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{{Infobox MOS
{{Infobox MOS}}
| Name = superdiatonic
| Periods = 1
| nLargeSteps = 7
| nSmallSteps = 2
| Equalized = 5
| Paucitonic = 4
| Collapsed = LLLLsLLLs
| Neutral = 5L 4s
}}
 
This page is about of a [[MOS scale]] with 7 large steps and 2 small steps ('''7L 2s''') arranged LLLLsLLLs (or any rotation of that, such as LLsLLLsLL).


{{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 ==
== Name ==
The name '''superdiatonic''' has been established by [[Armodue]] theorists, and so [[TAMNAMS]] adopts it as well.
The [[TAMNAMS]] name for this pattern is '''armotonic''', in reference to Armodue theory. '''Superdiatonic''' is also in use.


== Temperaments ==
== Scale properties ==
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#Mavila|mavila]] is an important harmonic entropy minimum here. So a general name for this MOS pattern could be "Mavila Superdiatonic" or simply 'Superdiatonic'.
{{TAMNAMS use}}


These scales are strongly associated with the [[Armodue]] project/system applied to septimal mavila and Hornbostel temperaments.
=== Intervals ===
{{MOS intervals}}


== Intervals ==
=== Generator chain ===
Note: In TAMNAMS, a k-step interval class in superdiatonic may be called a "k-step", "k-mosstep", or "k-armstep". TAMNAMS discourages 1-indexed terms such as "mos(k+1)th" for non-diatonic mosses.
{{MOS genchain}}


== Modes ==
=== Modes ===
* 8|0 LLLLsLLLs
{{MOS mode degrees}}
* 7|1 LLLsLLLLs
* 6|2 LLLsLLLsL
* 5|3 LLsLLLLsL
* 4|4 LLsLLLsLL
* 3|5 LsLLLLsLL
* 2|6 LsLLLsLLL
* 1|7 sLLLLsLLL
* 0|8 sLLLsLLLL


== Scale tree ==
=== Proposed mode 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.
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
}}


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


Generator ranges:
== Theory ==
* Chroma-positive generator: 666.6667 cents (5\9) to 685.7143 cents (4\7)
=== Temperament interpretations ===
* Chroma-negative generator: 514.2857 cents (3\7) to 533.3333 cents (4\9)
[[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.


{| class="wikitable"
== Scale tree ==
|-
{{MOS tuning spectrum
! colspan="3" | Generator
| 1/1 = Near exact-7/6 [[Pelogic_family#Armodue|Armodue]]
! | <span style="display: block; text-align: center;">'''Generator size (cents)'''</span>
| 4/3 = Near exact-20/17 [[Pentagoth]]
! | Pentachord steps
| 7/5 = Near exact-5/4 [[Mavila]]
! | Comments
| 3/2 = Near exact-13/11 Pentagoth
|-
| 7/4 = Near exact-7/4 [[Pelogic_family#Armodue|Armodue]]
| | 4\[[7edo|7]]
| 10/3 = Near exact-6/5 [[Mavila]]
| |
| 6/1 = [[Gravity]] ↓
| |
}}
| | 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|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"