Xenharmonic Wiki

Magic extensions: Difference between revisions

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==Tuning spectra==
[[Magic]] has various competing [[extension]]s to the 11- and 13-limit.


== Tuning spectra ==
=== Magic ===
=== Magic ===
 
{| class="wikitable center-all left-4"
Gencom: [2 5/4; 100/99 105/104 144/143 196/195]
 
Gencom mapping: [{{map|1 0 2 -1 6 -2}}, {{map|0 5 1 12 -8 18}}]
 
{| class="wikitable center-all"
|-
|-
! | ET<br>generator
! Edo<br>generator
! | [[eigenmonzo|eigenmonzo<br>(unchanged-interval]])
! [[Eigenmonzo|Eigenmonzo<br>(unchanged-interval)]]
! | major<br>third (¢)
! Generator (¢)
! | comments
! Comments
|-
|-
| |
|  
| | 14/13
| 14/13
| | 378.617
| 378.617
| |
|  
|-
|-
| |
|  
| | 6/5
| 6/5
| | 378.910
| 378.910
| |
|  
|-
|-
| | 6\19
| 6\19
| |
|  
| | 378.947
| 378.947
| |
|  
|-
|-
| |
|  
| | 15/13
| 15/13
| | 379.355
| 379.355
| |
|  
|-
|-
| |
|  
| | 18/13
| 18/13
| | 379.577
| 379.577
| |
|  
|-
|-
| |
|  
| | 13/10
| 13/10
| | 379.660
| 379.660
| |
|  
|-
|-
| |
|  
| | 10/9
| 10/9
| | 379.733
| 379.733
| |
|  
|-
|-
| |
|  
| | 13/12
| 13/12
| | 379.890
| 379.890
| |
|  
|-
|-
| |
|  
| | 27/20
| 27/20
| | 379.968
| 379.968
| | 5 limit least squares
| 5 limit least squares
|-
|-
| | 19\60
| 19\60
| |
|  
| | 380.000
| 380.000
| |
|  
|-
|-
| |
|  
| | 16/13
| 16/13
| | 380.029
| 380.029
| |
|  
|-
|-
| |
|  
| | 15/14
| 15/14
| | 380.093
| 380.093
| |
|  
|-
|-
| | 32\101
| 32\101
| |
|  
| | 380.198
| 380.198
| |
|  
|-
|-
| |
|  
| | 7/5
| 7/5
| | 380.228
| 380.228
| |
|  
|-
|-
| |
|  
| | 13/11
| 13/11
| | 380.354
| 380.354
| | 13 and 15 limit minimax
| 13 and 15 limit minimax
|-
|-
| |
|  
| | {{vector|0 56 -31 46 -94 88}}
