User:Moremajorthanmajor/7L 2s (major tenth-equivalent)
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This page is about a MOS scale with a period of 5/2 and 7 large steps and 2 small steps arranged LLLsLLLLs (or any rotation of that, such as LLsLLLsLL).
Name
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
Scale tree
| Generator | Generator size | ed16\12 (→ed4\3) | Comments | ||
|---|---|---|---|---|---|
| 4\7 | 960 | 914.285… | |||
| 25\44 | 937.5 | 909.09 | |||
| 71\125 | 936.263… | 908.8 | |||
| 46\81 | 935.593… | 908.641… | |||
| 67\118 | 934.883… | 908.474… | |||
| 21\37 | 933.3 | 908.108 | |||
| 80\141 | 932.038… | 907.801… | |||
| 59\104 | 931.579… | 907.692… | |||
| 38\67 | 930.612… | 907.462… | |||
| 55\97 | 929.577… | 907.216… | |||
| 72\127 | 929.032… | 907.086… | |||
| 89\157 | 928.695… | 907.006… | |||
| 17\30 | 927.27 | 906.6 | L/s = 4 | ||
| 115\203 | 926.174… | 906.403… | |||
| 98\173 | 925.984… | 906.358… | |||
| 81\143 | 925.714… | 906.293… | |||
| 64\113 | 925.301… | 906.194… | |||
| 47\83 | 924.591… | 906.024… | |||
| 30\53 | 923.076… | 905.660… | |||
| 73\129 | 922.105… | 905.426… | |||
| 43\76 | 921.428… | 905.263… | |||
| 56\99 | 920.547… | 905.05 | |||
| 69\122 | 920 | 904.918… | |||
| 82\145 | 919.626… | 904.827… | |||
| 95\168 | 919.354… | 904.761… | |||
| 919.340… | 904.758… | L/s = π | |||
| 108\191 | 919.148… | 904.712… | |||
| 121\214 | 918.987… | 904.672… | 28;9 Superdiatonic 1/28-tone | ||
| 134\237 | 918.857… | 904.642… | |||
| 13\23 | 917.647… | 904.347… | L/s = 4 | ||
| 100\177 | 916.030… | 903.954… | |||
| 87\154 | 915.789… | 903.896… | |||
| 74\131 | 915.463… | 903.816… | 17;6 1/17-tone | ||
| 61\108 | 915 | 903.703 | 14;5 1/14-tone | ||
| 48\85 | 914.286… | 903.529… | 11;4 1/11-tone | ||
| 913.820… | 903.415… | L/s = e | |||
| 35\62 | 913.043… | 903.225… | 8;3 1/8-tone | ||
| 912.286… | 903.040… | Split φ superdiatonic relation (34;13 - 55;21 - 89;34 - 144;55 - 233;89 - 377;144 - 610;233..) | |||
| 57\101 | 912 | 902.970… | 13;5 Superdiatonic 1/13-tone | ||
| 79\140 | 911.538… | 902.857… | |||
| 22\39 | 910.344… | 902.564… | Terra Rubra 1/5-tone | ||
| 75\133 | 909.09 | 902.255… | 17;7 Superdiatonic 1/17-tone | ||
| 53\94 | 908.571… | 902.127… | |||
| 31\55 | 907.317… | 901.81 | 7;3 Superdiatonic 1/7-tone | ||
| 71\126 | 906.382… | 901.587… | |||
| 40\71 | 905.660… | 901.408… | 9;4 Superdiatonic 1/9-tone | ||
| 49\87 | 904.615… | 901.149… | 11;5 Superdiatonic 1/11-tone | ||
| 58\103 | 903.896… | 900.970… | 13;6 Superdiatonic 1/13-tone | ||
| 67\119 | 903.370… | 900.840… | |||
| 76\135 | 902.970… | 900.740 | |||
| 85\151 | 902.654… | 900.662… | |||
| 94\167 | 902.4 | 900.598… | |||
| 103\183 | 902.189… | 900.564… | |||
| 112\199 | 902.013… | 900.502… | |||
| 121\215 | 901.863… | 900.465… | |||
| 9\16 | 900 | 900 | [BOUNDARY OF PROPRIETY: smaller generators are strictly proper] | ||
| 230\409 | 899.022… | 899.755… | |||
| 221\393 | 898.983… | 899.745… | |||
