Xenharmonic Wiki

Negri extensions: Difference between revisions

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VisualWikitext
m Cleanup (1/) and recategorize
-gencoms (irrelevant to tuning and trivial to derive). Misc. cleanup
Line 2: Line 2:


== Tuning spectra ==
== Tuning spectra ==
=== Undecimal negri ===


=== Negri ===
{| class="wikitable center-all left-4"
 
[[Gencom|Gencom]]: [2 15/14; 45/44 49/48 56/55 78/77]
 
Gencom mapping: [<1 2 2 3 4 4|, <0 -4 3 -2 -5 -3|]
 
{| class="wikitable center-all"
|-
|-
! | ET generator
! Edo<br>generator
! | [[eigenmonzo|eigenmonzo<br>(unchanged-interval]])
! [[Eigenmonzo|Eigenmonzo<br>(unchanged-interval]])
! | supersecor<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
| |
|  
|-
|-
| |
|  
| | 15/14
| 15/14
| | 119.443
| 119.443
| |
|  
|-
|-
| |
|  
| | 16/13
| 16/13
| | 119.824
| 119.824
| |
|  
|-
|-
| | 1\10
| 1\10
| |
|  
| | 120.000
| 120.000
| |
|  
|-
|-
| |
|  
| | 7/5
| 7/5
| | 123.498
| 123.498
| |
|  
|-
|-
| |
|  
| | 15/13
| 15/13
| | 123.871
| 123.871
| |
|  
|-
|-
| | 3\29
| 3\29
| |
|  
| | 124.138
| 124.138
| |
|  
|-
|-
| |
|  
| | 13/10
| 13/10
| | 124.298
| 124.298
| |
|  
|-
|-
| |
|  
| | 4/3
| 4/3
| | 124.511
| 124.511
| | 7 and 9 limit minimax
| 7- and 9-odd-limit minimax
|-
|-
| | 5\48
| 5\48
| |
|  
| | 125.000
| 125.000
| |
|  
|-
|-
| |
|  
| | 30517578125/26795786661
| 30517578125/26795786661
| | 125.469
| 125.469
| | 7 limit least squares
| 7-odd-limit least squares
|-
|-
| |
|  
| | {{vector|0 63 -26 -1}}
| {{vector|0 63 -26 -1}}
| | 125.579
| 125.579
| | 9 limit least squares
| 9-odd-limit least squares
|-
|-
| |
|  
| | 10/9
| 10/9
| | 125.673
| 125.673
| |
|  
|-
|-
| |
|  
| | 11337408/9765625
| 11337408/9765625
| | 126.238
| 126.238
| | 5 limit least squares
| 5-odd-limit least squares
|-
|-
| | 2\19
| 2\19
| |
|  
| | 126.316
| 126.316
| |
|  
|-
|-
| |
|  
| | 6/5
| 6/5
| | 126.337
| 126.337
| | 5 limit minimax
| 5-odd-limit minimax
|-
|-
| |
|  
| | {{vector|0 79 -40 -5 16 2}}
| {{vector|0 79 -40 -5 16 2}}
| | 126.445
| 126.445
| | 13 limit least squares
| 13-odd-limit least squares
|-
|-
| |
|  
| | {{vector|0 34 -17 -2 7}}
| {{vector|0 34 -17 -2 7}}
| | 126.511
| 126.511
| | 11 limit least squares
| 11-odd-limit least squares
|-
|-
| |
|  
| | {{vector|0 73 -46 -4 20 4}}
| {{vector|0 73 -46 -4 20 4}}
| | 126.619
| 126.619
| | 15 limit least squares
| 15-odd-limit least squares
|-
|-
| |
|  
| | 18/13
| 18/13
| | 127.324
| 127.324
| |
|  
|-
|-
| |
|  
| | 9/7
| 9/7
| | 127.486
| 127.486
| | 11, 13 and 15 limit minimax
| 11-, 13- and 15-odd-limit minimax
|-
|-
| | 5\47
| 5\47
| |
|  
| | 127.660
| 127.660
| |
|  
|-
|-
| |
|  
| | 14/13
| 14/13
| | 128.298
| 128.298
| |
|  
|-
|-
| | 3\28
| 3\28
| |
|  
| | 128.571
| 128.571
| |
|  
|-
|-
| |
|  
| | 5/4
| 5/4
| | 128.771
| 128.771
| |
|  
|-
|-
| |
|  
| | 11/10
| 11/10
| | 129.374
| 129.374
| |
|  
|-
|-
| |
|  
| | 11/8
| 11/8
| | 129.736
| 129.736
| |
|  
|-
|-
| |
|  
| | 7/6
| 7/6
| | 133.435
| 133.435
| |
|  
|-
|-
| |
|  
| | 15/11
| 15/11
| | 134.238
| 134.238
| |
|  
|-
|-
| |
|  
| | 13/12
| 13/12
| | 138.573
| 138.573
| |
|  
|-
|-
| |
|  
| | 14/11
| 14/11
| | 139.169
| 139.169
| |
|  
|-
|-
| |
|  
| | 13/11
| 13/11
| | 144.605
| 144.605
| |
|  
|-
|-
| |
|  
| | 12/11
| 12/11
| | 150.637
| 150.637
| |
|  
|}
|}