| {{vector|0 56 -31 46 -94 88}}
| | 380.377
| 380.377
| | 13 limit least squares
| 13 limit least squares
|-
|-
| |
|  
| | {{vector|0 36 -23 32}}
| {{vector|0 36 -23 32}}
| | 380.384
| 380.384
| | 9 limit least squares
| 9 limit least squares
|-
|-
| |
|  
| | {{vector|0 58 -29 52 -108 100}}
| {{vector|0 58 -29 52 -108 100}}
| | 380.389
| 380.389
| | 15 limit least squares
| 15 limit least squares
|-
|-
| |
|  
| | 4/3
| 4/3
| | 380.391
| 380.391
| | 5, 7 and 9 limit minimax
| 5, 7 and 9 limit minimax
|-
|-
| | 13\41
| 13\41
| |
|  
| | 380.488
| 380.488
| |
|  
|-
|-
| |
|  
| | {{vector|0 1 -7 15}}
| {{vector|0 1 -7 15}}
| | 380.506
| 380.506
| | 7 limit least squares
| 7 limit least squares
|-
|-
| |
|  
| | 11/9
| 11/9
| | 380.700
| 380.700
| | 11 limit minimax
| 11 limit minimax
|-
|-
| |
|  
| | {{vector|0 85 -14 52 -68}}
| {{vector|0 85 -14 52 -68}}
| | 380.714
| 380.714
| | 11 limit least squares
| 11 limit least squares
|-
|-
| |
|  
| | 8/7
| 8/7
| | 380.735
| 380.735
| |
|  
|-
|-
| | 33\104
| 33\104
| |
|  
| | 380.769
| 380.769
| |
|  
|-
|-
| |
|  
| | 12/11
| 12/11
| | 380.818
| 380.818
| |
|  
|-
|-
| |
|  
| | 14/11
| 14/11
| | 380.875
| 380.875
| |
|  
|-
|-
| | 20\63
| 20\63
| |
|  
| | 380.952
| 380.952
| |
|  
|-
|-
| |
|  
| | 7/6
| 7/6
| | 380.982
| 380.982
| |
|  
|-
|-
| |
|  
| | 11/8
| 11/8
| | 381.085
| 381.085
| |
|  
|-
|-
| |
|  
| | 15/11
| 15/11
| | 381.211
| 381.211
| |
|  
|-
|-
| |
|  
| | 16/15
| 16/15
| | 381.378
| 381.378
| |
|  
|-
|-
| |
|  
| | 11/10
| 11/10
| | 381.666
| 381.666
| |
|  
|-
|-
| | 7\22
| 7\22
| |
|  
| | 381.818
| 381.818
| |
|  
|-
|-
| |
|  
| | 9/7
| 9/7
| | 382.458
| 382.458
| |
|  
|-
|-
| |
|  
| | 5/4
| 5/4
| | 386.314
| 386.314
| |
|  
|}
|}


