7L 2s

7L 2s, named armotonic in TAMNAMS, is a 2/1-equivalent (octave-equivalent) moment of symmetry scale containing 7 large steps and 2 small steps, repeating every octave. Generators that produce this scale range from 666.7 ¢ to 685.7 ¢, or from 514.3 ¢ to 533.3 ¢. Scales of this form are strongly associated with Armodue theory, as applied to septimal mavila and Hornbostel temperaments.

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

Scale structure
Step pattern	LLLLsLLLs sLLLsLLLL
Equave	2/1 (1200.0 ¢)
Period	2/1 (1200.0 ¢)
Generator size
Bright	5\9 to 4\7 (666.7 ¢ to 685.7 ¢)
Dark	3\7 to 4\9 (514.3 ¢ to 533.3 ¢)
TAMNAMS information
Name	armotonic
Prefix	arm-
Abbrev.	arm
Related MOS scales
Parent	2L 5s
Sister	2L 7s
Daughters	9L 7s, 7L 9s
Neutralized	5L 4s
2-Flought	16L 2s, 7L 11s
Equal tunings
Equalized (L:s = 1:1)	5\9 (666.7 ¢)
Supersoft (L:s = 4:3)	19\34 (670.6 ¢)
Soft (L:s = 3:2)	14\25 (672.0 ¢)
Semisoft (L:s = 5:3)	23\41 (673.2 ¢)
Basic (L:s = 2:1)	9\16 (675.0 ¢)
Semihard (L:s = 5:2)	22\39 (676.9 ¢)
Hard (L:s = 3:1)	13\23 (678.3 ¢)
Superhard (L:s = 4:1)	17\30 (680.0 ¢)
Collapsed (L:s = 1:0)	4\7 (685.7 ¢)
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Name

The TAMNAMS name for this pattern is armotonic, in reference to Armodue theory. Superdiatonic is also in use.

Intervals

This article assumes TAMNAMS for naming step ratios, mossteps, and mosdegrees.

Intervals of 7L 2s

Intervals			Steps subtended	Range in cents
Generic	Specific	Abbrev.
0-armstep	Perfect 0-armstep	P0arms	0	0.0 ¢
1-armstep	Minor 1-armstep	m1arms	s	0.0 ¢ to 133.3 ¢
	Major 1-armstep	M1arms	L	133.3 ¢ to 171.4 ¢
2-armstep	Minor 2-armstep	m2arms	L + s	171.4 ¢ to 266.7 ¢
	Major 2-armstep	M2arms	2L	266.7 ¢ to 342.9 ¢
3-armstep	Minor 3-armstep	m3arms	2L + s	342.9 ¢ to 400.0 ¢
	Major 3-armstep	M3arms	3L	400.0 ¢ to 514.3 ¢
4-armstep	Perfect 4-armstep	P4arms	3L + s	514.3 ¢ to 533.3 ¢
	Augmented 4-armstep	A4arms	4L	533.3 ¢ to 685.7 ¢
5-armstep	Diminished 5-armstep	d5arms	3L + 2s	514.3 ¢ to 666.7 ¢
	Perfect 5-armstep	P5arms	4L + s	666.7 ¢ to 685.7 ¢
6-armstep	Minor 6-armstep	m6arms	4L + 2s	685.7 ¢ to 800.0 ¢
	Major 6-armstep	M6arms	5L + s	800.0 ¢ to 857.1 ¢
7-armstep	Minor 7-armstep	m7arms	5L + 2s	857.1 ¢ to 933.3 ¢
	Major 7-armstep	M7arms	6L + s	933.3 ¢ to 1028.6 ¢
8-armstep	Minor 8-armstep	m8arms	6L + 2s	1028.6 ¢ to 1066.7 ¢
	Major 8-armstep	M8arms	7L + s	1066.7 ¢ to 1200.0 ¢
9-armstep	Perfect 9-armstep	P9arms	7L + 2s	1200.0 ¢

Note names

7L 2s, when viewed under Armodue theory, can be notated using Armodue notation.

Theory

Temperament interpretations

Mavila is an important harmonic entropy minimum here, insofar as 678¢ can be considered a fifth. Other temperaments include septimal mavila and Hornbostel.

Modes

Modes of 7L 2s

UDP	Cyclic order	Step pattern
8|0	1	LLLLsLLLs
7|1	6	LLLsLLLLs
6|2	2	LLLsLLLsL
5|3	7	LLsLLLLsL
4|4	3	LLsLLLsLL
3|5	8	LsLLLLsLL
2|6	4	LsLLLsLLL
1|7	9	sLLLLsLLL
0|8	5	sLLLsLLLL

Scale tree

Template: Scale tree is deprecated. Please use Template: MOS tuning spectrum instead. Details: Use of a single Comments parameter has become unmaintainable. Existing scale trees should be migrated to the new template, where comments are entered using a step ratio p/q as a parameter: {{MOS tuning spectrum | 3/2 = Example comment | 4/3 = Another example comment }} The parameters tuning and depth have been replaced with Scale Signature and Depth, respectively.

Scale tree and tuning spectrum of 7L 2s

Generator(edo)						Cents		Step ratio		Comments
						Bright	Dark	L:s	Hardness
5\9						666.667	533.333	1:1	1.000	Equalized 7L 2s
					29\52	669.231	530.769	6:5	1.200
				24\43		669.767	530.233	5:4	1.250
					43\77	670.130	529.870	9:7	1.286
			19\34			670.588	529.412	4:3	1.333	Supersoft 7L 2s
					52\93	670.968	529.032	11:8	1.375
				33\59		671.186	528.814	7:5	1.400
					47\84	671.429	528.571	10:7	1.429
		14\25				672.000	528.000	3:2	1.500	Soft 7L 2s
					51\91	672.527	527.473	11:7	1.571
				37\66		672.727	527.273	8:5	1.600
					60\107	672.897	527.103	13:8	1.625
			23\41			673.171	526.829	5:3	1.667	Semisoft 7L 2s
					55\98	673.469	526.531	12:7	1.714
				32\57		673.684	526.316	7:4	1.750
					41\73	673.973	526.027	9:5	1.800
	9\16					675.000	525.000	2:1	2.000	Basic 7L 2s Scales with tunings softer than this are proper
					40\71	676.056	523.944	9:4	2.250
				31\55		676.364	523.636	7:3	2.333
					53\94	676.596	523.404	12:5	2.400
			22\39			676.923	523.077	5:2	2.500	Semihard 7L 2s
					57\101	677.228	522.772	13:5	2.600
				35\62		677.419	522.581	8:3	2.667
					48\85	677.647	522.353	11:4	2.750
		13\23				678.261	521.739	3:1	3.000	Hard 7L 2s
					43\76	678.947	521.053	10:3	3.333
				30\53		679.245	520.755	7:2	3.500
					47\83	679.518	520.482	11:3	3.667
			17\30			680.000	520.000	4:1	4.000	Superhard 7L 2s
					38\67	680.597	519.403	9:2	4.500
				21\37		681.081	518.919	5:1	5.000
					25\44	681.818	518.182	6:1	6.000
4\7						685.714	514.286	1:0	→ ∞	Collapsed 7L 2s