User:Moremajorthanmajor/7L 2s (major tenth-equivalent): Difference between revisions

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Revision as of 03:15, 2 June 2023

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

Comma list: 81/80

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

Comma list: 64/63

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

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