7L 2s
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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 mávila is an important harmonic entropy minimum here. So a general name for this MOS pattern could be "Mávila Superdiatonic" or simply 'Superdiatonic'.
These scales are strongly associated with the Armodue project/system applied too on Septimal-mávila 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 | |||
| 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-Mávila 1/13-tone | ||
| 50\89 | 674.157 | 11 11 11 6 | Armodue-Mávila 1/11-tone | ||
| 41\73 | 673.973 | 9 9 9 5 | Armodue-Mávila 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-Mávila 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-Mávila 1/17-tone | ||
| 101\180 | 673.333 | 22 22 22 13 | |||
| 23\41 | 673.171 | 5 5 5 3 | 5;3 Golden Armodue-Mávila 1/5-tone | ||
| 60\107 | 672.897 | 13 13 13 8 | 13;8 Golden Mávila 1/13-tone | ||
| 672.85 | φ φ φ 1 | GOLDEN MÁVILA (L/s = φ) | |||
| 97\173 | 672.832 | 21 21 21 13 | 21;13 Golden Mávila 1/21-tone (Phi is the step 120\173) | ||
| 37\66 | 672.727 | 8 8 8 5 | 8;5 Golden Mávila 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-Mávila 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 | |||