2L 2s

2L 2s, named biwood in TAMNAMS, is a 2/1-equivalent (octave-equivalent) moment of symmetry scale containing 2 large steps and 2 small steps, with a period of 1 large step and 1 small step that repeats every 600.0 ¢, or twice every octave. Generators that produce this scale range from 300 ¢ to 600 ¢, or from 0 ¢ to 300 ¢. Scales of the true MOS form, where every period is the same, are proper because there is only one small step per period.

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

Scale structure
Step pattern	LsLs sLsL
Equave	2/1 (1200.0 ¢)
Period	1\2 (600.0 ¢)
Generator size
Bright	1\4 to 1\2 (300.0 ¢ to 600.0 ¢)
Dark	0\2 to 1\4 (0.0 ¢ to 300.0 ¢)
TAMNAMS information
Name	biwood
Prefix	biwd-
Abbrev.	bw
Related MOS scales
Parent	none
Sister	2L 2s (self)
Daughters	4L 2s, 2L 4s
Neutralized	4edo
2-Flought	6L 2s, 2L 6s
Equal tunings
Equalized (L:s = 1:1)	1\4 (300.0 ¢)
Supersoft (L:s = 4:3)	4\14 (342.9 ¢)
Soft (L:s = 3:2)	3\10 (360.0 ¢)
Semisoft (L:s = 5:3)	5\16 (375.0 ¢)
Basic (L:s = 2:1)	2\6 (400.0 ¢)
Semihard (L:s = 5:2)	5\14 (428.6 ¢)
Hard (L:s = 3:1)	3\8 (450.0 ¢)
Superhard (L:s = 4:1)	4\10 (480.0 ¢)
Collapsed (L:s = 1:0)	1\2 (600.0 ¢)
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This scale is the parent of all half-octave-repeating MOS scales.

Names

TAMNAMS uses the name biwood, based on the n-wood series.

Modes

Scale degrees of the modes of 2L 2s

UDP	Cyclic order	Step pattern	Scale degree (biwddegree)
			0	1	2	3	4
2|0(2)	1	LsLs	Perf.	Maj.	Perf.	Maj.	Perf.
0|2(2)	2	sLsL	Perf.	Min.	Perf.	Min.	Perf.

Intervals

Intervals of 2L 2s

Intervals			Steps subtended	Range in cents
Generic	Specific	Abbrev.
0-biwdstep	Perfect 0-biwdstep	P0bws	0	0.0 ¢
1-biwdstep	Minor 1-biwdstep	m1bws	s	0.0 ¢ to 300.0 ¢
	Major 1-biwdstep	M1bws	L	300.0 ¢ to 600.0 ¢
2-biwdstep	Perfect 2-biwdstep	P2bws	L + s	600.0 ¢
3-biwdstep	Minor 3-biwdstep	m3bws	L + 2s	600.0 ¢ to 900.0 ¢
	Major 3-biwdstep	M3bws	2L + s	900.0 ¢ to 1200.0 ¢
4-biwdstep	Perfect 4-biwdstep	P4bws	2L + 2s	1200.0 ¢

Scale tree

Generator ranges:

• Chroma-positive generator: 300 cents (1\4) to 600 cents (1\2)
• Chroma-negative generator: 0 cents (0\2) to 300 cents (1\4)

Generator						Cents	L	s	L/s	Comments
1\4						300.000	1	1	1.000
					6\22	327.273	6	5	1.200
				5\18		333.333	5	4	1.250
					9\32	337.500	9	7	1.286
			4\14			342.857	4	3	1.333
					11\38	347.368	11	8	1.375
				7\24		350.000	7	5	1.400
					10\34	352.941	10	7	1.429
		3\10				360.000	3	2	1.500
					11\36	366.667	11	7	1.571	Baladic
				8\26		369.231	8	5	1.600
					13\42	371.429	13	8	1.625	Golden Lemba (370.8204¢)
			5\16			375.000	5	3	1.667
					12\38	378.947	12	7	1.714
				7\22		381.818	7	4	1.750
					9\28	385.714	9	5	1.800
	2\6					400.000	2	1	2.000	Basic 2L 2s
					9\26	415.385	9	4	2.250	Unidec is around here
				7\20		420.000	7	3	2.333
					12\34	423.529	12	5	2.400
			5\14			428.571	5	2	2.500
					13\36	433.333	13	5	2.600	Golden Hedgehog-supers (434.1641¢)
				8\22		436.364	8	3	2.667
					11\30	440.000	11	4	2.750
		3\8				450.000	3	1	3.000
					10\26	461.538	10	3	3.333	Fifive
				7\18		466.667	7	2	3.500
					11\28	471.429	11	3	3.667
			4\10			480.000	4	1	4.000
					9\22	490.909	9	2	4.500	Diaschismic / Pajara
				5\12		500.000	5	1	5.000	Injera is around here
					6\14	514.286	6	1	6.000	Vishnu↓
1\2						600.000	1	0	→ inf