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| <h2>IMPORTED REVISION FROM WIKISPACES</h2>
| | {{Infobox ET}} |
| This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br>
| | {{Wikipedia|58 equal temperament}} |
| : This revision was by author [[User:manuphonic|manuphonic]] and made on <tt>2015-12-10 14:38:58 UTC</tt>.<br>
| | {{ED intro}} |
| : The original revision id was <tt>569765105</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">The //58 equal temperament//, often abbreviated 58-tET, 58-EDO, or 58-ET, is the scale derived by dividing the [[octave]] into 58 equally-sized steps. Each step represents a frequency ratio of 20.69 cents. It tempers out 2048/2025, 126/125, 1728/1715, 144/143, 176/175, 896/891, 243/242, 5120/5103, 351/350, 364/363, 441/440, and 540/539, and is a strong system in the [[11-limit|11]], [[13-limit|13]] and [[17-limit]]s. It is the smallest [[edo|equal temperament]] which is [[consistent]] through the 17-limit, and is also the first et to map the entire 11-limit [[tonality diamond]] to distinct scale steps, and hence the first et which can define a version of the famous 43-note [[Harry Partch related scales|Genesis scale]] of [[Harry Partch]]. It supports [[hemififths]], [[myna]], [[diaschismic]], [[harry]], [[Hemifamity temperaments#Mystery|mystery]], [[Hemifamity temperaments#Buzzard|buzzard]] and [[Starling temperaments#Thuja|thuja]] [[Regular Temperaments|temperament]]s, and supplies the [[optimal patent val]] for 7-, 11- and 13-limit diaschismic, 11- and 13-limit hemififths, 11- and 13-limit thuja, and 13-limit myna. It also supplies the optimal patent val for the 13-limit rank three temperaments [[Starling family#Thrush|thrush]], [[Starling family#Thrush-Bluebird|bluebird]], [[Starling family#Aplonis|aplonis]] and [[Breed family#Jove,%20aka%20Wonder-Jofur|jofur]].
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| While the 17th harmonic is a cent and a half cent flat, the harmonics below it are all a little sharp, giving it the sound of a sharp system. 58 = 2*29, and 58 shares the same excellent fifth with [[29edo]].
| | == Theory == |
| | 58edo is a strong system in the [[11-limit|11-]], [[13-limit|13-]] and [[17-limit]]. It is the smallest [[edo]] which is [[consistent]] through the [[17-odd-limit]], and is also the smallest distinctly consistent in the [[11-odd-limit]] (the first equal temperament to map the entire 11-odd-limit [[tonality diamond]] to distinct scale steps), and hence the first which can define a tempered version of the famous 43-note [[Harry Partch related scales|Genesis scale]] of [[Harry Partch]]. |
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| =Scales= | | While the [[17/1|17th harmonic]] is a cent and a half flat, the harmonics below it are all a little sharp, giving it the sound of a sharp system. Since {{nowrap|58 {{=}} 2 × 29}}, 58edo shares the same excellent perfect fifth with [[29edo]]. It is the last edo to have exactly one [[5L 2s|diatonic]] perfect fifth and no [[5edo]] or [[7edo]] fifths. |
| [[hemif7]] | |
| [[hemif10]] | |
| [[hemif17]] | |
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| |
|
| ==Intervals==
| | The [[19/1|19th]] and [[23/1|23rd]] harmonics are very flat, so it makes sense to use their second-best approximations in the 58hi val. This val is, in fact, one of the first to be [[diamond monotone]] in the 23-odd-limit, past the idiosyncratic 53e val. However, its accuracy is questionable, with primes 19 and 23 being about 13 cents sharp, so one may want to use a larger system like [[62edo]] for the 23-limit instead, which has the added benefit of being meantone. |
| || degree of 58edo || cents value || ratios ||
| |
| || 0 || 0.00 || 1/1 ||
| |
| || 1 || 20.69 || 56/55, 64/63, 81/80, 128/125 ||
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| || 2 || 41.38 || 36/35, 49/48, 50/49, 55/54 ||
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| || 3 || 62.07 || 25/24, 26/25, 27/26, 28/27, 33/32 ||
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| || 4 || 82.76 || 21/20, 22/21 ||
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| || 5 || 103.45 || 16/15, 17/16, 18/17 ||
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| || 6 || 124.14 || 14/13, 15/14, 27/25 ||
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| || 7 || 144.83 || 12/11, 13/12 ||
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| || 8 || 165.52 || 11/10 ||
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| || 9 || 186.21 || 10/9 ||
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| || 10 || 206.9 || 9/8, 17/15 ||
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| || 11 || 227.59 || 8/7 ||
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| || 12 || 248.28 || 15/13 ||
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| || 13 || 268.97 || 7/6 ||
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| || 14 || 289.66 || 13/11, 20/17 ||
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| || 15 || 310.34 || 6/5 ||
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| || 16 || 331.03 || 17/14 ||
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| || 17 || 351.72 || 11/9, 16/13 ||
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| || 18 || 372.41 || 21/17 ||
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| || 19 || 393.1 || 5/4 ||
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| || 20 || 413.79 || 14/11 ||
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| || 21 || 434.48 || 9/7 ||
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| || 22 || 455.17 || 13/10, 17/13, 22/17 ||
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| || 23 || 475.86 || 21/16 ||
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| || 24 || 496.55 || 4/3 ||
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| || 25 || 517.24 || 27/20 ||
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| || 26 || 537.93 || 15/11 ||
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| || 27 || 558.62 || 11/8, 18/13 ||
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| || 28 || 579.31 || 7/5 ||
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| || 29 || 600 || 17/12, 24/17 ||
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| || 30 || 620.69 || 10/7 ||
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| || 31 || 641.38 || 13/9, 16/11 ||
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| || 32 || 662.07 || 22/15 ||
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| || 33 || 682.76 || 40/27 ||
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| || 34 || 703.45 || 3/2 ||
