Xenharmonic Wiki

Opossum: Difference between revisions

← Older edit
VisualWikitext
Wikispaces>genewardsmith
**Imported revision 382527810 - Original comment: **
m Text replacement - "Eigenmonzo<br>(unchanged-interval)" to "Unchanged interval<br>(eigenmonzo)"
 
(16 intermediate revisions by 5 users not shown)
Line 1: Line 1:
<h2>IMPORTED REVISION FROM WIKISPACES</h2>
'''Opossum''' is an alternative [[extension]] to [[porcupine]]. It is defined by [[tempering out]] [[28/27]] and [[126/125]].  
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 17:02:04 UTC</tt>.<br>
: The original revision id was <tt>382527810</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">See [[Trienstonic clan#Opossum]].


=Spectrum of Opossum Tunings by Eigenmonzos=
See [[Porcupine family #Opossum]] for technical data.
Gencom: [2 10/9; 28/27 40/39 55/54 66/65]
Gencom map: [&lt;1 2 3 4 4 4|, &lt;0 -3 -5 -9 -4 -2|]
||~ Eigenmonzo ||~ Neutral Second ||
|| 15/14 || 119.443 ||
|| 13/12 || 138.573 ||
|| 13/11 || 144.605 ||
|| 9/7 || 145.028 ||
|| 1\8 || 150.000 ||
|| 12/11 || 150.637 ||
|| 13/10 || 151.405 ||
|| 14/13 || 153.100 ||
|| 7/5 || 154.372 ||
|| 7/6 || 155.522 ||
|| 14/11 || 156.498 ||
|| 3\23 || 156.522 ||
|| 6/5 || 157.821 ||
|| |0 15 6 34 -1 -15&gt; || 158.421 (13 limit least squares) ||
|| 5\38 || 157.895 ||
|| 7\53 || 158.491 ||
|| 15/13 || 158.710 ||
|| |0 -5 3 19&gt; || 158.732 (7 limit least squares) ||
|| 8/7 || 159.019 (7, 9, 11, 13 and 15 limit minimax) ||
|| 18/13 || 159.154 ||
|| |0 32 23 35 -5 -21&gt; || 159.377 (15 limit least squares) ||
|| |0 3 2 22&gt; || 159.481 (9 limit least squares) ||
|| 1815912315/1476395008 || 159.564 (11 limit least squares) ||
|| 2\15 || 160.000 ||
|| 11/8 || 162.171 ||
|| 5/4 || 162.737 (5 limit minimax) ||
|| 262144/234375 || 162.996 (5 limit least squares) ||
|| 16/15 || 163.966 ||
|| 11/10 || 165.004 ||
|| 15/11 || 165.762 ||
|| 4/3 || 166.015 ||
|| 11/9 || 173.704 ||
|| 16/13 || 179.736 ||
|| 10/9 || 182.404 ||</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;Opossum&lt;/title&gt;&lt;/head&gt;&lt;body&gt;See &lt;a class="wiki_link" href="/Trienstonic%20clan#Opossum"&gt;Trienstonic clan&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 Opossum Tunings by Eigenmonzos"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:0 --&gt;Spectrum of Opossum Tunings by Eigenmonzos&lt;/h1&gt;
Gencom: [2 10/9; 28/27 40/39 55/54 66/65]&lt;br /&gt;
Gencom map: [&amp;lt;1 2 3 4 4 4|, &amp;lt;0 -3 -5 -9 -4 -2|]&lt;br /&gt;


== Interval chain ==
In the following table, odd harmonics 1–11 and their inverses are in '''bold'''.


