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| <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 16:36:51 UTC</tt>.<br>
| |
| : The original revision id was <tt>382519288</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: [<1 2 3 4 4 4|, <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 ||
| |
| || 12/11 || 150.637 ||
| |
| || 13/10 || 151.405 ||
| |
| || 14/13 || 153.100 ||
| |
| || 7/5 || 154.372 ||
| |
| || 7/6 || 155.522 ||
| |
| || 14/11 || 156.498 ||
| |
| || 6/5 || 157.821 ||
| |
| || 15/13 || 158.710 ||
| |
| || 8/7 || 159.019 (7, 9, 11, 13 and 15 limit minimax) ||
| |
| || 18/13 || 159.154 ||
| |
| || 11/8 || 162.171 ||
| |
| || 5/4 || 162.737 (5 limit minimax) ||
| |
| || 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"><html><head><title>Opossum</title></head><body>See <a class="wiki_link" href="/Trienstonic%20clan#Opossum">Trienstonic clan</a>.<br />
| |
| <br />
| |
| <!-- ws:start:WikiTextHeadingRule:0:&lt;h1&gt; --><h1 id="toc0"><a name="Spectrum of Opossum Tunings by Eigenmonzos"></a><!-- ws:end:WikiTextHeadingRule:0 -->Spectrum of Opossum Tunings by Eigenmonzos</h1>
| |
| Gencom: [2 10/9; 28/27 40/39 55/54 66/65]<br />
| |
| Gencom map: [&lt;1 2 3 4 4 4|, &lt;0 -3 -5 -9 -4 -2|]<br />
| |
|
| |
|
| | == Interval chain == |
| | In the following table, odd harmonics 1–11 and their inverses are in '''bold'''. |
|
| |
|
| <table class="wiki_table">
| | {| class="wikitable center-1 right-2" |
| <tr>
| | |- |
| <th>Eigenmonzo<br />
| | ! # |
| </th>
| | ! Cents* |
| <th>Neutral Second<br />
| | ! Approximate ratios* |
| </th>
| | |- |
| </tr>
| | | 0 |
| <tr>
| | | 0.0 |
| <td>15/14<br />
| | | '''1/1''' |
| </td>
| | |- |
| <td>119.443<br />
| | | 1 |
| </td>
| | | 160.0 |
| </tr>
| | | 10/9, 11/10, 12/11, 15/14 |
| <tr>
| | |- |
| <td>13/12<br />
| | | 2 |
| </td>
| | | 320.0 |
| <td>138.573<br />
| | | 6/5, 11/9 |
| </td>
| | |- |
| </tr>
| | | 3 |
| <tr>
| | | 480.0 |
| <td>13/11<br />
| | | '''4/3''', 9/7 |
| </td>
| | |- |
| <td>144.605<br />
| | | 4 |
| </td>
| | | 640.0 |
| </tr>
| | | 10/7, '''16/11''', 22/15 |
| <tr>
| | |- |
| <td>9/7<br />
| | | 5 |
| </td>
| | | 800.0 |
| <td>145.028<br />
| | | '''8/5''', 11/7 |
| </td>
| | |- |
| </tr>
| | | 6 |
| <tr>
| | | 960.0 |
| <td>12/11<br />
| | | 12/7, '''16/9''' |
| </td>
| | |- |
| <td>150.637<br />
| | | 7 |
| </td>
| | | 1120.0 |
| </tr>
| | | 40/21, 48/25, 64/33 |
| <tr>
| | |- |
| <td>13/10<br />
| | | 8 |
| </td>
| | | 80.0 |
| <td>151.405<br />
| | | 16/15, 36/35 |
| </td>
| | |- |
| </tr>
| | | 9 |
| <tr>
| | | 240.0 |
| <td>14/13<br />
| | | '''8/7''' |
| </td>
| | |} |
| <td>153.100<br />
| | <nowiki/>* In 15edo tuning, octave reduced |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>7/5<br />
| |
| </td>
| |
| <td>154.372<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>7/6<br />
| |
| </td>
| |
| <td>155.522<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>14/11<br />
| |
| </td>
| |
| <td>156.498<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>6/5<br />
| |
| </td>
| |
| <td>157.821<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>15/13<br />
| |
| </td>
| |
| <td>158.710<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>8/7<br />
| |
| </td>
| |
| <td>159.019 (7, 9, 11, 13 and 15 limit minimax)<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>18/13<br />
| |
| </td>
| |
| <td>159.154<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>11/8<br />
| |
| </td>
| |
| <td>162.171<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>5/4<br />
| |
| </td>
| |
| <td>162.737 (5 limit minimax)<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>16/15<br />
| |
| </td>
| |
| <td>163.966<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>11/10<br />
| |
| </td>
| |
| <td>165.004<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>15/11<br />
| |
| </td>
| |
| <td>165.762<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>4/3<br />
| |
| </td>
| |
| <td>166.015<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>11/9<br />
| |
| </td>
| |
| <td>173.704<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>16/13<br />
| |
| </td>
| |
| <td>179.736<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>10/9<br />
| |
| </td>
| |
| <td>182.404<br />
| |
| </td>
| |
| </tr>
| |
| </table>
| |
|
| |
|
| </body></html></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]] |
Opossum is an alternative extension to porcupine. It is defined by tempering out 28/27 and 126/125.
See Porcupine family #Opossum for technical data.
Interval chain
In the following table, odd harmonics 1–11 and their inverses are in bold.
| #
|
Cents*
|
Approximate ratios*
|
| 0
|
0.0
|
1/1
|
| 1
|
160.0
|
10/9, 11/10, 12/11, 15/14
|
| 2
|
320.0
|
6/5, 11/9
|
| 3
|
480.0
|
4/3, 9/7
|
| 4
|
640.0
|
10/7, 16/11, 22/15
|
| 5
|
800.0
|
8/5, 11/7
|
| 6
|
960.0
|
12/7, 16/9
|
| 7
|
1120.0
|
40/21, 48/25, 64/33
|
| 8
|
80.0
|
16/15, 36/35
|
| 9
|
240.0
|
8/7
|
* In 15edo tuning, octave reduced
Tunings
Least-squares tunings
| Target
|
Generator
|
Eigenmonzo
|
| 5-odd-limit
|
~10/9 = 162.996 ¢
|
262144/234375
|
| 7-odd-limit
|
~10/9 = 158.732 ¢
|
[0 -5 3 19⟩
|
| 9-odd-limit
|
~12/11 = 159.481 ¢
|
[0 3 2 22⟩
|
| 11-odd-limit
|
~12/11 = 159.564 ¢
|
[-27 2 1 9 -1⟩
|
| 13-odd-limit
|
~12/11 = 158.421 ¢
|
[0 15 6 34 -1 -15⟩
|
| 15-odd-limit
|
~12/11 = 159.377 ¢
|
[0 32 23 35 -5 -21⟩
|
Tuning spectrum
Edo
generator
|
Unchanged interval
(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
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
|
|