=== Necromancy ===
=== Necromancy ===
 
{| class="wikitable center-all left-4"
Gencom: [2 5/4; 100/99 225/224 245/243 275/273]
 
Gencom mapping: [{{map|1 0 2 -1 6 11}}, {{map|0 5 1 12 -8 -23}}]
 
{| class="wikitable center-all"
|-
|-
! | ET<br>generator
! Edo<br>generator
! | eigenmonzo<br>(unchanged-interval)
! Eigenmonzo<br>(unchanged-interval)
! | major<br>third (¢)
! Generator (¢)
! | comments
! Comments
|-
|-
| |
|  
| | 6/5
| 6/5
| | 378.910
| 378.910
| |
|  
|-
|-
| | 6\19
| 6\19
| |
|  
| | 378.947
| 378.947
| |
|  
|-
|-
| |
|  
| | 10/9
| 10/9
| | 379.733
| 379.733
| |
|  
|-
|-
| |
|  
| | 27/20
| 27/20
| | 379.968
| 379.968
| | 5 limit least squares
| 5 limit least squares
|-
|-
| | 19\60
| 19\60
| |
|  
| | 380.000
| 380.000
| |
|  
|-
|-
| |
|  
| | 15/14
| 15/14
| | 380.093
| 380.093
| |
|  
|-
|-
| | 32\101
| 32\101
| |
|  
| | 380.198
| 380.198
| |
|  
|-
|-
| |
|  
| | 7/5
| 7/5
| | 380.228
| 380.228
| |
|  
|-
|-
| |
|  
| | {{vector|0 36 -23 32}}
| {{vector|0 36 -23 32}}
| | 380.384
| 380.384
| | 9 limit least squares
| 9 limit least squares
|-
|-
| |
|  
| | 4/3
| 4/3
| | 380.391
| 380.391
| | 5, 7 and 9 limit minimax
| 5, 7 and 9 limit minimax
|-
|-
| | 13\41
| 13\41
| |
|  
| | 380.488
| 380.488
| |
|  
|-
|-
| |
|  
| | {{vector|0 1 -7 15}}
| {{vector|0 1 -7 15}}
| | 380.506
| 380.506
| | 7 limit least squares
| 7 limit least squares
|-
|-
| |
|  
| | 11/9
| 11/9
| | 380.700
| 380.700
| | 11 limit minimax
| 11 limit minimax
|-
|-
| |
|  
| | 18/13
| 18/13
| | 380.709
| 380.709
| | 13 and 15 limit minimax
| 13 and 15 limit minimax
|-
|-
| |
|  
| | {{vector|0 85 -14 52 -68}}
| {{vector|0 85 -14 52 -68}}
| | 380.714
| 380.714
| | 11 limit least squares
