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Augene: Difference between revisions

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→Spectrum of Augene Tunings by Eigenmonzos: improve and standardize tuning spectra tables
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→Tuning spectrum: improve and standardize tuning spectra tables
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The first few augene MOSes are [[3L_3s|3L 3s]], [[3L_6s|3L 6s]], [[3L_9s|3L 9s]], [[12L_3s|12L 3s]]... and the first EDOs that reasonably support augene are [[12edo|12edo]], [[15edo|15edo]], and especially [[27edo|27edo]].
The first few augene MOSes are [[3L_3s|3L 3s]], [[3L_6s|3L 6s]], [[3L_9s|3L 9s]], [[12L_3s|12L 3s]]... and the first EDOs that reasonably support augene are [[12edo|12edo]], [[15edo|15edo]], and especially [[27edo|27edo]].


== Tuning spectrum ==
==Tuning spectrum==
 
Gencom: [2 7/6; 99/98 121/120 176/175 275/273]
 
Gencom map: [<1 0 3 1 3 8|, <0 7 -3 8 2 -19|]


{| class="wikitable center-all"
{| class="wikitable center-all"
Line 9: Line 13:
! | ET<br>generator
! | ET<br>generator
! | [[eigenmonzo|eigenmonzo<br>(unchanged interval]])
! | [[eigenmonzo|eigenmonzo<br>(unchanged interval]])
! | fifth<br>(¢)
! | subminor<br>third (¢)
! | comments
! | comments
|-
|-
| |  
| |
| | 14/13
| | 7/6
| | 671.702
| | 266.871
| |  
| |
|-
|-
| | 12\28
| |
| |  
| | 15/11
| | 685.714
| | 268.475
| |  
| |
|-
|-
| |  
| |
| | 16/15
| | 14/11
| | 688.269
| | 269.585
| |  
| |
|-
|-
| |  
| |
| | 13/11
| | 12/11
| | 689.210
| | 270.127
| |  
| |
|-
|-
| | 7\12
| |
| |  
| | 15/14
| | 700.000
| | 270.139
| |  
| |
|-
|-
| | 31\53
| | 7\31
| |  
| |
| | 701.887
| | 270.968
| |  
| |
|-
|-
| |  
| |
| | 4/3
| | 11/9
| | 701.955
| | 271.049
| |  
| |
|-
|-
| | 30\51
| |
| |  
| | 8/7
| | 705.882
| | 271.103
| |
| |
|-
| |
| | 15/14
| | 706.481
| |
|-
| | 23\39
| |
| | 707.692
| |  
|-
|-
| |  
| |
| | 7/5
| | 7/5
| | 708.744
| | 271.137
| |  
| |
|-
|-
| |  
| |
| | 9/7
| | 5/4
| | 708.771
| | 271.229
| |  
| |
|-
|-
| |  
| |
| | 10/9
| | 1361367/1000000
| | 708.798
| | 271.326
| | 9 limit minimax
| | 7 limit least squares
|-
|-
| | 39\66
| |
| |  
| | 14/13
| | 709.091
| | 271.418
| |  
| | 13 and 15 limit minimax
|-
|-
| |  
| | 19\84
| | 7/6
| |
| | 711.043
| | 271.429
| |  
| |
|-
|-
| | 16\27
| |
| |  
| | {{vector|0 119 -46 20 -16}}
| | 711.111
| | 271.445
| |  
| | 11 limit least squares
|-
|-
| |  
| |  
| | 15/11
| | <math>x^{10} + 2x^3 = 8</math>
| | 712.317
| | 271.508
| |  
| | equal beating
|-
|-
| | 57\96
| |
| |  
| | 16/13
| | 712.5
| | 271.551
| |
| |
|-
| |
| | 11/9
| | 713.148
| | 11 limit minimax
|-
| | 25\42
| |
| | 714.286
| |  
|-
|-
| |  
| |
| | 8/7
| | {{vector|0 90 -41 14}}
| | 715.587
| | 271.561
| | 7, 13 and 15 limit minimax
| | 9 limit least squares
|-
|-
| |  
| |
| | 6/5
| | 6/5
| | 715.641
| | 271.564
| | 5 limit minimax
| | 5 limit minimax
|-
|-
| | 34\57
| |
| |  
| | {{vector|0 -211 30 -47 -5 142}}
| | 715.789
| | 271.567
| |  
| | 13 limit least squares
|-
|-
| | 25\72
| |
| |  
| | {{vector|0 -236 5 -51 -3 165}}
| | 716.667
| | 271.570
| |  
| | 15 limit least squares
|-
|-
| |  
| |
| | 12/11
| | 1220703125/1033121304
| | 716.879
| | 271.590
| |  
| | 5 limit least squares
|-
|-
| |  
| |
| | 11/10
| | 13/12
| | 717.498
| | 271.593
| |  
| |
|-
|-
| | 9\15
| |
| |  
| | 13/10
| | 720.000
| | 271.612
| |  
| |
|-
|-
| |  
| |
| | 18/13
| | 18/13
| | 721.127
| | 271.618
| |  
| |
|-
| |
| | 10/9
| | 271.623
| | 9 limit minimax
|-
|-
| |  
| |
| | 15/13
| | 15/13
| | 723.871
| | 271.641
| |  
| |
|-
| | 12\53
| |
| | 271.698
| |
|-
| |
| | 4/3
| | 271.708
| |
|-
| |
| | 13/11
| | 271.942
| |
|-
| |
| | 16/15
| | 272.067
| |
|-
|-
| |  
| |
| | 11/8
| | 9/7
| | 724.341
| | 272.514
| |  
| |
|-
|-
| |  
| | 5\22
| | 13/12
| |
| | 730.714
| | 272.727
| |  
| |
|-
|-
| |  
| |
| | 13/10
| | 11/10
| | 745.786
| | 273.001
| |  
| |
|-
|-
| |  
| |
| | 16/13
| | 11/8
| | 759.472
| | 275.659
| |  
| |
|}
|}


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