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| || 35 || 724.14 || 32/21 ||
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| || 36 || 744.83 || 20/13, 26/17, 17/11 ||
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| || 37 || 765.52 || 14/9 ||
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| || 38 || 786.21 || 11/7 ||
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| || 39 || 806.9 || 8/5 ||
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| || 40 || 827.59 || 34/21 ||
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| || 41 || 848.28 || 13/8, 18/11 ||
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| || 42 || 868.97 || 28/17 ||
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| || 43 || 889.66 || 5/3 ||
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| || 44 || 910.34 || 22/13, 17/10 ||
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| || 45 || 931.03 || 12/7 ||
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| || 46 || 951.72 || 26/15 ||
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| || 47 || 972.41 || 7/4 ||
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| || 48 || 993.1 || 16/9 ||
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| || 49 || 1013.79 || 9/5 ||
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| || 50 || 1034.48 || 20/11 ||
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| || 51 || 1055.17 || 11/6, 24/13 ||
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| || 52 || 1075.86 || 13/7, 28/15 ||
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| || 53 || 1096.55 || 15/8, 32/17, 17/9 ||
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| || 54 || 1117.24 || 40/21, 21/11 ||
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| || 55 || 1137.93 || ||
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| || 56 || 1158.62 || ||
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| || 57 || 1179.31 || ||
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| ==Rank two temperaments==
| |
| ||~ Period ||~ Generator ||~ Name ||
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| || 1\1 || 1\58 || ||
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| || || 3\58 || ||
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| || || 5\58 || ||
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| || || 7\58 || ||
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| || || 9\58 || ||
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| || || 11\58 || Gorgik ||
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| || || 13\58 || ||
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| || || 15\58 || Myna ||
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| || || 17\58 || Hemififths ||
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| || || 19\58 || ||
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| || || 21\58 || ||
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| || || 23\58 || Buzzard ||
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| || || 25\58 || ||
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| || || 27\58 || Thuja ||
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| || 1\2 || 1\58 || ||
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| || || 2\58 || ||
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| || || 3\58 || ||
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| || || 4\58 || Harry ||
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| || || 5\58 || Srutal/Diaschismic ||
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| || || 6\58 || ||
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| || || 7\58 || ||
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| || || 8\58 || Echidna, Supers ||
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| || || 9\58 || Secant ||
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| || || 10\58 || ||
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| || || 11\58 || ||
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| || || 12\58 || Sruti ||
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| || || 13\58 || ||
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| || || 14\58 || ||
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| || 1\29 || 1\58 || Mystery ||</pre></div>
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| <h4>Original HTML content:</h4>
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| <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>58edo</title></head><body>The <em>58 equal temperament</em>, often abbreviated 58-tET, 58-EDO, or 58-ET, is the scale derived by dividing the <a class="wiki_link" href="/octave">octave</a> into 58 equally-sized steps. Each step represents a frequency ratio of 20.69 cents. It tempers out 2048/2025, 126/125, 1728/1715, 144/143, 176/175, 896/891, 243/242, 5120/5103, 351/350, 364/363, 441/440, and 540/539, and is a strong system in the <a class="wiki_link" href="/11-limit">11</a>, <a class="wiki_link" href="/13-limit">13</a> and <a class="wiki_link" href="/17-limit">17-limit</a>s. It is the smallest <a class="wiki_link" href="/edo">equal temperament</a> which is <a class="wiki_link" href="/consistent">consistent</a> through the 17-limit, and is also the first et to map the entire 11-limit <a class="wiki_link" href="/tonality%20diamond">tonality diamond</a> to distinct scale steps, and hence the first et which can define a version of the famous 43-note <a class="wiki_link" href="/Harry%20Partch%20related%20scales">Genesis scale</a> of <a class="wiki_link" href="/Harry%20Partch">Harry Partch</a>. It supports <a class="wiki_link" href="/hemififths">hemififths</a>, <a class="wiki_link" href="/myna">myna</a>, <a class="wiki_link" href="/diaschismic">diaschismic</a>, <a class="wiki_link" href="/harry">harry</a>, <a class="wiki_link" href="/Hemifamity%20temperaments#Mystery">mystery</a>, <a class="wiki_link" href="/Hemifamity%20temperaments#Buzzard">buzzard</a> and <a class="wiki_link" href="/Starling%20temperaments#Thuja">thuja</a> <a class="wiki_link" href="/Regular%20Temperaments">temperament</a>s, and supplies the <a class="wiki_link" href="/optimal%20patent%20val">optimal patent val</a> for 7-, 11- and 13-limit diaschismic, 11- and 13-limit hemififths, 11- and 13-limit thuja, and 13-limit myna. It also supplies the optimal patent val for the 13-limit rank three temperaments <a class="wiki_link" href="/Starling%20family#Thrush">thrush</a>, <a class="wiki_link" href="/Starling%20family#Thrush-Bluebird">bluebird</a>, <a class="wiki_link" href="/Starling%20family#Aplonis">aplonis</a> and <a class="wiki_link" href="/Breed%20family#Jove,%20aka%20Wonder-Jofur">jofur</a>.<br />
