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Orwell extensions: Difference between revisions

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=== Tridecimal orwell ===
=== Tridecimal orwell ===
 
{| class="wikitable center-all left-4"
Gencom: [2 7/6; 99/98 121/120 176/175 275/273]
 
Gencom mapping: [<1 0 3 1 3 8|, <0 7 -3 8 2 -19|]
 
{| class="wikitable center-all"
|-
|-
! | ET<br>generator
! Edo<br>generators
! | [[eigenmonzo|eigenmonzo<br>(unchanged-interval]])
! [[Eigenmonzo|Eigenmonzo<br>(unchanged-interval)]]
! | subminor<br>third (¢)
! Generator (¢)
! | comments
! Comments
|-
|-
| |
|  
| | 7/6
| 7/6
| | 266.871
| 266.871
| |
|  
|-
|-
| |
|  
| | 15/11
| 15/11
| | 268.475
| 268.475
| |
|  
|-
|-
| |
|  
| | 14/11
| 14/11
| | 269.585
| 269.585
| |
|  
|-
|-
| |
|  
| | 12/11
| 12/11
| | 270.127
| 270.127
| |
|  
|-
|-
| |
|  
| | 15/14
| 15/14
| | 270.139
| 270.139
| |
|  
|-
|-
| | 7\31
| 7\31
| |
|  
| | 270.968
| 270.968
| |
|  
|-
|-
| |
|  
| | 11/9
| 11/9
| | 271.049
| 271.049
| |
|  
|-
|-
| |
|  
| | 8/7
| 8/7
| | 271.103
| 271.103
| |
|  
|-
|-
| |
|  
| | 7/5
| 7/5
| | 271.137
| 271.137
| |
|  
|-
|-
| |
|  
| | 5/4
| 5/4
| | 271.229
| 271.229
| |
|  
|-
|-
| |
|  
| | 1361367/1000000
| 1361367/1000000
| | 271.326
| 271.326
| | 7 limit least squares
| 7 limit least squares
|-
|-
| |
|  
| | 14/13
| 14/13
| | 271.418
| 271.418
| | 13 and 15 limit minimax
| 13 and 15 limit minimax
|-
|-
| | 19\84
| 19\84
| |
|  
| | 271.429
| 271.429
| |
|  
|-
|-
| |
|  
| | {{vector|0 119 -46 20 -16}}
| {{vector|0 119 -46 20 -16}}
| | 271.445
| 271.445
| | 11 limit least squares
| 11 limit least squares
|-
|-
| |
|  
| | <math>x^{10} + 2x^3 = 8</math>
| <math>x^{10} + 2x^3 = 8</math>
| | 271.508
| 271.508
| | equal beating
| equal beating
|-
|-
| |
|  
| | 16/13
| 16/13
| | 271.551
| 271.551
| |
|  
|-
|-
| |
|  
| | {{vector|0 90 -41 14}}
| {{vector|0 90 -41 14}}
| | 271.561
| 271.561
| | 9 limit least squares
| 9 limit least squares
|-
|-
| |
|  
| | 6/5
| 6/5
| | 271.564
| 271.564
| | 5 limit minimax
| 5 limit minimax
|-
|-
| |
|  
| | {{vector|0 -211 30 -47 -5 142}}
| {{vector|0 -211 30 -47 -5 142}}
| | 271.567
| 271.567
| | 13 limit least squares
| 13 limit least squares
|-
|-
| |
|  
| | {{vector|0 -236 5 -51 -3 165}}
| {{vector|0 -236 5 -51 -3 165}}
| | 271.570
| 271.570
| | 15 limit least squares
| 15 limit least squares
|-
|-
| |
|  
| | 1220703125/1033121304
| 1220703125/1033121304
| | 271.590
| 271.590
| | 5 limit least squares
| 5 limit least squares
|-
|-
| |
|  
| | 13/12
| 13/12
| | 271.593
| 271.593
| |
|  
|-
|-
| |
|  
| | 13/10
| 13/10
| | 271.612
| 271.612
| |
|  
|-
|-
| |
|  
| | 18/13
| 18/13
| | 271.618
| 271.618
| |
|  
|-
|-
| |
|  
| | 10/9
| 10/9
| | 271.623
| 271.623
| | 9 limit minimax
| 9 limit minimax
|-
|-
| |
|  
| | 15/13
| 15/13
| | 271.641
| 271.641
| |
|  
|-
|-
| | 12\53
| 12\53
| |
|  
| | 271.698
| 271.698
| |
|  
|-
|-
| |
|  
| | 4/3
| 4/3
| | 271.708
| 271.708
| |
|  
|-
|-
| |
|  
| | 13/11
| 13/11
| | 271.942
| 271.942
| |
|  
|-
|-
| |
|  
| | 16/15
| 16/15
| | 272.067
| 272.067
| |
|  
|-
|-
| |
|  
| | 9/7
| 9/7
| | 272.514
| 272.514
| |
|  
|-
|-
| | 5\22
| 5\22
| |
|  
| | 272.727
| 272.727
| |
|  
|-
|-
| |
|  
| | 11/10
| 11/10
| | 273.001
| 273.001
| |
|  
|-
|-
| |
|  
| | 11/8
| 11/8
| | 275.659
| 275.659
| |
|  
|}
|}


