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| <h2>IMPORTED REVISION FROM WIKISPACES</h2>
| | {{Infobox Regtemp |
| This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br>
| | | Title = Myna |
| : This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2015-05-01 15:54:21 UTC</tt>.<br>
| | | Subgroups = 2.3.5.7, 2.3.5.7.11 |
| : The original revision id was <tt>549464872</tt>.<br>
| | | Comma basis = [[126/125]], [[1728/1715]] (7-limit); <br> [[126/125]], [[176/175]], [[243/242]] (11-limit) |
| : The revision comment was: <tt></tt><br>
| | | Edo join 1 = 27 | Edo join 2 = 31 |
| The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.<br>
| | | Generator = 6/5 | Generator tuning = 310.1 | Optimization method = POTE |
| <h4>Original Wikitext content:</h4>
| | | MOS scales = [[3L 1s]], [[4L 3s]], [[4L 7s]], ... [[4L 23s]], [[27L 4s]] |
| <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 [[Starling temperaments#Myna%20temperament]].
| | | Mapping = 1; 10 9 7 25 |
| | | Pergen = (P8, ccP5/10) |
| | | Odd limit 1 = 7 | Mistuning 1 = ? | Complexity 1 = 23 |
| | | Odd limit 2 = (2.3.5.7.11) 21 | Mistuning 2 = ? | Complexity 2 = 58 |
| | }} |
|
| |
|
| Note: "myna" is pronounced /<span style="font-size: 120%;"><span class="IPA">ˈ</span></span>ma<span class="IPA">ɪ</span>n<span class="IPA">ə/, like [[@http://en.wikipedia.org/wiki/Myna|the bird]], but is also as a pun on "minor".</span>
| | '''Myna''' is a [[rank-2]] [[temperament]] that is [[generator|generated]] by a flattened minor third of [[6/5]], so that seven generators reach [[7/4]], nine reach [[5/4]] and ten reach [[3/2]]. It can be thought of in terms of a series of equidistances between thirds, that is, making [[8/7]] - [[7/6]] - 6/5 - [[49/40]] - [[5/4]] - [[9/7]] - [[21/16]] all equidistant (the distances between which are [[36/35]], [[49/48]], and [[50/49]]), or otherwise tuning the pental thirds outwards so that the chroma between them ([[25/24]]) is twice the size of the interval between the pental and septimal thirds, 36/35. This is one of two major options for how the thirds are organized in [[EDO]]s of medium size - the other one being [[keemic temperaments]], such as [[superkleismic]] and [[magic]], where the gap between 6/5 and 5/4 is compressed to equal that between 7/6 and 6/5 instead of widened to equal twice it. Both have their characteristic sets of damage, but myna leaves space for an exact neutral third in between 6/5 and 5/4; [[11-limit]] myna then arises from equating this neutral third to [[11/9]] and 13-limit myna adds the interpretation of [[16/13]] to it as well. |
|
| |
|
| =Spectrum of Myna Tunings by Eigenmonzos=
| | It can be described as the 27e & 31 temperament; [[27edo]] and [[31edo]] represent natural endpoints of its tuning range, and 27+31 = [[58edo]] and 58+31 = [[89edo]] are very good tunings. In terms of [[commas]], the most characteristic comma that myna [[tempering out|tempers out]] is [[126/125]], the starling comma, so that two generators reach [[10/7]] and four reach the distinctive 36/35[[~]]50/49 chroma. Additionally, {{S|6/S7}} = [[1728/1715]], the orwellisma, is tempered out to equate 36/35 with 49/48, and so is [[2401/2400]], the breedsma, to equate 49/48 and 50/49 (and find a neutral third at 49/40). In the 11-limit, [[176/175]], [[243/242]], [[441/440]], and [[540/539]] are tempered out; in the 13-limit, [[144/143]] and [[352/351]] are additionally tempered out. |