&lt;table class="wiki_table"&gt;
{| class="wikitable center-1 right-2"
    &lt;tr&gt;
|-
        &lt;th&gt;Eigenmonzo&lt;br /&gt;
! #
&lt;/th&gt;
! Cents*
        &lt;th&gt;Neutral Second&lt;br /&gt;
! Approximate ratios*
&lt;/th&gt;
|-
    &lt;/tr&gt;
| 0
    &lt;tr&gt;
| 0.0
        &lt;td&gt;15/14&lt;br /&gt;
| '''1/1'''
&lt;/td&gt;
|-
        &lt;td&gt;119.443&lt;br /&gt;
| 1
&lt;/td&gt;
| 160.0
    &lt;/tr&gt;
| 10/9, 11/10, 12/11, 15/14
    &lt;tr&gt;
|-
        &lt;td&gt;13/12&lt;br /&gt;
| 2
&lt;/td&gt;
| 320.0
        &lt;td&gt;138.573&lt;br /&gt;
| 6/5, 11/9
&lt;/td&gt;
|-
    &lt;/tr&gt;
| 3
    &lt;tr&gt;
| 480.0
        &lt;td&gt;13/11&lt;br /&gt;
| '''4/3''', 9/7
&lt;/td&gt;
|-
        &lt;td&gt;144.605&lt;br /&gt;
| 4
&lt;/td&gt;
| 640.0
    &lt;/tr&gt;
| 10/7, '''16/11''', 22/15
    &lt;tr&gt;
|-
        &lt;td&gt;9/7&lt;br /&gt;
| 5
&lt;/td&gt;
| 800.0
        &lt;td&gt;145.028&lt;br /&gt;
| '''8/5''', 11/7
&lt;/td&gt;
|-
    &lt;/tr&gt;
| 6
    &lt;tr&gt;
| 960.0
        &lt;td&gt;1\8&lt;br /&gt;
| 12/7, '''16/9'''
&lt;/td&gt;
|-
        &lt;td&gt;150.000&lt;br /&gt;
| 7
&lt;/td&gt;
| 1120.0
    &lt;/tr&gt;
| 40/21, 48/25, 64/33
    &lt;tr&gt;
|-
        &lt;td&gt;12/11&lt;br /&gt;
| 8
&lt;/td&gt;
| 80.0
        &lt;td&gt;150.637&lt;br /&gt;
| 16/15, 36/35
&lt;/td&gt;
|-
    &lt;/tr&gt;
| 9
    &lt;tr&gt;
| 240.0
        &lt;td&gt;13/10&lt;br /&gt;
| '''8/7'''
&lt;/td&gt;
|}
        &lt;td&gt;151.405&lt;br /&gt;
<nowiki/>* In 15edo tuning, octave reduced
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;14/13&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;153.100&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;154.372&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;155.522&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;14/11&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;156.498&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;3\23&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;156.522&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;157.821&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;|0 15 6 34 -1 -15&amp;gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;158.421 (13 limit least squares)&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;5\38&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;157.895&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;7\53&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;158.491&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;158.710&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;|0 -5 3 19&amp;gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;158.732 (7 limit least squares)&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;159.019 (7, 9, 11, 13 and 15 limit minimax)&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;159.154&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;|0 32 23 35 -5 -21&amp;gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;159.377 (15 limit least squares)&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;|0 3 2 22&amp;gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;159.481 (9 limit least squares)&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;1815912315/1476395008&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;159.564 (11 limit least squares)&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;2\15&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;160.000&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;162.171&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;5/4&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;162.737 (5 limit minimax)&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;262144/234375&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;162.996 (5 limit least squares)&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;163.966&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;165.004&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;165.762&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;166.015&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;173.704&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;179.736&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;182.404&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
&lt;/table&gt;


&lt;/body&gt;&lt;/html&gt;</pre></div>
== Tunings ==
{| class="wikitable center-1 mw-collapsible mw-collapsed"
|+ style="font-size: 105%; white-space: nowrap;" | Least-squares tunings
|-
! Target
! Generator
! Eigenmonzo
|-
| 5-odd-limit
| ~10/9 = 162.996{{c}}
| 262144/234375
|-
| 7-odd-limit
| ~10/9 = 158.732{{c}}
| {{Monzo| 0 -5 3 19 }}
|-
| 9-odd-limit
| ~12/11 = 159.481{{c}}
| {{Monzo| 0 3 2 22 }}
|-
| 11-odd-limit
| ~12/11 = 159.564{{c}}
| {{Monzo| -27 2 1 9 -1 }}
|-
| 13-odd-limit
| ~12/11 = 158.421{{c}}
| {{Monzo| 0 15 6 34 -1 -15 }}
|-
| 15-odd-limit
| ~12/11 = 159.377{{c}}
| {{Monzo| 0 32 23 35 -5 -21 }}
|}
 
=== Tuning spectrum ===
{| class="wikitable center-all left-4"
|-
! Edo<br>generator
! [[Eigenmonzo|Unchanged interval<br>(eigenmonzo)]]
! Generator (¢)
! Comments
|-
|
| 15/14
| 119.443
|
|-
|
| 13/12
| 138.573
|
|-
|
| 13/11
| 144.605
|
|-
|
| 9/7
| 145.028
|
|-
| 1\8
|
| 150.000
| 8d val, lower bound of 7-odd-limit diamond monotone
|-
|
| 11/6
| 150.637
|
|-
|
| 13/10
| 151.405
|
|-
|
| 13/7
| 153.100
|
|-
|
| 7/5
| 154.372
|
|-
|
| 7/6
| 155.522
|
|-
|
| 11/7
| 156.498
|
|-
| 3\23
|
| 156.522
| 23bcf val
|-
|
| 5/3
| 157.821
|
|-
| 5\38
|
| 157.895
| 38bceff val
|-
| 7\53
|
| 158.491
| 53bcefff val
|-
|
| 15/13
| 158.710
|
|-
|
| 7/4
| 159.019
| 7-, 9-, 11-, 13- and 15-odd-limit minimax
|-
|
| 13/9
| 159.154
|
|-
| 2\15
|
| 160.000
| Upper bound of 7-odd-limit diamond monotone<br>9- and 11-odd-limit diamond monotone (singleton)
|-
|
| 11/8
| 162.171
|
|-
|
| 5/4
| 162.737
| 5-odd-limit minimax
|-
|
| 15/8
| 163.966
|
|-
|
| 11/10
| 165.004
|
|-
|
| 15/11
| 165.762
|
|-
|
| 3/2
| 166.015
|
|-
|
| 11/9
| 173.704
|
|-
|
| 13/8
| 179.736
|
|-
|
| 9/5
| 182.404
|
|}
 
[[Category:Opossum| ]] <!-- main article -->
[[Category:Rank-2 temperaments]]
[[Category:Exotemperaments]]
[[Category:Porcupine family]]
[[Category:Trienstonic clan]]
[[Category:Starling temperaments]]
Retrieved from "https://en.xen.wiki/w/Opossum"