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| {{Infobox MOS | | {{Infobox MOS}} |
| | Name = mavila, superdiatonic
| | |
| | Periods = 1
| | {{MOS intro}} |
| | nLargeSteps = 7
| | Scales of this form are strongly associated with [[Armodue theory]], as applied to septimal mavila and Hornbostel temperaments. [[Trismegistus]] is also a usable temperament. |
| | nSmallSteps = 2
| | == Name == |
| | Equalized = 5
| | The [[TAMNAMS]] name for this pattern is '''armotonic''', in reference to Armodue theory. '''Superdiatonic''' is also in use. |
| | Paucitonic = 4
| | |
| | Pattern = LLLsLLLLs
| | == Scale properties == |
| }} | | {{TAMNAMS use}} |
| | |
| | === Intervals === |
| | {{MOS intervals}} |
| | |
| | === Generator chain === |
| | {{MOS genchain}} |
|
| |
|
| '''7L 2s''', '''mavila superdiatonic''' or '''superdiatonic''' refers to the structure of octave-equivalent [[MOS]] scales with generators ranging from 4\7 (four degrees of [[7edo]] = 685.71¢) to 5\9 (five degrees of [[9edo]] = 666.67¢). In the case of 9edo, L and s are the same size; in the case of 7edo, s becomes so small it disappears (and all that remains are the seven equal L's).
| | === Modes === |
| | {{MOS mode degrees}} |
|
| |
|
| From a regular temperament perspective (i.e. approximating [[low JI]] intervals), this MOS pattern is essentially synonymous to [[mavila]]. If you're looking for highly accurate scales (that is, ones that approximate low 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]] is an important harmonic entropy minimum here. So a general name for this MOS pattern could be "mavila superdiatonic" or simply 'Superdiatonic'.
| | === 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. |
| | {{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 |
| | }} |
|
| |
|
| These scales are strongly associated with the [[Armodue|Armodue]] project/system based on the septimal-mavila and Hornbostel temperaments.
| | == Note names== |
| | 7L 2s, when viewed under Armodue theory, can be notated using Armodue notation. |
|
| |
|
| 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.
| | == 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. |
|
| |
|
| {| 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>
| | | 5/4 = Near exact-16/15 [[Amavil]] |
| ! | Pentachord steps
| | | 4/3 = Near exact-20/17 [[Pentagoth]] |
| ! | Comments
| | | 7/5 = Near exact-5/4 [[Mavila]] |
| |-
| | | 3/2 = Near exact-13/11 Pentagoth |
| | | 4\[[7edo|7]]
| | | 7/4 = Near exact-7/4 [[Pelogic_family#Armodue|Armodue]] |
| | | | | | 10/3 = Near exact-6/5 [[Mavila]] |
| | |
| | | 6/1 = [[Gravity]] ↓ |
| | | 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 Mavila/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>
| | [[Category:9-tone scales]] |
| |-
| | [[Category:Mavila]] |
| | |
| |
| | | 113\200
| |
| | |
| |
| | | 678
| |
| | | 26 26 26 9
| |
| | | HORNBOSTEL (& [[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' & '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
| |
| | |
| |
| |-
| |
| | | 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
| |
| | |
| |
| |}
| |
| == Primodal theory ==
| |
| === Neji versions of mavila modes ===
| |
| * 40:48:52:54:59:64:70:77:80 Pental Superionian
| |
| === 9nejis ===
| |
| === 16nejis ===
| |
| === 23nejis ===
| |
| === 25nejis ===
| |
| [[Category:diatonic]]
| |
| [[Category:mavila]]
| |
| [[Category:Abstract MOS patterns]]
| |
| [[Category:scale]]
| |
| [[Category:scales]]
| |
| [[Category:superdiatonic]] | |
| [[Category:theory]]
| |
7L 2s, named armotonic in TAMNAMS, is a 2/1-equivalent (octave-equivalent) moment of symmetry scale containing 7 large steps and 2 small steps, repeating every octave. Generators that produce this scale range from 666.7 ¢ to 685.7 ¢, or from 514.3 ¢ to 533.3 ¢.
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.
Scale properties
- This article uses TAMNAMS conventions for the names of this scale's intervals and scale degrees. The use of 1-indexed ordinal names is reserved for interval regions.