=== Negril ===
=== Negril ===


[[Gencom|Gencom]]: [2 15/14; 49/48 65/64 91/90 875/858]
{| class="wikitable center-all left-4"
 
Gencom mapping: [{{map|1 2 2 3 2 4}}, {{map|0 -4 3 -2 14 -3}}]
 
{| class="wikitable center-all"
|-
|-
! | ET<br>generator
! Edo<br>generator
! | eigenmonzo<br>(unchanged-interval)
! Eigenmonzo<br>(unchanged-interval)
! | supersecor<br>(¢)
! Generator (¢)
! | comments
! Comments
|-
|-
| |
|  
| | 16/15
| 16/15
| | 111.731
| 111.731
| |
|  
|-
|-
| |
|  
| | 8/7
| 8/7
| | 115.587
| 115.587
| |
|  
|-
|-
| |
|  
| | 15/14
| 15/14
| | 119.443
| 119.443
| |
|  
|-
|-
| |
|  
| | 16/13
| 16/13
| | 119.824
| 119.824
| |
|  
|-
|-
| | 1\10
| 1\10
| |
|  
| | 120.000
| 120.000
| |
|  
|-
|-
| |
|  
| | 7/5
| 7/5
| | 123.498
| 123.498
| |
|  
|-
|-
| |
|  
| | 15/13
| 15/13
| | 123.871
| 123.871
| |
|  
|-
|-
| |
|  
| | 14/11
| 14/11
| | 123.906
| 123.906
| |
|  
|-
|-
| |
|  
| | 11/10
| 11/10
| | 124.091
| 124.091
| |
|  
|-
|-
| | 3\29
| 3\29
| |
|  
| | 124.138
| 124.138
| |
|  
|-
|-
| |
|  
| | 13/11
| 13/11
| | 124.164
| 124.164
| |
|  
|-
|-
| |
|  
| | 15/11
| 15/11
| | 124.203
| 124.203
| |
|  
|-
|-
| |
|  
| | 13/10
| 13/10
| | 124.298
| 124.298
| |
|  
|-
|-
| |
|  
| | 4/3
| 4/3
| | 124.511
| 124.511
| | 7, 9, 11, 13 and 15 limit minimax
| 7, 9, 11, 13 and 15 limit minimax
|-
|-
| |
|  
| | {{vector|0 -149 8 -15 113 -23}}
| {{vector|0 -149 8 -15 113 -23}}
| | 124.700
| 124.700
| | 15 limit least squares
| 15-odd-limit least squares
|-
|-
| |
|  
| | {{vector|0 -136 21 -14 98 -21}}
| {{vector|0 -136 21 -14 98 -21}}
| | 124.764
| 124.764
| | 13 limit least squares
| 13 limit least squares
|-
|-
| |
|  
| | {{vector|0 -125 15 -15 81}}
| {{vector|0 -125 15 -15 81}}
| | 124.854
| 124.854
| | 11 limit least squares
| 11-odd-limit least squares
|-
|-
| |
|  
| | 11/9
| 11/9
| | 124.882
| 124.882
| |
|  
|-
|-
| |
|  
| | 12/11
| 12/11
| | 124.965
| 124.965
| |
|  
|-
|-
| | 5\48
| 5\48
| |
|  
| | 125.000
| 125.000
| |
|  
|-
|-
| |
|  
| | 11/8
| 11/8
| | 125.094
| 125.094
| |
|  
|-
|-
| |
|  
| | 30517578125/26795786661
| 30517578125/26795786661
| | 125.469
| 125.469
| | 7 limit least squares
| 7 limit least squares
|-
|-
| |
|  
| | {{vector|0 63 -26 -1}}
| {{vector|0 63 -26 -1}}
| | 125.579
| 125.579
| | 9 limit least squares
| 9-odd-limit least squares
|-
|-
| |
|  
| | 10/9
| 10/9
| | 125.673
| 125.673
| |
|  
|-
|-
| |
|  
| | 11337408/9765625
| 11337408/9765625
| | 126.238
| 126.238
| | 5 limit least squares
| 5-odd-limit least squares
|-
|-
| | 2\19
| 2\19
| |
|  
| | 126.316
| 126.316
| |
|  
|-
|-
| |
|  
| | 6/5
| 6/5
| | 126.337
| 126.337
| | 5 limit minimax
| 5-odd-limit minimax
|-
|-
| |
|  
| | 18/13
| 18/13
| | 127.324
| 127.324
| |
|  
|-
|-
| |
|  
| | 9/7
| 9/7
| | 127.486
| 127.486
| |
|  
|-
|-
| | 5\47
| 5\47
| |
|  
| | 127.660
| 127.660
| |
|  
|-
|-
| |
|  
| | 14/13
| 14/13
| | 128.298
| 128.298
| |
|  
|-
|-
| | 3\28
| 3\28
| |
|  
| | 128.571
| 128.571
| |
|  
|-
|-
| |
|  
| | 5/4
| 5/4
| | 128.771
| 128.771
| |
|  
|-
|-
| |
|  
| | 7/6
| 7/6
| | 133.435
| 133.435
| |
|  
|-
|-
| |
|  
| | 13/12
| 13/12
| | 138.573
| 138.573
| |
|  
|}
|}


