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Augene is a regular temperament of the [[Augmented_family#x-Augene|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|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...
'''Augene''' is a [[regular temperament]] of the [[augmented family]], which means that [[128/125]] is [[tempering out|tempered out]] and three [[5/4]]'s 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 [[optimal ET 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 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]].
It is also the unique [[7-limit]] [[regular temperament]] that tempers out the [[essential tempering commas]] of the [[5-odd-limit|5-]] ([[128/125]]) and [[7-odd-limit]] ([[64/63]], [[126/125]]).


== 11-limit interval chain ==
The first few augene [[mos scale]]s are [[3L 3s]], [[3L 6s]], [[3L 9s]], [[12L 3s]], … and the first edos that reasonably support augene are [[12edo]], [[15edo]], and especially [[27edo]].
{| class="wikitable"
 
|+Generator based off of 11-limit minimax
See [[Augmented family #Augene]] for technical data. See [[Augene extensions]] for a discussion on 13-limit extensions.
!Gen.
 
!Period 1
== Interval chain ==
!Period 2
In the following table, odd harmonics 1–11 are in '''bold'''.
!Period 3 (0)
 
{| class="wikitable center-1 right-2 right-4 right-6"
|-
! rowspan="2" | #
! colspan="2" | Period 0
! colspan="2" | Period 1
! colspan="2" | Period 2
|-
|-
|0
! Cents*
|400.000
! Approx. ratios
|800.000
! Cents*
|1200.000
! Approx. ratios
! Cents*
! Approx. ratios
|-
|-
|1
| 0
|313.148
| 0.0
|713.148
| 1/1
|1113.148
| 400.0
| '''5/4''', 14/11
| 800.0
| '''8/5''', 11/7
|-
|-
|2
| 1
|226.296
| 1113.1
|626.296
| 15/8, 40/21
|1026.296
| 313.1
| 6/5
| 713.1
| '''3/2'''
|-
| 2
| 1026.3
| 9/5, 20/11
| 226.3
| '''8/7''', '''9/8'''
| 626.3
| 10/7, '''16/11'''
|-
|-
|3
| 3
|139.444
| 939.4
|539.444
| 12/7
|939.444
| 139.4
| 12/11, 15/14
| 539.4
| 15/11
|-
|-
|4
| 4
|52.592
| 852.6
|452.592
| 18/11
|852.592
| 52.6
| 45/44
| 452.6
| 9/7
|-
|-
|5
| 5
|1165.740
| 765.7
|365.740
| 54/35
|765.740
| 1165.7
| 27/14, 96/49
| 365.7
| 27/22
|}
|}
<nowiki/>* In 11-odd-limit minimax tuning, octave reduced


== Tuning spectrum ==
== Tunings ==
 
{| class="wikitable mw-collapsible mw-collapsed"
{| class="wikitable center-all"
|+ style="font-size: 105%; white-space: nowrap;" | 7-limit prime-optimized tunings
|-
|-
! | ET<br>generator
! rowspan="2" |  
! | [[eigenmonzo|eigenmonzo<br>(unchanged interval]])
! colspan="3" | Euclidean
! | fifth<br>(¢)
! | comments
|-
|-
| |
! Constrained
| | 14/13
! Constrained & skewed
| | 671.702
! Destretched
| |
|-
|-
| | 12\28
! Tenney
| |  
| CTE: ~3/2 = 709.5949{{c}}
| | 685.714
| CWE: ~3/2 = 709.3249{{c}}
| |  
| POTE: ~3/2 = 709.2568{{c}}
|}
{| class="wikitable mw-collapsible mw-collapsed"
|+ style="font-size: 105%; white-space: nowrap;" | 11-limit prime-optimized tunings
|-
|-
| |
! rowspan="2" |  
| | 16/15
! colspan="3" | Euclidean
| | 688.269
| |
|-
|-
| |
! Constrained
| | 13/11
! Constrained & skewed
| | 689.210
! Destretched
| |
|-
|-
| | 7\12
! Tenney
| |
| CTE: ~3/2 = 713.5701{{c}}
| | 700.000
| CWE: ~3/2 = 711.6031{{c}}
| |
| POTE: ~3/2 = 711.1766{{c}}
|-
|}
| | 31\53
 