| 11 limit least squares
|-
|-
| |
|  
| | 13/11
| 13/11
| | 380.719
| 380.719
| |
|  
|-
|-
| |
|  
| | 8/7
| 8/7
| | 380.735
| 380.735
| |
|  
|-
|-
| |
|  
| | 13/12
| 13/12
| | 380.765
| 380.765
| |
|  
|-
|-
| | 33\104
| 33\104
| |
|  
| | 380.769
| 380.769
| |
|  
|-
|-
| |
|  
| | {{vector|0 -179 -10 -87 53 158}}
| {{vector|0 -179 -10 -87 53 158}}
| | 380.785
| 380.785
| | 13 limit least squares
| 13 limit least squares
|-
|-
| |
|  
| | 14/13
| 14/13
| | 380.809
| 380.809
| |
|  
|-
|-
| |
|  
| | {{vector|0 -222 -53 -93 67 187}}
| {{vector|0 -222 -53 -93 67 187}}
| | 380.817
| 380.817
| | 15 limit least squares
| 15 limit least squares
|-
|-
| |
|  
| | 12/11
| 12/11
| | 380.818
| 380.818
| |
|  
|-
|-
| |
|  
| | 16/13
| 16/13
| | 380.847
| 380.847
| |
|  
|-
|-
| |
|  
| | 14/11
| 14/11
| | 380.875
| 380.875
| |
|  
|-
|-
| | 20\63
| 20\63
| |
|  
| | 380.952
| 380.952
| |
|  
|-
|-
| |
|  
| | 15/13
| 15/13
| | 380.957
| 380.957
| |
|  
|-
|-
| |
|  
| | 7/6
| 7/6
| | 380.982
| 380.982
| |
|  
|-
|-
| |
|  
| | 13/10
| 13/10
| | 381.074
| 381.074
| |
|  
|-
|-
| |
|  
| | 11/8
| 11/8
| | 381.085
| 381.085
| |
|  
|-
|-
| |
|  
| | 15/11
| 15/11
| | 381.211
| 381.211
| |
|  
|-
|-
| |
|  
| | 16/15
| 16/15
| | 381.378
| 381.378
| |
|  
|-
|-
| |
|  
| | 11/10
| 11/10
| | 381.666
| 381.666
| |
|  
|-
|-
| | 7\22
| 7\22
| |
|  
| | 381.818
| 381.818
| |
|  
|-
|-
| |
|  
| | 9/7
| 9/7
| | 382.458
| 382.458
| |
|  
|-
|-
| |
|  
| | 5/4
| 5/4
| | 386.314
| 386.314
| |
|  
|}
|}


=== Sorcery ===
=== Sorcery ===


Gencom: [2 5/4; 65/64 78/77 91/90 100/99]
{| class="wikitable center-all left-4"
 
Gencom mapping: [{{map|1 0 2 -1 6 4}}, {{map|0 5 1 12 -8 -1}}]
 