Intervals
Intervals of 7L 2s
| Intervals
|
Steps subtended
|
Range in cents
|
| Generic
|
Specific
|
Abbrev.
|
| 0-armstep
|
Perfect 0-armstep
|
P0arms
|
0
|
0.0 ¢
|
| 1-armstep
|
Minor 1-armstep
|
m1arms
|
s
|
0.0 ¢ to 133.3 ¢
|
| Major 1-armstep
|
M1arms
|
L
|
133.3 ¢ to 171.4 ¢
|
| 2-armstep
|
Minor 2-armstep
|
m2arms
|
L + s
|
171.4 ¢ to 266.7 ¢
|
| Major 2-armstep
|
M2arms
|
2L
|
266.7 ¢ to 342.9 ¢
|
| 3-armstep
|
Minor 3-armstep
|
m3arms
|
2L + s
|
342.9 ¢ to 400.0 ¢
|
| Major 3-armstep
|
M3arms
|
3L
|
400.0 ¢ to 514.3 ¢
|
| 4-armstep
|
Perfect 4-armstep
|
P4arms
|
3L + s
|
514.3 ¢ to 533.3 ¢
|
| Augmented 4-armstep
|
A4arms
|
4L
|
533.3 ¢ to 685.7 ¢
|
| 5-armstep
|
Diminished 5-armstep
|
d5arms
|
3L + 2s
|
514.3 ¢ to 666.7 ¢
|
| Perfect 5-armstep
|
P5arms
|
4L + s
|
666.7 ¢ to 685.7 ¢
|
| 6-armstep
|
Minor 6-armstep
|
m6arms
|
4L + 2s
|
685.7 ¢ to 800.0 ¢
|
| Major 6-armstep
|
M6arms
|
5L + s
|
800.0 ¢ to 857.1 ¢
|
| 7-armstep
|
Minor 7-armstep
|
m7arms
|
5L + 2s
|
857.1 ¢ to 933.3 ¢
|
| Major 7-armstep
|
M7arms
|
6L + s
|
933.3 ¢ to 1028.6 ¢
|
| 8-armstep
|
Minor 8-armstep
|
m8arms
|
6L + 2s
|
1028.6 ¢ to 1066.7 ¢
|
| Major 8-armstep
|
M8arms
|
7L + s
|
1066.7 ¢ to 1200.0 ¢
|
| 9-armstep
|
Perfect 9-armstep
|
P9arms
|
7L + 2s
|
1200.0 ¢
|
Generator chain
Generator chain of 7L 2s
| Bright gens |
Scale degree |
Abbrev.
|
| 15 |
Augmented 3-armdegree |
A3armd
|
| 14 |
Augmented 7-armdegree |
A7armd
|
| 13 |
Augmented 2-armdegree |
A2armd
|
| 12 |
Augmented 6-armdegree |
A6armd
|
| 11 |
Augmented 1-armdegree |
A1armd
|
| 10 |
Augmented 5-armdegree |
A5armd
|
| 9 |
Augmented 0-armdegree |
A0armd
|
| 8 |
Augmented 4-armdegree |
A4armd
|
| 7 |
Major 8-armdegree |
M8armd
|
| 6 |
Major 3-armdegree |
M3armd
|
| 5 |
Major 7-armdegree |
M7armd
|
| 4 |
Major 2-armdegree |
M2armd
|
| 3 |
Major 6-armdegree |
M6armd
|
| 2 |
Major 1-armdegree |
M1armd
|
| 1 |
Perfect 5-armdegree |
P5armd
|
| 0 |
Perfect 0-armdegree Perfect 9-armdegree |
P0armd P9armd
|
| −1 |
Perfect 4-armdegree |
P4armd
|
| −2 |
Minor 8-armdegree |
m8armd
|
| −3 |
Minor 3-armdegree |
m3armd
|
| −4 |
Minor 7-armdegree |
m7armd
|
| −5 |
Minor 2-armdegree |
m2armd
|
| −6 |
Minor 6-armdegree |
m6armd
|
| −7 |
Minor 1-armdegree |
m1armd
|
| −8 |
Diminished 5-armdegree |
d5armd
|
| −9 |
Diminished 9-armdegree |
d9armd
|
| −10 |
Diminished 4-armdegree |
d4armd
|
| −11 |
Diminished 8-armdegree |
d8armd
|
| −12 |
Diminished 3-armdegree |
d3armd
|
| −13 |
Diminished 7-armdegree |
d7armd
|
| −14 |
Diminished 2-armdegree |
d2armd
|
| −15 |
Diminished 6-armdegree |
d6armd
|
Modes
Scale degrees of the modes of 7L 2s
| UDP
|
Cyclic order
|
Step pattern
|
Scale degree (armdegree)
|
| 0
|
1
|
2
|
3
|
4
|
5
|
6
|
7
|
8
|
9
|
| 8|0
|
1
|
LLLLsLLLs
|
Perf.
