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→Tuning Spectra: improve and standardize tuning spectra tables
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The basic 7-limit [[Miracle|miracle]] temperament has various extensions to the 11 and 13 limits.
The basic 7-limit [[Miracle|miracle]] temperament has various extensions to the 11 and 13 limits.


=Tuning Spectra=
== Tuning spectra ==


==Spectrum of Miraculous Tunings by Eigenmonzos==
=== Miraculous ===


Gencom: [2 15/14; 105/104 144/143 196/195 275/273]
Gencom: [2 15/14; 105/104 144/143 196/195 275/273]


Gencom map: [<1 1 3 3 2 4|, <0 6 -7 -2 15 -3|]
Gencom map: [{{map|1 1 3 3 2 4}}, {{map|0 6 -7 -2 15 -3}}]


{| class="wikitable"
{| class="wikitable center-all"
|-
|-
! | Eigenmonzo
! | ET<br>generator
! | Secor
! | [[eigenmonzo|eigenmonzo<br>(unchanged interval]])
! | secor<br>(¢)
! | comments
|-
|-
| |
| | 16/15
| | 16/15
| | 111.731
| | 111.731
| |
|-
|-
| |
| | 13/10
| | 13/10
| | 113.553
| | 113.553
| |
|-
|-
| |
| | 8/7
| | 8/7
| | 115.587
| | 115.587
| |
|-
|-
| |
| | 11/9
| | 11/9
| | 115.803
| | 115.803
| |
|-
|-
| | 3\31
| | 3\31
| |
| | 116.129
| | 116.129
| |
|-
|-
| |
| | 5/4
| | 5/4
| | 116.241
| | 116.241
| |
|-
|-
| |
| | 15/11
| | 15/11
| | 116.441
| | 116.441
| |
|-
|-
| |
| | 7/5
| | 7/5
| | 116.502
| | 116.502
| |
|-
|-
| | 10\103
| | 10\103
| |
| | 116.505
| | 116.505
| |
|-
|-
| | 17\175
| | 17\175
| |
| | 116.571
| | 116.571
| |
|-
|-
| | |0 -27 25 5&gt;
| |
| | 116.573 (7 limit least squares)
| | {{vector|0 -27 25 5}}
| | 116.573
| | 7 limit least squares
|-
|-
| | |0 -19 20&gt;
| |
| | 116.578 (5 limit least squares)
| | {{vector|0 -19 20}}
| | 116.578
| | 5 limit least squares
|-
|-
| |
| | 6/5
| | 6/5
| | 116.588 (5 and 7 limit minimax)
| | 116.588
| | 5 and 7 limit minimax
|-
|-
| |
| | 11/10
| | 11/10
| | 116.591
| | 116.591
| |
|-
|-
| |
| | 12/11
| | 12/11
| | 116.596
| | 116.596
| |
|-
|-
| |
| | 14/11
| | 14/11
| | 116.617
| | 116.617
| |
|-
|-
| |
| |
| | 116.633
| | POTE11
| | POTE11
| | 116.633
|-
|-
| |
| | 7/6
| | 7/6
| | 116.641
| | 116.641
| |
|-
|-
| | 7\72
| | 7\72
| |
| | 116.667
| | 116.667
| |
|-
|-
| | |0 17 -11 -6 11&gt;
| |
| | 116.672 (11 limit least squares)
| | {{vector|0 17 -11 -6 11}}
| | 116.672
| | 11 limit least squares
|-
|-
| |
| |
| | 116.673
| | POTE5
| | POTE5
| | 116.673
|-
|-
| |
| |
| | 116.675
| | POTE7
| | POTE7
| | 116.675
|-
|-
| |
| | 10/9
| | 10/9
| | 116.716 (9, 11 and 13 limit minimax)
| | 116.716
| | 9, 11 and 13 limit minimax
|-
|-
| | |0 117 -44 -19&gt;
| |
| | 116.721 (9 limit least squares)
| | {{vector|0 117 -44 -19}}
| | 116.721
| | 9 limit least squares
|-
|-
| |
| |
| | 116.747
| | POTE13
| | POTE13
| | 116.747
|-
|-
| |
| | 11/8
| | 11/8
| | 116.755
| | 116.755
| |
|-
|-
| |
| | 9/7
| | 9/7
| | 116.792
| | 116.792
| |
|-
|-
| | 11\113
| | 11\113
| |
| | 116.814
| | 116.814
| |
|-
|-
| | |0 127 -84 -36 100 -44&gt;
| |
| | 116.820 (15 limit least squares)
| | {{vector|0 127 -84 -36 100 -44}}
| | 116.820
| | 15 limit least squares
|-
|-
| | |0 141 -70 -35 84 -42&gt;
| |
| | 116.846 (13 limit least squares)
| | {{vector|0 141 -70 -35 84 -42}}
| | 116.846
| | 13 limit least squares
|-
|-
| |
| | 4/3
| | 4/3
| | 116.993 (15 limit minimax)
| | 116.993
| | 15 limit minimax
|-
|-
| | 4\41
| | 4\41
| |
| | 117.073
| | 117.073
| |
|-
|-
| |
| | 13/11
| | 13/11
| | 117.266
| | 117.266
| |
|-
|-
| |
| | 18/13
| | 18/13
| | 117.559
| | 117.559
| |
|-
|-
| |
| | 13/12
| | 13/12
| | 117.936
| | 117.936
| |
|-
|-
| |
| | 15/14
| | 15/14
| | 119.443
| | 119.443
| |
|-
|-
| |
| | 16/13
| | 16/13
| | 119.824
| | 119.824
| |
|-
|-
| |
| | 15/13
| | 15/13
| | 123.871
| | 123.871
| |
|-
|-
| |
| | 14/13
| | 14/13
| | 128.298
| | 128.298
| |
|}
|}


