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

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#redirect [[7L_2s_(5/2-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
 
[[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==
{| class="wikitable"
|-
! colspan="3" |Generator
! |Generator size
! |ed16\12 (→ed4\3)
!Comments
|-
| |4\[[7ed5/2|7]]
| |
| |
| |<u>960</u>
| |''914.285…''
|-
|25\44
|
|
|<u>937.5</u>
|''909.{{Overline|09}}''
|
|-
|
|71\125
|
|<u>936.263…</u>
|''908.8''
|
|-
|
|46\81
|
|<u>935.593…</u>
|''908.641…''
|
|-
|
|67\118
|
|<u>934.883…</u>
|''908.474…''
|
|-
| |21\37
| |
| |
| |<u>933.{{Overline|3}}</u>
|''908.{{Overline|108}}''
| |
|-
|
|80\141
|
|<u>932.038…</u>
|''907.801…''
|
|-
|
|59\104
|
|<u>931.579…</u>
|''907.692…''
|
|-
|
|38\67
|
|<u>930.612…</u>
|''907.462…''
|
|-
|
|55\97
|
|<u>929.577…</u>
|''907.216…''
|
|-
|
|72\127
|
|<u>929.032…</u>
|''907.086…''
|
|-
|
|89\157
|
|<u>928.695…</u>
|''907.006…''
|
|-
| |17\30
| |
| |
| |<u>927.{{Overline|27}}</u>
|''906.{{Overline|6}}''
| |L/s = 4
|-
|
|115\203
|
|<u>926.174…</u>
|''906.403…''
|
|-
|
|98\173
|
|<u>925.984…</u>
|''906.358…''
|
|-
|
|81\143
|
|<u>925.714…</u>
|''906.293…''
|
|-
|
|64\113
|
|<u>925.301…</u>
|''906.194…''
|
|-
|
|47\83
|
|<u>924.591…</u>
|''906.024…''
|
|-
| |
| |30\53
| |
| |<u>923.076…</u>
|''905.660…''
| |
|-
|
|
|73\129
|<u>922.105…</u>
|''905.426…''
|
|-
| |
| |43\76
| |
| |<u>921.428…</u>
|''905.263…''
| |
|-
| |
| |56\99
| |
| |<u>920.547…</u>
|''905.{{Overline|05}}''
| |
|-
| |
| |69\122
| |
| |<u>920</u>
|''904.918…''
| |
|-
| |
| |82\145
| |
| |<u>919.626…</u>
|''904.827…''
| |
|-
| |
| |95\168
| |
| |<u>919.354…</u>
|''904.761…''
| |
|-
| |
| |
| |
| |<u>919.340…</u>
|''904.758…''
| |L/s = π
|-
| |
| |108\191
| |
| |<u>919.148…</u>
|''904.712…''
| |
|-
| |
| |121\214
| |
| |<u>918.987…</u>
|''904.672…''
| |28;9 Superdiatonic 1/28-tone
|-
| |
| |134\237
| |
| |<u>918.857…</u>
|''904.642…''
| |
|-
| |13\23
| |
| |
| |<u>917.647…</u>
|''904.347…''
| |L/s = 4
|-
| |
| |100\177
| |
| |<u>916.030…</u>
|''903.954…''
| |
|-
| |
| |87\154
| |
| |<u>915.789…</u>
|''903.896…''
| |
|-
| |
| |74\131
| |
| |<u>915.463…</u>
|''903.816…''
| |17;6 1/17-tone
|-
| |
| |61\108
| |
| |<u>915</u>
|''903.{{Overline|703}}''
| |14;5 1/14-tone
|-
| |
| |48\85
| |
| |<u>914.286…</u>
|''903.529…''
| |11;4 1/11-tone
|-
| |
| |
| |
| |<u>913.820…</u>
|''903.415…''
| |L/s = e
|-
| |
| |35\62
| |
| |<u>913.043…</u>
|''903.225…''
| |8;3 1/8-tone
|-
| |
| |
| |
| |<u>912.286…</u>
|''903.040…''
| |Split φ superdiatonic relation (34;13 - 55;21 - 89;34 - 144;55 - 233;89 - 377;144 - 610;233..)
|-
| |
| |
| |57\101
| |<u>912</u>
|''902.970…''
| |13;5 Superdiatonic 1/13-tone
|-
|
|
|79\140
|<u>911.538…</u>
|''902.857…''
|
|-
| |
| |22\39
| |
| |<u>910.344…</u>
|''902.564…''
