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{{Infobox MOS
{{Infobox MOS}}
| Name = superdiatonic, armotonic
| nLargeSteps = 7
| nSmallSteps = 2
| Equalized = 5
| Collapsed = 4
| Pattern = LLLLsLLLs
| Neutral = 5L 4s
}}


{{MOS intro}}
{{MOS intro}}
Scales of this form are strongly associated with [[Armodue theory]], as applied to septimal mavila and Hornbostel temperaments.
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==
== Name ==
The [[TAMNAMS]] name for this pattern is '''superdiatonic''', in reference to the diatonic mos (5L 2s) having two additional large steps added, or '''armotonic''', in reference to Armodue theory.
The [[TAMNAMS]] name for this pattern is '''armotonic''', in reference to Armodue theory. '''Superdiatonic''' is also in use.


==Intervals==
== Scale properties ==
:''This article assumes [[TAMNAMS]] for naming step ratios, mossteps, and mosdegrees.''
{{TAMNAMS use}}
{{MOS intervals|MOS Prefix=arm}}


== Note names==
=== Intervals ===
7L 2s, when viewed under Armodue theory, can be notated using Armodue notation.
{{MOS intervals}}


==Theory==
=== Generator chain ===
{{MOS genchain}}


=== Temperament interpretations ===
=== Modes ===
[[Pelogic family#Mavila|Mavila]] is an important harmonic entropy minimum here, insofar as 678¢ can be considered a fifth. Other temperaments include septimal mavila and Hornbostel.
{{MOS mode degrees}}


==Modes==
=== Proposed mode names ===
{{MOS modes|Mode Names=Superlydian; Superionian; Supermixolidyan; Supercorintihan; Superolympian; Superdorian; Superaeolian; Superphrygian; Superlocrian}}
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.
{{MOS modes
| Table Headers=
Super- Mode Names $
Ad- Mode Names (ground) $
| Table Entries=
Superlydian $
TBD $
Superionian $
Adlocrian $
Supermixolydian $
Adphrygian $
Supercorinthian $
Adaeolian $
Superolympian $
Addorian $
Superdorian $
Admixolydian $
Superaeolian $
Adionian $
Superphrygian $
Adlydian $
Superlocrian $
TBD
}}


==Scale tree==
== Note names==
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.
7L 2s, when viewed under Armodue theory, can be notated using Armodue notation.


== Theory ==
=== Temperament interpretations ===
[[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.


Generator ranges:
== Scale tree ==
*Chroma-positive generator: 666.6667 cents (5\9) to 685.7143 cents (4\7)
{{MOS tuning spectrum
* Chroma-negative generator: 514.2857 cents (3\7) to 533.3333 cents (4\9)
| 1/1 = Near exact-7/6 [[Pelogic_family#Armodue|Armodue]]
 
| 4/3 = Near exact-20/17 [[Pentagoth]]
{| class="wikitable"
| 7/5 = Near exact-5/4 [[Mavila]]
|-
| 3/2 = Near exact-13/11 Pentagoth
! colspan="3" | Generator
| 7/4 = Near exact-7/4 [[Pelogic_family#Armodue|Armodue]]
! |<span style="display: block; text-align: center;">'''Generator size (cents)'''</span>
| 10/3 = Near exact-6/5 [[Mavila]]
! | Pentachord steps
| 6/1 = [[Gravity]] ↓
! |Comments
}}
|-
| |4\[[7edo|7]]
| |
| |
| |685.714
| |1 1 1 0
| |
|-
|53\93
|
|
| 683.871
|13 13 13 1
|
|-
| |
| |102\[[179edo|179]]
| |
| | 683.798
| |25 25 25 2
| | Approximately 0.03 cents away from [[95/64]]
|-
| 49\86
|
|
|683.721
|12 12 12 1
|
|-
|
|94\165
|
|683.636
|23 23 23 2
|
|-
|45\79
|
|
|683.544
|11 11 11 1
|
|-
|
|86\151
|
| 683.444
|21 21 21 2
|
|-
| 41\72
|
|
|683.333
| 10 10 10 1
|
|-
|
|78\137
|
|683.212
|19 19 19 2
|
|-
|37\65
|
|
|683.077
| 9 9 9 1
|
|-
|
|70\123
|
|682.927
|17 17 17 2
|
|-
| |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.
|-
|
|62\109
|
|682.569
|15 15 15 2
|
|-
|29\51
|
|
|682.353
|7 7 7 1
|
|-
|
|54\95
|
|682.105
| 13 13 13 2
|
|-
|25\44
|
|
|681.818
|6 6 6 1
|
|-
|
|46\81
|
|681.4815
|11 11 11 2
|
|-
| | 21\37
| |
| |
| |681.081
| |5 5 5 1
| |
|-
|
|59\104
|
|680.769
|14 14 14 3
|
|-
|
|38\67
|
|680.597
|9 9 9 2
|
|-
|
|55\97
|
|680.412
|13 13 13 3
|
|-
| |17\30
| |
| |
| |680
| |4 4 4 1
| |L/s = 4
|-
|
|47\83
|
|679.518
|11 11 11 3
|
|-
| |
| |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>
|-
| |
| |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>
|-
| |
| |
| |
| | 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-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]] 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-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
| |<span style="background-color: #ffffff; color: #222222; font-family: arial,sans-serif; font-size: small;">φ φ φ 1</span>
| |GOLDEN MAVILA (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 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
|-
| |
| |
| |
| |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-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
| |
|-
|
|
|80\143
| 671.329
|17 17 17 12
|
|-
| |
| |33\59
| |
| |671.186
| | 7 7 7 5
| |
|-
|
|52\93
|
|670.968
| 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 11 9
|
|-
|29\52
|
|
|669.231
| 6 6 6 5
|
|-
|
|63\113
|
|669.0265
|13 13 13 11
|
|-
|34\61
|
|
|668.8525
|7 7 7 6
|
|-
|
| 73\131
|
|668.702
|15 15 15 13
|
|-
| 39\70
|
|
|668.571
|8 8 8 7
|
|-
|
|83\149
|
| 668.456
|17 17 17 15
|
|-
| 44\79
|
|
| 668.354
|9 9 9 8
|
|-
|
|93\167
|
|668.2365
|19 19 19 17
|
|-
|49\88
|
|
|668.182
| 10 10 10 9
|
|-
|
|103\185
|
|668.108
|21 21 21 9
|
|-
|54\97
|
|
| 668.041
|11 11 11 10
|
|-
|
| 113\203
|
|667.98
|23 23 23 21
|
|-
|59\106
|
|
|667.925
|12 12 12 11
|
|-
|
|123\221
|
| 667.873
|25 25 25 23
|
|-
|64\115
|
|
|667.826
|13 13 13 12
|
|-
| |5\[[9edo|9]]
| |
| |
| | 666.667
| |1 1 1 1
| |
|}


[[Category:9-tone scales]]
[[Category:9-tone scales]]
[[Category:Mavila]]
[[Category:Mavila]]
[[Category:Superdiatonic]]
Retrieved from "https://en.xen.wiki/w/7L_2s"