{| class="wikitable center-all"
|-
|-
! | ET<br>generator
! Edo<br>generator
! | eigenmonzo<br>(unchanged-interval)
! Eigenmonzo<br>(unchanged-interval)
! | major<br>third (¢)
! Generator (¢)
! | comments
! Comments
|-
|-
| |
|  
| | 16/13
| 16/13
| | 359.472
| 359.472
| |
|  
|-
|-
| |
|  
| | 13/10
| 13/10
| | 372.893
| 372.893
| |
|  
|-
|-
| |
|  
| | 13/12
| 13/12
| | 376.905
| 376.905
| |
|  
|-
|-
| |
|  
| | 15/13
| 15/13
| | 378.249
| 378.249
| |
|  
|-
|-
| |
|  
| | 18/13
| 18/13
| | 378.489
| 378.489
| |
|  
|-
|-
| |
|  
| | 6/5
| 6/5
| | 378.910
| 378.910
| |
|  
|-
|-
| | 6\19
| 6\19
| |
|  
| | 378.947
| 378.947
| |
|  
|-
|-
| |
|  
| | 14/13
| 14/13
| | 379.100
| 379.100
| |
|  
|-
|-
| |
|  
| | 10/9
| 10/9
| | 379.733
| 379.733
| |
|  
|-
|-
| |
|  
| | 27/20
| 27/20
| | 379.968
| 379.968
| | 5 limit least squares
| 5 limit least squares
|-
|-
| | 19\60
| 19\60
| |
|  
| | 380.000
| 380.000
| |
|  
|-
|-
| |
|  
| | 15/14
| 15/14
| | 380.093
| 380.093
| |
|  
|-
|-
| | 32\101
| 32\101
| |
|  
| | 380.198
| 380.198
| |
|  
|-
|-
| |
|  
| | 7/5
| 7/5
| | 380.228
| 380.228
| |
|  
|-
|-
| |
|  
| | {{vector|0 36 -23 32}}
| {{vector|0 36 -23 32}}
| | 380.384
| 380.384
| | 9 limit least squares
| 9 limit least squares
|-
|-
| |
|  
| | 4/3
| 4/3
| | 380.391
| 380.391
| | 5, 7 and 9 limit minimax
| 5, 7 and 9 limit minimax
|-
|-
| |
|  
| | {{vector|0 -113 12 -65 75 26}}
| {{vector|0 -113 12 -65 75 26}}
| | 380.427
| 380.427
| | 13 limit least squares
| 13 limit least squares
|-
|-
| |
|  
| | {{vector|0 134 9 71 -89 -33}}
| {{vector|0 134 9 71 -89 -33}}
| | 380.457
| 380.457
| | 15 limit least squares
| 15 limit least squares
|-
|-
| | 13\41
| 13\41
| |
|  
| | 380.488
| 380.488
| |
|  
|-
|-
| |
|  
| | {{vector|0 1 -7 15}}
| {{vector|0 1 -7 15}}
| | 380.506
| 380.506
| | 7 limit least squares
| 7 limit least squares
|-
|-
| |
|  
| | 11/9
| 11/9
| | 380.700
| 380.700
| | 11, 13 and 15 limit minimax
| 11, 13 and 15 limit minimax
|-
|-
| |
|  
| | {{vector|0 85 -14 52 -68}}
| {{vector|0 85 -14 52 -68}}
| | 380.714
| 380.714
| | 11 limit least squares
| 11 limit least squares
|-
|-
| |
|  
| | 8/7
| 8/7
| | 380.735
| 380.735
| |
|  
|-
|-
| | 33\104
| 33\104
| |
|  
| | 380.769
| 380.769
| |
|  
|-
|-
| |
|  
| | 12/11
| 12/11
| | 380.818
| 380.818
| |
|  
|-
|-
| |
|  
| | 14/11
| 14/11
| | 380.875
| 380.875
| |
|  
|-
|-
| | 20\63
| 20\63
| |
|  
| | 380.952
| 380.952
| |
|  
|-
|-
| |
|  
| | 7/6
| 7/6
| | 380.982
| 380.982
| |
|  
|-
|-
| |
|  
| | 11/8
| 11/8
| | 381.085
| 381.085
| |
|  
|-
|-
| |
|  
| | 15/11
| 15/11
| | 381.211
| 381.211
| |
|  
|-
|-
| |
|  
| | 16/15
| 16/15
| | 381.378
| 381.378
| |
|  
|-
|-
| |
|  
| | 11/10
| 11/10
| | 381.666
| 381.666
| |
|  
|-
|-
| | 7\22
| 7\22
| |
|  
| | 381.818
| 381.818
| |
|  
|-
|-
| |
|  
| | 9/7
| 9/7
| | 382.458
| 382.458
| |
|  
|-
|-
| |
|  
| | 13/11
| 13/11
| | 384.173
| 384.173
| |
|  
|-
|-
| |
|  
| | 5/4
| 5/4
| | 386.314
| 386.314
| |
|  
|}
|}


