7L 2s: Difference between revisions

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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).
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).


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'.
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'.


These scales are strongly associated with the [[Armodue|Armodue]] project/system applied too on Septimal-mávila and Hornbostel temperaments.
These scales are strongly associated with the [[Armodue]] project/system applied too on Septimal-mavila and Hornbostel temperaments.


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.
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.
Line 44: Line 44:
| | 682.758
| | 682.758
| | 8 8 8 1
| | 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.
| | 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
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| | 674.286
| | 674.286
| | 13 13 13 7
| | 13 13 13 7
| | Armodue-Mávila 1/13-tone
| | Armodue-Mavila 1/13-tone
|-
|-
| |  
| |  
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| | 674.157
| | 674.157
| | 11 11 11 6
| | 11 11 11 6
| | Armodue-Mávila 1/11-tone
| | Armodue-Mavila 1/11-tone
|-
|-
| |  
| |  
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| | 673.973
| | 673.973
| | 9 9 9 5
| | 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>
| | 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>
|-
|-
| |  
| |  
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| | 673.684
| | 673.684
| | 7 7 7 4
| | 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>
| | 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>
|-
|-
| |  
| |  
Line 333: Line 333:
| | 673.381
| | 673.381
| | 17 17 17 10
| | 17 17 17 10
| | Armodue-Mávila 1/17-tone
| | Armodue-Mavila 1/17-tone
|-
|-
| |  
| |  
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| | 673.171
| | 673.171
| | 5 5 5 3
| | 5 5 5 3
| | 5;3 Golden Armodue-Mávila 1/5-tone
| | 5;3 Golden Armodue-Mavila 1/5-tone
|-
|-
| |  
| |  
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| | 672.897
| | 672.897
| | 13 13 13 8
| | 13 13 13 8
| | 13;8 Golden Mávila 1/13-tone
| | 13;8 Golden Mavila 1/13-tone
|-
|-
| |  
| |  
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| | 672.85
| | 672.85
| | <span style="background-color: #ffffff; color: #222222; font-family: arial,sans-serif; font-size: small;">φ φ φ 1</span>
| | <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>
| | GOLDEN MAVILA (L/s = <span style="background-color: #ffffff; color: #222222; font-family: arial,sans-serif; font-size: small;">φ)</span>
|-
|-
| |  
| |  
Line 368: Line 368:
| | 672.832
| | 672.832
| | 21 21 21 13
| | 21 21 21 13
| | 21;13 Golden Mávila 1/21-tone <span style="font-size: 12.8000001907349px;">(Phi is the step 120\173)</span>
| | 21;13 Golden Mavila 1/21-tone <span style="font-size: 12.8000001907349px;">(Phi is the step 120\173)</span>
|-
|-
| |  
| |  
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| | 672.727
| | 672.727
| | 8 8 8 5
| | 8 8 8 5
| | 8;5 Golden Mávila 1/8-tone
| | 8;5 Golden Mavila 1/8-tone
|-
|-
| |  
| |  
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| | 672
| | 672
| | 3 3 3 2
| | 3 3 3 2
| | 3;2 Golden Armodue-Mávila 1/3-tone
| | 3;2 Golden Armodue-Mavila 1/3-tone
|-
|-
| |  
| |  

Revision as of 22:59, 19 April 2021

↖ 6L 1s ↑ 7L 1s 8L 1s ↗
← 6L 2s 7L 2s 8L 2s →
↙ 6L 3s ↓ 7L 3s 8L 3s ↘ 
┌╥╥╥╥┬╥╥╥┬┐
│║║║║│║║║││
│││││││││││
└┴┴┴┴┴┴┴┴┴┘
Scale structure
Step pattern LLLLsLLLs
sLLLsLLLL
Equave 2/1 (1200.0 ¢)
Period 2/1 (1200.0 ¢)
Generator size
Bright 5\9 to 4\7 (666.7 ¢ to 685.7 ¢)
Dark 3\7 to 4\9 (514.3 ¢ to 533.3 ¢)
TAMNAMS information
Name armotonic
Prefix arm-
Abbrev. arm
Related MOS scales
Parent 2L 5s
Sister 2L 7s
Daughters 9L 7s, 7L 9s
Neutralized 5L 4s
2-Flought 16L 2s, 7L 11s
Equal tunings
Equalized (L:s = 1:1) 5\9 (666.7 ¢)
Supersoft (L:s = 4:3) 19\34 (670.6 ¢)
Soft (L:s = 3:2) 14\25 (672.0 ¢)
Semisoft (L:s = 5:3) 23\41 (673.2 ¢)
Basic (L:s = 2:1) 9\16 (675.0 ¢)
Semihard (L:s = 5:2) 22\39 (676.9 ¢)
Hard (L:s = 3:1) 13\23 (678.3 ¢)
Superhard (L:s = 4:1) 17\30 (680.0 ¢)
Collapsed (L:s = 1:0) 4\7 (685.7 ¢)

This page is about of a MOSScale with 7 large steps and 2 small steps arranged LLLsLLLLs (or any rotation of that, such as LLsLLLsLL).

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 mavila is an important harmonic entropy minimum here. So a general name for this MOS pattern could be "Mavila Superdiatonic" or simply 'Superdiatonic'.

These scales are strongly associated with the Armodue project/system applied too on Septimal-mavila and Hornbostel temperaments.

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.

Generator Generator size (cents) Pentachord steps Comments
4\7 685.714 1 1 1 0
102\179 683.798 25 25 25 2 Approximately 0.03 cents away from 95/64
33\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 (a slight exceeded representation of the ratio 262144/177147, the Pythagorean wolf Fifth)
134\237 678.481 31 31 31 10 HORNBOSTEL TEMPERAMENT (1/31-tone; Optimum high size of Hornbostel '6th')
13\23 678.261 3 3 3 1 HORNBOSTEL TEMPERAMENT (Armodue 1/3-tone)
126\223 678.027 29 29 29 10 HORNBOSTEL TEMPERAMENT

(Armodue 1/29-tone)

113\200 678 26 26 26 9 HORNBOSTEL (& OGOLEVETS) TEMPERAMENT (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')
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 (the Golden Tone System of Thorvald Kornerup and a temperament of the Alexei Ogolevets's list of temperaments)
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 (Optimum accuracy of Phi interval, the note '7')
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 φ+1 φ+1 φ+1 1 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 (Optimum low size of Hornbostel '6th')
75\133 676.692 17 17 17 7 17;7 Superdiatonic 1/17-tone (Note the very accuracy of the step 75 with the ratio 34/23 with an error of +0.011 Cents)
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 [BOUNDARY OF PROPRIETY: smaller generators are strictly proper]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 (with an approximation of the Perfect Fifth + 1/5 Pyth.Comma [706.65 Cents]: 43\73 is 706.85 Cents)
32\57 673.684 7 7 7 4 Armodue-Mavila 1/7-tone (the 'Commatic' version of Armodue, because its high accuracy of the 7/4 interval, the note '8')
673.577 √3 √3 √3 1
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 φ φ φ 1 GOLDEN MAVILA (L/s = φ)
97\173 672.832 21 21 21 13 21;13 Golden Mavila 1/21-tone (Phi is the step 120\173)
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\9 666.667 1 1 1 1
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