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| <h2>IMPORTED REVISION FROM WIKISPACES</h2>
| | {{Prime limit navigation|19}} |
| This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br>
| | The '''19-limit''' consists of [[just intonation]] [[interval]]s whose [[ratio]]s contain no [[prime factor]]s higher than 19. It is the 8th [[prime limit]] and is a superset of the [[17-limit]] and a subset of the [[23-limit]]. |
| : This revision was by author [[User:guest|guest]] and made on <tt>2012-05-09 08:56:09 UTC</tt>.<br>
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| : The original revision id was <tt>332427594</tt>.<br>
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| : The revision comment was: <tt></tt><br>
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| The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.<br>
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| <h4>Original Wikitext 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;white-space: pre-wrap ! important" class="old-revision-html">In 19-limit [[Just Intonation]], all ratios in the system will contain no primes higher than 19.
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| ==[[#x-17-limit Intervals]]19-limit Intervals==
| | The 19-limit is a [[rank and codimension|rank-8]] system, and can be modeled in a 7-dimensional [[lattice]], with the primes 3, 5, 7, 11, 13, 17, and 19 represented by each dimension. The prime 2 does not appear in the typical 19-limit lattice because [[octave equivalence]] is presumed. If octave equivalence is not presumed, an eighth dimension is needed. |
| ||~ Ratio ||~ Cents Value ||~ Name ||
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| || [[18_17|20/19]] || 88.801 || small septendecimal semitone ||
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| || [[17_16|19/18]] || 93.603 || large septendecimal semitone ||
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| || [[17_15|19/17]] || 192.558 || septendecimal whole tone ||
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| || [[20_17|22/19]] || 253.805 || septendecimal minor third ||
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| || [[17_14|19/16]] || 297.513 || septendecimal supraminor third ||
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| || [[22_17|24/19]] || 404.442 || septendecimal supermajor third ||
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| || [[17_13|19/15]] || 409.244 || septendecimal sub-fourth ||
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| || [[24_17|19/14]] || 528.687 || 1st septendecimal tritone ||
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| || [[17_12|26/19]] || 543.015 || 2nd septendecimal tritone ||
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| || [[26_17|19/13]] || 6 || septendecimal super-fifth ||
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| || [[17_11|28/19]] || 6 || septendecimal subminor sixth ||
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| || [[28_17|30/19]] || 7 || septendecimal submajor sixth ||
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| || [[17_10|19/12]] || 7 || septendecimal major sixth ||
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| || [[30_17|32/19]] || 9 || septendecimal minor seventh ||
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| || [[32_17|19/11]] || 9 || small septendecimal major seventh ||
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| || [[17_9|34/19]] || 10 || large septendecimal major seventh ||
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| || 36/19 || 11 || ||
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| || 19/10 || 11 || ||
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| see [[Harmonic Limit]]</pre></div>
| | These things are contained by the 19-limit, but not the 17-limit: |
| <h4>Original HTML content:</h4>
| | * The [[19-odd-limit|19-]] and [[21-odd-limit]]; |
| <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>19-limit</title></head><body>In 19-limit <a class="wiki_link" href="/Just%20Intonation">Just Intonation</a>, all ratios in the system will contain no primes higher than 19.<br />
| | * Mode 10 and 11 of the harmonic or subharmonic series. |
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| <!-- ws:start:WikiTextHeadingRule:0:&lt;h2&gt; --><h2 id="toc0"><a name="x-19-limit Intervals"></a><!-- ws:end:WikiTextHeadingRule:0 --><!-- ws:start:WikiTextAnchorRule:2:&lt;img src=&quot;/i/anchor.gif&quot; class=&quot;WikiAnchor&quot; alt=&quot;Anchor&quot; id=&quot;wikitext@@anchor@@x-17-limit Intervals&quot; title=&quot;Anchor: x-17-limit Intervals&quot;/&gt; --><a name="x-17-limit Intervals"></a><!-- ws:end:WikiTextAnchorRule:2 -->19-limit Intervals</h2>
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| <table class="wiki_table">
| | == Terminology and notation == |
| <tr>
| | [[Interval_region|Interval categories]] of [[harmonic class|HC19]] are relatively clear. [[19/16]] is most commonly considered a minor third, as 1–19/16–3/2 is an important {{w|tertian}} chord (the [[Functional Just System]] and [[Helmholtz–Ellis notation]] agree). However, 19/16 may act as an augmented second in certain cases. This is more complex on its own but may simplify certain combinations with other intervals, especially if [[17/16]] is considered an augmented unison and/or if [[23/16]] is considered an augmented fourth. Perhaps most interestingly, [[Sagittal notation]] provides an accidental to enharmonically spell intervals of HC19 this way. |
| <th>Ratio<br />
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| </th>
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| <th>Cents Value<br />
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| </th>
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| <th>Name<br />
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| </th>
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| </tr>
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| <tr>
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| <td><a class="wiki_link" href="/18_17">20/19</a><br />
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| </td>
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| <td>88.801<br />
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| </td>
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| <td>small septendecimal semitone<br />
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| </td>
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| </tr>
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| <tr>
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| <td><a class="wiki_link" href="/17_16">19/18</a><br />
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| </td>
