Pajara extensions: Difference between revisions

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→Tuning Spectra: improve and standardize tuning spectra tables
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=Tuning Spectra=
== Tuning spectra ==


==Spectrum of Pajara Tunings by Eigenmonzos==
=== Pajara ===


[[Gencom|Gencom]]: [7/5 3/2; 50/49 64/63 65/63 99/98]
[[Gencom|Gencom]]: [7/5 3/2; 50/49 64/63 65/63 99/98]


[[Gencom_map|Gencom map]]: [<2 2 7 8 14 5|, <0 1 -2 -2 -6 2|]
[[Gencom_map|Gencom map]]: [{{map|2 2 7 8 14 5}}, {{map|0 1 -2 -2 -6 2}}]


{| class="wikitable"
{| class="wikitable center-all"
|-
|-
! | Eigenmonzo
! | ET<br>generator
! | Fifth
! | [[eigenmonzo|eigenmonzo<br>(unchanged interval]])
! | fifth<br>(¢)
! | comments
|-
|-
| |
| | 4/3
| | 4/3
| | 701.955
| | 701.955
| |
|-
|-
| |
| | 14/11
| | 14/11
| | 704.377
| | 704.377
| |
|-
|-
| |
| | 10/9
| | 10/9
| | 704.399
| | 704.399
| |
|-
|-
| |
| | 6/5
| | 6/5
| | 705.214 (5 limit minimax)
| | 705.214
| | 5 limit minimax
|-
|-
| |
| | 3125/2592
| | 3125/2592
| | 705.447 (5 limit least squares)
| | 705.447
| | 5 limit least squares
|-
|-
| | 20\34
| | 20\34
| |
| | 705.882
| | 705.882
| |
|-
|-
| |
| | 11/9
| | 11/9
| | 706.574
| | 706.574
| |
|-
|-
| |
| | 5/4
| | 5/4
| | 706.843
| | 706.843
| |
|-
|-
| | |0 -50 5 5 29&gt;
| |
| | 707.106 (11 limit least squares)
| | {{vector|0 -50 5 5 29}}
| | 707.106
| | 11 limit least squares
|-
|-
| | 33\56
| | 33\56
| |
| | 707.143
| | 707.143
| |
|-
|-
| |
| | 12/11
| | 12/11
| | 707.234
| | 707.234
| |
|-
|-
| |
| | 35/27
| | 35/27
| | 707.246 (9 limit least squares)
| | 707.246
| | 9 limit least squares
|-
|-
| |
| | 15/11
| | 15/11
| | 707.390
| | 707.390
| |
|-
|-
| |
| | 11/8
| | 11/8
| | 708.114
| | 708.114
| |
|-
|-
| |
| | 11/10
| | 11/10
| | 708.749 (11 limit minimax)
| | 708.749
| | 11 limit minimax
|-
|-
| |
| | 9/7
| | 9/7
| | 708.771 (9 limit minimax)
| | 708.771
| | 9 limit minimax
|-
|-
| |
| | 71663616/52521875
| | 71663616/52521875
| | 708.814 (7 limit least squares)
| | 708.814
| | 7 limit least squares
|-
|-
| | |0 -49 9 9 37 -19&gt;
| |
| | 708.901 (13 limit least squares)
| | {{vector|0 -49 9 9 37 -19}}
| | 708.901
| | 13 limit least squares
|-
|-
| | |0 -51 7 10 42 -22&gt;
| |
| | 709.038 (15 limit least squares)
| | {{vector|0 -51 7 10 42 -22}}
| | 709.038
| | 15 limit least squares
|-
|-
| | 13\22
| | 13\22
| |
| | 709.091
| | 709.091
| |
|-
|-
| |
| | 7/6
| | 7/6
| | 711.043 (7 limit minimax)
| | 711.043
| | 7 limit minimax
|-
|-
| | 32\54
| | 32\54
| |
| | 711.111
| | 711.111
| |
|-
|-
| |
| | 13/11
| | 13/11
| | 711.151 (13 and 15 limit minimax)
| | 711.151
| | 13 and 15 limit minimax
|-
|-
| |
| | 16/15
| | 16/15
| | 711.731
| | 711.731
| |
|-
|-
| | 19\32
| | 19\32
| |
| | 712.500
| | 712.500
| |
|-
|-
| |
| | 13/10
| | 13/10
| | 713.553
| | 713.553
| |
|-
|-
| |
| | 8/7
| | 8/7
| | 715.587
| | 715.587
| |
|-
|-
| |
| | 15/13
| | 15/13
| | 717.420
| | 717.420
| |
|-
|-
| |
| | 14/13
| | 14/13
| | 717.925
| | 717.925
| |
|-
|-
| |
| | 15/14
| | 15/14
| | 719.443
| | 719.443
| |
|-
|-
| |
| | 16/13
| | 16/13
| | 720.264
| | 720.264
| |
|-
|-
| |
| | 13/12
| | 13/12
| | 738.573
| | 738.573
| |
|}
|}