==Spectrum of Benediction Tunings by Eigenmonzos==
=== Benediction ===


Gencom: [2 15/14; 225/224 243/242 351/350 441/440]
Gencom: [2 15/14; 225/224 243/242 351/350 441/440]


Gencom map: [&lt;1 1 3 3 2 7|, &lt;0 6 -7 -2 15 -34|]
Gencom map: [{{map|1 1 3 3 2 7}}, {{map|0 6 -7 -2 15 -34}}]


{| class="wikitable"
{| class="wikitable center-all"
|-
|-
! | Eigenmonzo
! | ET<br>generator
! | Secor
! | eigenmonzo<br>(unchanged interval)
! | secor<br>(¢)
! | comments
|-
|-
| |
| | 16/15
| | 16/15
| | 111.731
| | 111.731
| |
|-
|-
| |
| | 8/7
| | 8/7
| | 115.587
| | 115.587
| |
|-
|-
| |
| | 11/9
| | 11/9
| | 115.803
| | 115.803
| |
|-
|-
| | 3\31
| | 3\31
| |
| | 116.129
| | 116.129
| |
|-
|-
| |
| | 5/4
| | 5/4
| | 116.241
| | 116.241
| |
|-
|-
| |
| | 15/11
| | 15/11
| | 116.441
| | 116.441
| |
|-
|-
| |
| | 16/13
| | 16/13
| | 116.455
| | 116.455
| |
|-
|-
| |
| | 7/5
| | 7/5
| | 116.502
| | 116.502
| |
|-
|-
| | 10\103
| | 10\103
| |
| | 116.505
| | 116.505
| |
|-
|-
| |
| | 14/13
| | 14/13
| | 116.509
| | 116.509
| |
|-
|-
| |
| | 13/10
| | 13/10
| | 116.511
| | 116.511
| |
|-
|-
| |
| | 13/12
| | 13/12
| | 116.536
| | 116.536
| |
|-
|-
| |
| | 13/11
| | 13/11
| | 116.547
| | 116.547
| |
|-
|-
| | |0 -234 39 4 -115 228&gt;
| |
| | 116.56309 (13 limit least squares)
| | {{vector|0 -234 39 4 -115 228}}
| | 116.56309
| | 13 limit least squares
|-
|-
| | |0 -251 22 5 -131 261&gt;
| |
| | 116.56348 (15 limit least squares)
| | {{vector|0 -251 22 5 -131 261}}
| | 116.56348
| | 15 limit least squares
|-
|-
| | 17\175
| | 17\175
| |
| | 116.571
| | 116.571
| |
|-
|-
| | |0 -27 25 5&gt;
| |
| | 116.573 (7 limit least squares)
| | {{vector|0 -27 25 5}}
| | 116.573
| | 7 limit least squares
|-
|-
| |
| |
| | 116.574
| | POTE13
| | POTE13
| | 116.574
|-
|-
| | |0 -19 20&gt;
| |
| | 116.578 (5 limit least squares)
| | {{vector|0 -19 20}}
| | 116.578
| | 5 limit least squares
|-
|-
| |
| | 6/5
| | 6/5
| | 116.588 (5, 7 and 15 limit minimax)
| | 116.588
| | 5, 7 and 15 limit minimax
|-
|-
| |
| | 11/10
| | 11/10
| | 116.591
| | 116.591
| |
|-
|-
| |
| | 18/13
| | 18/13
| | 116.595 (13 limit minimax)
| | 116.595
| | 13 limit minimax
|-
|-
| |
| | 12/11
| | 12/11
| | 116.596
| | 116.596
| |
|-
|-
| |
| | 15/13
| | 15/13
| | 116.598
| | 116.598
| |
|-
|-
| |
| | 14/11
| | 14/11
| | 116.617
| | 116.617
| |
|-
|-
| |
| |
| | 116.633
| | POTE11
| | POTE11
| | 116.633
|-
|-
| |
| | 7/6
| | 7/6
| | 116.641
| | 116.641
| |
|-
|-
| | 7\72
| | 7\72
| |
| | 116.667
| | 116.667
| |
|-
|-
| | |0 17 -11 -6 11&gt;
| |
| | 116.672 (11 limit least squares)
| | {{vector|0 17 -11 -6 11}}
| | 116.672
| | 11 limit least squares
|-
|-
| |
| |
| | 116.673
| | POTE5
| | POTE5
| | 116.673
|-
|-
| |
| |
| | 116.675
| | POTE7
| | POTE7
| | 116.675
|-
|-
| |
| | 10/9
| | 10/9
| | 116.716 (9 and 11 limit minimax)
| | 116.716
| | 9 and 11 limit minimax
|-
|-
| | |0 117 -44 -19&gt;
| |
| | 116.721 (9 limit least squares)
| | {{vector|0 117 -44 -19}}
| | 116.721
| | 9 limit least squares
|-
|-
| |
| | 11/8
| | 11/8
| | 116.755
| | 116.755
| |
|-
|-
| |
| | 9/7
| | 9/7
| | 116.792
| | 116.792
| |
|-
|-
| | 11\113
| | 11\113
| |
| | 116.814
| | 116.814
| |
|-
|-
| |
| | 4/3
| | 4/3
| | 116.993
| | 116.993
| |
|-
|-
| | 4\41
| | 4\41
| |
| | 117.073
| | 117.073
| |
|-
|-
| |
| | 15/14
| | 15/14
| | 119.443
| | 119.443
| |
|}
|}