=== Negric ===
=== Negric ===


[[Gencom|Gencom]]: [2 15/14; 33/32 49/48 65/64 91/90]
{| class="wikitable center-all left-4"
 
Gencom mapping: [{{map|1 2 2 3 3 4}}, {{map|0 -4 3 -2 4 -3}}]
 
{| class="wikitable center-all"
|-
|-
! | ET<br>generator
! Edo<br>generator
! | eigenmonzo<br>(unchanged-interval)
! Eigenmonzo<br>(unchanged-interval)
! | supersecor<br>(¢)
! Generator (¢)
! | comments
! Comments
|-
|-
| |
|  
| | 16/15
| 16/15
| | 111.731
| 111.731
| |
|  
|-
|-
| |
|  
| | 8/7
| 8/7
| | 115.587
| 115.587
| |
|  
|-
|-
| |
|  
| | 15/14
| 15/14
| | 119.443
| 119.443
| |
|  
|-
|-
| |
|  
| | 16/13
| 16/13
| | 119.824
| 119.824
| |
|  
|-
|-
| | 1\10
| 1\10
| |
|  
| | 120.000
| 120.000
| |
|  
|-
|-
| |
|  
| | 7/5
| 7/5
| | 123.498
| 123.498
| |
|  
|-
|-
| |
|  
| | 15/13
| 15/13
| | 123.871
| 123.871
| |
|  
|-
|-
| | 3\29
| 3\29
| |
|  
| | 124.138
| 124.138
| |
|  
|-
|-
| |
|  
| | 13/10
| 13/10
| | 124.298
| 124.298
| |
|  
|-
|-
| |
|  
| | 4/3
| 4/3
| | 124.511
| 124.511
| | 7 and 9 limit minimax
| 7- and 9-odd-limit minimax
|-
|-
| | 5\48
| 5\48
| |
|  
| | 125.000
| 125.000
| |
|  
|-
|-
| |
|  
| | 30517578125/26795786661
| 30517578125/26795786661
| | 125.469
| 125.469
| | 7 limit least squares
| 7-odd-limit least squares
|-
|-
| |
|  
| | {{vector|0 63 -26 -1}}
| {{vector|0 63 -26 -1}}
| | 125.579
| 125.579
| | 9 limit least squares
| 9-odd-limit least squares
|-
|-
| |
|  
| | 10/9
| 10/9
| | 125.673
| 125.673
| |
|  
|-
|-
| |
|  
| | 11337408/9765625
| 11337408/9765625
| | 126.238
| 126.238
| | 5 limit least squares
| 5-odd-limit least squares
|-
|-
| | 2\19
| 2\19
| |
|  
| | 126.316
| 126.316
| |
|  
|-
|-
| |
|  
| | 6/5
| 6/5
| | 126.337