==Spectrum of Pajarous Tunings by Eigenmonzos==
=== Pajarous ===


[[Gencom|Gencom]]: [7/5 3/2; 50/49 55/54 64/63 65/63]
[[Gencom|Gencom]]: [7/5 3/2; 50/49 55/54 64/63 65/63]


[[Gencom_map|Gencom map]]: [&lt;2 2 7 8 1 5|, &lt;0 1 -2 -2 5 2|]
[[Gencom_map|Gencom map]]: [{{map|2 2 7 8 1 5}}, {{map|0 1 -2 -2 5 2}}]


{| class="wikitable"
{| class="wikitable center-all"
|-
|-
! | Eigenmonzo
! | ET<br>generator
! | Fifth
! | eigenmonzo<br>(unchanged interval)
! | fifth<br>(¢)
! | comments
|-
|-
| |
| | 4/3
| | 4/3
| | 701.955
| | 701.955
| |
|-
|-
| |
| | 13/11
| | 13/11
| | 703.597
| | 703.597
| |
|-
|-
| |
| | 10/9
| | 10/9
| | 704.399
| | 704.399
| |
|-
|-
| |
| | 6/5
| | 6/5
| | 705.214 (5 limit minimax)
| | 705.214
| | 5 limit minimax
|-
|-
| |
| | 3125/2592
| | 3125/2592
| | 705.447 (5 limit least squares)
| | 705.447
| | 5 limit least squares
|-
|-
| | 20\34
| | 20\34
| |
| | 705.882
| | 705.882
| |
|-
|-
| |
| | 5/4
| | 5/4
| | 706.843
| | 706.843
| |
|-
|-
| | 33\56
| | 33\56
| |
| | 707.143
| | 707.143
| |
|-
|-
| |
| | 35/27
| | 35/27
| | 707.246 (9 limit least squares)
| | 707.246
| | 9 limit least squares
|-
|-
| |
| | 9/7
| | 9/7
| | 708.771 (9, 13 and 15 limit minimax)
| | 708.771
| | 9, 13 and 15 limit minimax
|-
|-
| |
| | 71663616/52521875
| | 71663616/52521875
| | 708.814 (7 limit least squares)
| | 708.814
| | 7 limit least squares
|-
|-
| | 13\22
| | 13\22
| |
| | 709.091
| | 709.091
| |
|-
|-
| |
| | 11/10
| | 11/10
| | 709.286 (11 limit minimax)
| | 709.286
| | 11 limit minimax
|-
|-
| | |0 17 -16 -16 26&gt;
| |
| | 709.883 (11 limit least squares)
| | {{vector|0 17 -16 -16 26}}
| | 709.883
| | 11 limit least squares
|-
|-
| |
| | 11/8
| | 11/8
| | 710.264
| | 710.264
| |
|-
|-
| |
| | 15/11
| | 15/11
| | 710.508
| | 710.508
| |
|-
|-
| | |0 16 -20 -20 29 8&gt;
| |
| | 710.665 (13 limit least squares)
| | {{vector|0 16 -20 -20 29 8}}
| | 710.665
| | 13 limit least squares
|-
|-
| | |0 7 -29 -21 35 11&gt;
| |
| | 710.879 (15 limit least squares)
| | {{vector|0 7 -29 -21 35 11}}
| | 710.879
| | 15 limit least squares
|-
|-
| |
| | 7/6
| | 7/6
| | 711.043 (7 limit minimax)
| | 711.043
| | 7 limit minimax
|-
|-
| | 32\54
| | 32\54
| |
| | 711.111
| | 711.111
| |
|-
|-
| |
| | 16/15
| | 16/15
| | 711.731
| | 711.731
| |
|-
|-
| |
| | 14/11
| | 14/11
| | 711.785
| | 711.785
| |
|-
|-
| |
| | 12/11
| | 12/11
| | 712.341
| | 712.341
| |
|-
|-
| | 19\32
| | 19\32
| |
| | 712.500
| | 712.500
| |
|-
|-
| |
| | 13/10
| | 13/10
| | 713.553
| | 713.553
| |
|-
|-
| |
| | 8/7
| | 8/7
| | 715.587
| | 715.587
| |
|-
|-
| |
| | 11/9
| | 11/9
| | 715.803
| | 715.803
| |
|-
|-
| |
| | 15/13
| | 15/13
| | 717.420
| | 717.420
| |
|-
|-
| |
| | 14/13
| | 14/13
| | 717.925
| | 717.925
| |
|-
|-
| |
| | 15/14
| | 15/14
| | 719.443
| | 719.443
| |
|-
|-
| |
| | 16/13
| | 16/13
| | 720.264
| | 720.264
| |
|-
|-
| |
| | 13/12
| | 13/12
| | 738.573
| | 738.573
| |
|}
|}