==Spectrum of Manna Tunings by Eigenmonzos==
=== Manna ===


Gencom: [2 15/14; 225/224 243/242 325/324 385/384]
Gencom: [2 15/14; 225/224 243/242 325/324 385/384]


Gencom map: [&lt;1 1 3 3 2 0|, &lt;0 6 -7 -2 15 38|]
Gencom map: [{{map|1 1 3 3 2 0}}, {{map|0 6 -7 -2 15 38}}]


{| class="wikitable"
{| class="wikitable center-all"
|-
|-
! | Eigenmonzo
! | ET<br>generator
! | Secor
! | eigenmonzo<br>(unchanged interval)
! | secor<br>(¢)
! | comments
|-
|-
| |
| | 16/15
| | 16/15
| | 111.731
| | 111.731
| |
|-
|-
| |
| | 8/7
| | 8/7
| | 115.587
| | 115.587
| |
|-
|-
| |
| | 11/9
| | 11/9
| | 115.803
| | 115.803
| |
|-
|-
| | 3\31
| | 3\31
| |
| | 116.129
| | 116.129
| |
|-
|-
| |
| | 5/4
| | 5/4
| | 116.241
| | 116.241
| |
|-
|-
| |
| | 15/11
| | 15/11
| | 116.441
| | 116.441
| |
|-
|-
| |
| | 7/5
| | 7/5
| | 116.502
| | 116.502
| |
|-
|-
| | 10\103
| | 10\103
| |
| | 116.505
| | 116.505
| |
|-
|-
| | 17\175
| | 17\175
| |
| | 116.571
| | 116.571
| |
|-
|-
| | |0 -27 25 5&gt;
| |
| | 116.573 (7 limit least squares)
| | {{vector|0 -27 25 5}}
| | 116.573
| | 7 limit least squares
|-
|-
| | |0 -19 20&gt;
| |
| | 116.578 (5 limit least squares)
| | {{vector|0 -19 20}}
| | 116.578
| | 5 limit least squares
|-
|-
| |
| | 6/5
| | 6/5
| | 116.588 (5 and 7 limit minimax)
| | 116.588
| | 5 and 7 limit minimax
|-
|-
| |
| | 11/10
| | 11/10
| | 116.591
| | 116.591
| |
|-
|-
| |
| | 12/11
| | 12/11
| | 116.596
| | 116.596
| |
|-
|-
| |
| | 14/11
| | 14/11
| | 116.617
| | 116.617
| |
|-
|-
| |
| |
| | 116.633
| | POTE11
| | POTE11
| | 116.633
|-
|-
| |
| | 7/6
| | 7/6
| | 116.641
| | 116.641
| |
|-
|-
| | 7\72
| | 7\72
| |
| | 116.667
| | 116.667
| |
|-
|-
| | |0 17 -11 -6 11&gt;
| |
| | 116.672 (11 limit least squares)
| | {{vector|0 17 -11 -6 11}}
| | 116.672
| | 11 limit least squares
|-
|-
| |
| |
