	1.625
			11\36			581.153	1320.802	5:3	1.667	Semisoft 3L 7s⟨3/1⟩
					26\85	581.774	1320.181	12:7	1.714
				15\49		582.231	1319.724	7:4	1.750
					19\62	582.857	1319.098	9:5	1.800
	4\13					585.217	1316.738	2:1	2.000	Basic 3L 7s⟨3/1⟩ Scales with tunings softer than this are proper Canopus is around here
					17\55	587.877	1314.078	9:4	2.250
				13\42		588.700	1313.255	7:3	2.333
					22\71	589.338	1312.617	12:5	2.400
			9\29			590.262	1311.693	5:2	2.500	Semihard 3L 7s⟨3/1⟩
					23\74	591.148	1310.807	13:5	2.600
				14\45		591.719	1310.236	8:3	2.667
					19\61	592.412	1309.543	11:4	2.750
		5\16				594.361	1307.594	3:1	3.000	Hard 3L 7s⟨3/1⟩
					16\51	596.692	1305.263	10:3	3.333
				11\35		597.757	1304.198	7:2	3.500
					17\54	598.764	1303.191	11:3	3.667
			6\19			600.617	1301.338	4:1	4.000	Superhard 3L 7s⟨3/1⟩
					13\41	603.059	1298.896	9:2	4.500
				7\22		605.168	1296.788	5:1	5.000
					8\25	608.626	1293.329	6:1	6.000
1\3						633.985	1267.970	1:0	→ ∞	Collapsed 3L 7s⟨3/1⟩