Negri extensions: Difference between revisions

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→Spectrum of Negri Tunings by Eigenmonzos: improve and standardize tuning spectra tables
Line 3: Line 3:
=Tuning Spectra=
=Tuning Spectra=


==Spectrum of Negri Tunings by Eigenmonzos==
== Tuning spectrum ==


[[Gencom|Gencom]]: [2 15/14; 45/44 49/48 56/55 78/77]
[[Gencom|Gencom]]: [2 15/14; 45/44 49/48 56/55 78/77]
Line 9: Line 9:
[[Gencom_map|Gencom map]]: [<1 2 2 3 4 4|, <0 -4 3 -2 -5 -3|]
[[Gencom_map|Gencom map]]: [<1 2 2 3 4 4|, <0 -4 3 -2 -5 -3|]


{| class="wikitable"
{| class="wikitable center-all"
|-
|-
! | Eigenmonzo
! | ET generator
! | Supersecor
! | [[eigenmonzo|eigenmonzo<br>(unchanged interval]])
! | supersecor<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
| |
|-
|-
| |
| | 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 (7 and 9 limit minimax)
| | 124.511  
| | 7 and 9 limit minimax
|-
|-
| | 5\48
| | 5\48
| |
| | 125.000
| | 125.000
| |
|-
|-
| |
| | 30517578125/26795786661
| | 30517578125/26795786661
| | 125.469 (7 limit least squares)
| | 125.469  
| | 7 limit least squares
|-
|-
| | |0 63 -26 -1&gt;
| |
| | 125.579 (9 limit least squares)
| | {{vector|0 63 -26 -1}}
| | 125.579
| | 9 limit least squares
|-
|-
| |
| | 10/9
| | 10/9
| | 125.673
| | 125.673
| |
|-
|-
| |
| | 11337408/9765625
| | 11337408/9765625
| | 126.238 (5 limit least squares)
| | 126.238  
| | 5 limit least squares
|-
|-
| | 2\19
| | 2\19
| |
| | 126.316
| | 126.316
| |
|-
|-
| |
| | 6/5
| | 6/5
| | 126.337 (5 limit minimax)
| | 126.337
| | 5 limit minimax
|-
|-
| | |0 79 -40 -5 16 2&gt;
| |
| | 126.445 (13 limit least squares)
| | {{vector|0 79 -40 -5 16 2}}
| | 126.445
| | 13 limit least squares
|-
|-
| | |0 34 -17 -2 7&gt;
| |
| | 126.511 (11 limit least squares)
| | {{vector|0 34 -17 -2 7}}
| | 126.511
| | 11 limit least squares
|-
|-
| | |0 73 -46 -4 20 4&gt;
| |
| | 126.619 (15 limit least squares)
| | {{vector|0 73 -46 -4 20 4}}
| | 126.619
| | 15 limit least squares
|-
|-
| |
| | 18/13
| | 18/13
| | 127.324
| | 127.324
| |
|-
|-
| |
| | 9/7
| | 9/7
| | 127.486 (11, 13 and 15 limit minimax)
| | 127.486
| | 11, 13 and 15 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
| |
|}
|}


Revision as of 00:29, 30 September 2021

Negri temperament has various extensions to the 11 limit.

Tuning Spectra

Tuning spectrum

Gencom: [2 15/14; 45/44 49/48 56/55 78/77]

Gencom map: [<1 2 2 3 4 4|, <0 -4 3 -2 -5 -3|]

ET generator eigenmonzo
(unchanged interval) 		supersecor
(¢) 		comments
16/15 111.731
8/7 115.587
11/9 115.803
15/14 119.443
16/13 119.824
1\10 120.000
7/5 123.498
15/13 123.871
3\29 124.138
13/10 124.298
4/3 124.511 7 and 9 limit minimax
5\48 125.000
30517578125/26795786661 125.469 7 limit least squares
[0 63 -26 -1⟩ 125.579 9 limit least squares
10/9 125.673
11337408/9765625 126.238 5 limit least squares
2\19 126.316
6/5 126.337 5 limit minimax
[0 79 -40 -5 16 2⟩ 126.445 13 limit least squares
[0 34 -17 -2 7⟩ 126.511 11 limit least squares
[0 73 -46 -4 20 4⟩ 126.619 15 limit least squares
18/13 127.324
9/7 127.486 11, 13 and 15 limit minimax
5\47 127.660
14/13 128.298
3\28 128.571
5/4 128.771
11/10 129.374
11/8 129.736
7/6 133.435
15/11 134.238
13/12 138.573
14/11 139.169
13/11 144.605
12/11 150.637

