7L 2s

↖ 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 ¢)

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.

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

Scale degrees of the modes of 7L 2s

UDP	Cyclic order	Step pattern	Scale degree (armdegree)
			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.

Proposed mode names

The Ad- mode names are proposed by groundfault. This naming has the feature of matching up the middle 7 modes with the antidiatonic mode names in the generator arc.

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