| 126.337
| | 5 limit minimax
| 5-odd-limit minimax
|-
|-
| |
|  
| | 18/13
| 18/13
| | 127.324
| 127.324
| |
|  
|-
|-
| |
|  
| | 9/7
| 9/7
| | 127.486
| 127.486
| |
|  
|-
|-
| |
|  
| | {{vector|0 106 -31 4 -38 11}}
| {{vector|0 106 -31 4 -38 11}}
| | 127.602
| 127.602
| | 13 limit least squares
| 13-odd-limit least squares
|-
|-
| | 5\47
| 5\47
| |
|  
| | 127.660
| 127.660
| |
|  
|-
|-
| |
|  
| | {{vector|0 -95 25 -5 31}}
| {{vector|0 -95 25 -5 31}}
| | 127.706
| 127.706
| | 11 limit least squares
| 11 limit least squares
|-
|-
| |
|  
| | {{vector|0 109 -28 5 -43 13}}
| {{vector|0 109 -28 5 -43 13}}
| | 127.718
| 127.718
| | 15 limit least squares
| 15-odd-limit least squares
|-
|-
| |
|  
| | 14/13
| 14/13
| | 128.298
| 128.298
| |
|  
|-
|-
| | 3\28
| 3\28
| |
|  
| | 128.571
| 128.571
| |
|  
|-
|-
| |
|  
| | 5/4
| 5/4
| | 128.771
| 128.771
| |
|  
|-
|-
| |
|  
| | 11/9
| 11/9
| | 128.951
| 128.951
| | 11, 13 and 15 limit minimax
| 11-, 13- and 15-odd-limit minimax
|-
|-
| |
|  
| | 13/11
| 13/11
| | 130.113
| 130.113
| |
|  
|-
|-
| |
|  
| | 14/11
| 14/11
| | 130.415
| 130.415
| |
|  
|-
|-
| |
|  
| | 12/11
| 12/11
| | 131.170
| 131.170
| |
|  
|-
|-
| |
|  
| | 15/11
| 15/11
| | 132.610
| 132.610
| |
|  
|-
|-
| |
|  
| | 7/6
| 7/6
| | 133.435
| 133.435
| |
|  
|-
|-
| |
|  
| | 11/8
| 11/8
| | 137.829
| 137.829
| |
|  
|-
|-
| |
|  
| | 13/12
| 13/12
| | 138.573
| 138.573
| |
|  
|-
|-
| |
|  
| | 11/10
| 11/10
| | 165.004
| 165.004
| |
|  
|}
|}


=== Negroni ===
=== Negroni ===


[[Gencom|Gencom]]: [2 15/14; 49/48 55/54 65/64 91/90]
{| class="wikitable center-all left-4"
 
Gencom mapping: [{{map|1 2 2 3 5 4}}, {{map|0 -4 3 -2 -15 -3}}]
 
