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autopatrolled, emailconfirmed
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improve and standardize tuning spectra tables
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=Tuning Spectra=
==Tuning spectra==


==Spectrum of Magic Tunings by Eigenmonzos==
=== Magic ===


Gencom: [2 5/4; 100/99 105/104 144/143 196/195]
Gencom: [2 5/4; 100/99 105/104 144/143 196/195]


Gencom map: [<1 0 2 -1 6 -2|, <0 5 1 12 -8 18|]
Gencom map: [{{map|1 0 2 -1 6 -2}}, {{map|0 5 1 12 -8 18}}]


{| class="wikitable"
{| class="wikitable center-all"
|-
|-
! | Eigenmonzo
! | ET<br>generator
! | Major Third
! | [[eigenmonzo|eigenmonzo<br>(unchanged interval]])
! | major<br>third (¢)
! | 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 (5 limit least squares)
| | 379.968
| | 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 (13 and 15 limit minimax)
| | 380.354
| | 13 and 15 limit minimax
|-
|-
| | |0 56 -31 46 -94 88&gt;
| |
| | 380.377 (13 limit least squares)
| | {{vector|0 56 -31 46 -94 88}}
| | 380.377
| | 13 limit least squares
|-
|-
| | |0 36 -23 32&gt;
| |
| | 380.384 (9 limit least squares)
| | {{vector|0 36 -23 32}}
| | 380.384
| | 9 limit least squares
|-
|-
| | |0 58 -29 52 -108 100&gt;
| |
| | 380.389 (15 limit least squares)
| | {{vector|0 58 -29 52 -108 100}}
| | 380.389
| | 15 limit least squares
|-
|-
| |
| | 4/3
| | 4/3
| | 380.391 (5, 7 and 9 limit minimax)
| | 380.391
| | 5, 7 and 9 limit minimax
|-
|-
| | 13\41
| | 13\41
| |
| | 380.488
| | 380.488
| |
|-
|-
| | |0 1 -7 15&gt;
| |
| | 380.506 (7 limit least squares)
| | {{vector|0 1 -7 15}}
| | 380.506
| | 7 limit least squares
|-
|-
| |
| | 11/9
| | 11/9
| | 380.700 (11 limit minimax)
| | 380.700
| | 11 limit minimax
|-
|-
| | |0 85 -14 52 -68&gt;
| |
| | 380.714 (11 limit least squares)
| | {{vector|0 85 -14 52 -68}}
| | 380.714
| | 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
| |
|}
|}


==Spectrum of Necromancy Tunings by Eigenmonzos==
=== Necromancy ===


Gencom: [2 5/4; 100/99 225/224 245/243 275/273]
Gencom: [2 5/4; 100/99 225/224 245/243 275/273]


Gencom map: [&lt;1 0 2 -1 6 11|, &lt;0 5 1 12 -8 -23|]
Gencom map: [{{map|1 0 2 -1 6 11}}, {{map|0 5 1 12 -8 -23}}]


{| class="wikitable"
{| class="wikitable center-all"
|-
|-
! | Eigenmonzo
! | ET<br>generator
! | Major Third
! | eigenmonzo<br>(unchanged interval)
! | major<br>third (¢)
! | 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 (5 limit least squares)
| | 379.968
| | 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
| |
|-
|-
| | |0 36 -23 32&gt;
| |
| | 380.384 (9 limit least squares)
| | {{vector|0 36 -23 32}}
| | 380.384
| | 9 limit least squares
|-
|-
| |
| | 4/3
| | 4/3
| | 380.391 (5, 7 and 9 limit minimax)
| | 380.391
| | 5, 7 and 9 limit minimax
|-
|-
| | 13\41
| | 13\41
| |
| | 380.488
| | 380.488
| |
|-
|-
| | |0 1 -7 15&gt;
| |
| | 380.506 (7 limit least squares)
| | {{vector|0 1 -7 15}}
| | 380.506
| | 7 limit least squares
|-
|-
| |
| | 11/9
| | 11/9
| | 380.700 (11 limit minimax)
| | 380.700
| | 11 limit minimax
|-
|-
| |
| | 18/13
| | 18/13
| | 380.709 (13 and 15 limit minimax)
| | 380.709
| | 13 and 15 limit minimax
|-
|-
| | |0 85 -14 52 -68&gt;
| |
| | 380.714 (11 limit least squares)
| | {{vector|0 85 -14 52 -68}}
| | 380.714
| | 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
| |
|-
|-
| | |0 -179 -10 -87 53 158&gt;
| |
| | 380.785 (13 limit least squares)
| | {{vector|0 -179 -10 -87 53 158}}
| | 380.785
| | 13 limit least squares
|-
|-
| |
| | 14/13
| | 14/13
| | 380.809
| | 380.809
| |
|-
|-
| | |0 -222 -53 -93 67 187&gt;
| |
| | 380.817 (15 limit least squares)
| | {{vector|0 -222 -53 -93 67 187}}
| | 380.817
| | 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
| |
|}
|}


