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 ¢)

This page is about of a MOSScale with 7 large steps and 2 small steps arranged LLLsLLLLs (or any rotation of that, such as LLsLLLsLL).

Name

The name superdiatonic has been established by Armodue theorists, and so TAMNAMS adopts it as well.

Temperaments

If you're looking for highly accurate scales (that is, ones that approximate JI closely), there are much better scale patterns to look at. However, if your harmonic entropy is coarse enough (that is, 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 the Armodue project/system applied to septimal mavila and Hornbostel temperaments.

Intervals

Note: In TAMNAMS, a k-step interval class in superdiatonic may be called a "k-step", "k-mosstep", or "k-armstep". 1-indexed terms such as "mos(k+1)th" are discouraged for non-diatonic mosses.

Scale tree

Optional types of 'JI Blown Fifth' Generators: 31/21, 34/23, 65/44, 71/48, 99/67, 105/71, 108/73, 133/90, 145/98, 176/119 & 250/169.

Generator			Generator size (cents)	Pentachord steps	Comments
4\7			685.714	1 1 1 0
57\100			684	14 14 14 1
53\93			683.871	[13 13 1|13 13 13 1]
	102\179		683.798	[25 25 2|25 25 25 2]	Approximately 0.03 cents away from 95/64
49\86			683.721	[12 12 1|12 12 12 1]
	94\165		683.636	[23 23 2|23 23 23 2]
45\79			683.544	[11 11 1|11 11 11 1]
	86\151		683.444	[21 21 2|21 21 21 2]
41\72			683.333	[10 10 1|10 10 10 1]
	78\137		683.212	[19 19 2|19 19 19 2]
37\65			683.077	9 9 9 1
	70\123		682.927	[17 17 2|17 17 17 2]
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.
	62\109		682.569	[15 15 2|15 15 15 2]
29\51			682.353	7 7 7 1
	54\95		682.105	[13 13 2|13 13 13 2]
25\44			681.818	6 6 6 1
	46\81		[[1]]	[11 11 2|11 11 11 2]
21\37			681.081	5 5 5 1
	59\104		680.769	[14 14 3|14 14 14 3]
	38\67		680.597	9 9 9 2
	55\97		680.412	[13 13 3|13 13 13 3]
17\30			680	4 4 4 1	L/s = 4
	47\83		679.518	[11 11 3|11 11 11 3]
	30\53		679.245	7 7 7 2
	43\76		678.947	[10 10 3|10 10 10 3]
	56\99		678.788	[13 13 4|13 13 13 4]
	69\122		[[2]]	[16 16 5|16 16 16 5]
	82\145		678.621	[19 19 6|19 19 19 6]
	95\168		678.571	[22 22 7|22 22 22 7]
			678.569	π π π 1	L/s = π
	108\191		678.534	[25 25 8|25 25 25 8]
	121\214		678.505	[28 28 9|28 28 28 9]	28;9 Superdiatonic 1/28-tone (a slight exceeded representation of the ratio [[3]], the Pythagorean wolf Fifth)
	134\237		678.481	[31 31 10|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 10|29 29 29 10]	HORNBOSTEL TEMPERAMENT (Armodue 1/29-tone)
	113\200		678	[26 26 9|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 8|23 23 23 8]
	87\154		677.922	[20 20 7|20 20 20 7]
	74\131		677.863	[17 17 6|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 5|14 14 14 5]	Armodue-Hornbostel 1/14-tone
		109\193	677.720	[25 25 9|25 25 25 9]	Armodue-Hornbostel 1/25-tone
	48\85		677.647	[11 11 4|11 11 11 4]	Armodue-Hornbostel 1/11-tone (Optimum accuracy of Phi interval, the note '7')
			677.562	e e e 1	L/s = e
	35\62		677.419	8 8 8 3	Armodue-Hornbostel 1/8-tone
		92\163	677.301	[21 21 8|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 5|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 7|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 5|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 5|11 11 11 5]	11;5 Superdiatonic 1/11-tone
	58\103		675.728	[13 13 6|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 7|13 13 13 7]	Armodue-Mavila 1/13-tone
	50\89		674.157	[11 11 6|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')
			673.577	√3 √3 √3 1
	55\98		673.469	[12 12 7|12 12 12 7]
	78\139		673.381	[17 17 10|17 17 17 10]	Armodue-Mavila 1/17-tone
	101\180		673.333	[22 22 13|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 8|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 13|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 7|11 11 11 7]	11;7 Superdiatonic 1/11-tone
			672.523	π π π 2
		116\207	672.464	[25 25 16|25 25 25 16]	25;16 Superdiatonic 1/25-tone
	65\116		672.414	[14 14 9|14 14 14 9]	14;9 Superdiatonic 1/14-tone
	79\141		672.340	[17 17 11|17 17 17 11]	17;11 Superdiatonic 1/17-tone
	93\166		672.289	[20 20 13|20 20 20 13]
	107\191		672.251	[23 23 15|23 23 23 15]
	121\216		672.222	[26 26 17|26 26 26 17]	26;17 Superdiatonic 1/26-tone
	135\241		672.199	[29 29 19|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 21|31 31 31 21]	31;21 Superdiatonic 1/31-tone
	131\234		671.795	[28 28 19|28 28 28 19]	28;19 Superdiatonic 1/28-tone
	117\209		671.770	[25 25 17|25 25 25 17]
	103\184		671.739	[22 22 15|22 22 22 15]
	89\159		671.698	[19 19 13|19 19 19 13]
	75\134		671.642	[16 16 11|16 16 16 11]
	61\109		671.560	[13 13 9|13 13 13 9]
	47\84		671.429	[10 10 7|10 10 10 7]
		80\143	671.329	[17 17 12|17 17 17 12]
	33\59		671.186	7 7 7 5
	52\93		670.968	[11 11 8|11 11 11 8]
19\34			670.588	4 4 4 3
	43\77		670.13	9 9 9 7
24\43			669.767	5 5 5 4
	53\95		669.474	[11 11 9|11 11 11 9]
29\52			669.231	6 6 6 5
	63\113		[[4]]	[13 13 11|13 13 13 11]
34\61			[[5]]	7 7 7 6
	73\131		668.702	[15 15 13|15 15 15 13]
39\70			668.571	8 8 8 7
	83\149		668.456	[17 17 15|17 17 17 15]
44\79			668.354	9 9 9 8
	93\167		[[6]]	[19 19 17|19 19 19 17]
49\88			668.182	[10 10 9|10 10 10 9]
	103\185		668.108	[21 21 9|21 21 21 9]
54\97			668.041	[11 11 10|11 11 11 10]
	113\203		667.98	[23 23 21|23 23 23 21]
59\106			667.925	[12 12 11|12 12 12 11]
	123\221		667.873	[25 25 23|25 25 25 23]
64\115			667.826	[13 13 12|13 13 13 12]
69\124			667.742	14 14 14 13
5\9			666.667	1 1 1 1