Interseptimal interval: Difference between revisions
Wikispaces>Andrew_Heathwaite **Imported revision 263365698 - 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>2011-10-10 | : This revision was by author [[User:Andrew_Heathwaite|Andrew_Heathwaite]] and made on <tt>2011-10-10 19:35:03 UTC</tt>.<br> | ||
: The original revision id was <tt> | : The original revision id was <tt>263413734</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> | 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">In the theory of [[Margo Schulter]], //interseptimal// is a category of intervals which occupy regions intermediate between two septimal ratios such as [[8_7|8/7]] and [[7_6|7/6]], or [[12_7|12/7]] and [[7_4|7/4]]. There are four interseptimal regions given below, with approximate cents ranges from Schulter's article [[http://www.bestii.com/%7Emschulter/IntervalSpectrumRegions.txt|Regions of the Interval Spectrum]]: | <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 the theory of [[Margo Schulter]], //interseptimal// is a category of intervals which occupy regions intermediate between two septimal ratios such as [[8_7|8/7]] and [[7_6|7/6]], or [[12_7|12/7]] and [[7_4|7/4]]. There are four interseptimal regions given below, with approximate cents ranges from Schulter's article [[http://www.bestii.com/%7Emschulter/IntervalSpectrumRegions.txt|Regions of the Interval Spectrum]]: | ||
# Maj2-min3 | # Maj2-min3 -- intermediate between 8/7 and 7/6 -- 240¢-260¢ | ||
# Maj3-4 | # Maj3-4 -- intermediate between [[9_7|9/7]] and [[21_16|21/16]] -- 440¢-468¢ | ||
# 5-min6 | # 5-min6 -- intermediate between [[32_21|32/21]] and [[14_9|14/9]] -- 732¢-760¢ | ||
# Maj6-min7 | # Maj6-min7 -- intermediate between 12/7 and 7/4 -- 940¢-960¢ | ||
Interseptimal intervals are well-represented in [[24edo]] at 250¢, 450¢, 750¢ and 950¢. As they fall in ambiguous zones between simpler categories, they are inevitably xenharmonic. | Interseptimal intervals are well-represented in [[24edo]] at 250¢, 450¢, 750¢ and 950¢. As they fall in ambiguous zones between simpler categories, they are inevitably xenharmonic. | ||
==Examples== | |||
Some interseptimal intervals in all four ranges, both just and tempered, are listed below. | |||
===Maj2-min3 - 240¢-260¢=== | |||
||~ Interval ||~ Cents Value ||~ Prime Limit (if applicable) || | |||
|| 147/128 || 239.607 || 7 || | |||
|| 1\[[5edo]] || 240.000 || - || | |||
|| 54/47 || 240.358 || 47 || | |||
|| 23/20 || 241.961 || 23 || | |||
|| 1152/1001 || 243.238 || 13 || | |||
|| 38/33 || 244.240 || 19 || | |||
|| [[15_13|15/13]] || 247.741 || 13 || | |||
|| 6\[[29edo]] || 248.276 || - || | |||
|| 5\[[24edo]] || 250.000 || - || | |||
|| 52/45 || 250.304 || 13 || | |||
|| 37/32 || 251.344 || 37 || | |||
|| 4\[[19edo]] || 252.632 || - || | |||
|| 22/19 || 253.805 || 19 || | |||
|| 29/25 || 256.950 || 29 || | |||
|| 3\[[14edo]] || 257.143 || - || | |||
|| 297/256 || 257.183 || 11 || | |||
|| 36/31 || 258.874 || 31 || | |||
|| 5\[[23edo]] || 260.870 || - || | |||
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>Interseptimal</title></head><body>In the theory of <a class="wiki_link" href="/Margo%20Schulter">Margo Schulter</a>, <em>interseptimal</em> is a category of intervals which occupy regions intermediate between two septimal ratios such as <a class="wiki_link" href="/8_7">8/7</a> and <a class="wiki_link" href="/7_6">7/6</a>, or <a class="wiki_link" href="/12_7">12/7</a> and <a class="wiki_link" href="/7_4">7/4</a>. There are four interseptimal regions given below, with approximate cents ranges from Schulter's article <a class="wiki_link_ext" href="http://www.bestii.com/%7Emschulter/IntervalSpectrumRegions.txt" rel="nofollow">Regions of the Interval Spectrum</a>:<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>Interseptimal</title></head><body>In the theory of <a class="wiki_link" href="/Margo%20Schulter">Margo Schulter</a>, <em>interseptimal</em> is a category of intervals which occupy regions intermediate between two septimal ratios such as <a class="wiki_link" href="/8_7">8/7</a> and <a class="wiki_link" href="/7_6">7/6</a>, or <a class="wiki_link" href="/12_7">12/7</a> and <a class="wiki_link" href="/7_4">7/4</a>. There are four interseptimal regions given below, with approximate cents ranges from Schulter's article <a class="wiki_link_ext" href="http://www.bestii.com/%7Emschulter/IntervalSpectrumRegions.txt" rel="nofollow">Regions of the Interval Spectrum</a>:<br /> | ||