=== Winston ===
=== Winston ===


Gencom: [2 7/6; 66/65 99/98 105/104 121/120]
{| class="wikitable center-all left-4"
 
Gencom mapping: [{{map|1 0 3 1 3 1}}, {{map|0 7 -3 8 2 12}}]
 
{| class="wikitable center-all"
|-
|-
! | ET<br>generator
! Edo<br>generators
! | [[eigenmonzo|eigenmonzo<br>(unchanged-interval]])
! [[Eigenmonzo|Eigenmonzo<br>(unchanged-interval)]]
! | subminor<br>third (¢)
! Generator (¢)
! | comments
! Comments
|-
|-
| |
|  
| | 7/6
| 7/6
| | 266.871
| 266.871
| |
|  
|-
|-
| |
|  
| | 13/12
| 13/12
| | 267.715
| 267.715
| |
|  
|-
|-
| |
|  
| | 14/13
| 14/13
| | 267.925
| 267.925
| |
|  
|-
|-
| |
|  
| | 15/11
| 15/11
| | 268.475
| 268.475
| |
|  
|-
|-
| |
|  
| | 13/11
| 13/11
| | 268.921
| 268.921
| |
|  
|-
|-
| |
|  
| | 15/13
| 15/13
| | 269.032
| 269.032
| |
|  
|-
|-
| |
|  
| | 14/11
| 14/11
| | 269.585
| 269.585
| |
|  
|-
|-
| |
|  
| | 16/13
| 16/13
| | 270.044
| 270.044
| |
|  
|-
|-
| |
|  
| | 12/11
| 12/11
| | 270.127
| 270.127
| |
|  
|-
|-
| |
|  
| | 15/14
| 15/14
| | 270.139
| 270.139
| |
|  
|-
|-
| |
|  
| | 13/10
| 13/10
| | 270.281
| 270.281
| |
|  
|-
|-
| |
|  
| | {{vector|0 112 -67 20 -28 52}}
| {{vector|0 112 -67 20 -28 52}}
| | 270.860
| 270.860
| | 15 limit least squares
| 15 limit least squares
|-
|-
| |
|  
| | {{vector|0 118 -61 16 -26 44}}
| {{vector|0 118 -61 16 -26 44}}
| | 270.933
| 270.933
| | 13 limit least squares
| 13 limit least squares
|-
|-
| | 7\31
| 7\31
| |
|  
| | 270.968
| 270.968
| |
|  
|-
|-
| |
|  
| | 11/9
| 11/9
| | 271.049
| 271.049
| | 13 and 15 limit minimax
| 13 and 15 limit minimax
|-
|-
| |
|  
| | 8/7
| 8/7
| | 271.103
| 271.103
| |
|  
|-
|-
| |
|  
| | 7/5
| 7/5
| | 271.137
| 271.137
| |
|  
|-
|-
| |
|  
| | 5/4
| 5/4
| | 271.229
| 271.229
| |
|  
|-
|-
| |
|  
| | 1361367/1000000
| 1361367/1000000
| | 271.326
| 271.326
| | 7 limit least squares
| 7 limit least squares
|-
|-
| | 19\84
| 19\84
| |
|  
| | 271.429
| 271.429
| |
|  
|-
|-
| |
|  
| | {{vector|0 119 -46 20 -16}}
| {{vector|0 119 -46 20 -16}}
| | 271.445
| 271.445
| | 11 limit least squares
| 11 limit least squares
|-
|-
| |  
|  
| | <math>x^{10} + 2x^3 = 8</math>
| <math>x^{10} + 2x^3 = 8</math>
| | 271.508
| 271.508
| | equal beating
| equal beating
|-
|-
| |
|  
| | {{vector|0 90 -41 14}}
| {{vector|0 90 -41 14}}
| | 271.561
| 271.561
| | 9 limit least squares
| 9 limit least squares
|-
|-
| |
|  
| | 6/5
| 6/5
| | 271.564
| 271.564
| | 5 limit minimax
| 5 limit minimax
|-
|-
| |
|  
| | 1220703125/1033121304
| 1220703125/1033121304
| | 271.590
| 271.590
| | 5 limit least squares
| 5 limit least squares
|-
|-
| |
|  
| | 10/9
| 10/9
| | 271.623
| 271.623
| | 9 limit minimax
| 9 limit minimax
|-
|-
| | 12\53
| 12\53
| |
|  
| | 271.698
| 271.698
| |
|  
|-
|-
| |
|  
| | 4/3
| 4/3
| | 271.708
| 271.708
| |
|  
|-
|-
| |
|  
| | 16/15
| 16/15
| | 272.067
| 272.067
| |
|  
|-
|-
| |
|  
| | 9/7
| 9/7
| | 272.514
| 272.514
| |
|  
|-
|-
| | 5\22
| 5\22
| |
|  
| | 272.727
| 272.727
| |
|  
|-
|-
| |
|  
| | 11/10
| 11/10
| | 273.001
| 273.001
| |
|  
|-
|-
| |
|  
| | 11/8
| 11/8
| | 275.659
| 275.659
| |
|  
|-
|-
| |
|  
| | 18/13
| 18/13
| | 281.691
| 281.691
| |
|  
|}
|}