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| <td>93.603<br />
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| </td>
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| <td>large septendecimal semitone<br />
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| </td>
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| </tr>
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| <tr>
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| <td><a class="wiki_link" href="/17_15">19/17</a><br />
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| </td>
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| <td>192.558<br />
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| </td>
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| <td>septendecimal whole tone<br />
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| </td>
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| </tr>
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| <tr>
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| <td><a class="wiki_link" href="/20_17">22/19</a><br />
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| </td>
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| <td>253.805<br />
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| </td>
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| <td>septendecimal minor third<br />
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| </td>
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| </tr>
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| <tr>
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| <td><a class="wiki_link" href="/17_14">19/16</a><br />
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| </td>
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| <td>297.513<br />
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| </td>
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| <td>septendecimal supraminor third<br />
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| </td>
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| </tr>
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| <tr>
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| <td><a class="wiki_link" href="/22_17">24/19</a><br />
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| </td>
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| <td>404.442<br />
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| </td>
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| <td>septendecimal supermajor third<br />
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| </td>
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| </tr>
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| <tr>
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| <td><a class="wiki_link" href="/17_13">19/15</a><br />
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| </td>
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| <td>409.244<br />
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| </td>
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| <td>septendecimal sub-fourth<br />
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| </td>
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| </tr>
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| <tr>
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| <td><a class="wiki_link" href="/24_17">19/14</a><br />
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| </td>
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| <td>528.687<br />
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| </td>
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| <td>1st septendecimal tritone<br />
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| </td>
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| </tr>
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| <tr>
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| <td><a class="wiki_link" href="/17_12">26/19</a><br />
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| </td>
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| <td>543.015<br />
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| </td>
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| <td>2nd septendecimal tritone<br />
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| </td>
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| </tr>
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| <tr>
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| <td><a class="wiki_link" href="/26_17">19/13</a><br />
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| </td>
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| <td>6<br />
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| </td>
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| <td>septendecimal super-fifth<br />
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| </td>
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| </tr>
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| <tr>
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| <td><a class="wiki_link" href="/17_11">28/19</a><br />
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| </td>
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| <td>6<br />
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| </td>
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| <td>septendecimal subminor sixth<br />
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| </td>
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| </tr>
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| <tr>
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| <td><a class="wiki_link" href="/28_17">30/19</a><br />
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| </td>
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| <td>7<br />
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| </td>
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| <td>septendecimal submajor sixth<br />
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| </td>
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| </tr>
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| <tr>
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| <td><a class="wiki_link" href="/17_10">19/12</a><br />
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| </td>
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| <td>7<br />
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| </td>
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| <td>septendecimal major sixth<br />
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| </td>
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| </tr>
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| <tr>