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| <br />
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| While the 17th harmonic is a cent and a half cent flat, the harmonics below it are all a little sharp, giving it the sound of a sharp system. 58 = 2*29, and 58 shares the same excellent fifth with <a class="wiki_link" href="/29edo">29edo</a>.<br />
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| <br />
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| <!-- ws:start:WikiTextHeadingRule:0:&lt;h1&gt; --><h1 id="toc0"><a name="Scales"></a><!-- ws:end:WikiTextHeadingRule:0 -->Scales</h1>
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| <a class="wiki_link" href="/hemif7">hemif7</a><br />
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| <a class="wiki_link" href="/hemif10">hemif10</a><br />
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| <a class="wiki_link" href="/hemif17">hemif17</a><br />
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| <br />
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| <!-- ws:start:WikiTextHeadingRule:2:&lt;h2&gt; --><h2 id="toc1"><a name="Scales-Intervals"></a><!-- ws:end:WikiTextHeadingRule:2 -->Intervals</h2>
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|
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|
| |
|
| <table class="wiki_table">
| | === Prime harmonics === |
| <tr>
| | {{Harmonics in equal|58}} |
| <td>degree of 58edo<br />
| |
| </td>
| |
| <td>cents value<br />
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| </td>
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| <td>ratios<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>0<br />
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| </td>
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| <td>0.00<br />
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| </td>
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| <td>1/1<br />
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| </td>
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| </tr>
| |
| <tr>
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| <td>1<br />
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| </td>
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| <td>20.69<br />
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| </td>
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| <td>56/55, 64/63, 81/80, 128/125<br />
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| </td>
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| </tr>
| |
| <tr>
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| <td>2<br />
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| </td>
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| <td>41.38<br />
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| </td>
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| <td>36/35, 49/48, 50/49, 55/54<br />
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| </td>
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| </tr>
| |
| <tr>
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| <td>3<br />
| |
| </td>
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| <td>62.07<br />
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| </td>
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| <td>25/24, 26/25, 27/26, 28/27, 33/32<br />
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| </td>
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| </tr>
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| <tr>
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| <td>4<br />
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| </td>
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| <td>82.76<br />
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| </td>
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| <td>21/20, 22/21<br />
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| </td>
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| </tr>
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| <tr>
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| <td>5<br />
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| </td>
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| <td>103.45<br />
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| </td>
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| <td>16/15, 17/16, 18/17<br />
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| </td>
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| </tr>
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| <tr>
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| <td>6<br />
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| </td>
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| <td>124.14<br />
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| </td>
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| <td>14/13, 15/14, 27/25<br />
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| </td>
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| </tr>
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| <tr>
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| <td>7<br />
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| </td>
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| <td>144.83<br />
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| </td>
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| <td>12/11, 13/12<br />
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| </td>
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| </tr>
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| <tr>
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| <td>8<br />
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| </td>
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| <td>165.52<br />
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| </td>
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| <td>11/10<br />
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| </td>
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| </tr>
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| <tr>
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| <td>9<br />
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| </td>
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| <td>186.21<br />
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| </td>
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| <td>10/9<br />
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| </td>