Spectrum of Negril Tunings by Eigenmonzos

Gencom: [2 15/14; 49/48 65/64 91/90 875/858]

Gencom map: [<1 2 2 3 2 4|, <0 -4 3 -2 14 -3|]

Eigenmonzo Supersecor
16/15 111.731
8/7 115.587
15/14 119.443
16/13 119.824
1\10 120.000
7/5 123.498
15/13 123.871
14/11 123.906
11/10 124.091
3\29 124.138
13/11 124.164
15/11 124.203
13/10 124.298
4/3 124.511 (7, 9, 11, 13 and 15 limit minimax)
|0 -149 8 -15 113 -23> 124.700 (15 limit least squares)
|0 -136 21 -14 98 -21> 124.764 (13 limit least squares)
|0 -125 15 -15 81> 124.854 (11 limit least squares)
11/9 124.882
12/11 124.965
5\48 125.000
11/8 125.094
30517578125/26795786661 125.469 (7 limit least squares)
|0 63 -26 -1> 125.579 (9 limit least squares)
10/9 125.673
11337408/9765625 126.238 (5 limit least squares)
2\19 126.316
6/5 126.337 (5 limit minimax)
18/13 127.324
9/7 127.486
5\47 127.660
14/13 128.298
3\28 128.571
5/4 128.771
7/6 133.435
13/12 138.573

Spectrum of Negric Tunings by Eigenmonzos

Gencom: [2 15/14; 33/32 49/48 65/64 91/90]

Gencom map: [<1 2 2 3 3 4|, <0 -4 3 -2 4 -3|]

Eigenmonzo Supersecor
16/15 111.731
8/7 115.587
15/14 119.443
16/13 119.824
1\10 120.000
7/5 123.498
15/13 123.871
3\29 124.138
13/10 124.298
4/3 124.511 (7 and 9 limit minimax)
5\48 125.000
30517578125/26795786661 125.469 (7 limit least squares)
|0 63 -26 -1> 125.579 (9 limit least squares)
10/9 125.673
11337408/9765625 126.238 (5 limit least squares)
2\19 126.316
6/5 126.337 (5 limit minimax)
18/13 127.324
9/7 127.486
|0 106 -31 4 -38 11> 127.602 (13 limit least squares)
5\47 127.660
|0 -95 25 -5 31> 127.706 (11 limit least squares)
|0 109 -28 5 -43 13> 127.718 (15 limit least squares)
14/13 128.298
3\28 128.571
5/4 128.771
11/9 128.951 (11, 13 and 15 limit minimax)
13/11 130.113
14/11 130.415
12/11 131.170
15/11 132.610
7/6 133.435
11/8 137.829
13/12 138.573
11/10 165.004

Spectrum of Negroni Tunings by Eigenmonzos

Gencom: [2 15/14; 49/48 55/54 65/64 91/90]

Gencom map: [<1 2 2 3 5 4|, <0 -4 3 -2 -15 -3|]

Eigenmonzo Supersecor
16/15 111.731
8/7 115.587
15/14 119.443
16/13 119.824
1\10 120.000
11/9 121.799 (11, 13 and 15 limit minimax)
12/11 122.785
11/8 123.245
7/5 123.498
15/13 123.871
15/11 124.068
13/11 124.101
3\29 124.138
11/10 124.166
|0 19 -22 -7 32> 124.180 (11 limit least squares)
|0 33 -66 -14 90 -6> 124.186 (15 limit least squares)
|0 49 -50 -15 76 -8> 124.215 (13 limit least squares)
13/10 124.298
14/11 124.424
4/3 124.511 (7 and 9 limit minimx)
5\48 125.000
30517578125/26795786661 125.469 (7 limit least squares)
|0 63 -26 -1> 125.579 (9 limit least squares)
10/9 125.673
11337408/9765625 126.238 (5 limit least squares)
6/5 126.337 (5 limit minimax)
18/13 127.324
9/7 127.486
5\47 127.660
14/13 128.298
3\28 128.571
5/4 128.771
7/6 133.435
13/12 138.573
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