Xenharmonic Wiki

Miracle extensions: Difference between revisions

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m Cleanup (1/) and recategorize
Cleanup. -gencoms (trivial and irrelevant)
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== Tuning spectra ==
== Tuning spectra ==
=== Miraculous ===
=== Miraculous ===
 
{| class="wikitable center-all left-4"
Gencom: [2 15/14; 105/104 144/143 196/195 275/273]
 
Gencom mapping: [{{map|1 1 3 3 2 4}}, {{map|0 6 -7 -2 15 -3}}]
 
{| class="wikitable center-all"
|-
|-
! | ET<br>generator
! Edo<br>generator
! | [[eigenmonzo|eigenmonzo<br>(unchanged-interval]])
! [[Eigenmonzo|Eigenmonzo<br>(unchanged-interval)]]
! | secor<br>(¢)
! Generator (¢)
! | comments
! 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
| |
|  
|-
|-
| |
|  
| | {{vector|0 -27 25 5}}
| {{monzo| 0 -27 25 5 }}
| | 116.573
| 116.573
| | 7 limit least squares
| 7 limit least squares
|-
|-
| |
|  
| | {{vector|0 -19 20}}
| {{monzo| 0 -19 20 }}
| | 116.578
| 116.578
| | 5 limit least squares
| 5 limit least squares
|-
|-
| |
|  
| | 6/5
| 6/5
| | 116.588
| 116.588
| | 5 and 7 limit minimax
| 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
| 116.633
| | POTE11
| POTE11
|-
|-
| |
|  
| | 7/6
| 7/6
| | 116.641
| 116.641
| |
|  
|-
|-
| | 7\72
| 7\72
| |
|  
| | 116.667
| 116.667
| |
|  
|-
|-
| |
|  
| | {{vector|0 17 -11 -6 11}}
| {{monzo| 0 17 -11 -6 11 }}
| | 116.672
| 116.672
| | 11 limit least squares
| 11 limit least squares
|-
|-
| |
|  
| |
|  
| | 116.673
| 116.673
| | POTE5
| POTE5
|-
|-
| |
|  
| |
|  
| | 116.675
| 116.675
| | POTE7
| POTE7
|-
|-
| |
|  
| | 10/9
| 10/9
| | 116.716
| 116.716
| | 9, 11 and 13 limit minimax
| 9, 11 and 13 limit minimax
|-
|-
| |
|  
| | {{vector|0 117 -44 -19}}
| {{monzo| 0 117 -44 -19 }}
| | 116.721
| 116.721
| | 9 limit least squares
| 9 limit least squares
|-
|-
| |
|  
| |
|  
| | 116.747
| 116.747
| | POTE13
| POTE13
|-
|-
| |
|  
| | 11/8
| 11/8
| | 116.755
| 116.755
| |
|  
|-
|-
| |
|  
| | 9/7
| 9/7
| | 116.792
| 116.792
| |
|  
|-
|-
| | 11\113
| 11\113
| |
|  
| | 116.814
| 116.814
| |
|  
|-
|-
| |
|  
| | {{vector|0 127 -84 -36 100 -44}}
| {{monzo| 0 127 -84 -36 100 -44 }}
| | 116.820
| 116.820
| | 15 limit least squares
| 15 limit least squares
|-
|-
| |
|  
| | {{vector|0 141 -70 -35 84 -42}}
| {{monzo| 0 141 -70 -35 84 -42 }}
| | 116.846
| 116.846
| | 13 limit least squares
| 13 limit least squares
|-
|-
| |
|  
| | 4/3
| 4/3
| | 116.993
| 116.993
| | 15 limit minimax
| 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
| |
|  
|}
|}


=== Benediction ===
=== Benediction ===
 
{| class="wikitable center-all left-4"
Gencom: [2 15/14; 225/224 243/242 351/350 441/440]
 
Gencom mapping: [{{map|1 1 3 3 2 7}}, {{map|0 6 -7 -2 15 -34}}]
 