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| <td><a class="wiki_link" href="/30_17">32/19</a><br />
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| </td>
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| <td>9<br />
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| </td>
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| <td>septendecimal minor seventh<br />
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| </td>
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| </tr>
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| <tr>
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| <td><a class="wiki_link" href="/32_17">19/11</a><br />
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| </td>
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| <td>9<br />
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| </td>
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| <td>small septendecimal major seventh<br />
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| </td>
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| </tr>
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| <tr>
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| <td><a class="wiki_link" href="/17_9">34/19</a><br />
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| </td>
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| <td>10<br />
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| </td>
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| <td>large septendecimal major seventh<br />
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| </td>
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| </tr>
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| <tr>
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| <td>36/19<br />
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| </td>
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| <td>11<br />
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| </td>
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| <td><br />
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| </td>
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| </tr>
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| <tr>
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| <td>19/10<br />
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| </td>
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| <td>11<br />
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| </td>
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| <td><br />
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| </td>
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| </tr>
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| </table>
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| <br />
| | == Edo approximation == |
| see <a class="wiki_link" href="/Harmonic%20Limit">Harmonic Limit</a></body></html></pre></div> | | Here is a list of [[edo]]s with progressively better tunings for 19-limit intervals ([[monotonicity limit]] ≥ 19 and decreasing [[TE error]]): {{EDOs| 34dh, 38df, 41, 50, 53, 58h, 68, 72, 94, 103h, 111, 121, 130, 140, 152fg, 159, 161, 183, 190g, 193, 212gh, 217, 243e, 270, 311, 400, 422, 460, 525, 581, 742, 935, 954h }} and so on. For a more comprehensive list, see [[Sequence of equal temperaments by error]]. |
| | |
| | Here is a list of edos which provides relatively good tunings for 19-limit intervals ([[TE relative error]] < 5%): {{EDOs| 72, 111, 217, 243e, 270, 282, 311, 354, 364, 373g, 400, 422, 460, 494(h), 525, 540, 581, 597, 624, 643, 653, 692, 718, 742, 764h, 814, 836f, 882, 908, 925, 935, 954h and }} so on. |
| | |
| | : '''Note''': [[wart notation]] is used to specify the [[val]] chosen for the edo. In the above list, "34dh" means taking the second closest approximations of harmonics 7 and 19. |
| | |
| | == Intervals == |
| | |
| | Here are all the [[21-odd-limit]] intervals of 19-limit: |
| | |
| | {| class="wikitable" |
| | ! Ratio |
| | ! Cents Value |
| | ! colspan="2" | Color Name |
| | ! Interval Name |
| | |- |
| | | [[20/19]] |
| | | 88.801 |
| | | 19uy1 |
| | | nuyo 1son |
| | | small undevicesimal semitone |
| | |- |
| | | [[19/18]] |
| | | 93.603 |
| | | 19o2 |
| | | ino 2nd |
| | | large undevicesimal semitone |
| | |- |
| | | [[21/19]] |
| | | 173.268 |
| | | 19uz2 |
| | | nuzo 2nd |
| | | small undevicesimal whole tone |
| | |- |
| | | [[19/17]] |
| | | 192.558 |
| | | 19o17u2 |
| | | nosu 2nd |
| | | large undevicesimal whole tone, quasi-meantone |
| | |- |
| | | [[22/19]] |
| | | 253.805 |
| | | 19u1o2 |
| | | nulo 2nd |
| | | undevicesimal second-third |
| | |- |
| | | [[19/16]] |
| | | 297.513 |
| | | 19o3 |
| | | ino 3rd |
| | | undevicesimal minor third |
| | |- |
| | | [[24/19]] |
| | | 404.442 |
| | | 19u3 |
| | | inu 3rd |
| | | small undevicesimal major third |
| | |- |
| | | [[19/15]] |
| | | 409.244 |
| | | 19og4 |
| | | nogu 4th |
| | | large undevicesimal major third |
| | |- |
| | | [[19/14]] |
| | | 528.687 |
| | | 19or4 |
| | | noru 4th |
| | | undevicesimal acute fourth |
| | |- |
| | | [[26/19]] |
| | | 543.015 |
| | | 19u3o4 |
| | | nutho 4th |
| | | undevicesimal super fourth |
| | |- |
| | | [[19/13]] |
| | | 656.985 |
| | | 19o3u5 |
| | | nothu 5th |
| | | undevicesimal subfifth |
| | |- |
| | | [[28/19]] |
| | | 671.313 |
| | | 19uz5 |
| | | nuzo 5th |
| | | undevicesimal gravefifth |
| | |- |
| | | [[30/19]] |
| | | 790.756 |
| | | 19uy5 |
| | | nuyo 5th |
| | | small undevicesimal minor sixth |
| | |- |
| | | [[19/12]] |
| | | 795.558 |
| | | 19o6 |
| | | ino 6th |
| | | large undevicesimal minor sixth |
| | |- |
| | | [[32/19]] |
| | | 902.487 |
| | | 19u6 |
| | | inu 6th |
| | | undevicesimal major sixth |
| | |- |
| | | [[19/11]] |
| | | 946.195 |
| | | 19o1u7 |
| | | nolu 7th |
| | | undevicesimal sixth-seventh |
| | |- |
| | | [[34/19]] |
| | | 1007.442 |
| | | 19u17o7 |
| | | nuso 7th |
| | | small undevicesimal minor seventh |
| | |- |
| | | [[38/21]] |
| | | 1026.732 |
| | | 19or7 |
| | | noru 7th |
| | | large undevicesimal minor seventh |
| | |- |
| | | [[36/19]] |
| | | 1106.397 |
| | | 19u7 |
| | | inu 7th |
| | | small undevicesimal major seventh |
| | |- |
| | | [[19/10]] |
| | | 1111.199 |
| | | 19og8 |
| | | nogu 8ve |
| | | large undevicesimal major seventh |
| | |} |
| | |
| | == Music == |
| | ; [[Domin]] |
| | * [https://www.youtube.com/watch?v=WTo5YihoLqs ''Asuttan''] (2024) |
| | * [https://www.youtube.com/watch?v=OPt3Y9VSliU ''Asuttan Bouta''] (2024) |
| | |
| | ; [[Joseph Monzo]] |
| | * [https://www.youtube.com/watch?v=it5avwRE8PI ''Theme from Invisible Haircut''] (1990) |
| | |
| | [[Category:19-limit| ]] <!-- main article --> |