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| </tr>
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| <tr>
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| <td>10<br />
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| </td>
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| <td>206.9<br />
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| </td>
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| <td>9/8, 17/15<br />
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| </td>
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| </tr>
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| <tr>
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| <td>11<br />
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| </td>
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| <td>227.59<br />
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| </td>
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| <td>8/7<br />
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| </td>
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| </tr>
| |
| <tr>
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| <td>12<br />
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| </td>
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| <td>248.28<br />
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| </td>
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| <td>15/13<br />
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| </td>
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| </tr>
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| <tr>
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| <td>13<br />
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| </td>
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| <td>268.97<br />
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| </td>
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| <td>7/6<br />
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| </td>
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| </tr>
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| <tr>
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| <td>14<br />
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| </td>
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| <td>289.66<br />
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| </td>
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| <td>13/11, 20/17<br />
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| </td>
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| </tr>
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| <tr>
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| <td>15<br />
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| </td>
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| <td>310.34<br />
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| </td>
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| <td>6/5<br />
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| </td>
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| </tr>
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| <tr>
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| <td>16<br />
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| </td>
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| <td>331.03<br />
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| </td>
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| <td>17/14<br />
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| </td>
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| </tr>
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| <tr>
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| <td>17<br />
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| </td>
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| <td>351.72<br />
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| </td>
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| <td>11/9, 16/13<br />
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| </td>
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| </tr>
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| <tr>
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| <td>18<br />
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| </td>
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| <td>372.41<br />
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| </td>
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| <td>21/17<br />
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| </td>
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| </tr>
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| <tr>
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| <td>19<br />
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| </td>
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| <td>393.1<br />
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| </td>
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| <td>5/4<br />
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| </td>
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| </tr>
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| <tr>
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| <td>20<br />
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| </td>
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| <td>413.79<br />
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| </td>
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| <td>14/11<br />
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| </td>
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| </tr>
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| <tr>
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| <td>21<br />
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| </td>
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| <td>434.48<br />
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| </td>
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| <td>9/7<br />
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| </td>
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| </tr>
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| <tr>
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| <td>22<br />
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| </td>
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| <td>455.17<br />
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| </td>
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| <td>13/10, 17/13, 22/17<br />
