7L 2s: Difference between revisions

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Line 6: Line 6:
| Equalized = 5
| Equalized = 5
| Paucitonic = 4
| Paucitonic = 4
| Pattern = LLLsLLLLs
| Pattern = LLLLsLLLs
| Neutral = 5L 4s
| Neutral = 5L 4s
}}
}}


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 ('''7L 2s''') arranged LLLLsLLLs (or any rotation of that, such as LLsLLLsLL).
 
== Name ==
== Name ==
The name '''superdiatonic''' has been established by [[Armodue]] theorists, and so [[TAMNAMS]] adopts it as well.
The name '''superdiatonic''' has been established by [[Armodue]] theorists, and so [[TAMNAMS]] adopts it as well.
== Temperaments ==
== Temperaments ==
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'.
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]] project/system applied to septimal mavila and Hornbostel temperaments.
These scales are strongly associated with the [[Armodue]] project/system applied to septimal mavila and Hornbostel temperaments.
== Intervals ==
== Intervals ==
Note: In TAMNAMS, a k-step interval class in superdiatonic may be called a "k-step", "k-mosstep", or "k-armstep". 1-indexed terms such as "mos(k+1)th" are discouraged for non-diatonic mosses.
Note: In TAMNAMS, a k-step interval class in superdiatonic may be called a "k-step", "k-mosstep", or "k-armstep". 1-indexed terms such as "mos(k+1)th" are discouraged for non-diatonic mosses.
== Modes ==
* 8|0 LLLLsLLLs
* 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 ==
== Scale tree ==
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]]' Generators: 31/21, 34/23, 65/44, 71/48, 99/67, 105/71, 108/73, 133/90, 145/98, 176/119 & 250/169.
 
 
Generator ranges:
* Chroma-positive generator: 666.6667 cents (5\9) to 685.7143 cents (4\7)
* Chroma-negative generator: 514.2857 cents (3\7) to 533.3333 cents (4\9)


{| class="wikitable"
{| class="wikitable"
Line 794: Line 814:
| |  
| |  
|}
|}
[[Category:Abstract MOS patterns]]
[[Category:Abstract MOS patterns]]
[[Category:9-tone scales]]
[[Category:Mavila]]
[[Category:Mavila]]
[[Category:Superdiatonic]]
[[Category:Superdiatonic]]

Revision as of 13:51, 13 February 2022

↖ 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 (7L 2s) arranged LLLLsLLLs (or any rotation of that, such as LLsLLLsLL).

Name

The name superdiatonic has been established by Armodue theorists, and so TAMNAMS adopts it as well.

Temperaments

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 to septimal mavila and Hornbostel temperaments.

Intervals

Note: In TAMNAMS, a k-step interval class in superdiatonic may be called a "k-step", "k-mosstep", or "k-armstep". 1-indexed terms such as "mos(k+1)th" are discouraged for non-diatonic mosses.

Modes

  • 8|0 LLLLsLLLs
  • 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

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 ranges:

  • Chroma-positive generator: 666.6667 cents (5\9) to 685.7143 cents (4\7)
  • Chroma-negative generator: 514.2857 cents (3\7) to 533.3333 cents (4\9)
Generator Generator size (cents) Pentachord steps Comments
4\7 685.714 1 1 1 0
53\93 683.871 13 13 13 1
102\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\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 (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
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\9 666.667 1 1 1 1
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