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Negri extensions: Difference between revisions

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{{Breadcrumb|Negri}}
[[Negri]] has various competing [[extension]]s to the [[11-limit]]. This is evidenced by the fact that its [[support]]ing equal temperaments, [[10edo|10]] and [[19edo|19]], do less well in the 11-limit. The extensions are:  
[[Negri]] has various competing [[extension]]s to the [[11-limit]]. This is evidenced by the fact that its [[support]]ing equal temperaments, [[10edo|10]] and [[19edo|19]], do less well in the 11-limit. The extensions are:  
* '''Undecimal negri''' (10 & 19) – tempering out 45/44, 49/48, and 56/55
* '''Undecimal negri''' (10 & 19) – tempering out 45/44, 49/48, and 56/55
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! Edo<br>generator
! Edo<br>generator
! [[Eigenmonzo|Eigenmonzo<br>(unchanged-interval]])
! [[Eigenmonzo|Unchanged interval<br>(eigenmonzo)]]
! Generator (¢)
! Generator (¢)
! Comments
! Comments
|-
|-
|  
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| 16/15
| 15/8
| 111.731
| 111.731
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| 4/3
| 3/2
| 124.511
| 124.511
| 7- and 9-odd-limit minimax
| 7- and 9-odd-limit minimax
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|-
|  
|  
| 30517578125/26795786661
| {{monzo| 0 -13 15 -5 }}
| 125.469
| 125.469
| 7-odd-limit least squares
| 7-odd-limit least squares
|-
|-
|  
|  
| {{vector|0 63 -26 -1}}
| {{monzo| 0 63 -26 -1 }}
| 125.579
| 125.579
| 9-odd-limit least squares
| 9-odd-limit least squares
|-
|-
|  
|  
| 10/9
| 9/5
| 125.673
| 125.673
|  
|  
|-
|-
|  
|  
| 11337408/9765625
| {{monzo| 6 11 -10 }}
| 126.238
| 126.238
| 5-odd-limit least squares
| 5-odd-limit least squares
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|-
|-
|  
|  
| 6/5
| 5/3
| 126.337
| 126.337
| 5-odd-limit minimax
| 5-odd-limit minimax
|-
|-
|  
|  
| {{vector|0 79 -40 -5 16 2}}
| {{monzo| 0 79 -40 -5 16 2 }}
| 126.445
| 126.445
| 13-odd-limit least squares
| 13-odd-limit least squares
|-
|-
|  
|  
| {{vector|0 34 -17 -2 7}}
| {{monzo| 0 34 -17 -2 7 }}
| 126.511
| 126.511
| 11-odd-limit least squares
| 11-odd-limit least squares
|-
|-
|  
|  
| {{vector|0 73 -46 -4 20 4}}
| {{monzo| 0 73 -46 -4 20 4 }}
| 126.619
| 126.619
| 15-odd-limit least squares
| 15-odd-limit least squares
|-
|-
|  
|  
| 18/13
| 13/9
| 127.324
| 127.324
|  
|  
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| 14/13
| 13/7
| 128.298
| 128.298
|  
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| 11/8
| 11/8
| 129.736
| 129.736
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|-
| 1\9
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| 133.333
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| 14/11
| 11/7
| 139.169
| 139.169
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|  
|  
| 12/11
| 11/6
| 150.637
| 150.637
|  
|  
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|-
|-
! Edo<br>generator
! Edo<br>generator
! Eigenmonzo<br>(unchanged-interval)
! Unchanged interval<br>(eigenmonzo)
! Generator (¢)
! Generator (¢)
! Comments
! Comments
|-
|-
|  
|  
| 16/15
| 15/8
| 111.731
| 111.731
|  
|  
|-
|-
|  
|  
| 8/7
| 7/4
| 115.587
| 115.587
|  
|  
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|  
|  
| 16/13
| 13/8
| 119.824
| 119.824
|  
