Augene: Difference between revisions

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→Tuning spectrum: improve and standardize tuning spectra tables
Cmloegcmluin (talk | contribs)
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Undo revision 79017 by Cmloegcmluin (talk) - oops that was a total accident sorry
Tag: Undo
Line 3: Line 3:
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 13: Line 9:
! | ET<br>generator
! | ET<br>generator
! | [[eigenmonzo|eigenmonzo<br>(unchanged interval]])
! | [[eigenmonzo|eigenmonzo<br>(unchanged interval]])
! | subminor<br>third (¢)
! | fifth<br>(¢)
! | comments
! | comments
|-
|-
| |
| |  
| | 7/6
| | 14/13
| | 266.871
| | 671.702
| |
| |
|-
| | 12\28
| |
| | 685.714
| |
|-
| |
| | 16/15
| | 688.269
| |
|-
| |
| | 13/11
| | 689.210
| |
|-
| | 7\12
| |
| | 700.000
| |  
|-
|-
| |
| | 31\53
| | 15/11
| |  
| | 268.475
| | 701.887
| |
| |  
|-
|-
| |
| |  
| | 14/11
| | 4/3
| | 269.585
| | 701.955
| |
| |  
|-
|-
| |
| | 30\51
| | 12/11
| |  
| | 270.127
| | 705.882
| |
| |  
|-
|-
| |
| |  
| | 15/14
| | 15/14
| | 270.139
| | 706.481
| |
| |  
|-
|-
| | 7\31
| | 23\39
| |
| |  
| | 270.968
| | 707.692
| |
| |  
|-
|-
| |
| |  
| | 11/9
| | 7/5
| | 271.049
| | 708.744
| |
| |  
|-
|-
| |
| |  
| | 8/7
| | 9/7
| | 271.103
| | 708.771
| |
| |  
|-
|-
| |
| |  
| | 7/5
| | 10/9
| | 271.137
| | 708.798
| |
| | 9 limit minimax
|-
|-
| |
| | 39\66
| | 5/4
| |  
| | 271.229
| | 709.091
| |
| |  
|-
|-
| |
| |  
| | 1361367/1000000
| | 7/6
| | 271.326
| | 711.043
| | 7 limit least squares
| |  
|-
|-
| |
| | 16\27
| | 14/13
| |  
| | 271.418
| | 711.111
| | 13 and 15 limit minimax
| |  
|-
|-
| | 19\84
| |  
| |
| | 15/11
| | 271.429
| | 712.317
| |
| |  
|-
|-
| |
| | 57\96
| | {{vector|0 119 -46 20 -16}}
| |  
| | 271.445
| | 712.5
| | 11 limit least squares
| |  
|-
|-
| |  
| |  
| | <math>x^{10} + 2x^3 = 8</math>
| | 11/9
| | 271.508
| | 713.148
| | equal beating
| | 11 limit minimax
|-
|-
| |
| | 25\42
| | 16/13
| |  
| | 271.551
| | 714.286
| |
| |  
|-
|-
| |
| |  
| | {{vector|0 90 -41 14}}
| | 8/7
| | 271.561
| | 715.587
| | 9 limit least squares
| | 7, 13 and 15 limit minimax
|-
|-
| |
| |  
| | 6/5
| | 6/5
| | 271.564
| | 715.641
| | 5 limit minimax
| | 5 limit minimax
|-
|-
| |
| | 34\57
| | {{vector|0 -211 30 -47 -5 142}}
| |  
| | 271.567
| | 715.789
| | 13 limit least squares
| |  
|-
|-
| |
| | 25\72
| | {{vector|0 -236 5 -51 -3 165}}
| |  
| | 271.570
| | 716.667
| | 15 limit least squares
| |  
|-
|-
| |
| |  
| | 1220703125/1033121304
| | 12/11
| | 271.590
| | 716.879
| | 5 limit least squares
| |  
|-
|-
| |
| |  
| | 13/12
| | 11/10
| | 271.593
| | 717.498
| |
| |  
|-
|-
| |
| | 9\15
| | 13/10
| |  
| | 271.612
| | 720.000
| |
| |  
|-
|-
| |
| |  
| | 18/13
| | 18/13
| | 271.618
| | 721.127
| |
| |  
|-
|-
| |
| |  
| | 10/9
| | 271.623
| | 9 limit minimax
|-
| |
| | 15/13
| | 15/13
| | 271.641
| | 723.871
| |
| |  
|-
|-
| | 12\53
| |  
| |
| | 11/8
| | 271.698
| | 724.341
| |
| |  
|-
|-
| |
| |  
| | 4/3
| | 13/12
| | 271.708
| | 730.714
| |
| |  
|-
|-
| |
| |  
| | 13/11
| | 13/10
| | 271.942
| | 745.786
| |
| |  
|-
|-
| |
| |  
| | 16/15
| | 16/13
| | 272.067
| | 759.472
| |
| |  
|-
| |
| | 9/7
| | 272.514
| |
|-
| | 5\22
| |
| | 272.727
| |
|-
| |
| | 11/10
| | 273.001
| |
|-
| |
| | 11/8
| | 275.659
| |
|}
|}


Revision as of 18:25, 4 October 2021

Augene is a regular temperament of the augmented family, which means that 128/125 is tempered out and three 5/4s make a 2/1. Augene is distinguished from its relative august by tempering out 64/63, which means that tunings in which the fifth is larger than 7\12 (700 cents) are optimal. Therefore the MOS sequence of augene goes 12, 15, 27... in constrast to august's which goes 9, 12, 21...

The first few augene MOSes are 3L 3s, 3L 6s, 3L 9s, 12L 3s... and the first EDOs that reasonably support augene are 12edo, 15edo, and especially 27edo.

Tuning spectrum

ET
generator 		eigenmonzo
(unchanged interval) 		fifth
(¢) 		comments
14/13 671.702
12\28 685.714
16/15 688.269
13/11 689.210
7\12 700.000
31\53 701.887
4/3 701.955
30\51 705.882
15/14 706.481
23\39 707.692
7/5 708.744
9/7 708.771
10/9 708.798 9 limit minimax
39\66 709.091
7/6 711.043
16\27 711.111
15/11 712.317
57\96 712.5
11/9 713.148 11 limit minimax
25\42 714.286
8/7 715.587 7, 13 and 15 limit minimax
6/5 715.641 5 limit minimax
34\57 715.789
25\72 716.667
12/11 716.879
11/10 717.498
9\15 720.000
18/13 721.127
15/13 723.871
11/8 724.341
13/12 730.714
13/10 745.786
16/13 759.472

Music

Sad Like Winter Leaves by Igliashon Jones in Augene[12] tuned to 27edo

Galticeran Sonatina by Joel Grant Taylor in Augene[12] tuned to 27edo

Retrieved from "https://en.xen.wiki/index.php?title=Augene&oldid=79018"