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These scales are strongly associated with [[mavila]] system, which can be divided into two systems:
These scales are strongly associated with [[mavila]] system, which can be divided into two systems:
* the [[Armodue|Armodue]] project/system and its associated [[armodue]] temperament.
* the [[Armodue|Armodue]] project/system and its associated [[armodue]] temperament, with fifths sharper than 5\9 (666.7¢) and flatter than 9\16 (675¢).
* Hornbostel temperament.
* 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.
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 ==
{| class="wikitable"
{| class="wikitable"
|-
|-
! colspan="3" | Generator
! colspan="5" | Generator
! | <span style="display: block; text-align: center;">'''Generator size (cents)'''</span>
! | Generator size (cents)
! | Pentachord steps
! | L/s
! | Comments
! | Comments
|-
|-
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| |  
| |  
| |  
| |  
| |
| |
| | 685.714
| | 685.714
| | 1 1 1 0
| | 1/0
| |
|-
| |  
| |  
| |
| | 102\[[179edo|179]]
| | 683.798
| | 25 25 25 2
| | Approximately 0.03 cents away from [[95/64]]
|-
| | 33\[[58edo|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
| | 21\37
| |
| |
| |  
| | 681.08
| | 681.081
| | 5/1
| | 5 5 5 1
| |
| |  
|-
|-
| |
| |
| |
| | 17\30
| | 17\30
| |
| |
| |  
| | 680
| | 680
| | 4 4 4 1
| | 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 <span style="font-size: 12.8000001907349px;">(a slight exceeded representation of the ratio 262144/177147, the Pythagorean wolf Fifth)</span>
|-
| |
| | 134\237
| |  
| | 678.481
| | 31 31 31 10
| | HORNBOSTEL TEMPERAMENT <span style="font-size: 12.8000001907349px;">(1/31-tone; Optimum high size of Hornbostel '6th')</span>
|-
|-
| |
| |
| | 13\23
| | 13\23
| |  
| |
| |  
| |
| | 678.261
| | 678.261
| | 3 3 3 1
| | 3/1
| | HORNBOSTEL TEMPERAMENT <span style="font-size: 12.8000001907349px;">(Armodue 1/3-tone)</span>
| |
|-
|-
| |
| |  
| |  
| | 126\223
| |
| |
| | 678.027
| | 29 29 29 10
| | HORNBOSTEL TEMPERAMENT
 
<span style="font-size: 12.8000001907349px;">(Armodue 1/29-tone)</span>
|-
| |
| | 113\200
| |
| | 678
| | 26 26 26 9
| | HORNBOSTEL (&amp; [[Alexei_Stepanovich_Ogolevets|OGOLEVETS]]) TEMPERAMENT <span style="font-size: 12.8000001907349px;">(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' &amp; '8')</span>
|-
| |
| | 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 <span style="font-size: 12.8000001907349px;">(the Golden Tone System of Thorvald Kornerup and a temperament of the Alexei Ogolevets's list of temperaments)</span>
|-
| |
| | 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 <span style="font-size: 12.8000001907349px;">(Optimum accuracy of Phi interval, the note '7')</span>
|-
| |
| | 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
| | <span style="background-color: #ffffff; color: #222222; font-family: arial,sans-serif; font-size: small;">φ+1 φ+1 φ+1 1</span>
| | 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
| | 22\39
| |
| |
| |  
| | 676.923
| | 676.923
| | 5 5 5 2
| | 5/2
| | Armodue-Hornbostel 1/5-tone <span style="font-size: 12.8000001907349px;">(Optimum low size of Hornbostel '6th')</span>
|-
| |
| | 75\133
| |
| | 676.692
| | 17 17 17 7
| | 17;7 Superdiatonic 1/17-tone <span style="font-size: 12.8000001907349px;">(Note the very accuracy of the step 75 with the ratio 34/23 with an error of +0.011 Cents)</span>
|-
| |
| | 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
| | 9\16
| |  
| |  
| |  
| |  
| |
| | 675
| | 675
| | 2 2 2 1
| | 2/1
| | <span style="display: block; text-align: left;">'''[BOUNDARY OF PROPRIETY: smaller generators are strictly proper]'''</span>ARMODUE ESADECAFONIA (or Goldsmith Temperament)
| | Boundary of propriety; smaller generators are strictly proper
|-
| |
| | 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 <span style="font-size: 12.8000001907349px;">(with an approximation of the Perfect Fifth + 1/5 Pyth.Comma [706.65 Cents]: 43\73 is 706.85 Cents)</span>
|-
| |
| | 32\57
| |
| | 673.684
| | 7 7 7 4
| | Armodue-Mavila 1/7-tone <span style="font-size: 12.8000001907349px;">(the 'Commatic' version of Armodue, because its high accuracy of the [[7/4|7/4]] interval, the note '8')</span>
|-
| |
| | 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
| | 23\41
| |  
| |  
| |  
| |  
| | 673.171
| | 673.171
| | 5 5 5 3
| | 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
| | 672.85
| | <span style="background-color: #ffffff; color: #222222; font-family: arial,sans-serif; font-size: small;">φ φ φ 1</span>
| | φ/1
| | GOLDEN Mavila (L/s = <span style="background-color: #ffffff; color: #222222; font-family: arial,sans-serif; font-size: small;">φ)</span>
| | Golden mavila
|-
| |
| |
| | 97\173
| | 672.832
| | 21 21 21 13
| | 21;13 Golden Mavila 1/21-tone <span style="font-size: 12.8000001907349px;">(Phi is the step 120\173)</span>
|-
| |
| | 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
| | 14\25
| |  
| |  
| |  
| |
| | 672
| | 672
| | 3 3 3 2
| | 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
| | 19\34
| |
| |  
| |  
| | 670.588
| | 670.588
| | 4 4 4 3
| | 4/3
| |  
| |  
|-
|-
| |
| |
| |
| |
| | 24\43
| | 24\43
| |
| |
| | 669.767
| | 669.767
| | 5 5 5 4
| | 5/4
| |  
| |  
|-
|-
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| |  
| |  
| |  
| |  
| |
| |
| | 666.667
| | 666.667
| | 1 1 1 1
| | 1/1
| |  
| |  
|}
|}
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