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, mavila superdiatonic or superdiatonic refers to the structure of octave-equivalent MOS scales with generators ranging from 4\7 (four degrees of 7edo = 685.71¢) to 5\9 (five degrees of 9edo = 666.67¢). In the case of 9edo, L and s are the same size; in the case of 7edo, s becomes so small it disappears (and all that remains are the seven equal L's).

From a regular temperament perspective (i.e. approximating low JI intervals), this MOS pattern is essentially synonymous to mavila. If you're looking for highly accurate scales (that is, ones that approximate low JI closely), there are much better scale patterns to look at. However, if 678 cents is an acceptable 3/2 to you, then mavila is an important harmonic entropy minimum here. So a general name for this MOS pattern could be "mavila superdiatonic" or simply 'Superdiatonic'.

These scales are strongly associated with mavila system, which can be divided into two systems:

• the Armodue project/system and its associated armodue temperament, with fifths sharper than 5\9 (666.7¢) and flatter than 9\16 (675¢).
• Hornbostel temperament, with fifths sharper than 9\16 (675¢) and flatter than 4\7 (685.71¢).

Some high JI approximations of the generator: 31/21, 34/23, 65/44, 71/48, 99/67, 105/71, 108/73, 133/90, 145/98, 176/119, 250/169. These could be used to guide the construction of neji versions of superdiatonic scales or edos.

Scale tree

Generator					Generator size (cents)	L/s	Comments
4\7					685.714	1/0
				21\37	681.08	5/1
			17\30		680	4/1
		13\23			678.261	3/1
			22\39		676.923	5/2
	9\16				675	2/1	Boundary of propriety; smaller generators are strictly proper
		23\41			673.171	5/3
					672.85	φ/1	Golden mavila
		14\25			672	3/2
			19\34		670.588	4/3
				24\43	669.767	5/4
5\9					666.667	1/1

Primodal theory

Neji versions of superdiatonic modes

• 40:48:52:54:59:64:70:77:80 Pental Superionian