|  
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|  
| 14/11
| 11/7
| 123.906
| 123.906
|  
|  
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|-
|  
|  
| 4/3
| 3/2
| 124.511
| 124.511
| 7-, 9-, 11-, 13- and 15-odd-limit minimax
| 7-, 9-, 11-, 13- and 15-odd-limit minimax
|-
|-
|  
|  
| {{vector|0 -149 8 -15 113 -23}}
| {{monzo| 0 -149 8 -15 113 -23 }}
| 124.700
| 124.700
| 15-odd-limit least squares
| 15-odd-limit least squares
|-
|-
|  
|  
| {{vector|0 -136 21 -14 98 -21}}
| {{monzo| 0 -136 21 -14 98 -21 }}
| 124.764
| 124.764
| 13-odd-limit least squares
| 13-odd-limit least squares
|-
|-
|  
|  
| {{vector|0 -125 15 -15 81}}
| {{monzo| 0 -125 15 -15 81 }}
| 124.854
| 124.854
| 11-odd-limit least squares
| 11-odd-limit least squares
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|-
|-
|  
|  
| 12/11
| 11/6
| 124.965
| 124.965
|  
|  
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|-
|-
|  
|  
| 30517578125/26795786661
| {{monzo| 0 -13 15 -5 }}
| 125.469
| 125.469
| 7-odd-limit least squares
| 7-odd-limit least squares
|-
|-
|  
|  
| {{vector|0 63 -26 -1}}
| {{monzo| 0 63 -26 -1 }}
| 125.579
| 125.579
| 9-odd-limit least squares
| 9-odd-limit least squares
|-
|-
|  
|  
| 10/9
| 9/5
| 125.673
| 125.673
|  
|  
|-
|-
|  
|  
| 11337408/9765625
| {{monzo| 6 11 -10 }}
| 126.238
| 126.238
| 5-odd-limit least squares
| 5-odd-limit least squares
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|-
|-
|  
|  
| 6/5
| 5/3
| 126.337
| 126.337
| 5-odd-limit minimax
| 5-odd-limit minimax
|-
|-
|  
|  
| 18/13
| 13/9
| 127.324
| 127.324
|  
|  
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| 14/13
| 13/7
| 128.298
| 128.298
|  
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| 5/4
| 5/4
| 128.771
| 128.771
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|-
| 1\9
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| 133.333
|  
|  
|-
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|-
|-
! Edo<br>generator
! Edo<br>generator
! Eigenmonzo<br>(unchanged-interval)
! Unchanged interval<br>(eigenmonzo)
! Generator (¢)
! Generator (¢)
! Comments
! Comments
|-
|-
|  
|  
| 16/15
| 15/8
| 111.731
| 111.731
|  
|  
|-
|-
|  
|  
| 8/7
| 7/4
| 115.587
| 115.587
|  
|  
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|-
|  
|  
| 16/13
| 13/8
| 119.824
| 119.824
|  
|  
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|-
|-
|  
|  
| 4/3
| 3/2
| 124.511
| 124.511
| 7- and 9-odd-limit minimax
| 7- and 9-odd-limit minimax
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|-
|-
|  
|  
| 30517578125/26795786661
| {{monzo| 0 -13 15 -5 }}
| 125.469
| 125.469
| 7-odd-limit least squares
| 7-odd-limit least squares
|-
|-
|  
|  
| {{vector|0 63 -26 -1}}
| {{monzo| 0 63 -26 -1 }}
| 125.579
| 125.579
| 9-odd-limit least squares
| 9-odd-limit least squares
|-
|-
|  
|  
| 10/9
| 9/5
| 125.673
| 125.673
|  
|  
|-
|-
|  
|  
| 11337408/9765625
| {{monzo| 6 11 -10 }}
| 126.238
| 126.238
| 5-odd-limit least squares
| 5-odd-limit least squares
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|-
|-
|  
|  
| 6/5
| 5/3
| 126.337
| 126.337
| 5-odd-limit minimax
| 5-odd-limit minimax
|-
|-
|  
|  
| 18/13
| 13/9
| 127.324
| 127.324
|  
|  
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|-
|-
|  
|  
| {{vector|0 106 -31 4 -38 11}}
| {{monzo| 0 106 -31 4 -38 11 }}
