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

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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).
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==
==Name==
The author suggests the name '''Terra Rubra''' for this scale.


==Temperaments==
==Temperaments==
Line 10: Line 11:
[[Comma]] list: [[81/80]]
[[Comma]] list: [[81/80]]


[[POL2]] generator: ~3/2 = 696.8737
[[POL2]] generator: ~3/2 = 696.8737¢


[[Mapping]]: [⟨1 1 1], ⟨0 -2 -1]]
[[Mapping]]: [⟨1 1 1], ⟨0 -2 -1]]


[[Optimal ET sequence]]: 9ed5/2, 16ed5/2, 25ed5/2
[[Optimal ET sequence]]: [[9ed5/2]], [[16ed5/2]], [[25ed5/2]]


=== Terra Rubra-Superpyth ===
=== Terra Rubra-Superpyth ===
Line 21: Line 22:
[[Comma]] list: [[64/63]]
[[Comma]] list: [[64/63]]


[[POL2]] generator: ~3/2 = 708.4011
[[POL2]] generator: ~3/2 = 708.4011¢


[[Mapping]]: [⟨1 1 1], ⟨0 -2 -1]]
[[Mapping]]: [⟨1 1 1], ⟨0 -2 -1]]


[[Optimal ET sequence]]: 7ed18/7, 16ed18/7, 23ed18/7
[[Optimal ET sequence]]: [[7ed18/7]], [[16ed18/7]], [[23ed18/7]], [[30ed18/7]]