=== Blair ===
=== Blair ===


Gencom: [2 7/6; 65/64 78/77 91/90 99/98]
{| class="wikitable left-4"
 
Gencom mapping: [&lt;1 0 3 1 3 3|, &lt;0 7 -3 8 2 3|]
 
{| class="wikitable"
|-
|-
! | [[eigenmonzo|eigenmonzo<br>(unchanged-interval]])
! Edo<br>generators
! | subminor<br>third (¢)
! [[Eigenmonzo|Eigenmonzo<br>(unchanged-interval)]]
! Generator (¢)
! Comments
|-
|-
| | 15/13
|  
| | 247.741
| 15/13
| 247.741
|
|-
|-
| | 13/12
|  
| | 265.357
| 13/12
| 265.357
|
|-
|-
| | 14/13
|  
| | 265.660
| 14/13
| 265.660
|
|-
|-
| | 7/6
|  
| | 266.871
| 7/6
| 266.871
|
|-
|-
| | 15/11
|  
| | 268.475
| 15/11
| 268.475
|
|-
|-
| | 18/13
|  
| | 269.398
| 18/13
| 269.398
|
|-
|-
| | 14/11
|  
| | 269.585
| 14/11
| 269.585
|
|-
|-
| | 12/11
|  
| | 270.127
| 12/11
| 270.127
|
|-
|-
| | 15/14
|  
| | 270.139
| 15/14
| 270.139
|
|-
|-
| | 7\31
|  
| | 270.968
| 7\31
| 270.968
|
|-
|-
| | 11/9
|  
| | 271.049
| 11/9
| 271.049
|
|-
|-
| | 8/7
|  
| | 271.103
| 8/7
| 271.103
|
|-
|-
| | 7/5
|  
| | 271.137 (7, 11, 13 and 15 limit minimax)
| 7/5
| 271.137 (7, 11, 13 and 15 limit minimax)
|
|-
|-
| | 5/4
|  
| | 271.229
| 5/4
| 271.229
|
|-
|-
| | |0 148 -49 29 -19 -11&gt;
|  
| | 271.231 (15 limit least squares)
| |0 148 -49 29 -19 -11&gt;
| 271.231 (15 limit least squares)
|
|-
|-
| | |0 145 -52 25 -17 -10&gt;
|  
| | 271.261 (13 limit least squares)
| |0 145 -52 25 -17 -10&gt;
| 271.261 (13 limit least squares)
|
|-
|-
| | 1361367/1000000
|  
| | 271.326 (7 limit least squares)
| 1361367/1000000
| 271.326 (7 limit least squares)
|
|-
|-
| | 19\84
|  
| | 271.429
| 19\84
| 271.429
|
|-
|-
| | |0 119 -46 20 -16&gt;
|  
| | 271.445 (11 limit least squares)
| |0 119 -46 20 -16&gt;
| 271.445 (11 limit least squares)
|
|-
|-
| | x^10 + 2x^3 = 8
|  
| | 271.508 (equal beating)
| x^10 + 2x^3 = 8
| 271.508 (equal beating)
|
|-
|-
| | |0 90 -41 14&gt;
|  
| | 271.561 (9 limit least squares)
| |0 90 -41 14&gt;
| 271.561 (9 limit least squares)
|
|-
|-
| | 6/5
|  
| | 271.564 (5 limit minimax)
| 6/5
| 271.564 (5 limit minimax)
|
|-
|-
| | 1220703125/1033121304
|  
| | 271.590 (5 limit least squares)
| 1220703125/1033121304
| 271.590 (5 limit least squares)
|
|-
|-
| | 10/9
|  
| | 271.623 (9 limit minimax)
| 10/9
| 271.623 (9 limit minimax)
|
|-
|-
| | 12\53
|  
| | 271.698
| 12\53
| 271.698
|
|-
|-
| | 4/3
|  
| | 271.708
| 4/3
| 271.708
|
|-
|-
| | 16/15
|  
| | 272.067
| 16/15
| 272.067
|
|-
|-
| | 9/7
|  
| | 272.514
| 9/7
| 272.514
|
|-
|-
| | 5\22
|  
| | 272.727
| 5\22
| 272.727
|
|-
|-
| | 11/10
|  
| | 273.001
| 11/10
| 273.001
|
|-
|-
| | 11/8
|  
| | 275.659
| 11/8
| 275.659
|
|-
|-
| | 13/10
|  
| | 275.702
| 13/10
| 275.702
|
|-
|-
| | 16/13
|  
| | 280.176
| 16/13
| 280.176
|
|-
|-
| | 13/11
|  
| | 289.210
| 13/11
| 289.210
|
|}
|}


[[Category:Orwell]]
[[Category:Orwell]]
[[Category:Temperament extensions]]
[[Category:Temperament extensions]]
Retrieved from "https://en.xen.wiki/w/Orwell_extensions"