==Spectrum of Sorcery Tunings by Eigenmonzos==
=== Sorcery ===


Gencom: [2 5/4; 65/64 78/77 91/90 100/99]
Gencom: [2 5/4; 65/64 78/77 91/90 100/99]


Gencom map: [&lt;1 0 2 -1 6 4|, &lt;0 5 1 12 -8 -1|]
Gencom map: [{{map|1 0 2 -1 6 4}}, {{map|0 5 1 12 -8 -1}}]


{| class="wikitable"
{| class="wikitable center-all"
|-
|-
! | Eigenmonzo
! | ET<br>generator
! | Major Third
! | eigenmonzo<br>(unchanged interval)
! | major<br>third (¢)
! | 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 (5 limit least squares)
| | 379.968
| | 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
| |
|-
|-
| | |0 36 -23 32&gt;
| |
| | 380.384 (9 limit least squares)
| | {{vector|0 36 -23 32}}
| | 380.384
| | 9 limit least squares
|-
|-
| |
| | 4/3
| | 4/3
| | 380.391 (5, 7 and 9 limit minimax)
| | 380.391
| | 5, 7 and 9 limit minimax
|-
|-
| | |0 -113 12 -65 75 26&gt;
| |
| | 380.427 (13 limit least squares)
| | {{vector|0 -113 12 -65 75 26}}
| | 380.427
| | 13 limit least squares
|-
|-
| | |0 134 9 71 -89 -33&gt;
| |
| | 380.457 (15 limit least squares)
| | {{vector|0 134 9 71 -89 -33}}
| | 380.457
| | 15 limit least squares
|-
|-
| | 13\41
| | 13\41
| |
| | 380.488
| | 380.488
| |
|-
|-
| | |0 1 -7 15&gt;
| |
| | 380.506 (7 limit least squares)
| | {{vector|0 1 -7 15}}
| | 380.506
| | 7 limit least squares
|-
|-
| |
| | 11/9
| | 11/9
| | 380.700 (11, 13 and 15 limit minimax)
| | 380.700
| | 11, 13 and 15 limit minimax
|-
|-
| | |0 85 -14 52 -68&gt;
| |
| | 380.714 (11 limit least squares)
| | {{vector|0 85 -14 52 -68}}
| | 380.714
| | 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
| |
|}
|}


==Spectrum of Telepathy Tunings by Eigenmonzos==
=== Telepathy ===


Gencom: [2 5/4; 55/54 65/64 91/90 99/98]
Gencom: [2 5/4; 55/54 65/64 91/90 99/98]


Gencom map: [&lt;1 0 2 -1 -1 4|, &lt;0 5 1 12 14 -1|]
Gencom map: [{{map|1 0 2 -1 -1 4}}, {{map|0 5 1 12 14 -1}}]


{| class="wikitable"
{| class="wikitable center-all"
|-
|-
! | Eigenmonzo
! | ET<br>generator
! | Major Third
! | eigenmonzo<br>(unchanged interval)
! | major<br>third (¢)
! | 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 (5 limit least squares)
| | 379.968
| | 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
| |
|-
|-
| | |0 36 -23 32&gt;
| |
| | 380.384 (9 limit least squares)
| | {{vector|0 36 -23 32}}
| | 380.384
| | 9 limit least squares
|-
|-
| |
| | 4/3
| | 4/3
| | 380.391 (5, 7 and 9 limit minimax)
| | 380.391
| | 5, 7 and 9 limit minimax
|-
|-
| | 13\41
| | 13\41
| |
| | 380.488
| | 380.488
| |
|-
|-
| | |0 1 -7 15&gt;
| |
| | 380.506 (7 limit least squares)
| | {{vector|0 1 -7 15}}
| | 380.506
| | 7 limit least squares
|-
|-
| | |0 47 -34 43 57 -48&gt;
| |
| | 380.676 (13 limit least squares)
| | {{vector|0 47 -34 43 57 -48}}
| | 380.676
| | 13 limit least squares
|-
|-
| | |0 46 -35 49 65 -55&gt;
| |
| | 380.691 (15 limit least squares)
| | {{vector|0 46 -35 49 65 -55}}
| | 380.691
| | 15 limit least squares
|-
|-
| |
| | 13/11
| | 13/11
| | 380.719 (13 and 15 limit minimax)
| | 380.719
| | 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
| |
|-
|-
| | |0 19 -36 30 42&gt;
| |
| | 381.380 (11 limit least squares)
| | {{vector|0 19 -36 30 42}}
| | 381.380
| | 11 limit least squares
|-
|-
| | 7\22
| | 7\22
| |
| | 381.818
| | 381.818
| |
|-
|-
| |
| | 11/10
| | 11/10
| | 381.923 (11 limit minimax)
| | 381.923
| | 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
| |
|}
|}