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| </td>
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| </tr>
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| <tr>
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| <td>23<br />
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| </td>
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| <td>475.86<br />
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| </td>
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| <td>21/16<br />
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| </td>
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| </tr>
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| <tr>
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| <td>24<br />
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| </td>
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| <td>496.55<br />
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| </td>
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| <td>4/3<br />
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| </td>
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| </tr>
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| <tr>
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| <td>25<br />
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| </td>
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| <td>517.24<br />
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| </td>
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| <td>27/20<br />
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| </td>
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| </tr>
| |
| <tr>
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| <td>26<br />
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| </td>
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| <td>537.93<br />
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| </td>
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| <td>15/11<br />
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| </td>
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| </tr>
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| <tr>
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| <td>27<br />
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| </td>
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| <td>558.62<br />
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| </td>
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| <td>11/8, 18/13<br />
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| </td>
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| </tr>
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| <tr>
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| <td>28<br />
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| </td>
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| <td>579.31<br />
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| </td>
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| <td>7/5<br />
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| </td>
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| </tr>
| |
| <tr>
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| <td>29<br />
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| </td>
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| <td>600<br />
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| </td>
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| <td>17/12, 24/17<br />
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| </td>
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| </tr>
| |
| <tr>
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| <td>30<br />
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| </td>
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| <td>620.69<br />
| |
| </td>
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| <td>10/7<br />
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| </td>
| |
| </tr>
| |
| <tr>
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| <td>31<br />
| |
| </td>
| |
| <td>641.38<br />
| |
| </td>
| |
| <td>13/9, 16/11<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>32<br />
| |
| </td>
| |
| <td>662.07<br />
| |
| </td>
| |
| <td>22/15<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>33<br />
| |
| </td>
| |
| <td>682.76<br />
| |
| </td>
| |
| <td>40/27<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>34<br />
| |
| </td>
| |
| <td>703.45<br />
| |
| </td>
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| <td>3/2<br />
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| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>35<br />
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| </td>
| |
| <td>724.14<br />
| |
| </td>
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| <td>32/21<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>36<br />
| |
| </td>
| |
| <td>744.83<br />
| |
| </td>
| |
| <td>20/13, 26/17, 17/11<br />
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| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>37<br />
| |
| </td>
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| <td>765.52<br />
| |
| </td>
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| <td>14/9<br />
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| </td>
| |
| </tr>
| |
| <tr>
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| <td>38<br />
| |
| </td>
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| <td>786.21<br />
| |
| </td>
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| <td>11/7<br />
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| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>39<br />
| |
| </td>
| |
| <td>806.9<br />
| |
| </td>
| |
| <td>8/5<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>40<br />
| |
| </td>
| |
| <td>827.59<br />
| |
| </td>
| |
| <td>34/21<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>41<br />
| |
| </td>
| |
| <td>848.28<br />
| |
| </td>
| |
| <td>13/8, 18/11<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>42<br />
| |
| </td>
| |
| <td>868.97<br />
| |
| </td>
| |
| <td>28/17<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>43<br />
| |
| </td>
| |
| <td>889.66<br />
| |
| </td>
| |
| <td>5/3<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>44<br />
| |
| </td>
| |
| <td>910.34<br />
| |
| </td>
| |
| <td>22/13, 17/10<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>45<br />
| |
| </td>
| |
| <td>931.03<br />
| |
| </td>
| |
| <td>12/7<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>46<br />
| |
| </td>
| |
