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<h2>IMPORTED REVISION FROM WIKISPACES</h2>
'''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, ….
This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br>
: This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2012-11-14 20:08:16 UTC</tt>.<br>
: The original revision id was <tt>382582570</tt>.<br>
: The revision comment was: <tt></tt><br>
The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.<br>
<h4>Original Wikitext content:</h4>
<div style="width:100%; max-height:400pt; overflow:auto; background-color:#f8f9fa; border: 1px solid #eaecf0; padding:0em"><pre style="margin:0px;border:none;background:none;word-wrap:break-word;white-space: pre-wrap ! important" class="old-revision-html">Augene is a regular temperament of the [[augmented family#x-Augene]], 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]].
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]]).


=Spectrum of Augene Tunings by Eigenmonzos=
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]].
||~ Eigenmonzo ||~ Fifth ||
|| 14/13 || 671.702 ||
|| 16/15 || 688.269 ||
|| 13/11 || 689.210 ||
|| 4/3 || 701.955 ||
|| 15/14 || 706.481 ||
|| 7/5 || 708.744 ||
|| 9/7 || 708.771 ||
|| 10/9 || 708.798 (9 limit minimax) ||
|| 7/6 || 711.043 ||
|| 15/11 || 712.317 ||
|| 11/9 || 713.148 (11 limit minimax) ||
|| 8/7 || 715.587 (7, 13 and 15 limit minimax) ||
|| 6/5 || 715.641 (5 limit minimax) ||
|| 12/11 || 716.879 ||
|| 11/10 || 717.498 ||
|| 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=
See [[Augmented family #Augene]] for technical data. See [[Augene extensions]] for a discussion on 13-limit extensions.  
//[[http://micro.soonlabel.com/gene_ward_smith/Others/Igs/Sad%20Like%20Winter%20Leaves.mp3|Sad Like Winter Leaves]]// by [[http://soundcloud.com/cityoftheasleep/sad-like-winter-trees|Igliashon Jones]] in Augene[12] tuned to 27edo
//[[http://micro.soonlabel.com/gene_ward_smith/Others/Taylor/12of27sonatina.mp3|Galticeran Sonatina]]// by [[http://soundcloud.com/joelgranttaylor/galticeran_sonatina|Joel Grant Taylor]] in Augene[12] tuned to 27edo</pre></div>
<h4>Original HTML content:</h4>
<div style="width:100%; max-height:400pt; overflow:auto; background-color:#f8f9fa; border: 1px solid #eaecf0; padding:0em"><pre style="margin:0px;border:none;background:none;word-wrap:break-word;width:200%;white-space: pre-wrap ! important" class="old-revision-html">&lt;html&gt;&lt;head&gt;&lt;title&gt;Augene&lt;/title&gt;&lt;/head&gt;&lt;body&gt;Augene is a regular temperament of the &lt;a class="wiki_link" href="/augmented%20family#x-Augene"&gt;augmented family&lt;/a&gt;, which means that 128/125 is tempered out and three 5/4s make a 2/1. Augene is distinguished from its relative &lt;a class="wiki_link" href="/august"&gt;august&lt;/a&gt; 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...&lt;br /&gt;
&lt;br /&gt;
The first few augene MOSes are &lt;a class="wiki_link" href="/3L%203s"&gt;3L 3s&lt;/a&gt;, &lt;a class="wiki_link" href="/3L%206s"&gt;3L 6s&lt;/a&gt;, &lt;a class="wiki_link" href="/3L%209s"&gt;3L 9s&lt;/a&gt;, &lt;a class="wiki_link" href="/12L%203s"&gt;12L 3s&lt;/a&gt;... and the first EDOs that reasonably support augene are &lt;a class="wiki_link" href="/12edo"&gt;12edo&lt;/a&gt;, &lt;a class="wiki_link" href="/15edo"&gt;15edo&lt;/a&gt;, and especially &lt;a class="wiki_link" href="/27edo"&gt;27edo&lt;/a&gt;.&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:0:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc0"&gt;&lt;a name="Spectrum of Augene Tunings by Eigenmonzos"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:0 --&gt;Spectrum of Augene Tunings by Eigenmonzos&lt;/h1&gt;


&lt;table class="wiki_table"&gt;
== Interval chain ==
    &lt;tr&gt;
In the following table, odd harmonics 1–11 are in '''bold'''.  
        &lt;th&gt;Eigenmonzo&lt;br /&gt;
&lt;/th&gt;
        &lt;th&gt;Fifth&lt;br /&gt;
&lt;/th&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;14/13&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;671.702&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;16/15&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;688.269&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;13/11&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;689.210&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;4/3&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;701.955&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;15/14&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;706.481&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;7/5&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;708.744&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;9/7&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;708.771&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;10/9&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;708.798 (9 limit minimax)&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;7/6&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;711.043&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;15/11&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;712.317&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;11/9&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;713.148 (11 limit minimax)&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;8/7&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;715.587 (7, 13 and 15 limit minimax)&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;6/5&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;715.641 (5 limit minimax)&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;12/11&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;716.879&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;11/10&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;717.498&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;18/13&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;721.127&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;15/13&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;723.871&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;11/8&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;724.341&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;13/12&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;730.714&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;13/10&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;745.786&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;16/13&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;759.472&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
&lt;/table&gt;