==Spectrum of Witchcraft Tunings by Eigenmonzos==
=== Witchcraft ===


Gencom: [2 5/4; 105/104 196/195 245/243 275/273]
Gencom: [2 5/4; 105/104 196/195 245/243 275/273]


Gencom map: [&lt;1 0 2 -1 -7 -2|, &lt;0 5 1 12 33 18|]
Gencom map: [{{map|1 0 2 -1 -7 -2}}, {{map|0 5 1 12 33 18}}]


{| class="wikitable"
{| class="wikitable center-all"
|-
|-
! | Eigenmonzo
! | ET<br>generator
! | Major Third
! | eigenmonzo<br>(unchanged interval)
! | major<br>third (¢)
! | 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 (5 limit least squares)
| | 379.968
| | 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 (15 limit minimax)
| | 380.113
| | 15 limit minimax
|-
|-
| |
| | 14/11
| | 14/11
| | 380.119 (13 limit minimax)
| | 380.119
| | 13 limit minimax
|-
|-
| |
| | 11/10
| | 11/10
| | 380.156
| | 380.156
| |
|-
|-
| | |0 -106 -111 11 179 59&gt;
| |
| | 380.193 (15 limit least squares)
| | {{vector|0 -106 -111 11 179 59}}
| | 380.193
| | 15 limit least squares
|-
|-
| | 32\101
| | 32\101
| |
| | 380.198
| | 380.198
| |
|-
|-
| | |0 -67 -72 5 152 47&gt;
| |
| | 380.218 (13 limit least squares)
| | {{vector|0 -67 -72 5 152 47}}
| | 380.218
| | 13 limit least squares
|-
|-
| |
| | 7/5
| | 7/5
| | 380.228
| | 380.228
| |
|-
|-
| | |0 -38 -55 11 137&gt;
| |
| | 380.278 (11 limit least squares)
| | {{vector|0 -38 -55 11 137}}
| | 380.278
| | 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 (11 limit minimax)
| | 380.343
| | 11 limit minimax
|-
|-
| | |0 36 -23 32&gt;
| |
| | 380.384 (9 limit least squares)
| | {{vector|0 36 -23 32}}
| | 380.384
| | 9 limit least squares
|-
|-
| |
| | 4/3
| | 4/3
| | 380.391 (5, 7 and 9 limit minimax)
| | 380.391
| | 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
| |
|}
|}


==Spectrum of Muggles Tunings by Eigenmonzos==
=== Muggles ===


Gencom: [2 5/4; 45/44 65/64 78/77 126/125]
Gencom: [2 5/4; 45/44 65/64 78/77 126/125]


Gencom map: [&lt;1 0 2 5 0 4|, &lt;0 5 1 -7 11 -1|]
Gencom map: [{{map|1 0 2 5 0 4}}, {{map|0 5 1 -7 11 -1}}]


{| class="wikitable"
{| class="wikitable center-all"
|-
|-
! | Eigenmonzo
! | ET<br>generator
! | Major Third
! | eigenmonzo<br>(unchanged interval)
! | major<br>third (¢)
! | 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 (11, 13 and 15 limit minimax)
| | 377.393
| | 11, 13 and 15 limit minimax
|-
|-
| | |0 113 -12 -68 58 -26&gt;
| |
| | 377.630 (13 limit least squares)
| | {{vector|0 113 -12 -68 58 -26}}
| | 377.630
| | 13 limit least squares
|-
|-
| | |0 -21 -5 27&gt;
| |
| | 377.640 (7 limit least squares)
| | {{vector|0 -21 -5 27}}
| | 377.640
| | 7 limit least squares
|-
|-
| | |0 134 9 -81 63 -33&gt;
| |
| | 377.718 (15 limit least squares)
| | {{vector|0 134 9 -81 63 -33}}
| | 377.718
| | 15 limit least squares
|-
|-
| | |0 85 -14 -62 46&gt;
| |
| | 377.758 (11 limit least squares)
| | {{vector|0 85 -14 -62 46}}
| | 377.758
| | 11 limit least squares
|-
|-
| |
| | 7/6
| | 7/6
| | 377.761 (7 limit minimax)
| | 377.761
| | 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 (9 limit minimax)
| | 378.534
| | 9 limit minimax
|-
|-
| | |0 93 -4 -44&gt;
| |
| | 378.554 (9 limit least squares)
| | {{vector|0 93 -4 -44}}
| | 378.554
| | 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 (5 limit least squares)
| | 379.968
| | 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 (5 limit minimax)
| | 380.391
| | 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
| |
|}
|}

