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
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 (with relation to root)		Size		Abbrev.
Generic	Specific	L's and s's	Range in cents
0-armstep (root)	Perfect 0-armstep	0	0.0¢	P0ms
1-armstep	Minor 1-armstep	s	0.0¢ to 133.3¢	m1ms
	Major 1-armstep	L	133.3¢ to 171.4¢	M1ms
2-armstep	Minor 2-armstep	L + s	171.4¢ to 266.7¢	m2ms
	Major 2-armstep	2L	266.7¢ to 342.9¢	M2ms
3-armstep	Minor 3-armstep	2L + s	342.9¢ to 400.0¢	m3ms
	Major 3-armstep	3L	400.0¢ to 514.3¢	M3ms
4-armstep	Perfect 4-armstep	3L + s	514.3¢ to 533.3¢	P4ms
	Augmented 4-armstep	4L	533.3¢ to 685.7¢	A4ms
5-armstep	Diminished 5-armstep	3L + 2s	514.3¢ to 666.7¢	d5ms
	Perfect 5-armstep	4L + s	666.7¢ to 685.7¢	P5ms
6-armstep	Minor 6-armstep	4L + 2s	685.7¢ to 800.0¢	m6ms
	Major 6-armstep	5L + s	800.0¢ to 857.1¢	M6ms
7-armstep	Minor 7-armstep	5L + 2s	857.1¢ to 933.3¢	m7ms
	Major 7-armstep	6L + s	933.3¢ to 1028.6¢	M7ms
8-armstep	Minor 8-armstep	6L + 2s	1028.6¢ to 1066.7¢	m8ms
	Major 8-armstep	7L + s	1066.7¢ to 1200.0¢	M8ms
9-armstep (octave)	Perfect 9-armstep	7L + 2s	1200.0¢	P9ms

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	Rotational order	Step pattern	Mode names
8|0	1	LLLLsLLLs	Superlydian
7|1	6	LLLsLLLLs	Superionian
6|2	2	LLLsLLLsL	Supermixolidyan
5|3	7	LLsLLLLsL	Supercorintihan
4|4	3	LLsLLLsLL	Superolympian
3|5	8	LsLLLLsLL	Superdorian
2|6	4	LsLLLsLLL	Superaeolian
1|7	9	sLLLLsLLL	Superphrygian
0|8	5	sLLLsLLLL	Superlocrian

Scale tree

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 near exact-7/6 Armodue
					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 near exact-20/17 Pentagoth
					52\93	670.968	529.032	11:8	1.375
				33\59		671.186	528.814	7:5	1.400	near exact-5/4 Mavila
					47\84	671.429	528.571	10:7	1.429
		14\25				672.000	528.000	3:2	1.500	Soft 7L 2s near exact-13/11 Pentagoth
					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	near exact-7/4 Armodue
					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	near exact-6/5 Mavila
				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