{| class="wikitable center-all"
|-
|-
! | ET<br>generator
! Edo<br>generator
! | eigenmonzo<br>(unchanged-interval)
! Eigenmonzo<br>(unchanged-interval)
! | supersecor<br>(¢)
! Generator (¢)
! | comments
! Comments
|-
|-
| |
|  
| | 16/15
| 16/15
| | 111.731
| 111.731
| |
|  
|-
|-
| |
|  
| | 8/7
| 8/7
| | 115.587
| 115.587
| |
|  
|-
|-
| |
|  
| | 15/14
| 15/14
| | 119.443
| 119.443
| |
|  
|-
|-
| |
|  
| | 16/13
| 16/13
| | 119.824
| 119.824
| |
|  
|-
|-
| | 1\10
| 1\10
| |
|  
| | 120.000
| 120.000
| |
|  
|-
|-
| |
|  
| | 11/9
| 11/9
| | 121.799
| 121.799
| | 11, 13 and 15 limit minimax
| 11-, 13- and 15-odd-limit minimax
|-
|-
| |
|  
| | 12/11
| 12/11
| | 122.785
| 122.785
| |
|  
|-
|-
| |
|  
| | 11/8
| 11/8
| | 123.245
| 123.245
| |
|  
|-
|-
| |
|  
| | 7/5
| 7/5
| | 123.498
| 123.498
| |
|  
|-
|-
| |
|  
| | 15/13
| 15/13
| | 123.871
| 123.871
| |
|  
|-
|-
| |
|  
| | 15/11
| 15/11
| | 124.068
| 124.068
| |
|  
|-
|-
| |
|  
| | 13/11
| 13/11
| | 124.101
| 124.101
| |
|  
|-
|-
| | 3\29
| 3\29
| |
|  
| | 124.138
| 124.138
| |
|  
|-
|-
| |
|  
| | 11/10
| 11/10
| | 124.166
| 124.166
| |
|  
|-
|-
| |
|  
| | {{vector|0 19 -22 -7 32}}
| {{vector|0 19 -22 -7 32}}
| | 124.180
| 124.180
| | 11 limit least squares
| 11-odd-limit least squares
|-
|-
| |
|  
| | {{vector|0 33 -66 -14 90 -6}}
| {{vector|0 33 -66 -14 90 -6}}
| | 124.186
| 124.186
| | 15 limit least squares
| 15-odd-limit least squares
|-
|-
| |
|  
| | {{vector|0 49 -50 -15 76 -8}}
| {{vector|0 49 -50 -15 76 -8}}
| | 124.215
| 124.215
| | 13 limit least squares
| 13-odd-limit least squares
|-
|-
| |
|  
| | 13/10
| 13/10
| | 124.298
| 124.298
| |
|  
|-
|-
| |
|  
| | 14/11
| 14/11
| | 124.424
| 124.424
| |
|  
|-
|-
| |
|  
| | 4/3
| 4/3
| | 124.511
| 124.511
| | 7 and 9 limit minimax
| 7- and 9-odd-limit minimax
|-
|-
| | 5\48
| 5\48
| |
|  
| | 125.000
| 125.000
| |
|  
|-
|-
| |
|  
| | 30517578125/26795786661
| 30517578125/26795786661
| | 125.469
| 125.469
| | 7 limit least squares
| 7-odd-limit least squares
|-
|-
| |
|  
| | {{vector|0 63 -26 -1}}
| {{vector|0 63 -26 -1}}
| | 125.579
| 125.579
| | 9 limit least squares
| 9-odd-limit least squares
|-
|-
| |
|  
| | 10/9
| 10/9
| | 125.673
| 125.673
| |
|  
|-
|-
| |
|  
| | 11337408/9765625
| 11337408/9765625
| | 126.238
| 126.238
| | 5 limit least squares
| 5-odd-limit least squares
|-
|-
| |
|  
| | 6/5
| 6/5
| | 126.337
| 126.337
| | 5 limit minimax
| 5-odd-limit minimax
|-
|-
| |
|  
| | 18/13
| 18/13
| | 127.324
| 127.324
| |
|  
|-
|-
| |
|  
| | 9/7
| 9/7
| | 127.486
| 127.486
| |
|  
|-
|-
| | 5\47
| 5\47
| |
|  
| | 127.660
| 127.660
| |
|  
|-
|-
| |
|  
| | 14/13
| 14/13
| | 128.298
| 128.298
| |
|  
|-
|-
| | 3\28
| 3\28
| |
|  
| | 128.571
| 128.571
| |
|  
|-
|-
| |
|  
| | 5/4
| 5/4
| | 128.771
| 128.771
| |
|  
|-
|-
| |
|  
| | 7/6
| 7/6
| | 133.435
| 133.435
| |
|  
|-
|-
| |
|  
| | 13/12
| 13/12
| | 138.573
| 138.573
| |
|  
|}
|}


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