| <td>951.72<br />
| |
| </td>
| |
| <td>26/15<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>47<br />
| |
| </td>
| |
| <td>972.41<br />
| |
| </td>
| |
| <td>7/4<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>48<br />
| |
| </td>
| |
| <td>993.1<br />
| |
| </td>
| |
| <td>16/9<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>49<br />
| |
| </td>
| |
| <td>1013.79<br />
| |
| </td>
| |
| <td>9/5<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>50<br />
| |
| </td>
| |
| <td>1034.48<br />
| |
| </td>
| |
| <td>20/11<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>51<br />
| |
| </td>
| |
| <td>1055.17<br />
| |
| </td>
| |
| <td>11/6, 24/13<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>52<br />
| |
| </td>
| |
| <td>1075.86<br />
| |
| </td>
| |
| <td>13/7, 28/15<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>53<br />
| |
| </td>
| |
| <td>1096.55<br />
| |
| </td>
| |
| <td>15/8, 32/17, 17/9<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>54<br />
| |
| </td>
| |
| <td>1117.24<br />
| |
| </td>
| |
| <td>40/21, 21/11<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>55<br />
| |
| </td>
| |
| <td>1137.93<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>56<br />
| |
| </td>
| |
| <td>1158.62<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>57<br />
| |
| </td>
| |
| <td>1179.31<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| </tr>
| |
| </table>
| |
|
| |
|
| <!-- ws:start:WikiTextHeadingRule:4:&lt;h2&gt; --><h2 id="toc2"><a name="Scales-Rank two temperaments"></a><!-- ws:end:WikiTextHeadingRule:4 -->Rank two temperaments</h2>
| | === As a tuning of other temperaments === |
|
| | As an equal temperament, 58et [[tempering out|tempers out]] [[2048/2025]] in the [[5-limit]]; [[126/125]], [[1728/1715]], and [[5120/5103]] in the [[7-limit]]; [[176/175]], [[243/242]], [[441/440]], [[540/539]], and [[896/891]] in the 11-limit; [[144/143]], [[351/350]], [[364/363]] in the 13-limit. It [[support]]s [[hemififths]], [[myna]], [[diaschismic]], [[harry]], [[mystery]], [[buzzard]], [[thuja]] [[regular temperament|temperament]]s plus a number of [[gravity family]] [[extension]]s, and supplies the [[optimal patent val]] for the 7-, 11- and 13-limit diaschismic, 11- and 13-limit hemififths, 11- and 13-limit thuja, and 13-limit myna. It also supplies the optimal patent val for the 13-limit rank-3 temperaments [[thrush]], [[bluebird]], [[aplonis]] and [[jofur]]. |
|
| |
|
| <table class="wiki_table">
| | Of all edos which map the syntonic comma ([[81/80]]) to 1 step by patent val, 58edo is the one with the step size closest to 81/80, with one step of 58edo being less than 1{{cent}} narrower than the just interval. |
| <tr>
| |
| <th>Period<br />
| |
| </th>
| |
| <th>Generator<br />
| |
| </th>
| |
| <th>Name<br />
| |
| </th>
| |
| </tr>
| |
| <tr>
| |
| <td>1\1<br />
| |
| </td>
| |
| <td>1\58<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><br />
| |
| </td>
| |
| <td>3\58<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><br />
| |
| </td>
| |
| <td>5\58<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><br />
| |
| </td>
| |
| <td>7\58<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><br />
| |
| </td>
| |
| <td>9\58<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><br />
| |
| </td>
| |
| <td>11\58<br />
| |
| </td>
| |
| <td>Gorgik<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><br />
| |
| </td>
| |
| <td>13\58<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><br />
| |
| </td>
| |
| <td>15\58<br />
| |
| </td>
| |
| <td>Myna<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><br />
| |
| </td>
| |
| <td>17\58<br />
| |
| </td>
| |
| <td>Hemififths<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><br />
| |
| </td>
| |
| <td>19\58<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><br />
| |
| </td>
| |
| <td>21\58<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><br />
| |
| </td>
| |
| <td>23\58<br />
| |
| </td>
| |
| <td>Buzzard<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><br />
| |
| </td>
| |
| <td>25\58<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><br />
| |
| </td>
| |
| <td>27\58<br />
| |
| </td>
| |
| <td>Thuja<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>1\2<br />
| |
| </td>
| |
| <td>1\58<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><br />
| |
| </td>
| |
| <td>2\58<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><br />
| |
| </td>
| |
| <td>3\58<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><br />
| |
| </td>
| |
| <td>4\58<br />
| |
| </td>
| |
| <td>Harry<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><br />
| |
| </td>
| |
| <td>5\58<br />
| |
| </td>
| |
| <td>Srutal/Diaschismic<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><br />
| |
| </td>
| |
| <td>6\58<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><br />
| |
| </td>
| |
| <td>7\58<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><br />
| |
| </td>
| |
| <td>8\58<br />
| |
| </td>
| |
| <td>Echidna, Supers<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><br />
| |
| </td>
| |
| <td>9\58<br />
| |
| </td>
| |
| <td>Secant<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><br />
| |
| </td>
| |
| <td>10\58<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><br />
| |
| </td>
| |
| <td>11\58<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><br />
| |
| </td>
| |
| <td>12\58<br />
| |
| </td>
| |
| <td>Sruti<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><br />
| |
| </td>
| |
| <td>13\58<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><br />
| |
| </td>
| |
| <td>14\58<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>1\29<br />
| |
| </td>
| |
| <td>1\58<br />
| |
| </td>
| |
| <td>Mystery<br />
| |
| </td>
| |
| </tr>
| |
| </table>
| |
|
| |
|
| </body></html></pre></div>
| | === Subsets and supersets === |
| | 58edo contains [[2edo]] and [[29edo]] as subsets. |
| | |
| | == Intervals == |
| | {| class="wikitable center-all right-2 left-3 left-4"" |
| | |- |
| | ! # |
| | ! Cents |
| | ! Approximate ratios* |
| | ! [[Ups and downs notation]] |
| | |- |
| | | 0 |
| | | 0.0 |
| | | [[1/1]] |
| | | {{UDnote|step=0}} |
| | |- |
| | | 1 |
| | | 20.7 |
| | | [[56/55]], [[64/63]], [[81/80]], [[91/90]], [[105/104]] |
| | | {{UDnote|step=1}} |
| | |- |
| | | 2 |
| | | 41.4 |
| | | [[36/35]], [[40/39]], [[45/44]], [[49/48]], [[50/49]], [[55/54]] |
| | | {{UDnote|step=2}} |
| | |- |
| | | 3 |
| | | 62.1 |
| | | [[26/25]], [[27/26]], [[28/27]], [[33/32]] |
| | | {{UDnote|step=3}} |
| | |- |
| | | 4 |
| | | 82.8 |
