7L 2s
↖ 6L 1s | ↑ 7L 1s | 8L 1s ↗ |
← 6L 2s | 7L 2s | 8L 2s → |
↙ 6L 3s | ↓ 7L 3s | 8L 3s ↘ |
┌╥╥╥╥┬╥╥╥┬┐ │║║║║│║║║││ │││││││││││ └┴┴┴┴┴┴┴┴┴┘
sLLLsLLLL
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.
Name
The TAMNAMS name for this pattern is armotonic, in reference to Armodue theory. Superdiatonic is also in use.
Intervals
- This article assumes TAMNAMS for naming step ratios, mossteps, and mosdegrees.
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 ¢ |
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 678¢ can be considered a fifth. Other temperaments include septimal mavila and Hornbostel.
Modes
UDP | Cyclic order |
Step pattern |
---|---|---|
8|0 | 1 | LLLLsLLLs |
7|1 | 6 | LLLsLLLLs |
6|2 | 2 | LLLsLLLsL |
5|3 | 7 | LLsLLLLsL |
4|4 | 3 | LLsLLLsLL |
3|5 | 8 | LsLLLLsLL |
2|6 | 4 | LsLLLsLLL |
1|7 | 9 | sLLLLsLLL |
0|8 | 5 | 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 |