User:Moremajorthanmajor/7L 2s (major tenth-equivalent)
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 | L | s | Comments | ||
|---|---|---|---|---|---|---|
| 4\7 | 960 | 1 | 0 | |||
| 25\44 | 937.5 | 6 | 1 | |||
| 71\125 | 936.263… | 17 | 3 | |||
| 46\81 | 935.593… | 11 | 2 | |||
| 67\118 | 934.883… | 16 | 3 | |||
| 21\37 | 933.3 | 5 | 1 | |||
| 80\141 | 932.038… | 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 | 928.695… | 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 | 924.591… | 11 | 3 | |||
| 30\53 | 923.076… | 7 | 2 | |||
| 73\129 | 922.105… | 17 | 5 | |||
| 43\76 | 921.428… | 10 | 3 | |||
| 56\99 | 920.547… | 13 | 4 | |||
| 69\122 | 920 | 16 | 5 | |||
| 82\145 | 919.626… | 19 | 6 | |||
| 95\168 | 919.354… | 22 | 7 | |||
| 919.340… | L/s = π | |||||
| 108\191 | 919.148… | 25 | 8 | |||
| 121\214 | 918.987… | 28 | 9 | |||
| 134\237 | 918.857… | 31 | 10 | |||
| 13\23 | 917.647… | 3 | 1 | |||
| 100\177 | 916.030… | 23 | 8 | |||
| 87\154 | 915.789… | 20 | 7 | |||
| 74\131 | 915.463… | 17 | 6 | |||
| 61\108 | 915 | 14 | 5 | |||
| 48\85 | 914.286… | 11 | 4 | |||
| 913.820… | L/s = e | |||||
| 35\62 | 913.043… | 8 | 3 | |||
| 912.286… | Split φ superdiatonic relation | |||||
| 57\101 | 912 | 13 | 5 | |||
| 79\140 | 911.538… | 18 | 7 | |||
| 22\39 | 910.344… | 5 | 2 | |||
| 75\133 | 909.09 | 17 | 7 | |||
| 53\94 | 908.571… | 12 | 5 | |||
| 31\55 | 907.317… | 7 | 3 | |||
| 71\126 | 906.382… | 16 | 7 | |||
| 40\71 | 905.660… | 9 | 4 | |||
| 49\87 | 904.615… | 11 | 5 | |||
| 58\103 | 903.896… | 13 | 6 | |||
| 9\16 | 900 | 2 | 1 | [BOUNDARY OF PROPRIETY: smaller generators are strictly proper] | ||
| 59\105 | 896.202… | 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… | ||||||
| 55\98 | 891.891 | 12 | 7 | |||
| 23\41 | 890.323… | 5 | 3 | Golden Terra Rubra 1/5-tone | ||
| 83\148 | 889.285… | 18 | 11 | |||
| 60\107 | 888.8 | 13 | 8 | Golden Terra Rubra 1/13-tone | ||
| 888.643… | GOLDEN Terra Rubra (L/s = φ) | |||||
| 37\66 | 888 | 8 | 5 | Golden Terra Rubra 1/8-tone | ||
| 88\157 | 887.394… | 19 | 12 | |||
| 51\91 | 886.956… | 11 | 7 | |||
| 65\116 | 886.36 | 14 | 9 | |||
| 79\141 | 885.981… | 17 | 11 | |||
| 93\166 | 885.714… | 20 | 13 | |||
| 14\25 | 884.210… | 3 | 2 | Golden Terra Rubra 1/3-tone | ||
| 117\209 | 883.018… | 25 | 17 | |||
| 103\184 | 882.857… | 22 | 15 | |||
| 89\159 | 882.644… | 19 | 13 | |||
| 75\134 | 882.353… | 16 | 11 | |||
| 61\109 | 881.927… | 13 | 9 | |||
| 47\84 | 881.25 | 10 | 7 | |||
| 80\143 | 880.733… | 17 | 12 | |||
| 33\59 | 880 | 7 | 5 | |||
| 85\152 | 879.310… | 18 | 13 | |||
| 52\93 | 878.873… | 11 | 8 | |||
| 71\127 | 878.350… | 15 | 11 | |||
| 90\161 | 878.048… | 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 | 871.232… | 11 | 9 | |||
| 29\52 | 870 | 6 | 5 | |||
| 5\9 | 857.142… | 1 | 0 | |||
See also
7L 2s (5/2-equivalent) - idealized meantone tuning
7L 2s (18/7-equivalent) - idealized Archytas tuning