{| class="wikitable center-all"
|-
|-
! | ET<br>generator
! Edo<br>generator
! | eigenmonzo<br>(unchanged-interval)
! Eigenmonzo<br>(unchanged-interval)
! | secor<br>(¢)
! Generator (¢)
! | comments
! 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
| |
|  
|-
|-
| |
|  
| | {{vector|0 -234 39 4 -115 228}}
| {{monzo| 0 -234 39 4 -115 228 }}
| | 116.56309
| 116.56309
| | 13 limit least squares
| 13 limit least squares
|-
|-
| |
|  
| | {{vector|0 -251 22 5 -131 261}}
| {{monzo| 0 -251 22 5 -131 261 }}
| | 116.56348
| 116.56348
| | 15 limit least squares
| 15 limit least squares
|-
|-
| | 17\175
| 17\175
| |
|  
| | 116.571
| 116.571
| |
|  
|-
|-
| |
|  
| | {{vector|0 -27 25 5}}
| {{monzo| 0 -27 25 5 }}
| | 116.573
| 116.573
| | 7 limit least squares
| 7 limit least squares
|-
|-
| |
|  
| |
|  
| | 116.574
| 116.574
| | POTE13
| POTE13
|-
|-
| |
|  
| | {{vector|0 -19 20}}
| {{monzo| 0 -19 20 }}
| | 116.578
| 116.578
| | 5 limit least squares
| 5 limit least squares
|-
|-
| |
|  
| | 6/5
| 6/5
| | 116.588
| 116.588
| | 5, 7 and 15 limit minimax
| 5, 7 and 15 limit minimax
|-
|-
| |
|  
| | 11/10
| 11/10
| | 116.591
| 116.591
| |
|  
|-
|-
| |
|  
| | 18/13
| 18/13
| | 116.595
| 116.595
| | 13 limit minimax
| 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
| 116.633
| | POTE11
| POTE11
|-
|-
| |
|  
| | 7/6
| 7/6
| | 116.641
| 116.641
| |
|  
|-
|-
| | 7\72
| 7\72
| |
|  
| | 116.667
| 116.667
| |
|  
|-
|-
| |
|  
| | {{vector|0 17 -11 -6 11}}
| {{monzo| 0 17 -11 -6 11 }}
| | 116.672
| 116.672
| | 11 limit least squares
| 11 limit least squares
|-
|-
| |
|  
| |
|  
| | 116.673
| 116.673
| | POTE5
| POTE5
|-
|-
| |
|  
| |
|  
| | 116.675
| 116.675
| | POTE7
| POTE7
|-
|-
| |
|  
| | 10/9
| 10/9
| | 116.716
| 116.716
| | 9 and 11 limit minimax
| 9 and 11 limit minimax
|-
|-
| |
|  
| | {{vector|0 117 -44 -19}}
| {{monzo| 0 117 -44 -19 }}
| | 116.721
| 116.721
| | 9 limit least squares
| 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
| |
|  
|}
|}


=== Manna ===
=== Manna ===
 
{| class="wikitable center-all left-4"
Gencom: [2 15/14; 225/224 243/242 325/324 385/384]
 
Gencom mapping: [{{map|1 1 3 3 2 0}}, {{map|0 6 -7 -2 15 38}}]
 
{| class="wikitable center-all"
|-
|-
! | ET<br>generator
! Edo<br>generator
! | eigenmonzo<br>(unchanged-interval)
! Eigenmonzo<br>(unchanged-interval)
! | secor<br>(¢)
! Generator (¢)
! | comments
! 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
| |
|  
|-
|-
| |
|  
| | {{vector|0 -27 25 5}}
| {{monzo| 0 -27 25 5 }}
| | 116.573
| 116.573
| | 7 limit least squares
| 7 limit least squares
|-
|-
| |
|  
| | {{vector|0 -19 20}}
| {{monzo| 0 -19 20 }}
| | 116.578
| 116.578
| | 5 limit least squares
| 5 limit least squares
|-
|-
| |
|  
| | 6/5
| 6/5
| | 116.588
| 116.588
| | 5 and 7 limit minimax
| 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
| 116.633
| | POTE11
| POTE11
|-
|-
| |
|  
| | 7/6
| 7/6
| | 116.641
| 116.641
| |
|  
|-
|-
| | 7\72
| 7\72
| |
|  
| | 116.667
| 116.667
| |
|  
|-
|-
| |
|  
| | {{vector|0 17 -11 -6 11}}
| {{monzo| 0 17 -11 -6 11 }}
| | 116.672
| 116.672
| | 11 limit least squares
| 11 limit least squares
|-
|-
| |
|  
| |
|  
| | 116.673
| 116.673
| | POTE5
| POTE5
|-
|-
| |
|  
| |
|  
| | 116.675
| 116.675
| | POTE7
| POTE7
|-
|-
| |
|  
| | 10/9
| 10/9
| | 116.716
| 116.716
| | 9 and 11 limit minimax
| 9 and 11 limit minimax
|-
|-
| |
|  
| | {{vector|0 117 -44 -19}}
| {{monzo| 0 117 -44 -19 }}
| | 116.721
| 116.721
| | 9 limit least squares
| 9 limit least squares
|-
|-
| |
|  
| | 15/13
| 15/13
| | 116.725
| 116.725
| | 15 limit minimax
| 15 limit minimax
|-
|-
| |
|  
| |
|  
| | 116.739
| 116.739
| | POTE13
| POTE13
|-
|-
| |
|  
| | 11/8
| 11/8
| | 116.755
| 116.755
| |
|  
|-
|-
| |
|  
| | 13/10
| 13/10
| | 116.760
| 116.760
| | 13 limit minimax
| 13 limit minimax
|-
|-
| |
|  
| | {{vector|0 -37 -166 -77 59 243}}
| {{monzo| 0 -37 -166 -77 59 243 }}
| | 116.764
| 116.764
| | 15 limit least squares
| 15 limit least squares
|-
|-
| |
|  
| | {{vector|0 18 -111 -76 43 204}}
| {{monzo| 0 18 -111 -76 43 204 }}
| | 116.780
| 116.780
| | 13 limit least squares
| 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
| |
|  
|}
|}