| |Terra Rubra 1/5-tone
|-
| |
| |
| |75\133
| |<u>909.{{Overline|09}}</u>
|''902.255…''
| |17;7 Superdiatonic 1/17-tone
|-
| |
| |
| |53\94
| |<u>908.571…</u>
|''902.127…''
| |
|-
| |
| |31\55
| |
| |<u>907.317…</u>
|''901.{{Overline|81}}''
| |7;3 Superdiatonic 1/7-tone
|-
|
|
|71\126
|<u>906.382…</u>
|''901.587…''
|
|-
| |
| |40\71
| |
| |<u>905.660…</u>
|''901.408…''
| |9;4 Superdiatonic 1/9-tone
|-
| |
| |49\87
| |
| |<u>904.615…</u>
|''901.149…''
| |11;5 Superdiatonic 1/11-tone
|-
| |
| |58\103
| |
| |<u>903.896…</u>
|''900.970…''
| |13;6 Superdiatonic 1/13-tone
|-
|
|67\119
|
|<u>903.370…</u>
|''900.840…''
|
|-
|
|76\135
|
|<u>902.970…</u>
|''900.{{Overline|740}}''
|
|-
|
|85\151
|
|<u>902.654…</u>
|''900.662…''
|
|-
|
|94\167
|
|<u>902.4</u>
|''900.598…''
|
|-
|
|103\183
|
|<u>902.189…</u>
|''900.564…''
|
|-
|
|112\199
|
|<u>902.013…</u>
|''900.502…''
|
|-
|
|121\215
|
|<u>901.863…</u>
|''900.465…''
|
|-
| |9\16
| |
| |
| |<u>900</u>
|''900''
| |<span style="display: block; text-align: left;">'''[BOUNDARY OF PROPRIETY: smaller generators are strictly proper]'''</span>
|-
|
|230\409
|
|<u>899.022…</u>
|''899.755…''
|
|-
|
|221\393
|
|<u>898.983…</u>
|''899.745…''
|
|-
|
|212\377
|
|<u>898.939…</u>
|''899.734…''
|
|-
|
|203\361
|
|<u>898.892…</u>
|''899.722…''
|
|-
|
|194\345
|
|<u>898.841…</u>
|''899.710…''
|
|-
|
|185\329
|
|<u>898.785…</u>
|''899.696…''
|
|-
|
|176\313
|
|<u>898.723…</u>
|''899.680…''
|
|-
|
|167\297
|
|<u>898.654…</u>
|''899.663…''
|
|-
|
|158\281
|
|<u>898.578…</u>
|''899.644…''
|
|-
|
|149\265
|
|<u>898.492…</u>
|''899.622…''
|
|-
|
|140\249
|
|<u>898.395…</u>
|''899.598…''
|
|-
|
|131\233
|
|<u>898.285…</u>
|''899.570…''
|
|-
|
|122\217
|
|<u>898.159…</u>
|''899.539…''
|
|-
|
|113\201
|
|<u>898.013…</u>
|''899.502…''
|
|-
|
|104\185
|
|<u>897.841…</u>
|''899.459…''
|
|-
|
|95\169
|
|<u>897.637…</u>
|''899.408…''
|
|-
|
|86\153
|
|<u>897.391…</u>
|''899.346…''
|
|-
|
|77\137
|
|<u>897.087…</u>
|''899.270…''
|
|-
|
|68\121
|
|<u>896.703…</u>
|''899.173…''
|
|-
| |
| |59\105
| |
| |<u>896.202…</u>
|''899.047…''
| |Terra Rubra 1/13-tone
|-
| |
| |50\89
| |
| |<u>895.522…</u>
|''898.876…''
| |Terra Rubra 1/11-tone
|-
| |
| |41\73
| |
| |<u>894.{{Overline|54}}</u>
|''898.630…''
| |Terra Rubra 1/9-tone
|-
| |
| |32\57
| |
| |<u>893.023…</u>
|''898.245…''
| |Terra Rubra 1/7-tone <span style="font-size: 12.8000001907349px;">(the 'Commatic' version of Terra Rubra, because its high accuracy of the 16/15 interval, the note '2b')</span>
|-
| |
| |
| |
| |<u>892.459…</u>
|''898.102…''
| |
|-
| |
| |
| |55\98
| |<u>891.{{Overline|891}}</u>
|''897.959…''
| |
|-
| |
| |
| |78\139
| |<u>891.428…</u>
|''897.841…''
| |Terra Rubra 1/17-tone
|-
| |
| |23\41
| |
| |<u>890.323…</u>
|''897.560…''
| |5;3 Golden Terra Rubra 1/5-tone
|-
|
|
|83\148