&lt;br /&gt;
{| class="wikitable center-1 right-2 right-4 right-6"
&lt;!-- ws:start:WikiTextHeadingRule:2:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc1"&gt;&lt;a name="Music"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:2 --&gt;Music&lt;/h1&gt;
|-
&lt;em&gt;&lt;a class="wiki_link_ext" href="http://micro.soonlabel.com/gene_ward_smith/Others/Igs/Sad%20Like%20Winter%20Leaves.mp3" rel="nofollow"&gt;Sad Like Winter Leaves&lt;/a&gt;&lt;/em&gt; by &lt;a class="wiki_link_ext" href="http://soundcloud.com/cityoftheasleep/sad-like-winter-trees" rel="nofollow"&gt;Igliashon Jones&lt;/a&gt; in Augene[12] tuned to 27edo&lt;br /&gt;
! rowspan="2" | #
&lt;em&gt;&lt;a class="wiki_link_ext" href="http://micro.soonlabel.com/gene_ward_smith/Others/Taylor/12of27sonatina.mp3" rel="nofollow"&gt;Galticeran Sonatina&lt;/a&gt;&lt;/em&gt; by &lt;a class="wiki_link_ext" href="http://soundcloud.com/joelgranttaylor/galticeran_sonatina" rel="nofollow"&gt;Joel Grant Taylor&lt;/a&gt; in Augene[12] tuned to 27edo&lt;/body&gt;&lt;/html&gt;</pre></div>
! colspan="2" | Period 0
! colspan="2" | Period 1
! colspan="2" | Period 2
|-
! Cents*
! Approx. ratios
! Cents*
! Approx. ratios
! Cents*
! Approx. ratios
|-
| 0
| 0.0
| 1/1
| 400.0
| '''5/4''', 14/11
| 800.0
| '''8/5''', 11/7
|-
| 1
| 1113.1
| 15/8, 40/21
| 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
| 939.4
| 12/7
| 139.4
| 12/11, 15/14
| 539.4
| 15/11
|-
| 4
| 852.6
| 18/11
| 52.6
| 45/44
| 452.6
| 9/7
|-
| 5
| 765.7
| 54/35
| 1165.7
| 27/14, 96/49
| 365.7
| 27/22
|}
<nowiki/>* In 11-odd-limit minimax tuning, octave reduced
 
== Tunings ==
{| class="wikitable mw-collapsible mw-collapsed"
|+ style="font-size: 105%; white-space: nowrap;" | 7-limit prime-optimized tunings
|-
! rowspan="2" |
! colspan="3" | Euclidean
|-
! Constrained
! Constrained & skewed
! Destretched
|-
! Tenney
| CTE: ~3/2 = 709.5949{{c}}
| 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" |
! colspan="3" | Euclidean
|-
! Constrained
! Constrained & skewed
! Destretched
|-
! Tenney
| CTE: ~3/2 = 713.5701{{c}}
| CWE: ~3/2 = 711.6031{{c}}
| POTE: ~3/2 = 711.1766{{c}}
|}
 
=== Tuning spectrum ===
{| class="wikitable center-all left-4"
|-
! Edo<br>generator
! [[Eigenmonzo|Eigenmonzo<br>(unchanged-interval)]]*
! Generator (¢)
! Comments
|-
|
| 15/8
| 688.269
| -1/3 comma
|-
| 7\12
|
| 700.000
|
|-
|
| 3/2
| 701.955
| Untempered
|-
| 30\51
|
| 705.882
| 51cdeee val
|-
|
| 15/14
| 706.481
|
|-
| 23\39
|
| 707.692
| 39dee val
|-
|
| 7/5
| 708.744
|
|-
|
| 9/7
| 708.771
|
|-
|
| 9/5
| 708.798
| 1/6 comma, 9-odd-limit minimax
|-
| 39\66
|
| 709.091
| 66cdeee val
|-
|
| 7/6
| 711.043
|
|-
| 16\27
|
| 711.111
| 27e val
|-
|
| 15/11
| 712.317
|
|-
| 41\69
|
| 713.043
| 69bcee val
|-
|
| 11/9
| 713.148
| 11-odd-limit minimax
|-
| 25\42
|
| 714.286
| 42e val
|-
|
| 7/4
| 715.587
| 7-odd-limit minimax
|-
|
| 5/3
| 715.641
| 1/3 comma, 5-odd-limit minimax
|-
| 34\57
|
| 715.789
| 53bce val
|-
|
| 11/6
| 716.879
|
|-
|
| 11/10
| 717.498
|
|-
| 9\15
|
| 720.000
|
|-
|
| 11/8
| 724.341
|
|}
<nowiki/>* Besides the octave
 
== Music ==
; [[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
 
; [[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:Augene| ]] <!-- Main article -->
[[Category:Rank-2 temperaments]]
[[Category:Augmented family]]
[[Category:Archytas clan]]
[[Category:Starling temperaments]]
Retrieved from "https://en.xen.wiki/w/Augene"