==Spectrum of Pajaro Tunings by Eigenmonzos==
=== Pajaro ===


[[Gencom|Gencom]]: [7/5 3/2; 40/39 50/49 55/54 64/63]
[[Gencom|Gencom]]: [7/5 3/2; 40/39 50/49 55/54 64/63]


[[Gencom_map|Gencom map]]: [&lt;2 2 7 8 1 11|, &lt;0 1 -2 -2 5 -3|]
[[Gencom_map|Gencom map]]: [{{map|2 2 7 8 1 11}}, {{map|0 1 -2 -2 5 -3}}]


{| class="wikitable"
{| class="wikitable center-all"
|-
|-
! | Eigenmonzo
! | ET<br>generator
! | Fifth
! | eigenmonzo<br>(unchanged interval)
! | fifth<br>(¢)
! | comments
|-
|-
| |
| | 4/3
| | 4/3
| | 701.955
| | 701.955
| |
|-
|-
| |
| | 10/9
| | 10/9
| | 704.399
| | 704.399
| |
|-
|-
| |
| | 6/5
| | 6/5
| | 705.214 (5 limit minimax)
| | 705.214
| | 5 limit minimax
|-
|-
| |
| | 3125/2592
| | 3125/2592
| | 705.447 (5 limit least squares)
| | 705.447
| | 5 limit least squares
|-
|-
| | 20\34
| | 20\34
| |
| | 705.882
| | 705.882
| |
|-
|-
| |
| | 5/4
| | 5/4
| | 706.843
| | 706.843
| |
|-
|-
| | 33\56
| | 33\56
| |
| | 707.143
| | 707.143
| |
|-
|-
| |
| | 35/27
| | 35/27
| | 707.246 (9 limit least squares)
| | 707.246
| | 9 limit least squares
|-
|-
| |
| | 9/7
| | 9/7
| | 708.771 (9 limit minimax)
| | 708.771
| | 9 limit minimax
|-
|-
| |
| | 71663616/52521875
| | 71663616/52521875
| | 708.814 (7 limit least squares)
| | 708.814
| | 7 limit least squares
|-
|-
| | 13\22
| | 13\22
| |
| | 709.091
| | 709.091
| |
|-
|-
| |
| | 11/10
| | 11/10
| | 709.286 (11 limit minimax)
| | 709.286
| | 11 limit minimax
|-
|-
| | |0 17 -16 -16 26&gt;
| |
| | 709.883 (11 limit least squares)
| | {{vector|0 17 -16 -16 26}}
| | 709.883
| | 11 limit least squares
|-
|-
| |
| | 11/8
| | 11/8
| | 710.264
| | 710.264
| |
|-
|-
| |
| | 15/11
| | 15/11
| | 710.508
| | 710.508
| |
|-
|-
| |
| | 7/6
| | 7/6
| | 711.043 (7 limit minimax)
| | 711.043
| | 7 limit minimax
|-
|-
| | 32\54
| | 32\54
| |
| | 711.111
| | 711.111
| |
|-
|-
| | |0 31 -15 -15 34 -22&gt;
| |
| | 711.580 (13 limit least squares)
| | {{vector|0 31 -15 -15 34 -22}}
| | 711.580
| | 13 limit least squares
|-
|-
| | |0 27 -19 -16 40 -24&gt;
| |
| | 711.631 (15 limit least squares)
| | {{vector|0 27 -19 -16 40 -24}}
| | 711.631
| | 15 limit least squares
|-
|-
| |
| | 16/15
| | 16/15
| | 711.731
| | 711.731
| |
|-
|-
| |
| | 14/11
| | 14/11
| | 711.785
| | 711.785
| |
|-
|-
| |
| | 12/11
| | 12/11
| | 712.341
| | 712.341
| |
|-
|-
| | 19\32
| | 19\32
| |
| | 712.500
| | 712.500
| |
|-
|-
| |
| | 18/13
| | 18/13
| | 712.676 (13 and 15 limit minimax)
| | 712.676
| | 13 and 15 limit minimax
|-
|-
| |
| | 13/11
| | 13/11
| | 713.849
| | 713.849
| |
|-
|-
| |
| | 13/12
| | 13/12
| | 715.357
| | 715.357
| |
|-
|-
| |
| | 8/7
| | 8/7
| | 715.587
| | 715.587
| |
|-
|-
| |
| | 11/9
| | 11/9
| | 715.803
| | 715.803
| |
|-
|-
| |
| | 15/14
| | 15/14
| | 719.443
| | 719.443
| |
|-
|-
| |
| | 16/13
| | 16/13
| | 719.824
| | 719.824
| |
|-
|-
| |
| | 15/13
| | 15/13
| | 723.871
| | 723.871
| |
|-
|-
| |
| | 14/13
| | 14/13
| | 728.298
| | 728.298
| |
|-
|-
| |
| | 13/10
| | 13/10
| | 745.786
| | 745.786
| |
|}
|}


==Spectrum of Pajaric Tunings by Eigenmonzos==
=== Pajaric ===


[[Gencom|Gencom]]: [7/5 3/2; 40/39 45/44 50/49 56/55]
[[Gencom|Gencom]]: [7/5 3/2; 40/39 45/44 50/49 56/55]


[[Gencom_map|Gencom map]]: [&lt;2 2 7 8 7 11|, &lt;0 1 -2 -2 0 -3|]
[[Gencom_map|Gencom map]]: [{{map|2 2 7 8 7 11}}, {{map|0 1 -2 -2 0 -3}}]


