Superfourth: Difference between revisions
Wikispaces>Andrew_Heathwaite **Imported revision 262968896 - Original comment: ** |
Wikispaces>Andrew_Heathwaite **Imported revision 262976924 - Original comment: ** |
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<h2>IMPORTED REVISION FROM WIKISPACES</h2> | <h2>IMPORTED REVISION FROM WIKISPACES</h2> | ||
This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br> | This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br> | ||
: This revision was by author [[User:Andrew_Heathwaite|Andrew_Heathwaite]] and made on <tt>2011-10-09 | : This revision was by author [[User:Andrew_Heathwaite|Andrew_Heathwaite]] and made on <tt>2011-10-09 11:52:38 UTC</tt>.<br> | ||
: The original revision id was <tt> | : The original revision id was <tt>262976924</tt>.<br> | ||
: The revision comment was: <tt></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> | 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> | <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">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. | <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">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. | 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]]</pre></div> | See: [[Interval Category]], [[Gallery of Just Intervals]]</pre></div> | ||
<h4>Original HTML content:</h4> | <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>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 /> | <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>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 /> | <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 /> | 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 /> | <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></pre></div> | 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></pre></div> | ||