| 127.602
| 127.602
| 13-odd-limit least squares
| 13-odd-limit least squares
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|-
|-
|  
|  
| {{vector|0 -95 25 -5 31}}
| {{monzo| 0 -95 25 -5 31 }}
| 127.706
| 127.706
| 11 limit least squares
| 11 limit least squares
|-
|-
|  
|  
| {{vector|0 109 -28 5 -43 13}}
| {{monzo| 0 109 -28 5 -43 13 }}
| 127.718
| 127.718
| 15-odd-limit least squares
| 15-odd-limit least squares
|-
|-
|  
|  
| 14/13
| 13/7
| 128.298
| 128.298
|  
|  
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|-
|  
|  
| 14/11
| 11/7
| 130.415
| 130.415
|  
|  
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|-
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| 12/11
| 11/6
| 131.170
| 131.170
|  
|  
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| 15/11
| 15/11
| 132.610
| 132.610
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|-
| 1\9
|
| 133.333
|  
|  
|-
|-
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|-
|-
! Edo<br>generator
! Edo<br>generator
! Eigenmonzo<br>(unchanged-interval)
! Unchanged interval<br>(eigenmonzo)
! Generator (¢)
! Generator (¢)
! Comments
! Comments
|-
|-
|  
|  
| 16/15
| 15/8
| 111.731
| 111.731
|  
|  
|-
|-
|  
|  
| 8/7
| 7/4
| 115.587
| 115.587
|  
|  
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|-
|  
|  
| 16/13
| 13/8
| 119.824
| 119.824
|  
|  
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|-
|  
|  
| 12/11
| 11/6
| 122.785
| 122.785
|  
|  
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|-
|-
|  
|  
| {{vector|0 19 -22 -7 32}}
| {{monzo| 0 19 -22 -7 32 }}
| 124.180
| 124.180
| 11-odd-limit least squares
| 11-odd-limit least squares
|-
|-
|  
|  
| {{vector|0 33 -66 -14 90 -6}}
| {{monzo| 0 33 -66 -14 90 -6 }}
| 124.186
| 124.186
| 15-odd-limit least squares
| 15-odd-limit least squares
|-
|-
|  
|  
| {{vector|0 49 -50 -15 76 -8}}
| {{monzo| 0 49 -50 -15 76 -8 }}
| 124.215
| 124.215
| 13-odd-limit least squares
| 13-odd-limit least squares
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|-
|-
|  
|  
| 14/11
| 11/7
| 124.424
| 124.424
|  
|  
|-
|-
|  
|  
| 4/3
| 3/2
| 124.511
| 124.511
| 7- and 9-odd-limit minimax
| 7- and 9-odd-limit minimax
Line 860: Line 877:
|-
|-
|  
|  
| 30517578125/26795786661
| {{monzo| 0 -13 15 -5 }}
| 125.469
| 125.469
| 7-odd-limit least squares
| 7-odd-limit least squares
|-
|-
|  
|  
| {{vector|0 63 -26 -1}}
| {{monzo| 0 63 -26 -1 }}
| 125.579
| 125.579
| 9-odd-limit least squares
| 9-odd-limit least squares
|-
|-
|  
|  
| 10/9
| 9/5
| 125.673
| 125.673
|  
|  
|-
|-
|  
|  
| 11337408/9765625
| {{monzo| 6 11 -10 }}
| 126.238
| 126.238
| 5-odd-limit least squares
| 5-odd-limit least squares
|-
|-
|  
|  
| 6/5
| 5/3
| 126.337
| 126.337
| 5-odd-limit minimax
| 5-odd-limit minimax
|-
|-
|  
|  
| 18/13
| 13/9
| 127.324
| 127.324
|  
|  
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|-
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|  
|  
| 14/13
| 13/7
| 128.298
| 128.298
|  
|  
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| 5/4
| 5/4
| 128.771
| 128.771
|
|-
| 1\9
|
| 133.333
|  
|  
|-
|-
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[[Category:Negri]]
[[Category:Negri]]
[[Category:Temperament extensions]]
[[Category:Temperament extensions]]
[[Category:Rank-2 temperaments]]
Retrieved from "https://en.xen.wiki/w/Negri_extensions"