{| class="wikitable"
{| class="wikitable center-all"
|-
|-
! | Eigenmonzo
! | ET<br>generator
! | Fifth
! | eigenmonzo<br>(unchanged interval)
! | fifth<br>(¢)
! | comments
|-
|-
| |
| | 15/11
| | 15/11
| | 663.049
| | 663.049
| |
|-
|-
| |
| | 11/10
| | 11/10
| | 682.502
| | 682.502
| |
|-
|-
| |
| | 14/11
| | 14/11
| | 691.246
| | 691.246
| |
|-
|-
| |
| | 4/3
| | 4/3
| | 701.955
| | 701.955
| |
|-
|-
| |
| | 13/11
| | 13/11
| | 703.597
| | 703.597
| |
|-
|-
| |
| | 10/9
| | 10/9
| | 704.399
| | 704.399
| |
|-
|-
| |
| | 6/5
| | 6/5
| | 705.214 (5 limit minimax)
| | 705.214
| | 5 limit minimax
|-
|-
| |
| | 3125/2592
| | 3125/2592
| | 705.447 (5 limit least squares)
| | 705.447
| | 5 limit least squares
|-
|-
| | 20\34
| | 20\34
| |
| | 705.882
| | 705.882
| |
|-
|-
| | |0 -32 11 11 -1&gt;
| |
| | 706.676 (11 limit least squares)
| | {{vector|0 -32 11 11 -1}}
| | 706.676
| | 11 limit least squares
|-
|-
| |
| | 5/4
| | 5/4
| | 706.843 (11, 13 and 15 limit minimax)
| | 706.843
| | 11, 13 and 15 limit minimax
|-
|-
| | 33\56
| | 33\56
| |
| | 707.143
| | 707.143
| |
|-
|-
| |
| | 35/27
| | 35/27
| | 707.246 (9 limit least squares)
| | 707.246
| | 9 limit least squares
|-
|-
| |
| | 9/7
| | 9/7
| | 708.771 (9 limit minimax)
| | 708.771
| | 9 limit minimax
|-
|-
| |
| | 71663616/52521875
| | 71663616/52521875
| | 708.814 (7 limit least squares)
| | 708.814
| | 7 limit least squares
|-
|-
| | 13\22
| | 13\22
| |
| | 709.091
| | 709.091
| |
|-
|-
| | |0 -46 10 10 -4 17&gt;
| |
| | 709.889 (13 limit least squares)
| | {{vector|0 -46 10 10 -4 17}}
| | 709.889
| | 13 limit least squares
|-
|-
| | |0 -47 9 11 -5 19&gt;
| |
| | 710.032 (15 limit least squares)
| | {{vector|0 -47 9 11 -5 19}}
| | 710.032
| | 15 limit least squares
|-
|-
| |
| | 7/6
