2L 7s

↖ 1L 6s	↑ 2L 6s	3L 6s ↗
← 1L 7s	2L 7s	3L 7s →
↙ 1L 8s	↓ 2L 8s	3L 8s ↘

┌╥┬┬┬╥┬┬┬┬┐ │║│││║│││││ │││││││││││ └┴┴┴┴┴┴┴┴┴┘
Scale structure
Step pattern	LsssLssss ssssLsssL
Equave	2/1 (1200.0¢)
Period	2/1 (1200.0¢)
Generator size
Bright	4\9 to 1\2 (533.3¢ to 600.0¢)
Dark	1\2 to 5\9 (600.0¢ to 666.7¢)
TAMNAMS information
Name	balzano
Prefix	bal-
Abbrev.	bz
Related MOS scales
Parent	2L 5s
Sister	7L 2s
Daughters	9L 2s, 2L 9s
Neutralized	4L 5s
2-Flought	11L 7s, 2L 16s
Equal tunings
Equalized (L:s = 1:1)	4\9 (533.3¢)
Supersoft (L:s = 4:3)	13\29 (537.9¢)
Soft (L:s = 3:2)	9\20 (540.0¢)
Semisoft (L:s = 5:3)	14\31 (541.9¢)
Basic (L:s = 2:1)	5\11 (545.5¢)
Semihard (L:s = 5:2)	11\24 (550.0¢)
Hard (L:s = 3:1)	6\13 (553.8¢)
Superhard (L:s = 4:1)	7\15 (560.0¢)
Collapsed (L:s = 1:0)	1\2 (600.0¢)

2L 7s, named balzano in TAMNAMS, is a 2/1-equivalent (octave-equivalent) moment of symmetry scale containing 2 large steps and 7 small steps, repeating every octave. Generators that produce this scale range from 533.3¢ to 600¢, or from 600¢ to 666.7¢.

Names

This scale is called balzano in TAMNAMS nomenclature.

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 diatonic interval categories.

Intervals

Intervals of 2L 7s

Intervals			Steps subtended	Range in cents
Generic	Specific	Abbrev.
0-balstep	Perfect 0-balstep	P0bzs	0	0.0¢
1-balstep	Minor 1-balstep	m1bzs	s	0.0¢ to 133.3¢
	Major 1-balstep	M1bzs	L	133.3¢ to 600.0¢
2-balstep	Minor 2-balstep	m2bzs	2s	0.0¢ to 266.7¢
	Major 2-balstep	M2bzs	L + s	266.7¢ to 600.0¢
3-balstep	Minor 3-balstep	m3bzs	3s	0.0¢ to 400.0¢
	Major 3-balstep	M3bzs	L + 2s	400.0¢ to 600.0¢
4-balstep	Diminished 4-balstep	d4bzs	4s	0.0¢ to 533.3¢
	Perfect 4-balstep	P4bzs	L + 3s	533.3¢ to 600.0¢
5-balstep	Perfect 5-balstep	P5bzs	L + 4s	600.0¢ to 666.7¢
	Augmented 5-balstep	A5bzs	2L + 3s	666.7¢ to 1200.0¢
6-balstep	Minor 6-balstep	m6bzs	L + 5s	600.0¢ to 800.0¢
	Major 6-balstep	M6bzs	2L + 4s	800.0¢ to 1200.0¢
7-balstep	Minor 7-balstep	m7bzs	L + 6s	600.0¢ to 933.3¢
	Major 7-balstep	M7bzs	2L + 5s	933.3¢ to 1200.0¢
8-balstep	Minor 8-balstep	m8bzs	L + 7s	600.0¢ to 1066.7¢
	Major 8-balstep	M8bzs	2L + 6s	1066.7¢ to 1200.0¢
9-balstep	Perfect 9-balstep	P9bzs	2L + 7s	1200.0¢

Modes

Scale degrees of the modes of 2L 7s 

UDP	Cyclic order	Step pattern	Scale degree (baldegree)
			0	1	2	3	4	5	6	7	8	9
8|0	1	LsssLssss	Perf.	Maj.	Maj.	Maj.	Perf.	Aug.	Maj.	Maj.	Maj.	Perf.
7|1	5	LssssLsss	Perf.	Maj.	Maj.	Maj.	Perf.	Perf.	Maj.	Maj.	Maj.	Perf.
6|2	9	sLsssLsss	Perf.	Min.	Maj.	Maj.	Perf.	Perf.	Maj.	Maj.	Maj.	Perf.
5|3	4	sLssssLss	Perf.	Min.	Maj.	Maj.	Perf.	Perf.	Min.	Maj.	Maj.	Perf.
4|4	8	ssLsssLss	Perf.	Min.	Min.	Maj.	Perf.	Perf.	Min.	Maj.	Maj.	Perf.
3|5	3	ssLssssLs	Perf.	Min.	Min.	Maj.	Perf.	Perf.	Min.	Min.	Maj.	Perf.
2|6	7	sssLsssLs	Perf.	Min.	Min.	Min.	Perf.	Perf.	Min.	Min.	Maj.	Perf.
1|7	2	sssLssssL	Perf.	Min.	Min.	Min.	Perf.	Perf.	Min.	Min.	Min.	Perf.
0|8	6	ssssLsssL	Perf.	Min.	Min.	Min.	Dim.	Perf.	Min.	Min.	Min.	Perf.

Scale tree

Scale Tree and Tuning Spectrum of 2L 7s

Generator(edo)						Cents		Step ratio		Comments
						Bright	Dark	L:s	Hardness
4\9						533.333	666.667	1:1	1.000	Equalized 2L 7s
					21\47	536.170	663.830	6:5	1.200
				17\38		536.842	663.158	5:4	1.250
					30\67	537.313	662.687	9:7	1.286
			13\29			537.931	662.069	4:3	1.333	Supersoft 2L 7s
					35\78	538.462	661.538	11:8	1.375
				22\49		538.776	661.224	7:5	1.400
					31\69	539.130	660.870	10:7	1.429
		9\20				540.000	660.000	3:2	1.500	Soft 2L 7s
					32\71	540.845	659.155	11:7	1.571
				23\51		541.176	658.824	8:5	1.600
					37\82	541.463	658.537	13:8	1.625
			14\31			541.935	658.065	5:3	1.667	Semisoft 2L 7s Casablanca
					33\73	542.466	657.534	12:7	1.714
				19\42		542.857	657.143	7:4	1.750
					24\53	543.396	656.604	9:5	1.800
	5\11					545.455	654.545	2:1	2.000	Basic 2L 7s Scales with tunings softer than this are proper
					21\46	547.826	652.174	9:4	2.250
				16\35		548.571	651.429	7:3	2.333
					27\59	549.153	650.847	12:5	2.400
			11\24			550.000	650.000	5:2	2.500	Semihard 2L 7s
					28\61	550.820	649.180	13:5	2.600
				17\37		551.351	648.649	8:3	2.667
					23\50	552.000	648.000	11:4	2.750
		6\13				553.846	646.154	3:1	3.000	Hard 2L 7s
					19\41	556.098	643.902	10:3	3.333
				13\28		557.143	642.857	7:2	3.500
					20\43	558.140	641.860	11:3	3.667	Thuja
			7\15			560.000	640.000	4:1	4.000	Superhard 2L 7s
					15\32	562.500	637.500	9:2	4.500
				8\17		564.706	635.294	5:1	5.000
					9\19	568.421	631.579	6:1	6.000
1\2						600.000	600.000	1:0	→ ∞	Collapsed 2L 7s