Revision as of 00:30, 30 September 2021

Tuning spectra

Magic

Gencom: [2 5/4; 100/99 105/104 144/143 196/195]

Gencom map: [⟨1 0 2 -1 6 -2], ⟨0 5 1 12 -8 18]]

ET
generator 		eigenmonzo
(unchanged interval) 		major
third (¢) 		comments
14/13 378.617
6/5 378.910
6\19 378.947
15/13 379.355
18/13 379.577
13/10 379.660
10/9 379.733
13/12 379.890
27/20 379.968 5 limit least squares
19\60 380.000
16/13 380.029
15/14 380.093
32\101 380.198
7/5 380.228
13/11 380.354 13 and 15 limit minimax
[0 56 -31 46 -94 88⟩ 380.377 13 limit least squares
[0 36 -23 32⟩ 380.384 9 limit least squares
[0 58 -29 52 -108 100⟩ 380.389 15 limit least squares
4/3 380.391 5, 7 and 9 limit minimax
13\41 380.488
[0 1 -7 15⟩ 380.506 7 limit least squares
11/9 380.700 11 limit minimax
[0 85 -14 52 -68⟩ 380.714 11 limit least squares
8/7 380.735
33\104 380.769
12/11 380.818
14/11 380.875
20\63 380.952
7/6 380.982
11/8 381.085
15/11 381.211
16/15 381.378
11/10 381.666
7\22 381.818
9/7 382.458
5/4 386.314

Necromancy

Gencom: [2 5/4; 100/99 225/224 245/243 275/273]

Gencom map: [⟨1 0 2 -1 6 11], ⟨0 5 1 12 -8 -23]]

ET
generator 		eigenmonzo
(unchanged interval) 		major
third (¢) 		comments
6/5 378.910
6\19 378.947
10/9 379.733
27/20 379.968 5 limit least squares
19\60 380.000
15/14 380.093
32\101 380.198
7/5 380.228
[0 36 -23 32⟩ 380.384 9 limit least squares
4/3 380.391 5, 7 and 9 limit minimax
13\41 380.488
[0 1 -7 15⟩ 380.506 7 limit least squares
11/9 380.700 11 limit minimax
18/13 380.709 13 and 15 limit minimax
[0 85 -14 52 -68⟩ 380.714 11 limit least squares
13/11 380.719
8/7 380.735
13/12 380.765
33\104 380.769
[0 -179 -10 -87 53 158⟩ 380.785 13 limit least squares
14/13 380.809
[0 -222 -53 -93 67 187⟩ 380.817 15 limit least squares
12/11 380.818
16/13 380.847
14/11 380.875
20\63 380.952
15/13 380.957
7/6 380.982
13/10 381.074
11/8 381.085
15/11 381.211
16/15 381.378
11/10 381.666
7\22 381.818
9/7 382.458
5/4 386.314

Sorcery

Gencom: [2 5/4; 65/64 78/77 91/90 100/99]

Gencom map: [⟨1 0 2 -1 6 4], ⟨0 5 1 12 -8 -1]]

ET
generator 		eigenmonzo
(unchanged interval) 		major
third (¢) 		comments
16/13 359.472
13/10 372.893
13/12 376.905
15/13 378.249
18/13 378.489
6/5 378.910
6\19 378.947
14/13 379.100
10/9 379.733
27/20 379.968 5 limit least squares
19\60 380.000
15/14 380.093
32\101 380.198
7/5 380.228
[0 36 -23 32⟩ 380.384 9 limit least squares
4/3 380.391 5, 7 and 9 limit minimax
[0 -113 12 -65 75 26⟩ 380.427 13 limit least squares
[0 134 9 71 -89 -33⟩ 380.457 15 limit least squares
13\41 380.488
[0 1 -7 15⟩ 380.506 7 limit least squares
11/9 380.700 11, 13 and 15 limit minimax
[0 85 -14 52 -68⟩ 380.714 11 limit least squares
8/7 380.735
33\104 380.769
12/11 380.818
14/11 380.875
20\63 380.952
7/6 380.982
11/8 381.085
15/11 381.211
16/15 381.378
11/10 381.666
7\22 381.818
9/7 382.458
13/11 384.173
5/4 386.314