|
Maj.
|
Maj.
|
Maj.
|
Aug.
|
Perf.
|
Maj.
|
Maj.
|
Maj.
|
Perf.
|
| 7|1
|
6
|
LLLsLLLLs
|
Perf.
|
Maj.
|
Maj.
|
Maj.
|
Perf.
|
Perf.
|
Maj.
|
Maj.
|
Maj.
|
Perf.
|
| 6|2
|
2
|
LLLsLLLsL
|
Perf.
|
Maj.
|
Maj.
|
Maj.
|
Perf.
|
Perf.
|
Maj.
|
Maj.
|
Min.
|
Perf.
|
| 5|3
|
7
|
LLsLLLLsL
|
Perf.
|
Maj.
|
Maj.
|
Min.
|
Perf.
|
Perf.
|
Maj.
|
Maj.
|
Min.
|
Perf.
|
| 4|4
|
3
|
LLsLLLsLL
|
Perf.
|
Maj.
|
Maj.
|
Min.
|
Perf.
|
Perf.
|
Maj.
|
Min.
|
Min.
|
Perf.
|
| 3|5
|
8
|
LsLLLLsLL
|
Perf.
|
Maj.
|
Min.
|
Min.
|
Perf.
|
Perf.
|
Maj.
|
Min.
|
Min.
|
Perf.
|
| 2|6
|
4
|
LsLLLsLLL
|
Perf.
|
Maj.
|
Min.
|
Min.
|
Perf.
|
Perf.
|
Min.
|
Min.
|
Min.
|
Perf.
|
| 1|7
|
9
|
sLLLLsLLL
|
Perf.
|
Min.
|
Min.
|
Min.
|
Perf.
|
Perf.
|
Min.
|
Min.
|
Min.
|
Perf.
|
| 0|8
|
5
|
sLLLsLLLL
|
Perf.
|
Min.
|
Min.
|
Min.
|
Perf.
|
Dim.
|
Min.
|
Min.
|
Min.
|
Perf.
|
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.
Modes of 7L 2s
| UDP |
Cyclic order |
Step pattern |
Super- Mode Names |
Ad- Mode Names (ground)
|
| 8|0 |
1 |
LLLLsLLLs |
Superlydian |
TBD
|
| 7|1 |
6 |
LLLsLLLLs |
Superionian |
Adlocrian
|
| 6|2 |
2 |
LLLsLLLsL |
Supermixolydian |
Adphrygian
|
| 5|3 |
7 |
LLsLLLLsL |
Supercorinthian |
Adaeolian
|
| 4|4 |
3 |
LLsLLLsLL |
Superolympian |
Addorian
|
| 3|5 |
8 |
LsLLLLsLL |
Superdorian |
Admixolydian
|
| 2|6 |
4 |
LsLLLsLLL |
Superaeolian |
Adionian
|
| 1|7 |
9 |
sLLLLsLLL |
Superphrygian |
Adlydian
|
| 0|8 |
5 |
sLLLsLLLL |
Superlocrian |
TBD
|
Note names
7L 2s, when viewed under Armodue theory, can be notated using Armodue notation.
Theory
Temperament interpretations
Mavila is an important harmonic entropy minimum here, insofar as 670-680 ¢ can be considered a fifth. Other temperaments include septimal mavila, hornbostel, and trismegistus.