| | 7/6
| | 711.043 (7 limit minimax)
| | 711.043
| | 7 limit minimax
|-
|-
| | 32\54
| | 32\54
| |
| | 711.111
| | 711.111
| |
|-
|-
| |
| | 16/15
| | 16/15
| | 711.731
| | 711.731
| |
|-
|-
| | 19\32
| | 19\32
| |
| | 712.500
| | 712.500
| |
|-
|-
| |
| | 18/13
| | 18/13
| | 712.676
| | 712.676
| |
|-
|-
| |
| | 13/12
| | 13/12
| | 715.357
| | 715.357
| |
|-
|-
| |
| | 8/7
| | 8/7
| | 715.587
| | 715.587
| |
|-
|-
| |
| | 15/14
| | 15/14
| | 719.443
| | 719.443
| |
|-
|-
| |
| | 16/13
| | 16/13
| | 719.824
| | 719.824
| |
|-
|-
| |
| | 15/13
| | 15/13
| | 723.871
| | 723.871
| |
|-
|-
| |
| | 11/9
| | 11/9
| | 726.296
| | 726.296
| |
|-
|-
| |
| | 14/13
| | 14/13
| | 728.298
| | 728.298
| |
|-
|-
| |
| | 13/10
| | 13/10
| | 745.786
| | 745.786
| |
|-
|-
| |
| | 12/11
| | 12/11
| | 750.637
| | 750.637
| |
|}
|}

Revision as of 00:23, 30 September 2021

Tuning spectra

Pajara

Gencom: [7/5 3/2; 50/49 64/63 65/63 99/98]

Gencom map: [⟨2 2 7 8 14 5], ⟨0 1 -2 -2 -6 2]]

ET
generator 		eigenmonzo
(unchanged interval) 		fifth
(¢) 		comments
4/3 701.955
14/11 704.377
10/9 704.399
6/5 705.214 5 limit minimax
3125/2592 705.447 5 limit least squares
20\34 705.882
11/9 706.574
5/4 706.843
[0 -50 5 5 29⟩ 707.106 11 limit least squares
33\56 707.143
12/11 707.234
35/27 707.246 9 limit least squares
15/11 707.390
11/8 708.114
11/10 708.749 11 limit minimax
9/7 708.771 9 limit minimax
71663616/52521875 708.814 7 limit least squares
[0 -49 9 9 37 -19⟩ 708.901 13 limit least squares
[0 -51 7 10 42 -22⟩ 709.038 15 limit least squares
13\22 709.091
7/6 711.043 7 limit minimax
32\54 711.111
13/11 711.151 13 and 15 limit minimax
16/15 711.731
19\32 712.500
13/10 713.553
8/7 715.587
15/13 717.420
14/13 717.925
15/14 719.443
16/13 720.264
13/12 738.573