| ||~ Eigenmonzo ||~ Minor Third ||
| |
| || 7/5 || 308.744 ||
| |
| || 11/9 || 309.482 ||
| |
| || 5/4 || 309.590 ||
| |
| || 8\31 || 309.677 ||
| |
| || 8/7 || 309.832 ||
| |
| || 16/15 || 309.909 ||
| |
| || 15/14 || 309.953 ||
| |
| || 12/11 || 309.958 ||
| |
| || 11/8 || 310.053 ||
| |
| || 23\89 || 310.112 ||
| |
| || 14/11 || 310.138 ||
| |
| || 4/3 || 310.196 (5, 7, 9 and 11 limit minimax; 5, 7, 11 and 13 limit POTT) ||
| |
| || 11/10 || 310.313 ||
| |
| || 15/13 || 310.323 (15 limit minimax) ||
| |
| || 15\58 || 310.345 ||
| |
| || 13/11 || 310.360 (13 limit minimax) ||
| |
| || 9/7 || 310.391 ||
| |
| || 13/10 || 310.413 ||
| |
| || 15/11 || 310.508 ||
| |
| || 18/13 || 310.535 ||
| |
| || 22\85 || 310.588 ||
| |
| || 10/9 || 310.691 ||
| |
| || 14/13 || 310.692 ||
| |
| || 13/12 || 310.762 ||
| |
| || 7/6 || 311.043 ||
| |
| || 7\27 || 311.111 ||
| |
| || 16/13 || 311.894 ||
| |
| || 6/5 || 315.641 ||</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>Myna</title></head><body>See <a class="wiki_link" href="/Starling%20temperaments#Myna%20temperament">Starling temperaments</a>.<br />
| |
| <br />
| |
| Note: &quot;myna&quot; is pronounced /<span style="font-size: 120%;"><span class="IPA">ˈ</span></span>ma<span class="IPA">ɪ</span>n<span class="IPA">ə/, like <a class="wiki_link_ext" href="http://en.wikipedia.org/wiki/Myna" rel="nofollow" target="_blank">the bird</a>, but is also as a pun on &quot;minor&quot;.</span><br />
| |
| <br />
| |
| <!-- ws:start:WikiTextHeadingRule:0:&lt;h1&gt; --><h1 id="toc0"><a name="Spectrum of Myna Tunings by Eigenmonzos"></a><!-- ws:end:WikiTextHeadingRule:0 -->Spectrum of Myna Tunings by Eigenmonzos</h1>
| |
|
| |
|
| |
|
| <table class="wiki_table">
| | Note: "myna" is pronounced /'maɪnə/, like [[Wikipedia:Myna|the bird]], but is also as a pun on "minor". |
| <tr>
| |
| <th>Eigenmonzo<br />
| |
| </th>
| |
| <th>Minor Third<br />
| |
| </th>
| |
| </tr>
| |
| <tr>
| |
| <td>7/5<br />
| |
| </td>
| |
| <td>308.744<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>11/9<br />
| |
| </td>
| |
| <td>309.482<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>5/4<br />
| |
| </td>
| |
| <td>309.590<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>8\31<br />
| |
| </td>
| |
| <td>309.677<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>8/7<br />
| |
| </td>
| |
| <td>309.832<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>16/15<br />
| |
| </td>
| |
| <td>309.909<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>15/14<br />
| |
| </td>
| |
| <td>309.953<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>12/11<br />
| |
| </td>
| |
| <td>309.958<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>11/8<br />
| |
| </td>
| |
| <td>310.053<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>23\89<br />
| |
| </td>
| |
| <td>310.112<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>14/11<br />