| 212\377 | 898.939… | 899.734… | |||
| 203\361 | 898.892… | 899.722… | |||
| 194\345 | 898.841… | 899.710… | |||
| 185\329 | 898.785… | 899.696… | |||
| 176\313 | 898.723… | 899.680… | |||
| 167\297 | 898.654… | 899.663… | |||
| 158\281 | 898.578… | 899.644… | |||
| 149\265 | 898.492… | 899.622… | |||
| 140\249 | 898.395… | 899.598… | |||
| 131\233 | 898.285… | 899.570… | |||
| 122\217 | 898.159… | 899.539… | |||
| 113\201 | 898.013… | 899.502… | |||
| 104\185 | 897.841… | 899.459… | |||
| 95\169 | 897.637… | 899.408… | |||
| 86\153 | 897.391… | 899.346… | |||
| 77\137 | 897.087… | 899.270… | |||
| 68\121 | 896.703… | 899.173… | |||
| 59\105 | 896.202… | 899.047… | Terra Rubra 1/13-tone | ||
| 50\89 | 895.522… | 898.876… | Terra Rubra 1/11-tone | ||
| 41\73 | 894.54 | 898.630… | Terra Rubra 1/9-tone | ||
| 32\57 | 893.023… | 898.245… | Terra Rubra 1/7-tone (the 'Commatic' version of Terra Rubra, because its high accuracy of the 16/15 interval, the note '2b') | ||
| 892.459… | 898.102… | ||||
| 55\98 | 891.891 | 897.959… | |||
| 78\139 | 891.428… | 897.841… | Terra Rubra 1/17-tone | ||
| 23\41 | 890.323… | 897.560… | 5;3 Golden Terra Rubra 1/5-tone | ||
| 83\148 | 889.285… | 897.297 | |||
| 60\107 | 888.8 | 897.196… | 13;8 Golden Terra Rubra 1/13-tone | ||
| 888.643… | 897.133… | GOLDEN Terra Rubra (L/s = φ) | |||
| 97\173 | 888.549… | 897.109… | 21;13 Golden Terra Rubra 1/21-tone | ||
| 37\66 | 888 | 896.96 | 8;5 Golden Terra Rubra 1/8-tone | ||
| 88\157 | 887.394… | 896.815… | |||
| 51\91 | 886.956… | 896.703… | 11;7 Superdiatonic 1/11-tone | ||
| 886.933… | 896.697… | ||||
| 65\116 | 886.36 | 896.551… | 14;9 Superdiatonic 1/14-tone | ||
| 79\141 | 885.981… | 896.453… | 17;11 Superdiatonic 1/17-tone | ||
| 93\166 | 885.714… | 896.385… | |||
| 107\191 | 885.517… | 896.335… | |||
| 121\216 | 885.365… | 896.296 | 26;17 Superdiatonic 1/26-tone | ||
| 135\241 | 885.245… | 896.265… | 29;19 Superdiatonic 1/29-tone | ||
| 14\25 | 884.210… | 896 | 3;2 Golden Terra Rubra 1/3-tone | ||
| 145\259 | 883.248… | 895.752… | 31;21 Superdiatonic 1/31-tone | ||
| 131\234 | 883.146… | 895.726… | 28;19 Superdiatonic 1/28-tone | ||
| 117\209 | 883.018… | 895.693… | |||
| 103\184 | 882.857… | 895.652… | |||
| 89\159 | 882.644… | 895.579… | |||
| 75\134 | 882.353… | 895.522… | |||
| 61\109 | 881.927… | 895.412… | |||
| 47\84 | 881.25 | 895.238… | |||
| 80\143 | 880.733… | 895.104… | |||
| 33\59 | 880 | 894.915… | |||
| 85\152 | 879.310… | 894.736… | |||
| 52\93 | 878.873… | 894.623… | |||
| 71\127 | 878.350… | 894.488… | |||
| 19\34 | 876.923… | 894.117… | |||
| 62\111 | 875.294… | 893.693 | |||
| 43\77 | 874.576… | 893.506… | |||
| 67\120 | 873.913… | 893.3 | |||
| 24\43 | 872.72 | 893.023… | |||
| 53\95 | 871.232… | 892.631… | |||
| 29\52 | 870 | 892.307… | |||
| 5\9 | 857.142… | 888.8 | |||
See also
7L 2s (5/2-equivalent) - idealized meantone tuning
7L 2s (18/7-equivalent) - idealized Archytas tuning