=== Telepathy ===
=== Telepathy ===
 
{| class="wikitable center-all left-4"
Gencom: [2 5/4; 55/54 65/64 91/90 99/98]
 
Gencom mapping: [{{map|1 0 2 -1 -1 4}}, {{map|0 5 1 12 14 -1}}]
 
{| class="wikitable center-all"
|-
|-
! | ET<br>generator
! Edo<br>generator
! | eigenmonzo<br>(unchanged-interval)
! Eigenmonzo<br>(unchanged-interval)
! | major<br>third (¢)
! Generator (¢)
! | comments
! Comments
|-
|-
| |
|  
| | 16/13
| 16/13
| | 359.472
| 359.472
| |
|  
|-
|-
| |
|  
| | 13/10
| 13/10
| | 372.893
| 372.893
| |
|  
|-
|-
| |
|  
| | 13/12
| 13/12
| | 376.905
| 376.905
| |
|  
|-
|-
| |
|  
| | 15/13
| 15/13
| | 378.249
| 378.249
| |
|  
|-
|-
| |
|  
| | 18/13
| 18/13
| | 378.489
| 378.489
| |
|  
|-
|-
| |
|  
| | 6/5
| 6/5
| | 378.910
| 378.910
| |
|  
|-
|-
| | 6\19
| 6\19
| |
|  
| | 378.947
| 378.947
| |
|  
|-
|-
| |
|  
| | 14/13
| 14/13
| | 379.100
| 379.100
| |
|  
|-
|-
| |
|  
| | 10/9
| 10/9
| | 379.733
| 379.733
| |
|  
|-
|-
| |
|  
| | 27/20
| 27/20
| | 379.968
| 379.968
| | 5 limit least squares
| 5 limit least squares
|-
|-
| | 19\60
| 19\60
| |
|  
| | 380.000
| 380.000
| |
|  
|-
|-
| |
|  
| | 15/14
| 15/14
| | 380.093
| 380.093
| |
|  
|-
|-
| | 32\101
| 32\101
| |
|  
| | 380.198
| 380.198
| |
|  
|-
|-
| |
|  
| | 7/5
| 7/5
| | 380.228
| 380.228
| |
|  
|-
|-
| |
|  
| | {{vector|0 36 -23 32}}
| {{vector|0 36 -23 32}}
| | 380.384
| 380.384
| | 9 limit least squares
| 9 limit least squares
|-
|-
| |
|  
| | 4/3
| 4/3
| | 380.391
| 380.391
| | 5, 7 and 9 limit minimax
| 5, 7 and 9 limit minimax
|-
|-
| | 13\41
| 13\41
| |
|  
| | 380.488
| 380.488
| |
|  
|-
|-
| |
|  
| | {{vector|0 1 -7 15}}
| {{vector|0 1 -7 15}}
| | 380.506
| 380.506
| | 7 limit least squares
| 7 limit least squares
|-
|-
| |
|  
| | {{vector|0 47 -34 43 57 -48}}
| {{vector|0 47 -34 43 57 -48}}
| | 380.676
| 380.676
| | 13 limit least squares
| 13 limit least squares
|-
|-
| |
|  
| | {{vector|0 46 -35 49 65 -55}}
| {{vector|0 46 -35 49 65 -55}}
| | 380.691
| 380.691
| | 15 limit least squares
| 15 limit least squares
|-
|-
| |
|  
| | 13/11
| 13/11
| | 380.719
| 380.719
| | 13 and 15 limit minimax
| 13 and 15 limit minimax
|-
|-
| |
|  
| | 8/7
| 8/7
| | 380.735
| 380.735
| |
|  
|-
|-
| | 33\104
| 33\104
| |
|  
| | 380.769
| 380.769
| |
|  
|-
|-
| | 20\63
| 20\63
| |
|  
| | 380.952
| 380.952
| |
|  
|-
|-
| |
|  
| | 7/6
| 7/6
| | 380.982
| 380.982
| |
|  
|-
|-
| |
|  
| | 16/15
| 16/15
| | 381.378
| 381.378
| |
|  
|-
|-
| |
|  
| | {{vector|0 19 -36 30 42}}
| {{vector|0 19 -36 30 42}}
| | 381.380
| 381.380
| | 11 limit least squares
| 11 limit least squares
|-
|-
| | 7\22
| 7\22
| |
|  
| | 381.818
| 381.818
| |
|  
|-
|-
| |
|  
| | 11/10
| 11/10
| | 381.923
| 381.923
| | 11 limit minimax
| 11 limit minimax
|-
|-
| |
|  
| | 11/8
| 11/8
| | 382.237
| 382.237
| |
|  
|-
|-
| |
|  
| | 9/7
| 9/7
| | 382.458
| 382.458
| |
|  
|-
|-
| |
|  
| | 15/11
| 15/11
| | 382.881
| 382.881
| |
|  
|-
|-
| |
|  
| | 12/11
| 12/11
| | 383.263
| 383.263
| |
|  
|-
|-
| |
|  
| | 5/4
| 5/4
| | 386.314
| 386.314
| |
|  
|-
|-
| |
|  
| | 11/9
| 11/9
| | 386.852
| 386.852
| |
|  
|-
|-
| |
|  
| | 14/11
| 14/11
| | 391.246
| 391.246
| |
|  
|}
|}


