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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).

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 mávila is an important harmonic entropy minimum here. So a general name for this MOS pattern could be "Mávila Superdiatonic" or simply 'Superdiatonic'.
These scales are strongly associated with the Armodue project/system applied too on Septimal-mávila and Hornbostel temperaments.

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

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




678.569
π π π 1
L/s = π

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')



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 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-Mávila 1/13-tone

50\89

674.157
11 11 11 6
Armodue-Mávila 1/11-tone

41\73

673.973
9 9 9 5
Armodue-Mávila 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-Mávila 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 12 7


78\139

673.381
17 17 17 10
Armodue-Mávila 1/17-tone

101\180

673.333
22 22 22 13

23\41


673.171
5 5 5 3
5;3 Golden Armodue-Mávila 1/5-tone

60\107

672.897
13 13 13 8
13;8 Golden Mávila 1/13-tone



672.85
φ φ φ 1
GOLDEN MÁVILA (L/s = φ)


97\173
672.832
21 21 21 13
21;13 Golden Mávila 1/21-tone (Phi is the step 120\173)

37\66

672.727
8 8 8 5
8;5 Golden Mávila 1/8-tone

51\91

672.527
11 11 11 7
11;7 Superdiatonic 1/11-tone



672.523
π π π 2



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-Mávila 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