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This page is about of a [[MOSScales|MOSScale]] with 7 large steps and 2 small steps arranged LLLsLLLLs (or any rotation of that, such as LLsLLLsLL).
{{Infobox MOS}}


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 [[Pelogic_family|mávila]] is an important harmonic entropy minimum here. So a general name for this MOS pattern could be "Mávila Superdiatonic" or simply 'Superdiatonic'.
{{MOS intro}}
Scales of this form are strongly associated with [[Armodue theory]], as applied to septimal mavila and Hornbostel temperaments. [[Trismegistus]] is also a usable temperament.
== Name ==
The [[TAMNAMS]] name for this pattern is '''armotonic''', in reference to Armodue theory. '''Superdiatonic''' is also in use.


These scales are strongly associated with the [[Armodue|Armodue]] project/system applied too on Septimal-mávila and Hornbostel temperaments.
== Scale properties ==
{{TAMNAMS use}}


Optional types of 'JI [[Blown_Fifth|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.
=== Intervals ===
{{MOS intervals}}


{| class="wikitable"
=== Generator chain ===
|-
{{MOS genchain}}
! colspan="3" | Generator
! | <span style="display: block; text-align: center;">'''Generator size (cents)'''</span>
! | Pentachord steps
! | Comments
|-
| | 4\[[7edo|7]]
| |
| |
| | 685.714
| | 1 1 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 Mávila/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
| |
|-
| |
| |
| |
| | 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 <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
| |
| |
| | 678.261
| | 3 3 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>
=== Modes ===
|-
{{MOS mode degrees}}
| |
 
| | 113\200
=== Proposed mode names ===
| |
The Ad- mode names proposed by [[groundfault]] have the feature of matching up the middle 7 modes with the antidiatonic mode names in the generator arc.
| | 678
{{MOS modes
| | 26 26 26 9
| Table Headers=
| | 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>
Super- Mode Names $
|-
Ad- Mode Names (ground) $
| |
| Table Entries=
| | 100\177
Superlydian $
| |
TBD $
| | 677.966
Superionian $
| | 23 23 23 8
Adlocrian $
| |
Supermixolydian $
|-
Adphrygian $
| |
Supercorinthian $
| | 87\154
Adaeolian $
| |
Superolympian $
| | 677.922
Addorian $
| | 20 20 20 7
Superdorian $
| |
Admixolydian $
|-
Superaeolian $
| |
Adionian $
| | 74\131
Superphrygian $
| |
Adlydian $
| | 677.863
Superlocrian $
| | 17 17 17 6
TBD
| | 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>
}}
|-
 
| |
== Note names==
| | 61\108
7L&nbsp;2s, when viewed under Armodue theory, can be notated using Armodue notation.
| |
 
| | 677.778
== Theory ==
| | 14 14 14 5
=== Temperament interpretations ===
| | Armodue-Hornbostel 1/14-tone
[[Pelogic family#Mavila|Mavila]] is an important harmonic entropy minimum here, insofar as 670-680{{c}} can be considered a fifth. Other temperaments include septimal mavila, hornbostel, and trismegistus.
|-
 
| |
== Scale tree ==
| | 109\193
{{MOS tuning spectrum
| |
| 1/1 = Near exact-7/6 [[Pelogic_family#Armodue|Armodue]]
| | 677.720
| 4/3 = Near exact-20/17 [[Pentagoth]]
| | 25 25 25 9
| 7/5 = Near exact-5/4 [[Mavila]]
| | Armodue-Hornbostel 1/25-tone
| 3/2 = Near exact-13/11 Pentagoth
|-
| 7/4 = Near exact-7/4 [[Pelogic_family#Armodue|Armodue]]
| |
| 10/3 = Near exact-6/5 [[Mavila]]
| | 48\85
| 6/1 = [[Gravity]] ↓
| |
}}
| | 677.647
 
| | 11 11 11 4
[[Category:9-tone scales]]
| | Armodue-Hornbostel 1/11-tone <span style="font-size: 12.8000001907349px;">(Optimum accuracy of Phi interval, the note '7')</span>
[[Category:Mavila]]
|-
| |
| |
| |
| | 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
| | <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
| |
| |
| | 676.923
| | 5 5 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
| |
| |
| | 675
| | 2 2 2 1
| | <span style="display: block; text-align: left;">'''[BOUNDARY OF PROPRIETY: smaller generators are strictly proper]'''</span>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 <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-Mávila 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>
|-
| |
| |
| |
| | 673.577
| | <span style="background-color: #ffffff;">√3 √3 √3 1</span>
| |
|-
| |
| | 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
| | <span style="background-color: #ffffff; color: #222222; font-family: arial,sans-serif; font-size: small;">φ φ φ 1</span>
| | GOLDEN MÁVILA (L/s = <span style="background-color: #ffffff; color: #222222; font-family: arial,sans-serif; font-size: small;">φ)</span>
|-
| |
| |
| | 97\173
| | 672.832
| | 21 21 21 13
| | 21;13 Golden Mávila 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 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\[[9edo|9]]
| |
| |
| | 666.667
| | 1 1 1 1
| |
|}
[[Category:diatonic]]
[[Category:mavila]]
[[Category:Abstract MOS patterns]]
[[Category:scale]]
[[Category:scales]]
[[Category:superdiatonic]]
[[Category:theory]]
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