Xenharmonic Wiki

Superfourth

Revision as of 11:52, 9 October 2011 by Wikispaces>Andrew_Heathwaite (**Imported revision 262976924 - Original comment: **)

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A "superfourth" is an interval too wide to sound like a [[perfect fourth]] and too narrow to sound like a [[tritone]]. [[Margo Schulter]], in her article [[http://www.bestii.com/%7Emschulter/IntervalSpectrumRegions.txt|Regions of the Interval Spectrum]], proposes an approximate range for a superfourth to be from 528¢ to 560¢. Some of the simplest superfourths in [[Just Intonation]] are [[11_8|11/8]] (about 551.3¢) and [[15_11|15/11]] (about 537¢), both undecimal (11-based) superfourths, and [[48_35|48/35]] (about 546.8¢), a septimal superfourth.

The inversion of a superfourth is a [[subfifth]].

Of course, it should never be taken for granted that these categories are subjective and culturally influenced, and the borders are "fuzzy". Other description are possible and legitimate.

==Examples== 
Below is a list of some intervals in the superfourth range, both just and tempered.

||~ Interval ||~ Cents Value ||~ Prime Limit (if applicable) ||
|| 6\[[88cET]] or 11\[[25edo]] || 528.000 || - ||
|| [[19_14|19/14]] || 528.687 || 19 ||
|| 34/25 || 532.328 || 17 ||
|| 4\[[9edo]] || 533.333 || - ||
|| 64/47 || 534.493 || 47 ||
|| [[15_11|15/11]] || 536.951 || 11 ||
|| 13\[[29edo]] || 537.931 || - ||
|| 56/41 || 539.764 || 41 ||
|| 9\[[20edo]] || 540.000 || - ||
|| 41/30 || 540.794 || 41 ||
|| 14\[[31edo]] || 541.935 || - ||
|| [[26_19|26/19]] || 543.015 || 19 ||
|| 5\[[11edo]] || 545.455 || - ||
|| 37/27 || 545.479 || 37 ||
|| [[48_35|48/35]] || 546.815 || 7 ||
|| 11\[[24edo]] || 550.000 || - ||
|| [[11_8|11/8]] || 551.318 || 11 ||
|| 6\[[13edo]] || 553.846 || - ||
|| 62/45 || 554.812 || 31 ||
|| 40/29 || 556.737 || 29 ||
|| 13\[[28edo]] || 557.143 || - ||
|| 29/21 || 558.796 || 29 ||
|| 47/34 || 560.551 || 47 ||
|| 7\[[15edo]] || 560.000 || - ||


See: [[Interval Category]], [[Gallery of Just Intervals]]

Original HTML content:

<html><head><title>Superfourth</title></head><body>A &quot;superfourth&quot; is an interval too wide to sound like a <a class="wiki_link" href="/perfect%20fourth">perfect fourth</a> and too narrow to sound like a <a class="wiki_link" href="/tritone">tritone</a>. <a class="wiki_link" href="/Margo%20Schulter">Margo Schulter</a>, in her article <a class="wiki_link_ext" href="http://www.bestii.com/%7Emschulter/IntervalSpectrumRegions.txt" rel="nofollow">Regions of the Interval Spectrum</a>, proposes an approximate range for a superfourth to be from 528¢ to 560¢. Some of the simplest superfourths in <a class="wiki_link" href="/Just%20Intonation">Just Intonation</a> are <a class="wiki_link" href="/11_8">11/8</a> (about 551.3¢) and <a class="wiki_link" href="/15_11">15/11</a> (about 537¢), both undecimal (11-based) superfourths, and <a class="wiki_link" href="/48_35">48/35</a> (about 546.8¢), a septimal superfourth.<br />
<br />
The inversion of a superfourth is a <a class="wiki_link" href="/subfifth">subfifth</a>.<br />
<br />
Of course, it should never be taken for granted that these categories are subjective and culturally influenced, and the borders are &quot;fuzzy&quot;. Other description are possible and legitimate.<br />
<br />
<!-- ws:start:WikiTextHeadingRule:0:&lt;h2&gt; --><h2 id="toc0"><a name="x-Examples"></a><!-- ws:end:WikiTextHeadingRule:0 -->Examples</h2>
 Below is a list of some intervals in the superfourth range, both just and tempered.<br />
<br />