| |
| </td>
| |
| <td>310.138<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>4/3<br />
| |
| </td>
| |
| <td>310.196 (5, 7, 9 and 11 limit minimax; 5, 7, 11 and 13 limit POTT)<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>11/10<br />
| |
| </td>
| |
| <td>310.313<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>15/13<br />
| |
| </td>
| |
| <td>310.323 (15 limit minimax)<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>15\58<br />
| |
| </td>
| |
| <td>310.345<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>13/11<br />
| |
| </td>
| |
| <td>310.360 (13 limit minimax)<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>9/7<br />
| |
| </td>
| |
| <td>310.391<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
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| <td>13/10<br />
| |
| </td>
| |
| <td>310.413<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>15/11<br />
| |
| </td>
| |
| <td>310.508<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>18/13<br />
| |
| </td>
| |
| <td>310.535<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>22\85<br />
| |
| </td>
| |
| <td>310.588<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>10/9<br />
| |
| </td>
| |
| <td>310.691<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>14/13<br />
| |
| </td>
| |
| <td>310.692<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>13/12<br />
| |
| </td>
| |
| <td>310.762<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>7/6<br />
| |
| </td>
| |
| <td>311.043<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>7\27<br />
| |
| </td>
| |
| <td>311.111<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>16/13<br />
| |
| </td>
| |
| <td>311.894<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>6/5<br />
| |
| </td>
| |
| <td>315.641<br />
| |
| </td>
| |
| </tr>
| |
| </table>
| |
|
| |
|
| </body></html></pre></div> | | See [[Starling temperaments #Myna]] for more technical data. |
| | |
| | == Interval chain == |
| | In the following table, prime harmonics are in '''bold'''. |
| | |
| | {| class="wikitable center-1 right-2" |
| | |- |
| | ! # |
| | ! Cents* |
| | ! Approximate Ratios |
| | |- |
| | | 0 |
| | | 0.0 |
| | | '''1/1''' |
| | |- |
| | | 1 |
| | | 310.3 |
| | | 6/5 |
| | |- |
| | | 2 |
| | | 620.6 |
| | | 10/7 |
| | |- |
| | | 3 |
| | | 930.8 |
| | | 12/7 |
| | |- |
| | | 4 |
| | | 41.1 |
| | | 36/35, 40/39, 45/44, 49/48, 50/49 |
| | |- |
| | | 5 |
| | | 351.4 |
| | | 11/9, '''16/13''' |
| | |- |
| | | 6 |
| | | 661.7 |
| | | 22/15, 35/24 |
| | |- |
| | | 7 |
| | | 971.9 |
| | | '''7/4''' |
| | |- |
| | | 8 |
| | | 82.2 |
| | | 21/20, 22/21, 25/24 |
| | |- |
| | | 9 |
| | | 392.5 |
| | | '''5/4''' |
| | |- |
| | | 10 |
| | | 702.8 |
| | | '''3/2''' |
| | |- |
| | | 11 |
| | | 1013.0 |
| | | 9/5 |
| | |- |
| | | 12 |
| | | 123.3 |
| | | 14/13, 15/14, 27/25 |
| | |- |
| | | 13 |
| | | 433.6 |
| | | 9/7 |
| | |- |
| | | 14 |
| | | 743.9 |
| | | 20/13 |
| | |- |
| | | 15 |
| | | 1054.1 |
| | | 11/6, 24/13 |
| | |- |
| | | 16 |
| | | 164.4 |
| | | 11/10 |
| | |- |
| | | 17 |
| | | 474.7 |
| | | 21/16 |
| | |- |
| | | 18 |