Scale tree
Scale tree and tuning spectrum of 7L 2s
| Generator(edo)
|
Cents
|
Step ratio
|
Comments
|
| Bright
|
Dark
|
L:s
|
Hardness
|
| 5\9
|
|
|
|
|
|
666.667
|
533.333
|
1:1
|
1.000
|
Equalized 7L 2s Near exact-7/6 Armodue
|
|
|
|
|
|
|
29\52
|
669.231
|
530.769
|
6:5
|
1.200
|
|
|
|
|
|
|
24\43
|
|
669.767
|
530.233
|
5:4
|
1.250
|
Near exact-16/15 Amavil
|
|
|
|
|
|
|
43\77
|
670.130
|
529.870
|
9:7
|
1.286
|
|
|
|
|
|
19\34
|
|
|
670.588
|
529.412
|
4:3
|
1.333
|
Supersoft 7L 2s Near exact-20/17 Pentagoth
|
|
|
|
|
|
|
52\93
|
670.968
|
529.032
|
11:8
|
1.375
|
|
|
|
|
|
|
33\59
|
|
671.186
|
528.814
|
7:5
|
1.400
|
Near exact-5/4 Mavila
|
|
|
|
|
|
|
47\84
|
671.429
|
528.571
|
10:7
|
1.429
|
|
|
|
|
14\25
|
|
|
|
672.000
|
528.000
|
3:2
|
1.500
|
Soft 7L 2s Near exact-13/11 Pentagoth
|
|
|
|
|
|
|
51\91
|
672.527
|
527.473
|
11:7
|
1.571
|
|
|
|
|
|
|
37\66
|
|
672.727
|
527.273
|
8:5
|
1.600
|
|
|
|
|
|
|
|
60\107
|
672.897
|
527.103
|
13:8
|
1.625
|
|
|
|
|
|
23\41
|
|
|
673.171
|
526.829
|
5:3
|
1.667
|
Semisoft 7L 2s
|
|
|
|
|
|
|
55\98
|
673.469
|
526.531
|
12:7
|
1.714
|
|
|
|
|
|
|
32\57
|
|
673.684
|
526.316
|
7:4
|
1.750
|
Near exact-7/4 Armodue
|
|
|
|
|
|
|
41\73
|
673.973
|
526.027
|
9:5
|
1.800
|
|
|
|
9\16
|
|
|
|
|
675.000
|
525.000
|
2:1
|
2.000
|
Basic 7L 2s Scales with tunings softer than this are proper
|
|
|
|
|
|
|
40\71
|
676.056
|
523.944
|
9:4
|
2.250
|
|
|
|
|
|
|
31\55
|
|
676.364
|
523.636
|
7:3
|
2.333
|
|
|
|
|
|
|
|
53\94
|
676.596
|
523.404
|
12:5
|
2.400
|
|
|
|
|
|
22\39
|
|
|
676.923
|
523.077
|
5:2
|
2.500
|
Semihard 7L 2s
|
|
|
|
|
|
|
57\101
|
677.228
|
522.772
|
13:5
|
2.600
|
|
|
|
|
|
|
35\62
|
|
677.419
|
522.581
|
8:3
|
2.667
|
|
|
|
|
|
|
|
48\85
|
677.647
|
522.353
|
11:4
|
2.750
|
|
|
|
|
13\23
|
|
|
|
678.261
|
521.739
|
3:1
|
3.000
|
Hard 7L 2s
|
|
|
|
|
|
|
43\76
|
678.947
|
521.053
|
10:3
|
3.333
|
Near exact-6/5 Mavila
|
|
|
|
|
|
30\53
|
|
679.245
|
520.755
|
7:2
|
3.500
|
|
|
|
|
|
|
|
47\83
|
679.518
|
520.482
|
11:3
|
3.667
|
|
|
|
|
|
17\30
|
|
|
680.000
|
520.000
|
4:1
|
4.000
|
Superhard 7L 2s
|
|
|
|
|
|
|
38\67
|
680.597
|
519.403
|
9:2
|
4.500
|
|
|
|
|
|
|
21\37
|
|
681.081
|
518.919
|
5:1
|
5.000
|
|
|
|
|
|
|
|
25\44
|
681.818
|
518.182
|
6:1
|
6.000
|
Gravity ↓
|
| 4\7
|
|
|
|
|
|
685.714
|
514.286
|
1:0
|
→ ∞
|
Collapsed 7L 2s
|