==Scale tree==
==Scale tree==
{| class="wikitable"
{| class="wikitable"
|-
|-
! colspan="3" |Generator
!Generator
! |Generator size
! |Generator size
!L
!L
Line 37: Line 38:
|-
|-
| |4\[[7ed5/2|7]]
| |4\[[7ed5/2|7]]
| |
| |<u>960.000</u>
| |
| |<u>960</u>
|1
|1
|0
|0
Line 45: Line 44:
|-
|-
|25\44
|25\44
|
|<u>937.500</u>
|
|<u>937.5</u>
|6
|6
|1
|1
|
|
|-
|-
|
|71\129
|71\125
|<u>936.263</u>
|
|<u>936.263…</u>
|17
|17
|3
|3
|
|
|-
|-
|
|46\81
|46\81
|
|<u>935.593</u>
|<u>935.593…</u>
|11
|11
|2
|2
|
|
|-
|-
|
|67\118
|67\118
|
|<u>934.884</u>
|<u>934.883…</u>
|16
|16
|3
|3
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|-
|-
| |21\37
| |21\37
| |
| |<u>933.333</u>
| |
| |<u>933.{{Overline|3}}</u>
|5
|5
|1
|1
| |
| |
|-
|-
|
|80\141
|80\141
|
|<u>932.039</u>
|<u>932.038…</u>
|19
|19
|4
|4
|
|
|-
|-
|
|59\104
|59\104
|
|<u>931.579</u>
|<u>931.579…</u>
|14
|14
|3
|3
|
|
|-
|-
|
|38\67
|38\67
|
|<u>930.612</u>
|<u>930.612…</u>
|9
|9
|2
|2
|
|
|-
|-
|
|55\97
|55\97
|
|<u>929.577</u>
|<u>929.577…</u>
|13
|13
|3
|3
|
|
|-
|-
|
|72\127
|72\127
|
|<u>929.032</u>
|<u>929.032…</u>
|17
|17
|4
|4
|
|
|-
|-
|
|89\157
|89\157
|
|<u>928.696</u>
|<u>928.695…</u>
|21
|21
|5
|5
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|-
| |17\30
| |17\30
| |
| |<u>927.273</u>
| |
| |<u>927.{{Overline|27}}</u>
|4
|4
|1
|1
| |
| |
|-
|-
|
|115\203
|115\203
|
|<u>926.174</u>
|<u>926.174…</u>
|27
|27
|7
|7
|
|
|-
|-
|
|98\173
|98\173
|
|<u>925.984</u>
|<u>925.984…</u>
|23
|23
|6
|6
|
|
|-
|-
|
|81\143
|81\143
|
|<u>925.714</u>
|<u>925.714…</u>
|19
|19
|5
|5
|
|
|-
|-
|
|64\113
|64\113
|
|<u>925.301</u>
|<u>925.301…</u>
|15
|15
|4
|4
|
|
|-
|-
|
|47\83
|47\83
|
|<u>924.590</u>
|<u>924.591…</u>
|11
|11
|3
|3
|
|
|-
|-
| |
| |30\53
| |30\53
| |
| |<u>923.077</u>
| |<u>923.076…</u>
|7
|7
|2
|2
| |
| |
|-
|-
|
|
|73\129
|73\129
|<u>922.105…</u>
|<u>922.105</u>
|17
|17
|5
|5
|
|
|-
|-
| |
| |43\76
| |43\76
| |
| |<u>921.429</u>
| |<u>921.428…</u>
|10
|10
|3
|3
| |
| |
|-
|-
| |
| |56\99
| |56\99
| |
| |<u>920.548</u>
| |<u>920.547…</u>
|13
|13
|4
|4
| |
| |
|-
|-
| |
| |69\122
| |69\122
| |
| |<u>920.000</u>
| |<u>920</u>
|16
|16
|5
|5
| |
| |
|-
|-
| |
| |82\145
| |82\145
| |
| |<u>919.626</u>
| |<u>919.626…</u>
|19
|19
|6
|6
| |
| |
|-
|-
| |
| |95\168
| |95\168
| |
| |<u>919.355</u>
| |<u>919.354…</u>
|22
|22
|7
|7
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|-
|-
| |
| |
| |<u>919.340</u>
|π
|1
| |
| |
| |
| |<u>919.340…</u>
|
|
| |L/s = π
|-
|-
| |
| |108\191
| |108\191
| |
| |<u>919.149</u>
| |<u>919.148…</u>
|25
|25
|8
|8
| |
| |
|-
|-
| |
| |121\214
| |121\214
| |
| |<u>918.987</u>
| |<u>918.987…</u>
|28
|28
|9
|9
| |
|-
| |
| |134\237
| |
| |<u>918.857…</u>
|31
|10
| |
| |
|-
|-
| |13\23
| |13\23
| |
| |<u>917.647</u>
| |
| |<u>917.647…</u>
|3
|3
|1
|1
| |
| |
|-
|-
| |
| |100\177
| |100\177
| |
| |<u>916.031</u>
| |<u>916.030…</u>
|23
|23
|8
|8
| |
| |
|-
|-
| |
| |87\154
| |87\154
| |
| |<u>915.789</u>
| |<u>915.789…</u>
|20
|20
|7
|7
| |
| |
|-
|-
| |
| |74\131
| |74\131
| |
| |<u>915.464</u>
| |<u>915.463…</u>
|17
|17