Telepathy

Gencom: [2 5/4; 55/54 65/64 91/90 99/98]

Gencom map: [⟨1 0 2 -1 -1 4], ⟨0 5 1 12 14 -1]]

ET
generator 		eigenmonzo
(unchanged interval) 		major
third (¢) 		comments
16/13 359.472
13/10 372.893
13/12 376.905
15/13 378.249
18/13 378.489
6/5 378.910
6\19 378.947
14/13 379.100
10/9 379.733
27/20 379.968 5 limit least squares
19\60 380.000
15/14 380.093
32\101 380.198
7/5 380.228
[0 36 -23 32⟩ 380.384 9 limit least squares
4/3 380.391 5, 7 and 9 limit minimax
13\41 380.488
[0 1 -7 15⟩ 380.506 7 limit least squares
[0 47 -34 43 57 -48⟩ 380.676 13 limit least squares
[0 46 -35 49 65 -55⟩ 380.691 15 limit least squares
13/11 380.719 13 and 15 limit minimax
8/7 380.735
33\104 380.769
20\63 380.952
7/6 380.982
16/15 381.378
[0 19 -36 30 42⟩ 381.380 11 limit least squares
7\22 381.818
11/10 381.923 11 limit minimax
11/8 382.237
9/7 382.458
15/11 382.881
12/11 383.263
5/4 386.314
11/9 386.852
14/11 391.246

Witchcraft

Gencom: [2 5/4; 105/104 196/195 245/243 275/273]

Gencom map: [⟨1 0 2 -1 -7 -2], ⟨0 5 1 12 33 18]]

ET
generator 		eigenmonzo
(unchanged interval) 		major
third (¢) 		comments
14/13 378.617
6/5 378.910
6\19 378.947
15/13 379.355
18/13 379.577
13/10 379.660
10/9 379.733
27/20 379.968 5 limit least squares
13/12 379.890
19\60 380.000
16/13 380.029
15/14 380.093
15/11 380.113 15 limit minimax
14/11 380.119 13 limit minimax
11/10 380.156
[0 -106 -111 11 179 59⟩ 380.193 15 limit least squares
32\101 380.198
[0 -67 -72 5 152 47⟩ 380.218 13 limit least squares
7/5 380.228
[0 -38 -55 11 137⟩ 380.278 11 limit least squares
11/9 380.322
12/11 380.334
11/8 380.343 11 limit minimax
[0 36 -23 32⟩ 380.384 9 limit least squares
4/3 380.391 5, 7 and 9 limit minimax
13\41 380.488
13/11 380.719
8/7 380.735
33\104 380.769
20\63 380.952
7/6 380.982
16/15 381.378
7\22 381.818
9/7 382.458
5/4 386.314

Muggles

Gencom: [2 5/4; 45/44 65/64 78/77 126/125]

Gencom map: [⟨1 0 2 5 0 4], ⟨0 5 1 -7 11 -1]]

ET
generator 		eigenmonzo
(unchanged interval) 		major
third (¢) 		comments
11/9 347.408
16/13 359.472
15/11 372.610
13/10 372.893
12/11 374.894
8/7 375.882
13/11 375.899
11/10 376.500
14/11 376.805
13/12 376.905
7/5 377.186
11/8 377.393 11, 13 and 15 limit minimax
[0 113 -12 -68 58 -26⟩ 377.630 13 limit least squares
[0 -21 -5 27⟩ 377.640 7 limit least squares
[0 134 9 -81 63 -33⟩ 377.718 15 limit least squares
[0 85 -14 -62 46⟩ 377.758 11 limit least squares
7/6 377.761 7 limit minimax
15/13 378.249
15/14 378.419
18/13 378.489
9/7 378.534 9 limit minimax
[0 93 -4 -44⟩ 378.554 9 limit least squares
14/13 378.617
6/5 378.910
6\19 378.947
10/9 379.733
27/20 379.968 5 limit least squares
19\60 380.000
32\101 380.198
4/3 380.391 5 limit minimax
13\41 380.488
33\104 380.769
20\63 380.952
16/15 381.378
7\22 381.818
5/4 386.314
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