| | 116.673
| | POTE5
| | POTE5
| | 116.673
|-
|-
| |
| |
| | 116.675
| | POTE7
| | POTE7
| | 116.675
|-
|-
| |
| | 10/9
| | 10/9
| | 116.716 (9 and 11 limit minimax)
| | 116.716
| | 9 and 11 limit minimax
|-
|-
| | |0 117 -44 -19&gt;
| |
| | 116.721 (9 limit least squares)
| | {{vector|0 117 -44 -19}}
| | 116.721
| | 9 limit least squares
|-
|-
| |
| | 15/13
| | 15/13
| | 116.725 (15 limit minimax)
| | 116.725
| | 15 limit minimax
|-
|-
| |
| |
| | 116.739
| | POTE13
| | POTE13
| | 116.739
|-
|-
| |
| | 11/8
| | 11/8
| | 116.755
| | 116.755
| |
|-
|-
| |
| | 13/10
| | 13/10
| | 116.760 (13 limit minimax)
| | 116.760
| | 13 limit minimax
|-
|-
| | |0 -37 -166 -77 59 243&gt;
| |
| | 116.764 (15 limit least squares)
| | {{vector|0 -37 -166 -77 59 243}}
| | 116.764
| | 15 limit least squares
|-
|-
| | |0 18 -111 -76 43 204&gt;
| |
| | 116.780 (13 limit least squares)
| | {{vector|0 18 -111 -76 43 204}}
| | 116.780
| | 13 limit least squares
|-
|-
| |
| | 9/7
| | 9/7
| | 116.792
| | 116.792
| |
|-
|-
| |
| | 14/13
| | 14/13
| | 116.79254
| | 116.79254
| |
|-
|-
| |
| | 18/13
| | 18/13
| | 116.79299
| | 116.79299
| |
|-
|-
| | 11\113
| | 11\113
| |
| | 116.814
| | 116.814
| |
|-
|-
| |
| | 13/12
| | 13/12
| | 116.830
| | 116.830
| |
|-
|-
| |
| | 16/13
| | 16/13
| | 116.856
| | 116.856
| |
|-
|-
| |
| | 13/11
| | 13/11
| | 116.922
| | 116.922
| |
|-
|-
| |
| | 4/3
| | 4/3
| | 116.993
| | 116.993
| |
|-
|-
| | 4\41
| | 4\41
| |
| | 117.073
| | 117.073
| |
|-
|-
| |
| | 15/14
| | 15/14
| | 119.443
| | 119.443
| |
|}
|}


==Spectrum of Revelation Tunings by Eigenmonzos==
=== Revelation ===


Gencom: [2 15/14; 66/65 99/98 105/104 1001/1000]
Gencom: [2 15/14; 66/65 99/98 105/104 1001/1000]


Gencom map: [&lt;1 1 3 3 5 4|, &lt;0 6 -7 -2 -16 -3|]
Gencom map: [{{map|1 1 3 3 5 4}}, {{map|0 6 -7 -2 -16 -3}}]


