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

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| |<span style="display: block; text-align: left;">'''[BOUNDARY OF PROPRIETY: smaller generators are strictly proper]'''</span>
| |<span style="display: block; text-align: left;">'''[BOUNDARY OF PROPRIETY: smaller generators are strictly proper]'''</span>
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== See also ==
== See also ==
[[7L 2s (5/2-equivalent)]] - idealized meantone tuning
[[7L 2s (5/2-equivalent)]] - idealized meantone tuning
[[7L 2s (81/32-equivalent)]] - Pythagorean tuning


[[7L 2s (28/11-equivalent)]] - Neogothic tuning
[[7L 2s (28/11-equivalent)]] - Neogothic tuning


[[7L 2s (18/7-equivalent)]] - idealized Archytas tuning
[[7L 2s (18/7-equivalent)]] - idealized Archytas tuning

Latest revision as of 19:06, 29 December 2024

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

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, 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\37 933.333 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\30 927.273 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\133 909.091 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
… … … …
229\305 900.983 51 25
9\16 900.000 2 1 [BOUNDARY OF PROPRIETY: smaller generators are strictly proper]
230\397 899.023 51 26
… … … …
41\73 894.545 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\98 891.892 12 7
23\41 890.323 5 3 Golden Terra Rubra 1/5-tone
83\148 889.286 18 11
60\107 888.889 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\116 886.364 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\43 872.727 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

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