|6
|6
| |
| |
|-
|-
| |
| |61\108
| |61\108
| |
| |<u>915.000</u>
| |<u>915</u>
|14
|14
|5
|5
| |
| |
|-
|-
| |
| |48\85
| |48\85
| |
| |<u>914.286</u>
| |<u>914.286…</u>
|11
|11
|4
|4
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|-
|-
| |
| |
| |
| |<u>913.821</u>
| |
|e
| |<u>913.820…</u>
|1
|
|
| |L/s = e
| |L/s = e
|-
|-
| |
| |35\62
| |35\62
| |
| |<u>913.043</u>
| |<u>913.043…</u>
|8
|8
|3
|3
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|-
|-
| |
| |
| |
| |<u>912.287</u>
| |
|<span style="background-color: #ffffff; color: #222222; font-family: arial,sans-serif; font-size: small;">φ</span>+1
| |<u>912.286…</u>
|1
|
| |Split <span style="background-color: #ffffff; color: #222222; font-family: arial,sans-serif; font-size: small;">φ</span> superdiatonic relation
|
| |Split φ superdiatonic relation
|-
|-
| |
| |
| |57\101
| |57\101
| |<u>912</u>
| |<u>912.000</u>
|13
|13
|5
|5
| |
| |
|-
|-
|
|
|79\140
|79\140
|<u>911.538…</u>
|<u>911.538</u>
|18
|18
|7
|7
|
|
|-
|-
| |
| |22\39
| |22\39
| |
| |<u>910.345</u>
| |<u>910.344…</u>
|5
|5
|2
|2
| |
| |
|-
|-
| |
| |
| |75\133
| |75\133
| |<u>909.{{Overline|09}}</u>
| |<u>909.091</u>
|17
|17
|7
|7
| |
| |
|-
|-
| |
| |
| |53\94
| |53\94
| |<u>908.571…</u>
| |<u>908.571</u>
|12
|12
|5
|5
| |
| |
|-
|-
| |
| |31\55
| |31\55
| |
| |<u>907.317</u>
| |<u>907.317…</u>
|7
|7
|3
|3
| |
| |
|-
|-
|
|
|71\126
|71\126
|<u>906.382…</u>
|<u>906.383</u>
|16
|16
|7
|7
|
|
|-
|-
| |
| |40\71
| |40\71
| |
| |<u>905.660</u>
| |<u>905.660…</u>
|9
|9
|4
|4
| |
| |
|-
|-
| |
| |…
| |49\87
| |…
| |
|…
| |<u>904.615…</u>
|…
|11
|5
| |
| |
|-
|-
| |
|229\305
| |58\103
|<u>900.983</u>
| |
|51
| |<u>903.896…</u>
|25
|13
|
|6
| |
|-
|-
| |9\16
| |9\16
| |
| |<u>900.000</u>
| |
| |<u>900</u>
|2
|2
|1
|1
| |<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>
|-
|-
| |
|230\397
| |59\105
|<u>899.023</u>
| |
|51
| |<u>896.202…</u>
|26
|13
|
|7
| |
|-
|-
| |
|…
| |50\89
|…
| |
|…
| |<u>895.522…</u>
|…
|11
|
|6
| |
|-
|-
| |
| |41\73
| |41\73
| |
| |<u>894.545</u>
| |<u>894.{{Overline|54}}</u>
|9
|9
|5
|5
| |
| |
|-
|-
| |
| |32\57
| |32\57
| |
| |<u>893.023</u>
| |<u>893.023…</u>
|7
|7
|4
|4
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|-
|-
| |
| |
| |
| |<u>892.459</u>
| |
| |<u>892.459…</u>
|
|
|
|
| |
| |
|-
|-
| |
|87\155
| |
|<u>892.307</u>
|19
|11
|
|-
| |55\98
| |55\98
| |<u>891.{{Overline|891}}</u>
| |<u>891.892</u>
|12
|12
|7
|7
| |
| |
|-
|-
| |
| |23\41
| |23\41
| |
| |<u>890.323</u>
| |<u>890.323…</u>
|5
|5
|3
|3
| |Golden Terra Rubra 1/5-tone
| |Golden Terra Rubra 1/5-tone
|-
|-
|
|
|83\148
|83\148
|<u>889.285…</u>
|<u>889.286</u>
|18
|18
|11
|11
|
|
|-
|-
| |
| |
| |60\107
| |60\107
| |<u>888.{{Overline|8}}</u>
| |<u>888.889</u>
|13
|13
|8
|8
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|-
|-
| |
| |
| |
| |<u>888.643</u>
| |
|<span style="background-color: #ffffff; color: #222222; font-family: arial,sans-serif; font-size: small;">φ</span>
| |<u>888.643…</u>
|1
|
|
| |GOLDEN Terra Rubra (L/s = <span style="background-color: #ffffff; color: #222222; font-family: arial,sans-serif; font-size: small;">φ)</span>
