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

Equal tunings

Equalized (L:s = 1:1)

5\9 (666.7 ¢)

Supersoft (L:s = 4:3)

19\34 (670.6 ¢)

14\25 (672.0 ¢)

23\41 (673.2 ¢)

9\16 (675.0 ¢)

22\39 (676.9 ¢)

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.
Hornbostel temperament.

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.

Generator			Generator size (cents)	Pentachord steps	Comments
4\7			685.714	1 1 1 0
		102\179	683.798	25 25 25 2	Approximately 0.03 cents away from 95/64
33\58			682.758	8 8 8 1	2 generators equal 11/10, 6 equal 4/3, creating a hybrid Mavila/Porcupine scale with three perfect 5ths as well as the flat ones.
21\37			681.081	5 5 5 1
17\30			680	4 4 4 1	L/s = 4
	30\53		679.245	7 7 7 2
	43\76		678.947	10 10 10 3
	56\99		678.788	13 13 13 4
	69\122		678.6885	16 16 16 5
	82\145		678.621	19 19 19 6
	95\168		678.571	22 22 22 7
	108\191		678.534	25 25 25 8
	121\214		678.505	28 28 28 9	28;9 Superdiatonic 1/28-tone (a slight exceeded representation of the ratio 262144/177147, the Pythagorean wolf Fifth)
	134\237		678.481	31 31 31 10	HORNBOSTEL TEMPERAMENT (1/31-tone; Optimum high size of Hornbostel '6th')
13\23			678.261	3 3 3 1	HORNBOSTEL TEMPERAMENT (Armodue 1/3-tone)
	126\223		678.027	29 29 29 10	HORNBOSTEL TEMPERAMENT (Armodue 1/29-tone)
	113\200		678	26 26 26 9	HORNBOSTEL (& OGOLEVETS) TEMPERAMENT (Armodue 1/26-tone; Best equillibrium between 6/5, Phi (833.1 Cent) and Square root of Pi (990.9 Cent), the notes '3', '7' & '8')
	100\177		677.966	23 23 23 8
	87\154		677.922	20 20 20 7
	74\131		677.863	17 17 17 6	Armodue-Hornbostel 1/17-tone (the Golden Tone System of Thorvald Kornerup and a temperament of the Alexei Ogolevets's list of temperaments)
	61\108		677.778	14 14 14 5	Armodue-Hornbostel 1/14-tone
	109\193		677.720	25 25 25 9	Armodue-Hornbostel 1/25-tone
	48\85		677.647	11 11 11 4	Armodue-Hornbostel 1/11-tone (Optimum accuracy of Phi interval, the note '7')
	35\62		677.419	8 8 8 3	Armodue-Hornbostel 1/8-tone
	92\163		677.301	21 21 21 8	21;8 Superdiatonic 1/21-tone
			677.28	φ+1 φ+1 φ+1 1	Split φ superdiatonic relation (34;13 - 55;21 - 89;34 - 144;55 - 233;89 - 377;144 - 610;233..)
	57\101		677.228	13 13 13 5	13;5 Superdiatonic 1/13-tone
22\39			676.923	5 5 5 2	Armodue-Hornbostel 1/5-tone (Optimum low size of Hornbostel '6th')
	75\133		676.692	17 17 17 7	17;7 Superdiatonic 1/17-tone (Note the very accuracy of the step 75 with the ratio 34/23 with an error of +0.011 Cents)
	53\94		676.596	12 12 12 5
	31\55		676.364	7 7 7 3	7;3 Superdiatonic 1/7-tone
	40\71		676.056	9 9 9 4	9;4 Superdiatonic 1/9-tone
	49\87		675.862	11 11 11 5	11;5 Superdiatonic 1/11-tone
	58\103		675.728	13 13 13 6	13;6 Superdiatonic 1/13-tone
9\16			675	2 2 2 1	[BOUNDARY OF PROPRIETY: smaller generators are strictly proper]ARMODUE ESADECAFONIA (or Goldsmith Temperament)
	59\105		674.286	13 13 13 7	Armodue-Mavila 1/13-tone
	50\89		674.157	11 11 11 6	Armodue-Mavila 1/11-tone
	41\73		673.973	9 9 9 5	Armodue-Mavila 1/9-tone (with an approximation of the Perfect Fifth + 1/5 Pyth.Comma [706.65 Cents]: 43\73 is 706.85 Cents)
	32\57		673.684	7 7 7 4	Armodue-Mavila 1/7-tone (the 'Commatic' version of Armodue, because its high accuracy of the 7/4 interval, the note '8')
	55\98		673.469	12 12 12 7
	78\139		673.381	17 17 17 10	Armodue-Mavila 1/17-tone
	101\180		673.333	22 22 22 13
23\41			673.171	5 5 5 3	5;3 Golden Armodue-Mavila 1/5-tone
	60\107		672.897	13 13 13 8	13;8 Golden Mavila 1/13-tone
			672.85	φ φ φ 1	GOLDEN Mavila (L/s = φ)
		97\173	672.832	21 21 21 13	21;13 Golden Mavila 1/21-tone (Phi is the step 120\173)
	37\66		672.727	8 8 8 5	8;5 Golden Mavila 1/8-tone
	51\91		672.527	11 11 11 7	11;7 Superdiatonic 1/11-tone
		116\207	672.464	25 25 25 16	25;16 Superdiatonic 1/25-tone
	65\116		672.414	14 14 14 9	14;9 Superdiatonic 1/14-tone
	79\141		672.340	17 17 17 11	17;11 Superdiatonic 1/17-tone
	93\166		672.289	20 20 20 13
	107\191		672.251	23 23 23 15
	121\216		672.222	26 26 26 17	26;17 Superdiatonic 1/26-tone
	135\241		672.199	29 29 29 19	29;19 Superdiatonic 1/29-tone
14\25			672	3 3 3 2	3;2 Golden Armodue-Mavila 1/3-tone
	145\259		671.815	31 31 31 21	31;21 Superdiatonic 1/31-tone
	131\234		671.795	28 28 28 19	28;19 Superdiatonic 1/28-tone
	117\209		671.770	25 25 25 17
	103\184		671.739	22 22 22 15
	89\159		671.698	19 19 19 13
	75\134		671.642	16 16 16 11
	61\109		671.560	13 13 13 9
47\84			671.429	10 10 10 7
33\59			671.186	7 7 7 5
19\34			670.588	4 4 4 3
24\43			669.767	5 5 5 4
5\9			666.667	1 1 1 1

7L 2s

Contents

Primodal theory

Neji versions of superdiatonic modes

16nejis

23nejis

25nejis