=== Witchcraft ===
=== Witchcraft ===
 
{| class="wikitable center-all left-4"
Gencom: [2 5/4; 105/104 196/195 245/243 275/273]
 
Gencom mapping: [{{map|1 0 2 -1 -7 -2}}, {{map|0 5 1 12 33 18}}]
 
{| class="wikitable center-all"
|-
|-
! | ET<br>generator
! Edo<br>generator
! | eigenmonzo<br>(unchanged-interval)
! Eigenmonzo<br>(unchanged-interval)
! | major<br>third (¢)
! Generator (¢)
! | comments
! Comments
|-
|-
| |
|  
| | 14/13
| 14/13
| | 378.617
| 378.617
| |
|  
|-
|-
| |
|  
| | 6/5
| 6/5
| | 378.910
| 378.910
| |
|  
|-
|-
| | 6\19
| 6\19
| |
|  
| | 378.947
| 378.947
| |
|  
|-
|-
| |
|  
| | 15/13
| 15/13
| | 379.355
| 379.355
| |
|  
|-
|-
| |
|  
| | 18/13
| 18/13
| | 379.577
| 379.577
| |
|  
|-
|-
| |
|  
| | 13/10
| 13/10
| | 379.660
| 379.660
| |
|  
|-
|-
| |
|  
| | 10/9
| 10/9
| | 379.733
| 379.733
| |
|  
|-
|-
| |
|  
| | 27/20
| 27/20
| | 379.968
| 379.968
| | 5 limit least squares
| 5 limit least squares
|-
|-
| |
|  
| | 13/12
| 13/12
| | 379.890
| 379.890
| |
|  
|-
|-
| | 19\60
| 19\60
| |
|  
| | 380.000
| 380.000
| |
|  
|-
|-
| |
|  
| | 16/13
| 16/13
| | 380.029
| 380.029
| |
|  
|-
|-
| |
|  
| | 15/14
| 15/14
| | 380.093
| 380.093
| |
|  
|-
|-
| |
|  
| | 15/11
| 15/11
| | 380.113
| 380.113
| | 15 limit minimax
| 15 limit minimax
|-
|-
| |
|  
| | 14/11
| 14/11
| | 380.119
| 380.119
| | 13 limit minimax
| 13 limit minimax
|-
|-
| |
|  
| | 11/10
| 11/10
| | 380.156
| 380.156
| |
|  
|-
|-
| |
|  
| | {{vector|0 -106 -111 11 179 59}}
| {{vector|0 -106 -111 11 179 59}}
| | 380.193
| 380.193
| | 15 limit least squares
| 15 limit least squares
|-
|-
| | 32\101
| 32\101
| |
|  
| | 380.198
| 380.198
| |
|  
|-
|-
| |
|  
| | {{vector|0 -67 -72 5 152 47}}
| {{vector|0 -67 -72 5 152 47}}
| | 380.218
| 380.218
| | 13 limit least squares
| 13 limit least squares
|-
|-
| |
|  
| | 7/5
| 7/5
| | 380.228
| 380.228
| |
|  
|-
|-
| |
|  
| | {{vector|0 -38 -55 11 137}}
| {{vector|0 -38 -55 11 137}}
| | 380.278
| 380.278
| | 11 limit least squares
| 11 limit least squares
|-
|-
| |
|  
| | 11/9
| 11/9
| | 380.322
| 380.322
| |
|  
|-
|-
| |
|  
| | 12/11
| 12/11
| | 380.334
| 380.334
| |
|  
|-
|-
| |
|  
| | 11/8
| 11/8
| | 380.343
| 380.343
| | 11 limit minimax
| 11 limit minimax
|-
|-
| |
|  
| | {{vector|0 36 -23 32}}
| {{vector|0 36 -23 32}}
| | 380.384
| 380.384
| | 9 limit least squares
| 9 limit least squares
|-
|-
| |
|  
| | 4/3
| 4/3
| | 380.391
| 380.391
| | 5, 7 and 9 limit minimax
| 5, 7 and 9 limit minimax
|-
|-
| | 13\41
| 13\41
| |
|  
| | 380.488
| 380.488
| |
|  
|-
|-
| |
|  
| | 13/11
| 13/11
| | 380.719
| 380.719
| |
|  
|-
|-
| |
|  
| | 8/7
| 8/7
| | 380.735
| 380.735
| |
|  
|-
|-
| | 33\104
| 33\104
| |
|  
| | 380.769
| 380.769
| |
|  
|-
|-
| | 20\63
| 20\63
| |
|  
| | 380.952
| 380.952
| |
|  
|-
|-
| |
|  
| | 7/6
| 7/6
| | 380.982
| 380.982
| |
|  
|-
|-
| |
|  
| | 16/15
| 16/15
| | 381.378
| 381.378
| |
|  
|-
|-
| | 7\22
| 7\22
| |
|  
| | 381.818
| 381.818
| |
|  
|-
|-
| |
|  
| | 9/7
| 9/7
| | 382.458
| 382.458
| |
|  
|-
|-
| |
|  
| | 5/4
| 5/4
| | 386.314
| 386.314
| |
|  
|}
|}


=== Muggles ===
=== Muggles ===
 
{| class="wikitable center-all left-4"
Gencom: [2 5/4; 45/44 65/64 78/77 126/125]
 
Gencom mapping: [{{map|1 0 2 5 0 4}}, {{map|0 5 1 -7 11 -1}}]
 
