Negri extensions: Difference between revisions

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5,164 edits
→Tuning Spectra: improve and standardize tuning spectra tables
Line 1: Line 1:
[[Negri|Negri]] temperament has various extensions to the [[11-limit|11 limit]].
[[Negri|Negri]] temperament has various extensions to the [[11-limit|11 limit]].


=Tuning Spectra=
==Tuning spectra==


== Tuning spectrum ==
=== Negri ===


[[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 42: Line 42:
|-
|-
| | 1\10
| | 1\10
| |  
| |
| | 120.000
| | 120.000
| |
| |
Line 68: Line 68:
| |
| |
| | 4/3
| | 4/3
| | 124.511  
| | 124.511
| | 7 and 9 limit minimax
| | 7 and 9 limit minimax
|-
|-
Line 78: Line 78:
| |
| |
| | 30517578125/26795786661
| | 30517578125/26795786661
| | 125.469  
| | 125.469
| | 7 limit least squares
| | 7 limit least squares
|-
|-
Line 93: Line 93:
| |
| |
| | 11337408/9765625
| | 11337408/9765625
| | 126.238  
| | 126.238
| | 5 limit least squares
| | 5 limit least squares
|-
|-
Line 192: Line 192:
|}
|}


==Spectrum of Negril Tunings by Eigenmonzos==
=== Negril ===


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


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


{| class="wikitable"
{| class="wikitable center-all"
|-
|-
! | Eigenmonzo
! | ET<br>generator
! | Supersecor
! | eigenmonzo<br>(unchanged interval)
! | supersecor<br>(¢)
! | 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 (7, 9, 11, 13 and 15 limit minimax)
| | 124.511
| | 7, 9, 11, 13 and 15 limit minimax
|-
|-
| | |0 -149 8 -15 113 -23&gt;
| |
| | 124.700 (15 limit least squares)
| | {{vector|0 -149 8 -15 113 -23}}
| | 124.700
| | 15 limit least squares
|-
|-
| | |0 -136 21 -14 98 -21&gt;
| |
| | 124.764 (13 limit least squares)
| | {{vector|0 -136 21 -14 98 -21}}
| | 124.764
| | 13 limit least squares
|-
|-
| | |0 -125 15 -15 81&gt;
| |
| | 124.854 (11 limit least squares)
| | {{vector|0 -125 15 -15 81}}
| | 124.854
| | 11 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 (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
|-
|-
| |
| | 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
| |
|}
|}


==Spectrum of Negric Tunings by Eigenmonzos==
=== Negric ===


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


[[Gencom_map|Gencom map]]: [&lt;1 2 2 3 3 4|, &lt;0 -4 3 -2 4 -3|]
[[Gencom_map|Gencom map]]: [{{map|1 2 2 3 3 4}}, {{map|0 -4 3 -2 4 -3}}]


{| class="wikitable"
{| class="wikitable center-all"
|-
|-
! | Eigenmonzo
! | ET<br>generator
! | Supersecor
! | eigenmonzo<br>(unchanged interval)
! | supersecor<br>(¢)
! | 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 (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
|-
|-
| |
| | 18/13
| | 18/13
| | 127.324
| | 127.324
| |
|-
|-
| |
| | 9/7
| | 9/7
| | 127.486
| | 127.486
| |
|-
|-
| | |0 106 -31 4 -38 11&gt;
| |
| | 127.602 (13 limit least squares)
| | {{vector|0 106 -31 4 -38 11}}
| | 127.602
| | 13 limit least squares
|-
|-
| | 5\47
| | 5\47
| |
| | 127.660
| | 127.660
| |
|-
|-
| | |0 -95 25 -5 31&gt;
| |
| | 127.706 (11 limit least squares)
| | {{vector|0 -95 25 -5 31}}
| | 127.706
| | 11 limit least squares
|-
|-
| | |0 109 -28 5 -43 13&gt;
| |
| | 127.718 (15 limit least squares)
| | {{vector|0 109 -28 5 -43 13}}
| | 127.718
| | 15 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 (11, 13 and 15 limit minimax)
| | 128.951
| | 11, 13 and 15 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
| |
|}
|}


==Spectrum of Negroni Tunings by Eigenmonzos==
=== Negroni ===


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


[[Gencom_map|Gencom map]]: [&lt;1 2 2 3 5 4|, &lt;0 -4 3 -2 -15 -3|]
[[Gencom_map|Gencom map]]: [{{map|1 2 2 3 5 4}}, {{map|0 -4 3 -2 -15 -3}}]


{| class="wikitable"
{| class="wikitable center-all"
|-
|-
! | Eigenmonzo
! | ET<br>generator
! | Supersecor
! | eigenmonzo<br>(unchanged interval)
! | supersecor<br>(¢)
! | 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 (11, 13 and 15 limit minimax)
| | 121.799
| | 11, 13 and 15 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
| |
|-
|-
| | |0 19 -22 -7 32&gt;
| |
| | 124.180 (11 limit least squares)
| | {{vector|0 19 -22 -7 32}}
| | 124.180
| | 11 limit least squares
|-
|-
| | |0 33 -66 -14 90 -6&gt;
| |
| | 124.186 (15 limit least squares)
| | {{vector|0 33 -66 -14 90 -6}}
| | 124.186
| | 15 limit least squares
|-
|-
| | |0 49 -50 -15 76 -8&gt;
| |
| | 124.215 (13 limit least squares)
| | {{vector|0 49 -50 -15 76 -8}}
| | 124.215
| | 13 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 (7 and 9 limit minimx)
| | 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
|-
|-
| |
| | 6/5
| | 6/5
| | 126.337 (5 limit minimax)
| | 126.337
| | 5 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:eigenmonzo]]
[[Category:eigenmonzo]]

Revision as of 00:38, 30 September 2021

Negri temperament has various extensions to the 11 limit.

Tuning spectra

Negri

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

Negril

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]]

ET
generator 		eigenmonzo
(unchanged interval) 		supersecor
(¢) 		comments
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

Negric

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]]

ET
generator 		eigenmonzo
(unchanged interval) 		supersecor
(¢) 		comments
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

Negroni

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]]

ET
generator 		eigenmonzo
(unchanged interval) 		supersecor
(¢) 		comments
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 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
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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