| | | [[21/20]], [[22/21]], ''[[25/24]]'' |
| | | {{UDnote|step=4}} |
| | |- |
| | | 5 |
| | | 103.4 |
| | | [[16/15]], [[17/16]], [[18/17]] |
| | | {{UDnote|step=5}} |
| | |- |
| | | 6 |
| | | 124.1 |
| | | [[14/13]], [[15/14]] |
| | | {{UDnote|step=6}} |
| | |- |
| | | 7 |
| | | 144.8 |
| | | [[12/11]], [[13/12]] |
| | | {{UDnote|step=7}} |
| | |- |
| | | 8 |
| | | 165.5 |
| | | [[11/10]] |
| | | {{UDnote|step=8}} |
| | |- |
| | | 9 |
| | | 186.2 |
| | | [[10/9]] |
| | | {{UDnote|step=9}} |
| | |- |
| | | 10 |
| | | 206.9 |
| | | [[9/8]], [[17/15]] |
| | | {{UDnote|step=10}} |
| | |- |
| | | 11 |
| | | 227.6 |
| | | [[8/7]] |
| | | {{UDnote|step=11}} |
| | |- |
| | | 12 |
| | | 248.3 |
| | | [[15/13]] |
| | | {{UDnote|step=12}} |
| | |- |
| | | 13 |
| | | 269.0 |
| | | [[7/6]] |
| | | {{UDnote|step=13}} |
| | |- |
| | | 14 |
| | | 289.7 |
| | | [[13/11]], [[20/17]] |
| | | {{UDnote|step=14}} |
| | |- |
| | | 15 |
| | | 310.3 |
| | | [[6/5]] |
| | | {{UDnote|step=15}} |
| | |- |
| | | 16 |
| | | 331.0 |
| | | [[17/14]], [[40/33]] |
| | | {{UDnote|step=16}} |
| | |- |
| | | 17 |
| | | 351.7 |
| | | [[11/9]], [[16/13]] |
| | | {{UDnote|step=17}} |
| | |- |
| | | 18 |
| | | 372.4 |
| | | [[21/17]], [[26/21]] |
| | | {{UDnote|step=18}} |
| | |- |
| | | 19 |
| | | 393.1 |
| | | [[5/4]] |
| | | {{UDnote|step=19}} |
| | |- |
| | | 20 |
| | | 413.8 |
| | | [[14/11]] |
| | | {{UDnote|step=20}} |
| | |- |
| | | 21 |
| | | 434.5 |
| | | [[9/7]] |
| | | {{UDnote|step=21}} |
| | |- |
| | | 22 |
| | | 455.2 |
| | | [[13/10]], [[17/13]], [[22/17]] |
| | | {{UDnote|step=22}} |
| | |- |
| | | 23 |
| | | 475.9 |
| | | [[21/16]] |
| | | {{UDnote|step=23}} |
| | |- |
| | | 24 |
| | | 496.6 |
| | | [[4/3]] |
| | | {{UDnote|step=24}} |
| | |- |
| | | 25 |
| | | 517.2 |
| | | [[27/20]] |
| | | {{UDnote|step=25}} |
| | |- |
| | | 26 |
| | | 537.9 |
| | | [[15/11]] |
| | | {{UDnote|step=26}} |
| | |- |
| | | 27 |
| | | 558.6 |
| | | [[11/8]], [[18/13]] |
| | | {{UDnote|step=27}} |
| | |- |
| | | 28 |
| | | 579.3 |
| | | [[7/5]] |
| | | {{UDnote|step=28}} |
| | |- |
| | | 29 |
| | | 600.0 |
| | | [[17/12]], [[24/17]] |
| | | {{UDnote|step=29}} |
| | |- |
| | | 30 |
| | | 620.7 |
| | | [[10/7]] |
| | | {{UDnote|step=30}} |
| | |- |
| | | 31 |
| | | 641.4 |
| | | [[13/9]], [[16/11]] |
| | | {{UDnote|step=31}} |
| | |- |
| | | 32 |
| | | 662.1 |
| | | [[22/15]] |
| | | {{UDnote|step=32}} |
| | |- |
| | | 33 |
| | | 682.8 |
| | | [[40/27]] |
| | | {{UDnote|step=33}} |
| | |- |
| | | 34 |
| | | 703.4 |
| | | [[3/2]] |
| | | {{UDnote|step=34}} |
| | |- |
| | | 35 |
| | | 724.1 |
| | | [[32/21]] |
| | | {{UDnote|step=35}} |
| | |- |
| | | 36 |
| | | 744.8 |
| | | [[17/11]], [[20/13]], [[26/17]] |
| | | {{UDnote|step=36}} |
| | |- |
| | | 37 |
| | | 765.5 |
| | | [[14/9]] |
| | | {{UDnote|step=37}} |
| | |- |
| | | 38 |
| | | 786.2 |
| | | [[11/7]] |
| | | {{UDnote|step=38}} |
| | |- |
| | | 39 |
| | | 806.9 |
| | | [[8/5]] |
| | | {{UDnote|step=39}} |
| | |- |
| | | 40 |
| | | 827.6 |
| | | [[21/13]], [[34/21]] |
| | | {{UDnote|step=40}} |
| | |- |
| | | 41 |
| | | 848.3 |
| | | [[13/8]], [[18/11]] |
| | | {{UDnote|step=41}} |
| | |- |
| | | 42 |
| | | 869.0 |
| | | [[28/17]], [[33/20]] |
| | | {{UDnote|step=42}} |
| | |- |
| | | 43 |
| | | 889.7 |
| | | [[5/3]] |
| | | {{UDnote|step=43}} |
| | |- |
| | | 44 |
| | | 910.3 |
| | | [[17/10]], [[22/13]] |
| | | {{UDnote|step=44}} |
| | |- |
| | | 45 |
| | | 931.0 |
| | | [[12/7]] |
| | | {{UDnote|step=45}} |
| | |- |
| | | 46 |
| | | 951.7 |
| | | [[26/15]] |
| | | {{UDnote|step=46}} |
| | |- |
| | | 47 |
| | | 972.4 |
| | | [[7/4]] |
| | | {{UDnote|step=47}} |
| | |- |
| | | 48 |
| | | 993.1 |
| | | [[16/9]], [[30/17]] |
| | | {{UDnote|step=48}} |
| | |- |
| | | 49 |
| | | 1013.8 |
| | | [[9/5]] |
| | | {{UDnote|step=49}} |
| | |- |
| | | 50 |
| | | 1034.5 |
| | | [[20/11]] |
| | | {{UDnote|step=50}} |
| | |- |
| | | 51 |
| | | 1055.2 |
| | | [[11/6]], [[24/13]] |
| | | {{UDnote|step=51}} |
| | |- |
| | | 52 |
| | | 1075.9 |
| | | [[13/7]], [[28/15]] |
| | | {{UDnote|step=52}} |
| | |- |
| | | 53 |
| | | 1096.6 |
| | | [[15/8]], [[17/9]], [[32/17]] |
| | | {{UDnote|step=53}} |
| | |- |
| | | 54 |
| | | 1117.2 |
| | | [[21/11]], [[40/21]], ''[[48/25]]'' |
| | | {{UDnote|step=54}} |
| | |- |
| | | 55 |
| | | 1137.9 |
| | | [[25/13]], [[27/14]], [[52/27]], [[64/33]] |
| | | {{UDnote|step=55}} |
| | |- |
| | | 56 |
| | | 1158.6 |
| | | [[35/18]], [[39/20]], [[49/25]], [[88/45]], [[96/49]], [[108/55]] |
| | | {{UDnote|step=56}} |
| | |- |
| | | 57 |
| | | 1179.3 |
| | | [[55/28]], [[63/32]], [[160/81]], [[180/91]], [[208/105]] |
| | | {{UDnote|step=57}} |
| | |- |
| | | 58 |
| | | 1200.0 |
| | | [[2/1]] |
| | | {{UDnote|step=58}} |
| | |} |
| | <nowiki/>* As a 17-limit temperament, inconsistently mapped intervals in ''italic'' |
| | |
| | == Notation == |
| | === Stein–Zimmermann–Gould notation === |
| | [[Stein–Zimmermann–Gould notation]] for 58edo uses sharps and flats combined with quartertone accidentals and arrows: |
| | {{Sharpness-sharp6-szg}} |
| | |
| | If double arrows are not desirable, then arrows can be attached to quartertone accidentals: |
| | {{Sharpness-sharp6-qt-szg}} |
| | |
| | === Kite's ups and downs notation === |
| | 58edo can also be notated with [[Kite's ups and downs notation|Kite's ups and downs]], spoken as up, dup, trup, dudsharp, downsharp, sharp, upsharp etc. and down, dud, trud, dupflat etc. |
| | {{Ups and downs sharpness}} |
| | |
| | Half-sharps and half-flats can be used to avoid triple arrows: |
| | {{Ups and downs sharpness|58|true}} |
| | |
| | === Ivan Wyschnegradsky's notation === |
| | Since a sharp raises by six steps, Wyschnegradsky accidentals borrowed from [[72edo]] can also be used: |
| | {{Sharpness-sharp6-iw}} |
| | |
| | === Sagittal notation === |
| | ==== Evo flavor ==== |
| | {{Sagittal chart|Evo}} |
| | |
| | ==== Evo-SZ flavor ==== |
| | {{Sagittal chart|Evo-SZ}} |
| | |
| | ==== Revo flavor ==== |
| | {{Sagittal chart}} |
| | |
| | === Hemipyth notation === |
| | {| class="wikitable center-all right-2 center-3 mw-collapsible mw-collapsed" |
| | |+ style="font-size: 105%; white-space: nowrap;" | Hemipyth notation for 58edo (SW3-style) |
| | |- |
| | ! # |
| | ! Cents |
| | ! Note names<br>on D |
| | |- |
| | | 0 |
| | | 0.0 |
| | | D |
| | |- |
| | | 2 |
| | | 41.4 |
| | | α𝄳 |
| | |- |
| | | 5 |
| | | 103.4 |
| | | α |
| | |- |
| | | 7 |
| | | 144.8 |
| | | E𝄳 |
| | |- |
| | | 10 |
| | | 206.9 |
| | | E |
| | |- |
| | | 12 |
| | | 248.3 |
| | | β𝄳 |
| | |- |
| | | 14 |
| | | 289.7 |
| | | F |
| | |- |
| | | 15 |
| | | 310.3 |