Pajarous

Gencom: [7/5 3/2; 50/49 55/54 64/63 65/63]

Gencom map: [⟨2 2 7 8 1 5], ⟨0 1 -2 -2 5 2]]

ET
generator 		eigenmonzo
(unchanged interval) 		fifth
(¢) 		comments
4/3 701.955
13/11 703.597
10/9 704.399
6/5 705.214 5 limit minimax
3125/2592 705.447 5 limit least squares
20\34 705.882
5/4 706.843
33\56 707.143
35/27 707.246 9 limit least squares
9/7 708.771 9, 13 and 15 limit minimax
71663616/52521875 708.814 7 limit least squares
13\22 709.091
11/10 709.286 11 limit minimax
[0 17 -16 -16 26⟩ 709.883 11 limit least squares
11/8 710.264
15/11 710.508
[0 16 -20 -20 29 8⟩ 710.665 13 limit least squares
[0 7 -29 -21 35 11⟩ 710.879 15 limit least squares
7/6 711.043 7 limit minimax
32\54 711.111
16/15 711.731
14/11 711.785
12/11 712.341
19\32 712.500
13/10 713.553
8/7 715.587
11/9 715.803
15/13 717.420
14/13 717.925
15/14 719.443
16/13 720.264
13/12 738.573

Pajaro

Gencom: [7/5 3/2; 40/39 50/49 55/54 64/63]

Gencom map: [⟨2 2 7 8 1 11], ⟨0 1 -2 -2 5 -3]]

ET
generator 		eigenmonzo
(unchanged interval) 		fifth
(¢) 		comments
4/3 701.955
10/9 704.399
6/5 705.214 5 limit minimax
3125/2592 705.447 5 limit least squares
20\34 705.882
5/4 706.843
33\56 707.143
35/27 707.246 9 limit least squares
9/7 708.771 9 limit minimax
71663616/52521875 708.814 7 limit least squares
13\22 709.091
11/10 709.286 11 limit minimax
[0 17 -16 -16 26⟩ 709.883 11 limit least squares
11/8 710.264
15/11 710.508
7/6 711.043 7 limit minimax
32\54 711.111
[0 31 -15 -15 34 -22⟩ 711.580 13 limit least squares
[0 27 -19 -16 40 -24⟩ 711.631 15 limit least squares
16/15 711.731
14/11 711.785
12/11 712.341
19\32 712.500
18/13 712.676 13 and 15 limit minimax
13/11 713.849
13/12 715.357
8/7 715.587
11/9 715.803
15/14 719.443
16/13 719.824
15/13 723.871
14/13 728.298
13/10 745.786

Pajaric

Gencom: [7/5 3/2; 40/39 45/44 50/49 56/55]

Gencom map: [⟨2 2 7 8 7 11], ⟨0 1 -2 -2 0 -3]]

ET
generator 		eigenmonzo
(unchanged interval) 		fifth
(¢) 		comments
15/11 663.049
11/10 682.502
14/11 691.246
4/3 701.955
13/11 703.597
10/9 704.399
6/5 705.214 5 limit minimax
3125/2592 705.447 5 limit least squares
20\34 705.882
[0 -32 11 11 -1⟩ 706.676 11 limit least squares
5/4 706.843 11, 13 and 15 limit minimax
33\56 707.143
35/27 707.246 9 limit least squares
9/7 708.771 9 limit minimax
71663616/52521875 708.814 7 limit least squares
13\22 709.091
[0 -46 10 10 -4 17⟩ 709.889 13 limit least squares
[0 -47 9 11 -5 19⟩ 710.032 15 limit least squares
7/6 711.043 7 limit minimax
32\54 711.111
16/15 711.731
19\32 712.500
18/13 712.676
13/12 715.357
8/7 715.587
15/14 719.443
16/13 719.824
15/13 723.871
11/9 726.296
14/13 728.298
13/10 745.786
12/11 750.637
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