{| class="wikitable center-all"
|-
|-
! | ET<br>generator
! Edo<br>generator
! | eigenmonzo<br>(unchanged-interval)
! Eigenmonzo<br>(unchanged-interval)
! | major<br>third (¢)
! Generator (¢)
! | comments
! Comments
|-
|-
| |
|  
| | 11/9
| 11/9
| | 347.408
| 347.408
| |
|  
|-
|-
| |
|  
| | 16/13
| 16/13
| | 359.472
| 359.472
| |
|  
|-
|-
| |
|  
| | 15/11
| 15/11
| | 372.610
| 372.610
| |
|  
|-
|-
| |
|  
| | 13/10
| 13/10
| | 372.893
| 372.893
| |
|  
|-
|-
| |
|  
| | 12/11
| 12/11
| | 374.894
| 374.894
| |
|  
|-
|-
| |
|  
| | 8/7
| 8/7
| | 375.882
| 375.882
| |
|  
|-
|-
| |
|  
| | 13/11
| 13/11
| | 375.899
| 375.899
| |
|  
|-
|-
| |
|  
| | 11/10
| 11/10
| | 376.500
| 376.500
| |
|  
|-
|-
| |
|  
| | 14/11
| 14/11
| | 376.805
| 376.805
| |
|  
|-
|-
| |
|  
| | 13/12
| 13/12
| | 376.905
| 376.905
| |
|  
|-
|-
| |
|  
| | 7/5
| 7/5
| | 377.186
| 377.186
| |
|  
|-
|-
| |
|  
| | 11/8
| 11/8
| | 377.393
| 377.393
| | 11, 13 and 15 limit minimax
| 11, 13 and 15 limit minimax
|-
|-
| |
|  
| | {{vector|0 113 -12 -68 58 -26}}
| {{vector|0 113 -12 -68 58 -26}}
| | 377.630
| 377.630
| | 13 limit least squares
| 13 limit least squares
|-
|-
| |
|  
| | {{vector|0 -21 -5 27}}
| {{vector|0 -21 -5 27}}
| | 377.640
| 377.640
| | 7 limit least squares
| 7 limit least squares
|-
|-
| |
|  
| | {{vector|0 134 9 -81 63 -33}}
| {{vector|0 134 9 -81 63 -33}}
| | 377.718
| 377.718
| | 15 limit least squares
| 15 limit least squares
|-
|-
| |
|  
| | {{vector|0 85 -14 -62 46}}
| {{vector|0 85 -14 -62 46}}
| | 377.758
| 377.758
| | 11 limit least squares
| 11 limit least squares
|-
|-
| |
|  
| | 7/6
| 7/6
| | 377.761
| 377.761
| | 7 limit minimax
| 7 limit minimax
|-
|-
| |
|  
| | 15/13
| 15/13
| | 378.249
| 378.249
| |
|  
|-
|-
| |
|  
| | 15/14
| 15/14
| | 378.419
| 378.419
| |
|  
|-
|-
| |
|  
| | 18/13
| 18/13
| | 378.489
| 378.489
| |
|  
|-
|-
| |
|  
| | 9/7
| 9/7
| | 378.534
| 378.534
| | 9 limit minimax
| 9 limit minimax
|-
|-
| |
|  
| | {{vector|0 93 -4 -44}}
| {{vector|0 93 -4 -44}}
| | 378.554
| 378.554
| | 9 limit least squares
| 9 limit least squares
|-
|-
| |
|  
| | 14/13
| 14/13
| | 378.617
| 378.617
| |
|  
|-
|-
| |
|  
| | 6/5
| 6/5
| | 378.910
| 378.910
| |
|  
|-
|-
| | 6\19
| 6\19
| |
|  
| | 378.947
| 378.947
| |
|  
|-
|-
| |
|  
| | 10/9
| 10/9
| | 379.733
| 379.733
| |
|  
|-
|-
| |
|  
| | 27/20
| 27/20
| | 379.968
| 379.968
| | 5 limit least squares
| 5 limit least squares
|-
|-
| | 19\60
| 19\60
| |
|  
| | 380.000
| 380.000
| |
|  
|-
|-
| | 32\101
| 32\101
| |
|  
| | 380.198
| 380.198
| |
|  
|-
|-
| |
|  
| | 4/3
| 4/3
| | 380.391
| 380.391
| | 5 limit minimax
| 5 limit minimax
|-
|-
| | 13\41
| 13\41
| |
|  
| | 380.488
| 380.488
| |
|  
|-
|-
| | 33\104
| 33\104
| |
|  
| | 380.769
| 380.769
| |
|  
|-
|-
| | 20\63
| 20\63
| |
|  
| | 380.952
| 380.952
| |
|  
|-
|-
| |
|  
| | 16/15
| 16/15
| | 381.378
| 381.378
| |
|  
|-
|-
| | 7\22
| 7\22
| |
|  
| | 381.818
| 381.818
| |
|  
|-
|-
| |
|  
| | 5/4
| 5/4
| | 386.314
| 386.314
| |
|  
|}
|}


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