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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
! |ed16\12 (→ed4\3)
!L
!L
!s
!s
Line 38: Line 38:
|-
|-
| |4\[[7ed5/2|7]]
| |4\[[7ed5/2|7]]
| |
| |<u>960.000</u>
| |
| |<u>960</u>
| |''914.285…''
|1
|1
|0
|0
Line 47: Line 44:
|-
|-
|25\44
|25\44
|
|<u>937.500</u>
|
|<u>937.5</u>
|''909.{{Overline|09}}''
|6
|6
|1
|1
|
|
|-
|-
|
|71\129
|71\125
|<u>936.263</u>
|
|<u>936.263…</u>
|''908.8''
|17
|17
|3
|3
|
|
|-
|-
|
|46\81
|46\81
|
|<u>935.593</u>
|<u>935.593…</u>
|''908.641…''
|11
|11
|2
|2
|
|
|-
|-
|
|67\118
|67\118
|
|<u>934.884</u>
|<u>934.883…</u>
|''908.474…''
|16
|16
|3
|3
Line 83: Line 68:
|-
|-
| |21\37
| |21\37
| |
| |<u>933.333</u>
| |
| |<u>933.{{Overline|3}}</u>
|''908.{{Overline|108}}''
|5
|5
|1
|1
| |
| |
|-
|-
|
|80\141
|80\141
|
|<u>932.039</u>
|<u>932.038…</u>
|''907.801…''
|19
|19
|4
|4
|
|
|-
|-
|
|59\104
|59\104
|
|<u>931.579</u>
|<u>931.579…</u>
|''907.692…''
|14
|14
|3
|3
|
|
|-
|-
|
|38\67
|38\67
|
|<u>930.612</u>
|<u>930.612…</u>
|''907.462…''
|9
|9
|2
|2
|
|
|-
|-
|
|55\97
|55\97
|
|<u>929.577</u>
|<u>929.577…</u>
|''907.216…''
|13
|13
|3
|3
|
|
|-
|-
|
|72\127
|72\127
|
|<u>929.032</u>
|<u>929.032…</u>
|''907.086…''
|17
|17
|4
|4
|
|
|-
|-
|
|89\157
|89\157
|
|<u>928.696</u>
|<u>928.695…</u>
|''907.006…''
|21
|21
|5
|5
Line 146: Line 110:
|-
|-
| |17\30
| |17\30
| |
| |<u>927.273</u>
| |
| |<u>927.{{Overline|27}}</u>
|''906.{{Overline|6}}''
|4
|4
|1
|1
| |
| |
|-
|-
|
|115\203
|115\203
|
|<u>926.174</u>
|<u>926.174…</u>
|''906.403…''
|27
|27
|7
|7
|
|
|-
|-
|
|98\173
|98\173
|
|<u>925.984</u>
|<u>925.984…</u>
|''906.358…''
|23
|23
|6
|6
|
|
|-
|-
|
|81\143
|81\143
|
|<u>925.714</u>
|<u>925.714…</u>
|''906.293…''
|19
|19
|5
|5
|
|
|-
|-
|
|64\113
|64\113
|
|<u>925.301</u>
|<u>925.301…</u>
|''906.194…''
|15
|15
|4
|4
|
|
|-
|-
|
|47\83
|47\83
|
|<u>924.590</u>
|<u>924.591…</u>
|''906.024…''
|11
|11
|3
|3
|
|
|-
|-
| |
| |30\53
| |30\53
| |
| |<u>923.077</u>
| |<u>923.076…</u>
|''905.660…''
|7
|7
|2
|2
| |
| |
|-
|-
|
|
|73\129
|73\129
|<u>922.105…</u>
|<u>922.105</u>
|''905.426…''
|17
|17
|5
|5
|
|
|-
|-
| |
| |43\76
| |43\76
| |
| |<u>921.429</u>
| |<u>921.428…</u>
|''905.263…''
|10
|10
|3
|3
| |
| |
|-
|-
| |
| |56\99
| |56\99
| |
| |<u>920.548</u>
| |<u>920.547…</u>
|''905.{{Overline|05}}''
|13
|13
|4
|4
| |
| |
|-
|-
| |
| |69\122
| |69\122
| |
| |<u>920.000</u>
| |<u>920</u>
|''904.918…''
|16
|16
|5
|5
| |
| |
|-
|-
| |
| |82\145
| |82\145
| |
| |<u>919.626</u>
| |<u>919.626…</u>
|''904.827…''
|19
|19
|6
|6
| |
| |
|-
|-
| |
| |95\168
| |95\168
| |
| |<u>919.355</u>
| |<u>919.354…</u>
|''904.761…''
|22
|22
|7
|7
Line 263: Line 188:
|-
|-
| |
| |
| |<u>919.340</u>
|π
|1
| |
| |
| |
| |<u>919.340…</u>
|''904.758…''
|
|
| |L/s = π
|-
|-
| |
| |108\191
| |108\191
| |
| |<u>919.149</u>
| |<u>919.148…</u>
|''904.712…''
|25
|25
|8
|8
| |
| |
|-
|-
| |
| |121\214
| |121\214
| |
| |<u>918.987</u>
| |<u>918.987…</u>
|''904.672…''
|28
|28
|9
|9
| |
|-
| |
| |134\237
| |
| |<u>918.857…</u>