<ol><li>Maj2-min3 | <ol><li>Maj2-min3 -- intermediate between 8/7 and 7/6 -- 240¢-260¢</li><li>Maj3-4 -- intermediate between <a class="wiki_link" href="/9_7">9/7</a> and <a class="wiki_link" href="/21_16">21/16</a> -- 440¢-468¢</li><li>5-min6 -- intermediate between <a class="wiki_link" href="/32_21">32/21</a> and <a class="wiki_link" href="/14_9">14/9</a> -- 732¢-760¢</li><li>Maj6-min7 -- intermediate between 12/7 and 7/4 -- 940¢-960¢</li></ol><br /> | ||
Interseptimal intervals are well-represented in <a class="wiki_link" href="/24edo">24edo</a> at 250¢, 450¢, 750¢ and 950¢. As they fall in ambiguous zones between simpler categories, they are inevitably xenharmonic.<br /> | Interseptimal intervals are well-represented in <a class="wiki_link" href="/24edo">24edo</a> at 250¢, 450¢, 750¢ and 950¢. As they fall in ambiguous zones between simpler categories, they are inevitably xenharmonic.<br /> | ||
<br /> | |||
<!-- ws:start:WikiTextHeadingRule:0:&lt;h2&gt; --><h2 id="toc0"><a name="x-Examples"></a><!-- ws:end:WikiTextHeadingRule:0 -->Examples</h2> | |||
Some interseptimal intervals in all four ranges, both just and tempered, are listed below.<br /> | |||
<br /> | |||
<!-- ws:start:WikiTextHeadingRule:2:&lt;h3&gt; --><h3 id="toc1"><a name="x-Examples-Maj2-min3 - 240¢-260¢"></a><!-- ws:end:WikiTextHeadingRule:2 -->Maj2-min3 - 240¢-260¢</h3> | |||
<table class="wiki_table"> | |||
<tr> | |||
<th>Interval<br /> | |||
</th> | |||
<th>Cents Value<br /> | |||
</th> | |||
<th>Prime Limit (if applicable)<br /> | |||
</th> | |||
</tr> | |||
<tr> | |||
<td>147/128<br /> | |||
</td> | |||
<td>239.607<br /> | |||
</td> | |||
<td>7<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td>1\<a class="wiki_link" href="/5edo">5edo</a><br /> | |||
</td> | |||
<td>240.000<br /> | |||
</td> | |||
<td>-<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td>54/47<br /> | |||
</td> | |||
<td>240.358<br /> | |||
</td> | |||
<td>47<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td>23/20<br /> | |||
</td> | |||
<td>241.961<br /> | |||
</td> | |||
<td>23<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td>1152/1001<br /> | |||
</td> | |||
<td>243.238<br /> | |||
</td> | |||
<td>13<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td>38/33<br /> | |||
</td> | |||
<td>244.240<br /> | |||
</td> | |||
<td>19<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td><a class="wiki_link" href="/15_13">15/13</a><br /> | |||
</td> | |||
<td>247.741<br /> | |||
</td> | |||
<td>13<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td>6\<a class="wiki_link" href="/29edo">29edo</a><br /> | |||
</td> | |||
<td>248.276<br /> | |||
</td> | |||
<td>-<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td>5\<a class="wiki_link" href="/24edo">24edo</a><br /> | |||
</td> | |||
<td>250.000<br /> | |||
</td> | |||
<td>-<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td>52/45<br /> | |||
</td> | |||
<td>250.304<br /> | |||
</td> | |||
<td>13<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td>37/32<br /> | |||
</td> | |||
<td>251.344<br /> | |||
</td> | |||
<td>37<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td>4\<a class="wiki_link" href="/19edo">19edo</a><br /> | |||
</td> | |||
<td>252.632<br /> | |||
</td> | |||
<td>-<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td>22/19<br /> | |||
</td> | |||
<td>253.805<br /> | |||
</td> | |||
<td>19<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td>29/25<br /> | |||
</td> | |||
<td>256.950<br /> | |||
</td> | |||
<td>29<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td>3\<a class="wiki_link" href="/14edo">14edo</a><br /> | |||
</td> | |||
<td>257.143<br /> | |||
</td> | |||
<td>-<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td>297/256<br /> | |||
</td> | |||
<td>257.183<br /> | |||
</td> | |||
<td>11<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td>36/31<br /> | |||
</td> | |||
<td>258.874<br /> | |||
</td> | |||
<td>31<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td>5\<a class="wiki_link" href="/23edo">23edo</a><br /> | |||
</td> | |||
<td>260.870<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> | ||