|<u>889.285…</u>
|''897.{{Overline|297}}''
|
|-
| |
| |
| |60\107
| |<u>888.{{Overline|8}}</u>
|''897.196…''
| |13;8 Golden Terra Rubra 1/13-tone
|-
| |
| |
| |
| |<u>888.643…</u>
|''897.133…''
| |GOLDEN Terra Rubra (L/s = <span style="background-color: #ffffff; color: #222222; font-family: arial,sans-serif; font-size: small;">φ)</span>
|-
| |
| |
| |97\173
| |<u>888.549…</u>
|''897.109…''
| |21;13 Golden Terra Rubra 1/21-tone
|-
| |
| |37\66
| |
| |<u>888</u>
|''896.{{Overline|96}}''
| |8;5 Golden Terra Rubra 1/8-tone
|-
|
|
|88\157
|<u>887.394…</u>
|''896.815…''
|
|-
| |
| |51\91
| |
| |<u>886.956…</u>
|''896.703…''
| |11;7 Superdiatonic 1/11-tone
|-
| |
| |
| |
| |<u>886.933…</u>
|''896.697…''
| |
|-
| |
| |65\116
| |
| |<u>886.{{Overline|36}}</u>
|''896.551…''
| |14;9 Superdiatonic 1/14-tone
|-
| |
| |79\141
| |
| |<u>885.981…</u>
|''896.453…''
| |17;11 Superdiatonic 1/17-tone
|-
| |
| |93\166
| |
| |<u>885.714…</u>
|''896.385…''
| |
|-
| |
| |107\191
| |
| |<u>885.517…</u>
|''896.335…''
| |
|-
| |
| |121\216
| |
| |<u>885.365…</u>
|''896.{{Overline|296}}''
| |26;17 Superdiatonic 1/26-tone
|-
| |
| |135\241
| |
| |<u>885.245…</u>
|''896.265…''
| |29;19 Superdiatonic 1/29-tone
|-
| |14\25
| |
| |
| |<u>884.210…</u>
|''896''
| |3;2 Golden Terra Rubra 1/3-tone
|-
| |
| |145\259
| |
| |<u>883.248…</u>
|''895.752…''
| |31;21 Superdiatonic 1/31-tone
|-
| |
| |131\234
| |
| |<u>883.146…</u>
|''895.726…''
| |28;19 Superdiatonic 1/28-tone
|-
| |
| |117\209
| |
| |<u>883.018…</u>
|''895.693…''
| |
|-
| |
| |103\184
| |
| |<u>882.857…</u>
|''895.652…''
| |
|-
| |
| |89\159
| |
| |<u>882.644…</u>
|''895.579…''
| |
|-
| |
| |75\134
| |
| |<u>882.353…</u>
|''895.522…''
| |
|-
| |
| |61\109
| |
| |<u>881.927…</u>
|''895.412…''
| |
|-
| |
| |47\84
| |
| |<u>881.25</u>
|''895.238…''
| |
|-
|
|
|80\143
|<u>880.733…</u>
|''895.104…''
|
|-
| |
| |33\59
| |
| |<u>880</u>
|''894.915…''
| |
|-
|
|
|85\152
|<u>879.310…</u>
|''894.736…''
|
|-
|
|52\93
|
|<u>878.873…</u>
|''894.623…''
|
|-
|
|71\127
|
|<u>878.350…</u>
|''894.488…''
|
|-
| |19\34
| |
| |
| |<u>876.923…</u>
|''894.117…''
| |
|-
|
|62\111
|
|<u>875.294…</u>
|''893.{{Overline|693}}''
|
|-
|
|43\77
|
|<u>874.576…</u>
|''893.506…''
|
|-
|
|67\120
|
|<u>873.913…</u>
|''893.{{Overline|3}}''
|
|-
|24\43
|
|
|<u>872.{{Overline|72}}</u>
|''893.023…''
|
|-
|
|53\95
|
|<u>871.232…</u>
|''892.631…''
|
|-
|29\52
|
|
|<u>870</u>
|''892.307…''
|
|-
| |5\[[9edo|9]]
| |
| |
| |<u>857.142…</u>
|''888.{{Overline|8}}''
| |
|}
 
== See also ==
[[7L 2s (5/2-equivalent)]] - idealized meantone tuning
 
[[7L 2s (18/7-equivalent)]] - idealized Archytas tuning

Revision as of 15:05, 24 May 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 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

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