| |
=== Tuning spectrum ===
| | 701.887
{| class="wikitable center-all left-4"
| |
|-
| |
| | 4/3
| | 701.955
| |
|-
| | 30\51
| |
| | 705.882
| |
|-
| |
| | 15/14
| | 706.481
| |
|-
|-
| | 23\39
! Edo<br>generator
| |
! [[Eigenmonzo|Eigenmonzo<br>(unchanged-interval)]]*
| | 707.692
! Generator (¢)
| |
! Comments
|-
|-
| |  
|  
| | 7/5
| 15/8
| | 708.744
| 688.269
| |
| -1/3 comma
|-
|-
| |
| 7\12
| | 9/7
|  
| | 708.771
| 700.000
| |  
|  
|-
|-
| |  
|  
| | 10/9
| 3/2
| | 708.798
| 701.955
| | 9 limit minimax
| Untempered
|-
|-
| | 39\66
| 30\51
| |  
|  
| | 709.091
| 705.882
| |
| 51cdeee val
|-
|-
| |  
|  
| | 7/6
| 15/14
| | 711.043
| 706.481
| |  
|  
|-
|-
| | 16\27
| 23\39
| |  
|  
| | 711.111
| 707.692
| |
| 39dee val
|-
|-
| |  
|  
| | 15/11
| 7/5
| | 712.317
| 708.744
| |  
|  
|-
|-
| | 57\96
|  
| |
| 9/7
| | 712.5
| 708.771
| |  
|  
|-
|-
| |  
|  
| | 11/9
| 9/5
| | 713.148
| 708.798
| | 11 limit minimax
| 1/6 comma, 9-odd-limit minimax
|-
|-
| | 25\42
| 39\66
| |  
|  
| | 714.286
| 709.091
| |
| 66cdeee val
|-
|-
| |  
|  
| | 8/7
| 7/6
| | 715.587
| 711.043
| | 7, 13 and 15 limit minimax
|  
|-
|-
| |
| 16\27
| | 6/5
|  
| | 715.641
| 711.111
| | 5 limit minimax
| 27e val
|-
|-
| | 34\57
|  
| |
| 15/11
| | 715.789
| 712.317
| |  
|  
|-
|-
| | 25\72
| 41\69
| |  
|  
| | 716.667
| 713.043
| |
| 69bcee val
|-
|-
| |  
|  
| | 12/11
| 11/9
| | 716.879
| 713.148
| |
| 11-odd-limit minimax
|-
|-
| |
| 25\42
| | 11/10
|  
| | 717.498
| 714.286
| |
| 42e val
|-
|-
| | 9\15
|  
| |
| 7/4
| | 720.000
| 715.587
| |
| 7-odd-limit minimax
|-
|-
| |  
|  
| | 18/13
| 5/3
| | 721.127
| 715.641
| |
| 1/3 comma, 5-odd-limit minimax
|-
|-
| |
| 34\57
| | 15/13
|  
| | 723.871
| 715.789
| |
| 53bce val
|-
|-
| |  
|  
| | 11/8
| 11/6
| | 724.341
| 716.879
| |  
|  
|-
|-
| |  
|  
| | 13/12
| 11/10
| | 730.714
| 717.498
| |  
|  
|-
|-
| |
| 9\15
| | 13/10
|  
| | 745.786
| 720.000
| |  
|  
|-
|-
| |  
|  
| | 16/13
| 11/8
| | 759.472
| 724.341
| |  
|  
|}
|}
<nowiki/>* Besides the octave


=Music=
== Music ==
''[http://micro.soonlabel.com/gene_ward_smith/Others/Igs/Sad%20Like%20Winter%20Leaves.mp3 Sad Like Winter Leaves]'' by [https://soundcloud.com/cityoftheasleep/sad-like-winter-trees Igliashon Jones] in Augene[12] tuned to 27edo
; [[Igliashon Jones]]
* [https://web.archive.org/web/20201127012539/http://micro.soonlabel.com/gene_ward_smith/Others/Igs/Sad%20Like%20Winter%20Leaves.mp3 ''Sad Like Winter Leaves''] &ndash; in Augene[12] tuned to 27edo


''[http://micro.soonlabel.com/gene_ward_smith/Others/Taylor/12of27sonatina.mp3 Galticeran Sonatina]'' by [https://soundcloud.com/joelgranttaylor/galticeran_sonatina Joel Grant Taylor] in Augene[12] tuned to 27edo
; [[Joel Grant Taylor]]
* [https://web.archive.org/web/20201127012922/http://micro.soonlabel.com/gene_ward_smith/Others/Taylor/12of27sonatina.mp3 ''Galticeran Sonatina''] &ndash; in Augene[12] tuned to 27edo


[[Category:Temperaments]]
[[Category:Augene| ]] <!-- Main article -->
[[Category:Augene| ]] <!-- main article -->
[[Category:Rank-2 temperaments]]
[[Category:Augmented family]]
[[Category:Archytas clan]]
[[Category:Starling temperaments]]
Retrieved from "https://en.xen.wiki/w/Augene"