=== Revelation ===
=== Revelation ===
 
{| class="wikitable center-all left-4"
Gencom: [2 15/14; 66/65 99/98 105/104 1001/1000]
 
Gencom mapping: [{{map|1 1 3 3 5 4}}, {{map|0 6 -7 -2 -16 -3}}]
 
{| class="wikitable center-all"
|-
|-
! | ET<br>generator
! Edo<br>generator
! | eigenmonzo<br>(unchanged-interval)
! Eigenmonzo<br>(unchanged-interval)
! | secor<br>(¢)
! Generator (¢)
! | comments
! 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
| 116.164
| | 11, 13 and 15 limit minimax
| 11, 13 and 15 limit minimax
|-
|-
| |
|  
| | {{vector|0 -195 35 5 89}}
| {{monzo| 0 -195 35 5 89 }}
| | 116.198
| 116.198
| | 11 limit least squares
| 11 limit least squares
|-
|-
| |
|  
| | {{vector|0 -251 22 5 117 13}}
| {{monzo| 0 -251 22 5 117 13 }}
| | 116.229
| 116.229
| | 15 limit least squares
| 15 limit least squares
|-
|-
| |
|  
| | 5/4
| 5/4
| | 116.241
| 116.241
| |
|  
|-
|-
| |
|  
| | {{vector|0 -234 39 4 102 11}}
| {{monzo| 0 -234 39 4 102 11 }}
| | 116.249
| 116.249
| | 13 limit least squares
| 13 limit least squares
|-
|-
| |
|  
| |
|  
| | 116.268
| 116.268
| | POTE13
| POTE13
|-
|-
| |
|  
| |
|  
| | 116.277
| 116.277
| | POTE11
| POTE11
|-
|-
| |
|  
| | 7/5
| 7/5
| | 116.502
| 116.502
| |
|  
|-
|-
| | 10\103
| 10\103
| |
|  
| | 116.505
| 116.505
| |
|  
|-
|-
| | 17\175
| 17\175
| |
|  
| | 116.571
| 116.571
| |
|  
|-
|-
| |
|  
| | {{vector|0 -27 25 5}}
| {{monzo| 0 -27 25 5 }}
| | 116.573
| 116.573
| | 7 limit least squares
| 7 limit least squares
|-
|-
| |
|  
| | {{vector|0 -19 20}}
| {{monzo| 0 -19 20 }}
| | 116.578
| 116.578
| | 5 limit least squares
| 5 limit least squares
|-
|-
| |
|  
| | 6/5
| 6/5
| | 116.588
| 116.588
| | 5 and 7 limit minimax
| 5 and 7 limit minimax
|-
|-
| |
|  
| | 7/6
| 7/6
| | 116.641
| 116.641
| |
|  
|-
|-
| | 7\72
| 7\72
| |
|  
| | 116.667
| 116.667
| |
|  
|-
|-
| |
|  
| |
|  
| | 116.673
| 116.673
| | POTE5
| POTE5
|-
|-
| |
|  
| |
|  
| | 116.675
| 116.675
| | POTE7
| POTE7
|-
|-
| |
|  
| | 10/9
| 10/9
| | 116.716
| 116.716
| | 9 limit minimax
| 9 limit minimax
|-
|-
| |
|  
| | {{vector|0 117 -44 -19}}
| {{monzo| 0 117 -44 -19 }}
| | 116.721
| 116.721
| | 9 limit least squares
| 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:Miracle]]
[[Category:Miracle]]
[[Category:Temperament extensions]]
[[Category:Temperament extensions]]
Retrieved from "https://en.xen.wiki/w/Miracle_extensions"