{| class="wikitable"
{| class="wikitable center-all"
|-
|-
! | Eigenmonzo
! | ET<br>generator
! | Secor
! | eigenmonzo<br>(unchanged interval)
! | secor<br>(¢)
! | comments
|-
|-
| |
| | 16/15
| | 16/15
| | 111.731
| | 111.731
| |
|-
|-
| |
| | 13/10
| | 13/10
| | 113.553
| | 113.553
| |
|-
|-
| |
| | 13/11
| | 13/11
| | 114.555
| | 114.555
| |
|-
|-
| |
| | 11/10
| | 11/10
| | 115.000
| | 115.000
| |
|-
|-
| |
| | 14/11
| | 14/11
| | 115.536
| | 115.536
| |
|-
|-
| |
| | 11/8
| | 11/8
| | 115.543
| | 115.543
| |
|-
|-
| |
| | 8/7
| | 8/7
| | 115.587
| | 115.587
| |
|-
|-
| |
| | 15/11
| | 15/11
| | 115.797
| | 115.797
| |
|-
|-
| |
| | 12/11
| | 12/11
| | 115.938
| | 115.938
| |
|-
|-
| | 3\31
| | 3\31
| |
| | 116.129
| | 116.129
| |
|-
|-
| |
| | 11/9
| | 11/9
| | 116.164 (11, 13 and 15 limit minimax)
| | 116.164
| | 11, 13 and 15 limit minimax
|-
|-
| | |0 -195 35 5 89&gt;
| |
| | 116.198 (11 limit least squares)
| | {{vector|0 -195 35 5 89}}
| | 116.198
| | 11 limit least squares
|-
|-
| | |0 -251 22 5 117 13&gt;
| |
| | 116.229 (15 limit least squares)
| | {{vector|0 -251 22 5 117 13}}
| | 116.229
| | 15 limit least squares
|-
|-
| |
| | 5/4
| | 5/4
| | 116.241
| | 116.241
| |
|-
|-
| | |0 -234 39 4 102 11&gt;
| |
| | 116.249 (13 limit least squares)
| | {{vector|0 -234 39 4 102 11}}
| | 116.249
| | 13 limit least squares
|-
|-
| |
| |
| | 116.268
| | POTE13
| | POTE13
| | 116.268
|-
|-
| |
| |
| | 116.277
| | POTE11
| | POTE11
| | 116.277
|-
|-
| |
| | 7/5
| | 7/5
| | 116.502
| | 116.502
| |
|-
|-
| | 10\103
| | 10\103
| |
| | 116.505
| | 116.505
| |
|-
|-
| | 17\175
| | 17\175
| |
| | 116.571
| | 116.571
| |
|-
|-
| | |0 -27 25 5&gt;
| |
| | 116.573 (7 limit least squares)
| | {{vector|0 -27 25 5}}
| | 116.573
| | 7 limit least squares
|-
|-
| | |0 -19 20&gt;
| |
| | 116.578 (5 limit least squares)
| | {{vector|0 -19 20}}
| | 116.578
| | 5 limit least squares
|-
|-
| |
| | 6/5
| | 6/5
| | 116.588 (5 and 7 limit minimax)
| | 116.588
| | 5 and 7 limit minimax
|-
|-
| |
| | 7/6
| | 7/6
| | 116.641
| | 116.641
| |
|-
|-
| | 7\72
| | 7\72
| |
| | 116.667
| | 116.667
| |
|-
|-
| |
| |
| | 116.673
| | POTE5
| | POTE5
| | 116.673
|-
|-
| |
| |
| | 116.675
| | POTE7
| | POTE7
| | 116.675
|-
|-
| |
| | 10/9
| | 10/9
| | 116.716 (9 limit minimax)
| | 116.716
| | 9 limit minimax
|-
|-
| | |0 117 -44 -19&gt;
| |
| | 116.721 (9 limit least squares)
| | {{vector|0 117 -44 -19}}
| | 116.721
| | 9 limit least squares
|-
|-
| |
| | 9/7
| | 9/7
| | 116.792
| | 116.792
| |
|-
|-
| | 11\113
| | 11\113
| |
| | 116.814
| | 116.814
| |
|-
|-
| |
| | 4/3
| | 4/3
| | 116.993
| | 116.993
| |
|-
|-
| | 4\41
| | 4\41
| |
| | 117.073
| | 117.073
| |
|-
|-
| |
| | 18/13
| | 18/13
| | 117.559
| | 117.559
| |
|-
|-
| |
| | 13/12
| | 13/12
| | 117.936
| | 117.936
| |
|-
|-
| |
| | 15/14
| | 15/14
| | 119.443
| | 119.443
| |
|-
|-
| |
| | 16/13
| | 16/13
| | 119.824
| | 119.824
| |
|-
|-
| |
| | 15/13
| | 15/13
| | 123.871
| | 123.871
| |
|-
|-
| |
| | 14/13
| | 14/13
| | 128.298
| | 128.298
| |
|}
|}
[[Category:benediction]]
[[Category:benediction]]
Retrieved from "https://en.xen.wiki/w/Miracle_extensions"