| | | β |
| | |- |
| | | 17 |
| | | 351.7 |
| | | F‡ |
| | |- |
| | | 19 |
| | | 393.1 |
| | | γ |
| | |- |
| | | 22 |
| | | 455.2 |
| | | γ‡ |
| | |- |
| | | 24 |
| | | 496.6 |
| | | G |
| | |- |
| | | 27 |
| | | 558.6 |
| | | G‡ |
| | |- |
| | | 29 |
| | | 600.0 |
| | | δ |
| | |- |
| | | 31 |
| | | 641.4 |
| | | A𝄳 |
| | |- |
| | | 34 |
| | | 703.4 |
| | | A |
| | |- |
| | | 36 |
| | | 744.8 |
| | | ε𝄳 |
| | |- |
| | | 39 |
| | | 806.9 |
| | | ε |
| | |- |
| | | 41 |
| | | 848.3 |
| | | B𝄳 |
| | |- |
| | | 43 |
| | | 889.7 |
| | | ζ |
| | |- |
| | | 44 |
| | | 910.3 |
| | | B |
| | |- |
| | | 46 |
| | | 951.7 |
| | | ζ‡ |
| | |- |
| | | 48 |
| | | 993.1 |
| | | C |
| | |- |
| | | 51 |
| | | 1055.2 |
| | | C‡ |
| | |- |
| | | 53 |
| | | 1096.6 |
| | | η |
| | |- |
| | | 56 |
| | | 1158.6 |
| | | η‡ |
| | |- |
| | | 58 |
| | | 1200.0 |
| | | D |
| | |} |
| | |
| | == Approximation to JI == |
| | === Interval mappings === |
| | {{15-odd-limit|58}} |
| | |
| | == Regular temperament properties == |
| | {| class="wikitable center-4 center-5 center-6" |
| | |- |
| | ! rowspan="2" | [[Subgroup]] |
| | ! rowspan="2" | [[Comma list]] |
| | ! rowspan="2" | [[Mapping]] |
| | ! rowspan="2" | Optimal<br>8ve stretch (¢) |
| | ! colspan="2" | Tuning error |
| | |- |
| | ! [[TE error|Absolute]] (¢) |
| | ! [[TE simple badness|Relative]] (%) |
| | |- |
| | | 2.3.5 |
| | | 2048/2025, [[1594323/1562500]] |
| | | {{Mapping| 58 92 135 }} |
| | | −1.29 |
| | | 1.22 |
| | | 5.89 |
| | |- |
| | | 2.3.5.7 |
| | | 126/125, 1728/1715, 2048/2025 |
| | | {{Mapping| 58 92 135 163 }} |
| | | −1.29 |
| | | 1.05 |
| | | 5.10 |
| | |- |
| | | 2.3.5.7.11 |
| | | 126/125, 176/175, 243/242, 896/891 |
| | | {{Mapping| 58 92 135 163 201 }} |
| | | −1.45 |
| | | 1.00 |
| | | 4.83 |
| | |- |
| | | 2.3.5.7.11.13 |
| | | 126/125, 144/143, 176/175, 196/195, 364/363 |
| | | {{Mapping| 58 92 135 163 201 215 }} |
| | | −1.56 |
| | | 0.94 |
| | | 4.56 |
| | |- |
| | | 2.3.5.7.11.13.17 |
| | | 126/125, 136/135, 144/143, 176/175, 196/195, 364/363 |
| | | {{Mapping| 58 92 135 163 201 215 237 }} |
| | | −1.28 |
| | | 1.10 |
| | | 5.33 |
| | |} |
| | * 58et has a lower relative error than any previous equal temperaments in the 13-limit, and the next equal temperament that does better in this subgroup is [[72edo|72]]. |
| | |
| | === Rank-2 temperaments === |
| | {| class="wikitable center-all left-5" |
| | |+ style="font-size: 105%;" | Table of rank-2 temperaments by generator |
| | |- |
| | ! Periods<br>per 8ve |
| | ! Generator* |
| | ! Cents* |
| | ! Associated<br>ratio* |
| | ! Temperament |
| | |- |
| | | 1 |
| | | 3\58 |
| | | 62.1 |
| | | 28/27 |
| | | [[Unicorn]] / alicorn / qilin |
| | |- |
| | | 1 |
| | | 11\58 |
| | | 227.6 |
| | | 8/7 |
| | | [[Gorgik]] |
| | |- |
| | | 1 |
| | | 13\58 |
| | | 269.0 |
| | | 7/6 |
| | | [[Infraorwell]] |
| | |- |
| | | 1 |
| | | 15\58 |
| | | 310.3 |
| | | 6/5 |
| | | [[Myna]] |
| | |- |
| | | 1 |
| | | 17\58 |
| | | 351.7 |
| | | 49/40 |
| | | [[Hemififths]] |
| | |- |
| | | 1 |
| | | 19\58 |
| | | 393.1 |
| | | 64/51 |
| | | [[Emmthird]] |
| | |- |
| | | 1 |
| | | 23\58 |
| | | 475.9 |
| | | 21/16 |
| | | [[Buzzard]] / [[subfourth]] |
| | |- |
| | | 1 |
| | | 25\58 |
| | | 517.2 |
| | | 27/20 |
| | | [[Gravity]] / [[abergravity]] / [[gravid]] |
| | |- |
| | | 1 |
| | | 27\58 |
| | | 558.6 |
| | | 11/8 |
| | | [[Thuja]] |
| | |- |
| | | 2 |
| | | 3\58 |
| | | 62.1 |
| | | 28/27 |
| | | [[Monocerus]] |
| | |- |
| | | 2 |
| | | 1\58 |
| | | 20.7 |
| | | 81/80 |
| | | [[Bicommatic]] |
| | |- |
| | | 2 |
| | | 9\58 |
| | | 186.2 |
| | | 10/9 |
| | | [[Secant]] |
| | |- |
| | | 2 |
| | | 17\58<br>(12\58) |
| | | 351.7<br>(248.3) |
| | | 11/9<br>(15/13) |
| | | [[Sruti]] |
| | |- |
| | | 2 |
| | | 21\58<br>(8\58) |
| | | 434.5<br>(165.5) |
| | | 9/7<br>(11/10) |
| | | [[Echidna]] |
| | |- |
| | | 2 |
| | | 24\58<br>(5\58) |
| | | 496.6<br>(103.4) |
| | | 4/3<br>(17/16) |
| | | [[Diaschismic]] |
| | |- |
| | | 2 |
| | | 25\58<br>(4\58) |
| | | 517.2<br>(82.8) |
| | | 27/20<br>(21/20) |
| | | [[Harry]] |
| | |- |
| | | 29 |
| | | 19\58<br>(1\58) |
| | | 393.1<br>(20.7) |
| | | 5/4<br>(91/90) |
| | | [[Mystery]] |
| | |} |
| | <nowiki/>* [[Normal forms #Equave-reduced-generator form|Octave-reduced form]], reduced to the first half-octave, and [[normal forms #Minimal-generator form|minimal form]] in parentheses if distinct |
| | |
| | 58et can also be detempered to [[semihemi]] ({{nowrap| 58 & 140 }}), [[supers]] ({{nowrap| 58 & 152 }}), [[condor]] ({{nowrap| 58 & 159 }}), and [[eagle]] ({{nowrap| 58 & 212 }}). |
| | |
| | == Octave stretch or compression == |
| | 58edo's approximations of harmonics 3, 5, 7, 11, and 13 can all be improved if slightly [[stretched and compressed tuning|compressing the octave]] is acceptable, using tunings such as [[92edt]], [[150ed6]] or [[zpi|289zpi]]. |
| | |
| | == Scales == |
| | * [[Compdye]] |
| | * [[Maeve Gutierrez#Gutierrez-Lambeth quasi-subharmonic pentatonic|Gutierrez-Lambeth quasi-subharmonic pentatonic]] |
| | * [[Hemif7]] |
| | * [[Hemif10]] |
| | * [[Hemif17]] |
| | |
| | == Instruments == |
| | * [[Lumatone mapping for 58edo]] |
| | * [[Skip fretting system 58 2 15|15\58 × 2\58 isomorphic instrument layout]] |
| | * [[Skip fretting system 58 4 15|15\58 × 4\58 isomorphic instrument layout]] |
| | * [[Skip fretting system 58 2 17|17\58 × 2\58 isomorphic instrument layout]] |
| | |
| | == Music == |
| | ; [[Jeff Brown]] |
| | * [https://www.youtube.com/watch?v=0373hBH87LY ''Fruitbats in Formation''] (2023) |
| | |
| | ; [[Bryan Deister]] |
| | * [https://www.youtube.com/shorts/4J4MNno-4PA ''58edo improv''] (2025) |
| | * [https://www.youtube.com/shorts/7gkRyld5OU8 ''Waltz in 58edo''] (2025) |
| | * [https://www.youtube.com/shorts/H5XG4lrvrP8 ''58edo groove''] (2025) |
| | |
| | ; [[Francium]] |
| | * [https://www.youtube.com/watch?v=XXMjoUxVfLs ''We Wish You A Larry Christmas''] (2024) – in larry, 58edo tuning |
| | |
| | ; [[Cam Taylor]] |
| | * [https://www.youtube.com/watch?v=Keclakcqie8 ''58EDO, Mystery temperament and 2 rings of Pythagorean on the Lumatone''] (2021) |
| | |
| | ; [[Xotla]] |
| | * [https://www.youtube.com/watch?v=yTkPhjTEQMw "Wormhole Shmurmhole"], from [https://www.youtube.com/playlist?list=PL4HmfPDldHXueRjmTV-iJN3fsLn_O9jvT ''Just Another Microtonal Music Album''] (2025–2026) – in part, the rest being in 31edo |
| | |
| | [[Category:Buzzard]] |
| | [[Category:Diaschismic]] |
| | [[Category:Harry]] |
| | [[Category:Hemififths]] |
| | [[Category:Myna]] |
| | [[Category:Mystery]] |
| | [[Category:Harry Partch]] |
| | [[Category:Listen]] |