User:Moremajorthanmajor/7L 2s (major tenth-equivalent)
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This page is about a MOS scale with a period of a major tenth and 7 large steps and 2 small steps arranged LLLsLLLLs (or any rotation of that, such as LLsLLLsLL).
Name
The author suggests the name Terra Rubra for this scale.
Temperaments
Terra Rubra-Meantone
Subgroup: 5/2.2.3
POL2 generator: ~3/2 = 696.8737¢
Mapping: [⟨1 1 1], ⟨0 -2 -1]]
Optimal ET sequence: 9ed5/2, 16ed5/2, 25ed5/2
Terra Rubra-Superpyth
Subgroup: 18/7.2.3
POL2 generator: ~3/2 = 708.4011¢
Mapping: [⟨1 1 1], ⟨0 -2 -1]]
Optimal ET sequence: 7ed18/7, 16ed18/7, 23ed18/7, 30ed18/7
Scale tree
| Generator | Generator size | L | s | Comments |
|---|---|---|---|---|
| 4\7 | 960.000 | 1 | 0 | |
| 25\44 | 937.500 | 6 | 1 | |
| 71\129 | 936.263 | 17 | 3 | |
| 46\81 | 935.593 | 11 | 2 | |
| 67\118 | 934.884 | 16 | 3 | |
| 21\37 | 933.3 | 5 | 1 | |
| 80\141 | 932.039 | 19 | 4 | |
| 59\104 | 931.579 | 14 | 3 | |
| 38\67 | 930.612 | 9 | 2 | |
| 55\97 | 929.577 | 13 | 3 | |
| 72\127 | 929.032 | 17 | 4 | |
| 89\157 | 928.696 | 21 | 5 | |
| 17\30 | 927.27 | 4 | 1 | |
| 115\203 | 926.174 | 27 | 7 | |
| 98\173 | 925.984 | 23 | 6 | |
| 81\143 | 925.714 | 19 | 5 | |
| 64\113 | 925.301 | 15 | 4 | |
| 47\83 | 924.590 | 11 | 3 | |
| 30\53 | 923.077 | 7 | 2 | |
| 73\129 | 922.105 | 17 | 5 | |
| 43\76 | 921.429 | 10 | 3 | |
| 56\99 | 920.548 | 13 | 4 | |
| 69\122 | 920.000 | 16 | 5 | |
| 82\145 | 919.626 | 19 | 6 | |
| 95\168 | 919.355 | 22 | 7 | |
| 919.340 | π | 1 | ||
| 108\191 | 919.149 | 25 | 8 | |
| 121\214 | 918.987 | 28 | 9 | |
| 13\23 | 917.647 | 3 | 1 | |
| 100\177 | 916.031 | 23 | 8 | |
| 87\154 | 915.789 | 20 | 7 | |
| 74\131 | 915.464 | 17 | 6 | |
| 61\108 | 915.000 | 14 | 5 | |
| 48\85 | 914.286 | 11 | 4 | |
| 913.821 | e | 1 | L/s = e | |
| 35\62 | 913.043 | 8 | 3 | |
| 912.287 | φ+1 | 1 | Split φ superdiatonic relation | |
| 57\101 | 912.000 | 13 | 5 | |
| 79\140 | 911.538 | 18 | 7 | |
| 22\39 | 910.345 | 5 | 2 | |
| 75\133 | 909.09 | 17 | 7 | |
| 53\94 | 908.571 | 12 | 5 | |
| 31\55 | 907.317 | 7 | 3 | |
| 71\126 | 906.383 | 16 | 7 | |
| 40\71 | 905.660 | 9 | 4 | |
| 49\87 | 904.615 | 11 | 5 | |
| 58\103 | 903.896 | 13 | 6 | |
| 67\119 | 903.370 | 15 | 7 | |
| 76\135 | 902.9702 | 17 | 8 | |
| 85\151 | 902.655 | 19 | 9 | |
| 94\167 | 902.400 | 21 | 10 | |
| 103\183 | 902.190 | 23 | 11 | |
| 112\199 | 902.013 | 25 | 12 | |
| 121\215 | 901.863 | 27 | 13 | |
| 9\16 | 900.000 | 2 | 1 | [BOUNDARY OF PROPRIETY: smaller generators are strictly proper] |
| 122\217 | 898.160 | 27 | 14 | |
| 113\201 | 898.013 | 25 | 13 | |
| 104\185 | 897.842 | 23 | 12 | |
| 95\169 | 897.638 | 21 | 11 | |
| 86\153 | 897.391 | 19 | 10 | |
| 77\137 | 897.087 | 17 | 9 | |
| 68\121 | 896.703 | 15 | 8 | |
| 59\105 | 896.203 | 13 | 7 | |
| 50\89 | 895.522 | 11 | 6 | |
| 41\73 | 894.54 | 9 | 5 | |
| 32\57 | 893.023 | 7 | 4 | the 'Commatic' version of Terra Rubra, because its high accuracy of the 16/15 interval, the note '2b' |
| 892.459 | ||||
| 87\155 | 892.307 | 19 | 11 | |
| 55\98 | 891.891 | 12 | 7 | |
| 23\41 | 890.323 | 5 | 3 | Golden Terra Rubra 1/5-tone |
| 83\148 | 889.286 | 18 | 11 | |
| 60\107 | 888.8 | 13 | 8 | Golden Terra Rubra 1/13-tone |
| 888.643 | φ | 1 | GOLDEN Terra Rubra (L/s = φ) | |
| 37\66 | 888.000 | 8 | 5 | Golden Terra Rubra 1/8-tone |
| 88\157 | 887.395 | 19 | 12 | |
| 51\91 | 886.957 | 11 | 7 | |
| 65\116 | 886.36 | 14 | 9 | |
| 79\141 | 885.981 | 17 | 11 | |
| 93\166 | 885.714 | 20 | 13 | |
| 14\25 | 884.211 | 3 | 2 | Golden Terra Rubra 1/3-tone |
| 117\209 | 883.019 | 25 | 17 | |
| 103\184 | 882.857 | 22 | 15 | |
| 89\159 | 882.645 | 19 | 13 | |
| 75\134 | 882.353 | 16 | 11 | |
| 61\109 | 881.928 | 13 | 9 | |
| 47\84 | 881.250 | 10 | 7 | |
| 33\59 | 880.000 | 7 | 5 | |
| 85\152 | 879.310 | 18 | 13 | |
| 52\93 | 878.873 | 11 | 8 | |
| 71\127 | 878.351 | 15 | 11 | |
| 90\161 | 878.049 | 19 | 14 | |
| 109\195 | 877.852 | 23 | 17 | |
| 19\34 | 876.923 | 4 | 3 | |
| 62\111 | 875.294 | 13 | 10 | |
| 43\77 | 874.576 | 9 | 7 | |
| 67\120 | 873.913 | 14 | 11 | |
| 24\43 | 872.72 | 5 | 4 | |
| 53\95 | 871.233 | 11 | 9 | |
| 29\52 | 870.000 | 6 | 5 | |
| 5\9 | 857.142 | 1 | 0 |
See also
7L 2s (5/2-equivalent) - idealized meantone tuning
7L 2s (81/32-equivalent) - Pythagorean tuning
7L 2s (28/11-equivalent) - Neogothic tuning
7L 2s (18/7-equivalent) - idealized Archytas tuning