| |GOLDEN Terra Rubra (L/s = <span style="background-color: #ffffff; color: #222222; font-family: arial,sans-serif; font-size: small;">φ)</span>
|-
|-
| |
| |37\66
| |37\66
| |
| |<u>888.000</u>
| |<u>888</u>
|8
|8
|5
|5
| |Golden Terra Rubra 1/8-tone
| |Golden Terra Rubra 1/8-tone
|-
|-
|
|
|88\157
|88\157
|<u>887.394…</u>
|<u>887.395</u>
|19
|19
|12
|12
|
|
|-
|-
| |
| |51\91
| |51\91
| |
| |<u>886.957</u>
| |<u>886.956…</u>
|11
|11
|7
|7
| |
| |
|-
|-
| |
| |65\116
| |65\116
| |
| |<u>886.364</u>
| |<u>886.{{Overline|36}}</u>
|14
|14
|9
|9
| |
| |
|-
|-
| |
| |79\141
| |79\141
| |
| |<u>885.981</u>
| |<u>885.981…</u>
|17
|17
|11
|11
| |
| |
|-
|-
| |
| |93\166
| |93\166
| |
| |<u>885.714</u>
| |<u>885.714…</u>
|20
|20
|13
|13
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|-
|-
| |14\25
| |14\25
| |
| |<u>884.211</u>
| |
| |<u>884.210…</u>
|3
|3
|2
|2
| |Golden Terra Rubra 1/3-tone
| |Golden Terra Rubra 1/3-tone
|-
|-
| |
| |117\209
| |117\209
| |
| |<u>883.019</u>
| |<u>883.018…</u>
|25
|25
|17
|17
| |
| |
|-
|-
| |
| |103\184
| |103\184
| |
| |<u>882.857</u>
| |<u>882.857…</u>
|22
|22
|15
|15
| |
| |
|-
|-
| |
| |89\159
| |89\159
| |
| |<u>882.645</u>
| |<u>882.644…</u>
|19
|19
|13
|13
| |
| |
|-
|-
| |
| |75\134
| |75\134
| |
| |<u>882.353</u>
| |<u>882.353…</u>
|16
|16
|11
|11
| |
| |
|-
|-
| |
| |61\109
| |61\109
| |
| |<u>881.928</u>
| |<u>881.927…</u>
|13
|13
|9
|9
| |
| |
|-
|-
| |
| |47\84
| |47\84
| |
| |<u>881.250</u>
| |<u>881.25</u>
|10
|10
|7
|7
| |
| |
|-
|-
|
|
|80\143
|<u>880.733…</u>
|17
|12
|
|-
| |
| |33\59
| |33\59
| |
| |<u>880.000</u>
| |<u>880</u>
|7
|7
|5
|5
| |
| |
|-
|-
|
|
|85\152
|85\152
|<u>879.310…</u>
|<u>879.310</u>
|18
|18
|13
|13
|
|
|-
|-
|
|52\93
|52\93
|
|<u>878.873</u>
|<u>878.873…</u>
|11
|11
|8
|8
|
|
|-
|-
|
|71\127
|71\127
|
|<u>878.351</u>
|<u>878.350…</u>
|15
|15
|11
|11
|
|
|-
|-
|
|90\161
|90\161
|
|<u>878.049</u>
|<u>878.048…</u>
|19
|19
|14
|14
|
|
|-
|-
|
|109\195
|109\195
|
|<u>877.852</u>
|<u>877.852…</u>
|23
|23
|17
|17
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|-
|-
| |19\34
| |19\34
| |
| |<u>876.923</u>
| |
| |<u>876.923…</u>
|4
|4
|3
|3
| |
| |
|-
|-
|
|62\111
|62\111
|
|<u>875.294</u>
|<u>875.294…</u>
|13
|13
|10
|10
|
|
|-
|-
|
|43\77
|43\77
|
|<u>874.576</u>
|<u>874.576…</u>
|9
|9
|7
|7
|
|
|-
|-
|
|67\120
|67\120
|
|<u>873.913</u>
|<u>873.913…</u>
|14
|14
|11
|11
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|-
|-
|24\43
|24\43
|
|<u>872.727</u>
|
|<u>872.{{Overline|72}}</u>
|5
|5
|4
|4
|
|
|-
|-
|
|53\95
|53\95
|
|<u>871.233</u>
|<u>871.232…</u>
|11
|11
|9
|9
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|-
|29\52
|29\52
|
|<u>870.000</u>
|
|<u>870</u>
|6
|6
|5
|5
Line 725: Line 548:
|-
|-
| |5\[[9edo|9]]
| |5\[[9edo|9]]
| |
| |<u>857.142</u>
| |
| |<u>857.142…</u>
|1
|1
|0
|0
Line 735: Line 556:
== 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 (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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