| | | 785.0 |
| | | 11/7 |
| | |- |
| | | 19 |
| | | 1095.3 |
| | | 15/8 |
| | |- |
| | | 20 |
| | | 205.5 |
| | | 9/8 |
| | |- |
| | | 21 |
| | | 515.8 |
| | | 27/20 |
| | |- |
| | | 22 |
| | | 826.1 |
| | | 21/13 |
| | |- |
| | | 23 |
| | | 1136.4 |
| | | 27/14 |
| | |- |
| | | 24 |
| | | 246.6 |
| | | 15/13 |
| | |- |
| | | 25 |
| | | 556.9 |
| | | '''11/8''', 18/13 |
| | |- |
| | | 26 |
| | | 867.1 |
| | | 33/20 |
| | |- |
| | | 27 |
| | | 1177.5 |
| | | 55/28, 63/32, 77/39, 99/50 |
| | |} |
| | <nowiki />* In 13-limit POTE tuning |
| | |
| | == Chords == |
| | : ''Main article: [[Chords of myna]] and [[Chords of tridecimal myna]]'' |
| | |
| | == Scales == |
| | ; MOS scales |
| | * [[Myna7]] |
| | * [[Myna11]] |
| | * [[Myna15]] |
| | |
| | ; Transversal scales |
| | * [[Myna19trans]] |
| | * [[Myna19trans37]] |
| | * [[Myna23trans]] |
| | * [[Myna23trans37]] |
| | * [[Myna27trans]] |
| | * [[Myna27trans37]] |
| | |
| | == Tuning spectrum == |
| | {| class="wikitable center-all" |
| | |- |
| | ! ET<br />generator |
| | ! [[Eigenmonzo|Eigenmonzo<br />(unchanged interval)]]) |
| | ! Minor<br />third (¢) |
| | ! Comments |
| | |- |
| | | |
| | | 7/5 |
| | | 308.744 |
| | | |
| | |- |
| | | |
| | | 11/9 |
| | | 309.482 |
| | | |
| | |- |
| | | |
| | | 5/4 |
| | | 309.590 |
| | | |
| | |- |
| | | 8\31 |
| | | |
| | | 309.677 |
| | | |
| | |- |
| | | |
| | | 8/7 |
| | | 309.832 |
| | | |
| | |- |
| | | |
| | | 16/15 |
| | | 309.909 |
| | | |
| | |- |
| | | |
| | | 15/14 |
| | | 309.953 |
| | | |
| | |- |
| | | |
| | | 12/11 |
| | | 309.958 |
| | | |
| | |- |
| | | |
| | | 11/8 |
| | | 310.053 |
| | | |
| | |- |
| | | 23\89 |
| | | |
| | | 310.112 |
| | | |
| | |- |
| | | |
| | | 14/11 |
| | | 310.138 |
| | | |
| | |- |
| | | |
| | | 4/3 |
| | | 310.196 |
| | | 5-, 7-, 9- and 11-odd-imit minimax; <br>5-, 7-, 11- and 13-limit POTT |
| | |- |
| | | |
| | | 11/10 |
| | | 310.313 |
| | | |
| | |- |
| | | |
| | | 15/13 |
| | | 310.323 |
| | | 15-odd-limit minimax |
| | |- |
| | | 15\58 |
| | | |
| | | 310.345 |
| | | |
| | |- |
| | | |
| | | 13/11 |
| | | 310.360 |
| | | 13-odd-limit minimax |
| | |- |
| | | |
| | | 9/7 |
| | | 310.391 |
| | | |
| | |- |
| | | |
| | | 13/10 |
| | | 310.413 |
| | | |
| | |- |
| | | |
| | | 15/11 |
| | | 310.508 |
| | | |
| | |- |
| | | |
| | | 18/13 |
| | | 310.535 |
| | | |
| | |- |
| | | 22\85 |
| | | |
| | | 310.588 |
| | | |
| | |- |
| | | |
| | | 10/9 |
| | | 310.691 |
| | | |
| | |- |
| | | |
| | | 14/13 |
| | | 310.692 |
| | | |
| | |- |
| | | |
| | | 13/12 |
| | | 310.762 |
| | | |
| | |- |
| | | |
| | | 7/6 |
| | | 311.043 |
| | | |
| | |- |
| | | 7\27 |
| | | |
| | | 311.111 |
| | | |
| | |- |
| | | |
| | | 16/13 |
| | | 311.894 |
| | | |
| | |- |
| | | |
| | | 6/5 |
| | | 315.641 |
| | | |
| | |} |
| | |
| | == Music == |
| | * ''[http://clones.soonlabel.com/public/micro/gene_ward_smith/Others/Igs/89versionof23Myna.mp3 Myna Music]'' by [[Igliashon Jones]] |
| | |
| | [[Category:Myna| ]] <!-- Main article --> |
| | [[Category:Rank-2 temperaments]] |
| | [[Category:Starling temperaments]] |
| | [[Category:Orwellismic temperaments]] |
| | [[Category:Breedsmic temperaments]] |