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Augene: Difference between revisions

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**Imported revision 246771639 - Original comment: **
 
→Tunings: + prime-optimized tunings
 
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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:keenanpepper|keenanpepper]] and made on <tt>2011-08-18 15:10:09 UTC</tt>.<br>
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]]).
: The original revision id was <tt>246771639</tt>.<br>
 
: The revision comment was: <tt></tt><br>
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]].
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>
See [[Augmented family #Augene]] for technical data. See [[Augene extensions]] for a discussion on 13-limit extensions.
<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">See [[Augmented family#Augene]].</pre></div>
 
<h4>Original HTML content:</h4>
== Interval chain ==
<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;See &lt;a class="wiki_link" href="/Augmented%20family#Augene"&gt;Augmented family&lt;/a&gt;.&lt;/body&gt;&lt;/html&gt;</pre></div>
In the following table, odd harmonics 1–11 are in '''bold'''.
 
{| class="wikitable center-1 right-2 right-4 right-6"
|-
! rowspan="2" | #
! 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"