<table class="wiki_table">
    <tr>
        <th>Interval<br />
</th>
        <th>Cents Value<br />
</th>
        <th>Prime Limit (if applicable)<br />
</th>
    </tr>
    <tr>
        <td>6\<a class="wiki_link" href="/88cET">88cET</a> or 11\<a class="wiki_link" href="/25edo">25edo</a><br />
</td>
        <td>528.000<br />
</td>
        <td>-<br />
</td>
    </tr>
    <tr>
        <td><a class="wiki_link" href="/19_14">19/14</a><br />
</td>
        <td>528.687<br />
</td>
        <td>19<br />
</td>
    </tr>
    <tr>
        <td>34/25<br />
</td>
        <td>532.328<br />
</td>
        <td>17<br />
</td>
    </tr>
    <tr>
        <td>4\<a class="wiki_link" href="/9edo">9edo</a><br />
</td>
        <td>533.333<br />
</td>
        <td>-<br />
</td>
    </tr>
    <tr>
        <td>64/47<br />
</td>
        <td>534.493<br />
</td>
        <td>47<br />
</td>
    </tr>
    <tr>
        <td><a class="wiki_link" href="/15_11">15/11</a><br />
</td>
        <td>536.951<br />
</td>
        <td>11<br />
</td>
    </tr>
    <tr>
        <td>13\<a class="wiki_link" href="/29edo">29edo</a><br />
</td>
        <td>537.931<br />
</td>
        <td>-<br />
</td>
    </tr>
    <tr>
        <td>56/41<br />
</td>
        <td>539.764<br />
</td>
        <td>41<br />
</td>
    </tr>
    <tr>
        <td>9\<a class="wiki_link" href="/20edo">20edo</a><br />
</td>
        <td>540.000<br />
</td>
        <td>-<br />
</td>
    </tr>
    <tr>
        <td>41/30<br />
</td>
        <td>540.794<br />
</td>
        <td>41<br />
</td>
    </tr>
    <tr>
        <td>14\<a class="wiki_link" href="/31edo">31edo</a><br />
</td>
        <td>541.935<br />
</td>
        <td>-<br />
</td>
    </tr>
    <tr>
        <td><a class="wiki_link" href="/26_19">26/19</a><br />
</td>
        <td>543.015<br />
</td>
        <td>19<br />
</td>
    </tr>
    <tr>
        <td>5\<a class="wiki_link" href="/11edo">11edo</a><br />
</td>
        <td>545.455<br />
</td>
        <td>-<br />
</td>
    </tr>
    <tr>
        <td>37/27<br />
</td>
        <td>545.479<br />
</td>
        <td>37<br />
</td>
    </tr>
    <tr>
        <td><a class="wiki_link" href="/48_35">48/35</a><br />
</td>
        <td>546.815<br />
</td>
        <td>7<br />
</td>
    </tr>
    <tr>
        <td>11\<a class="wiki_link" href="/24edo">24edo</a><br />
</td>
        <td>550.000<br />
</td>
        <td>-<br />
</td>
    </tr>
    <tr>
        <td><a class="wiki_link" href="/11_8">11/8</a><br />
</td>
        <td>551.318<br />
</td>
        <td>11<br />
</td>
    </tr>
    <tr>
        <td>6\<a class="wiki_link" href="/13edo">13edo</a><br />
</td>
        <td>553.846<br />
</td>
        <td>-<br />
</td>
    </tr>
    <tr>
        <td>62/45<br />
</td>
        <td>554.812<br />
</td>
        <td>31<br />
</td>
    </tr>
    <tr>
        <td>40/29<br />
</td>
        <td>556.737<br />
</td>
        <td>29<br />
</td>
    </tr>
    <tr>
        <td>13\<a class="wiki_link" href="/28edo">28edo</a><br />
</td>
        <td>557.143<br />
</td>
        <td>-<br />
</td>
    </tr>
    <tr>
        <td>29/21<br />
</td>
        <td>558.796<br />
</td>
        <td>29<br />
</td>
    </tr>
    <tr>
        <td>47/34<br />
</td>
        <td>560.551<br />
</td>
        <td>47<br />
</td>
    </tr>
    <tr>
        <td>7\<a class="wiki_link" href="/15edo">15edo</a><br />
</td>
        <td>560.000<br />
</td>
        <td>-<br />
</td>
    </tr>
</table>

<br />
<br />
See: <a class="wiki_link" href="/Interval%20Category">Interval Category</a>, <a class="wiki_link" href="/Gallery%20of%20Just%20Intervals">Gallery of Just Intervals</a></body></html>
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