|''904.642…''
|31
|10
| |
| |
|-
|-
| |13\23
| |13\23
| |
| |<u>917.647</u>
| |
| |<u>917.647…</u>
|''904.347…''
|3
|3
|1
|1
| |
| |
|-
|-
| |
| |100\177
| |100\177
| |
| |<u>916.031</u>
| |<u>916.030…</u>
|''903.954…''
|23
|23
|8
|8
| |
| |
|-
|-
| |
| |87\154
| |87\154
| |
| |<u>915.789</u>
| |<u>915.789…</u>
|''903.896…''
|20
|20
|7
|7
| |
| |
|-
|-
| |
| |74\131
| |74\131
| |
| |<u>915.464</u>
| |<u>915.463…</u>
|''903.816…''
|17
|17
|6
|6
| |
| |
|-
|-
| |
| |61\108
| |61\108
| |
| |<u>915.000</u>
| |<u>915</u>
|''903.{{Overline|703}}''
|14
|14
|5
|5
| |
| |
|-
|-
| |
| |48\85
| |48\85
| |
| |<u>914.286</u>
| |<u>914.286…</u>
|''903.529…''
|11
|11
|4
|4
Line 353: Line 242:
|-
|-
| |
| |
| |
| |<u>913.821</u>
| |
|e
| |<u>913.820…</u>
|1
|''903.415…''
|
|
| |L/s = e
| |L/s = e
|-
|-
| |
| |35\62
| |35\62
| |
| |<u>913.043</u>
| |<u>913.043…</u>
|''903.225…''
|8
|8
|3
|3
Line 371: Line 254:
|-
|-
| |
| |
| |
| |<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
|''903.040…''
| |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>
|''902.970…''
|13
|13
|5
|5
| |
| |
|-
|-
|
|
|79\140
|79\140
|<u>911.538…</u>
|<u>911.538</u>
|''902.857…''
|18
|18
|7
|7
|
|
|-
|-
| |
| |22\39
| |22\39
| |
| |<u>910.345</u>
| |<u>910.344…</u>
|''902.564…''
|5
|5
|2
|2
| |
| |
|-
|-
| |
| |
| |75\133
| |75\133
| |<u>909.{{Overline|09}}</u>
| |<u>909.091</u>
|''902.255…''
|17
|17
|7
|7
| |
| |
|-
|-
| |
| |
| |53\94
| |53\94
| |<u>908.571…</u>
| |<u>908.571</u>
|''902.127…''
|12
|12
|5
|5
| |
| |
|-
|-
| |
| |31\55
| |31\55
| |
| |<u>907.317</u>
| |<u>907.317…</u>
|''901.{{Overline|81}}''
|7
|7
|3
|3
| |
| |
|-
|-
|
|
|71\126
|71\126
|<u>906.382…</u>
|<u>906.383</u>
|''901.587…''
|16
|16
|7
|7
|
|
|-
|-
| |
| |40\71
| |40\71
| |
| |<u>905.660</u>
| |<u>905.660…</u>
|''901.408…''
|9
|9
|4
|4
| |
| |
|-
|-
| |
| |…
| |49\87
| |…
| |
|…
| |<u>904.615…</u>
|…
|''901.149…''
|11
|5
| |
| |
|-
|-
| |
|229\305
| |58\103
|<u>900.983</u>
| |
|51
| |<u>903.896…</u>
|25
|''900.970…''
|
|13
|6
| |
|-
|-
| |9\16
| |9\16
| |
| |<u>900.000</u>
| |
| |<u>900</u>
|''900''
|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
|''899.047…''
|
|13
|7
| |
|-
|-
| |
|…
| |50\89
|…
| |
|…
| |<u>895.522…</u>
|…
|''898.876…''
|
|11
|6
| |
|-
|-
| |
| |41\73
| |41\73
| |
| |<u>894.545</u>
| |<u>894.{{Overline|54}}</u>
|''898.630…''
|9
|9
|5
|5
| |
| |
|-
|-
| |
| |32\57
| |32\57
| |
| |<u>893.023</u>
| |<u>893.023…</u>
|''898.245…''
|7
|7
|4
|4
Line 515: Line 350:
|-
|-
| |
| |
| |
| |<u>892.459</u>
| |
| |<u>892.459…</u>
|''898.102…''
|
|
|
|
| |
| |
|-
|-
| |
|87\155
| |
|<u>892.307</u>
|19
|11
|
|-
| |55\98
| |55\98
| |<u>891.{{Overline|891}}</u>
| |<u>891.892</u>
|''897.959…''
|12
|12
|7
|7
| |
| |
|-
|-
| |
| |23\41
| |23\41
| |
| |<u>890.323</u>
| |<u>890.323…</u>
|''897.560…''
|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>
|''897.{{Overline|297}}''
|18
|18
|11
|11
|
|
|-
|-
| |
| |
| |60\107
| |60\107
| |<u>888.{{Overline|8}}</u>
| |<u>888.889</u>
|''897.196…''
|13
|13
|8
|8
Line 560: Line 386:
|-
|-
| |
| |
| |
| |<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
|''897.133…''
|
|
| |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>
|''896.{{Overline|96}}''
|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>
|''896.815…''
|19
|19
|12
|12
|
|
|-
|-
| |
| |51\91
| |51\91
| |
| |<u>886.957</u>
| |<u>886.956…</u>
|''896.703…''
|11
|11
|7
|7
| |
| |
|-
|-
| |
| |65\116
| |65\116
| |
| |<u>886.364</u>
| |<u>886.{{Overline|36}}</u>
|''896.551…''
|14
|14
|9
|9
| |
| |
|-
|-
| |
| |79\141
| |79\141
| |
| |<u>885.981</u>
| |<u>885.981…</u>
|''896.453…''
|17
|17
|11
|11
| |
| |
|-
|-
| |
| |93\166
| |93\166
| |
| |<u>885.714</u>
| |<u>885.714…</u>
|''896.385…''
|20
|20
|13
|13
Line 623: Line 428:
|-
|-
| |14\25
| |14\25
| |
| |<u>884.211</u>
| |
| |<u>884.210…</u>
|''896''
|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>
|''895.693…''
|25
|25
|17
|17
| |
| |
|-
|-
| |
| |103\184
| |103\184
| |
| |<u>882.857</u>
| |<u>882.857…</u>
|''895.652…''
|22
|22
|15
|15
| |
| |
|-
|-
| |
| |89\159
| |89\159
| |
| |<u>882.645</u>
| |<u>882.644…</u>
|''895.579…''
|19
|19
|13
|13
| |
| |
|-
|-
| |
| |75\134
| |75\134
| |
| |<u>882.353</u>
| |<u>882.353…</u>
|''895.522…''
|16
|16
|11
|11
| |
| |
|-
|-
| |
| |61\109
| |61\109
| |
| |<u>881.928</u>
| |<u>881.927…</u>
|''895.412…''
|13
|13
|9
|9
| |
| |
|-
|-
| |
| |47\84
| |47\84
| |
| |<u>881.250</u>
| |<u>881.25</u>
|''895.238…''
|10
|10
|7
|7
| |
| |
|-
|-
|
|
|80\143
|<u>880.733…</u>
|''895.104…''
|17
|12
|
|-
| |
| |33\59
| |33\59
| |
| |<u>880.000</u>
| |<u>880</u>
|''894.915…''
|7
|7
|5
|5
| |
| |
|-
|-
|
|
|85\152
|85\152
|<u>879.310…</u>
|<u>879.310</u>
|''894.736…''
|18
|18
|13
|13
|
|
|-
|-
|
|52\93
|52\93
|
|<u>878.873</u>
|<u>878.873…</u>
|''894.623…''
|11
|11
|8
|8
|
|
|-
|-
|
|71\127
|71\127
|
|<u>878.351</u>
|<u>878.350…</u>
|''894.488…''
|15
|15
|11
|11
|
|
|-
|-
|
|90\161
|90\161
|
|<u>878.049</u>
|<u>878.048…</u>
|''894.409…''
|19
|19
|14
|14
|
|
|-
|-
|
|109\195
|109\195
|
|<u>877.852</u>
|<u>877.852…</u>
|''894.358…''
|23
|23
|17
|17
Line 749: Line 506:
|-
|-
| |19\34
| |19\34
| |
| |<u>876.923</u>
| |
| |<u>876.923…</u>
|''894.117…''
|4
|4
|3
|3
| |
| |
|-
|-
|
|62\111
|62\111
|
|<u>875.294</u>
|<u>875.294…</u>
|''893.{{Overline|693}}''
|13
|13
|10
|10
|
|
|-
|-
|
|43\77
|43\77
|
|<u>874.576</u>
|<u>874.576…</u>
|''893.506…''
|9
|9
|7
|7
|
|
|-
|-
|
|67\120
|67\120
|
|<u>873.913</u>
|<u>873.913…</u>
|''893.{{Overline|3}}''
|14
|14
|11
|11
Line 785: Line 530:
|-
|-
|24\43
|24\43
|
|<u>872.727</u>
|
|<u>872.{{Overline|72}}</u>
|''893.023…''
|5
|5
|4
|4
|
|
|-
|-
|
|53\95
|53\95
|
|<u>871.233</u>
|<u>871.232…</u>
|''892.631…''
|11
|11
|9
|9
Line 803: Line 542:
|-
|-
|29\52
|29\52
|
|<u>870.000</u>
|
|<u>870</u>
|''892.307…''
|6
|6
|5
|5
Line 812: Line 548:
|-
|-
| |5\[[9edo|9]]
| |5\[[9edo|9]]
| |
| |<u>857.142</u>
| |
| |<u>857.142…</u>
|''888.{{Overline|8}}''
|1
|1
|0
|0
Line 823: 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
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