Interseptimal interval: Difference between revisions

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<h2>IMPORTED REVISION FROM WIKISPACES</h2>

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: This revision was by author [[User:~~xenwolf~~|~~xenwolf~~]] and made on <tt>2016-02-~~16 16~~:36:49 UTC</tt>.<br>

: This revision was by author [[User:MasonGreen1|MasonGreen1]] and made on <tt>2016-03-14 01:42:29 UTC</tt>.<br>

: The original revision id was <tt>~~574999245~~</tt>.<br>

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# 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¢. They also appear in [[19edo]] and [[29edo]].

As they fall in ambiguous zones between simpler categories, they are inevitably xenharmonic. This also makes them difficult to name: do we classify a 250-cent interval as a second, a third, both, or neither? One option is to give each region a distinct name (analogous to using the word //tritone// rather than diminished fifth or augmented fourth). Possible names that could be used are:

# 240¢-260¢ -- semifourth -- an interval of this size is around half the size of a perfect fourth.

# 440¢-468¢ -- semisixth -- an interval of this size is around half the size of a major sixth.

# 732¢-760¢ -- semitenth -- an interval of this size is around half the size of a major tenth (i. e., compound major third). Another possible name is sesquifourth (since this is also about one and a half times the size of a perfect fourth).

# 940¢-960¢ -- semitwelfth -- an interval of this size is around half the size of a perfect twelfth (i e., a compound perfect fifth, or tritave). All even [[edt|edts]] have a semitwelfth of approximately 951 cents, analogous to the 600 cent tritone shared by all even edos.

This makes notating these intervals very easy as long as we have an agreed-upon symbol for "semi".

By analogy the tritone could also be called a semioctave, although the term tritone is so well-established that seems is little reason to change it now.

==Examples==

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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>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 -- 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¢. They also appear in <a class="wiki_link" href="/19edo">19edo</a> and <a class="wiki_link" href="/29edo">29edo</a>.<br />

<br />

As they fall in ambiguous zones between simpler categories, they are inevitably xenharmonic. This also makes them difficult to name: do we classify a 250-cent interval as a second, a third, both, or neither? One option is to give each region a distinct name (analogous to using the word <em>tritone</em> rather than diminished fifth or augmented fourth). Possible names that could be used are:<br />

<br />

<ol><li>240¢-260¢ -- semifourth -- an interval of this size is around half the size of a perfect fourth.</li><li>440¢-468¢ -- semisixth -- an interval of this size is around half the size of a major sixth.</li><li>732¢-760¢ -- semitenth -- an interval of this size is around half the size of a major tenth (i. e., compound major third). Another possible name is sesquifourth (since this is also about one and a half times the size of a perfect fourth).</li><li>940¢-960¢ -- semitwelfth -- an interval of this size is around half the size of a perfect twelfth (i e., a compound perfect fifth, or tritave). All even <a class="wiki_link" href="/edt">edts</a> have a semitwelfth of approximately 951 cents, analogous to the 600 cent tritone shared by all even edos.</li></ol><br />

This makes notating these intervals very easy as long as we have an agreed-upon symbol for &quot;semi&quot;.<br />

<br />

By analogy the tritone could also be called a semioctave, although the term tritone is so well-established that seems is little reason to change it now.<br />

<br />

<h2 id="toc0"><a name="x-Examples"></a>Examples</h2>

@@ Line 1: / Line 1: @@
 <h2>IMPORTED REVISION FROM WIKISPACES</h2>
 This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br>
-: This revision was by author [[User:xenwolf|xenwolf]] and made on <tt>2016-02-16 16:36:49 UTC</tt>.<br>
+: This revision was by author [[User:MasonGreen1|MasonGreen1]] and made on <tt>2016-03-14 01:42:29 UTC</tt>.<br>
-: The original revision id was <tt>574999245</tt>.<br>
+: The original revision id was <tt>577376761</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>
@@ Line 12: / Line 12: @@
 # 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¢. They also appear in [[19edo]] and [[29edo]].
+As they fall in ambiguous zones between simpler categories, they are inevitably xenharmonic. This also makes them difficult to name: do we classify a 250-cent interval as a second, a third, both, or neither? One option is to give each region a distinct name (analogous to using the word //tritone// rather than diminished fifth or augmented fourth). Possible names that could be used are:
+# 240¢-260¢ -- semifourth -- an interval of this size is around half the size of a perfect fourth.
+# 440¢-468¢ -- semisixth -- an interval of this size is around half the size of a major sixth.
+# 732¢-760¢ -- semitenth -- an interval of this size is around half the size of a major tenth (i. e., compound major third). Another possible name is sesquifourth (since this is also about one and a half times the size of a perfect fourth).
+# 940¢-960¢ -- semitwelfth -- an interval of this size is around half the size of a perfect twelfth (i e., a compound perfect fifth, or tritave). All even [[edt|edts]] have a semitwelfth of approximately 951 cents, analogous to the 600 cent tritone shared by all even edos.
+This makes notating these intervals very easy as long as we have an agreed-upon symbol for "semi".
+By analogy the tritone could also be called a semioctave, although the term tritone is so well-established that seems is little reason to change it now.
 ==Examples==
@@ Line 122: / Line 134: @@
 <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">&lt;html&gt;&lt;head&gt;&lt;title&gt;Interseptimal&lt;/title&gt;&lt;/head&gt;&lt;body&gt;In the theory of &lt;a class="wiki_link" href="/Margo%20Schulter"&gt;Margo Schulter&lt;/a&gt;, &lt;em&gt;interseptimal&lt;/em&gt; is a category of intervals which occupy regions intermediate between two septimal ratios such as &lt;a class="wiki_link" href="/8_7"&gt;8/7&lt;/a&gt; and &lt;a class="wiki_link" href="/7_6"&gt;7/6&lt;/a&gt;, or &lt;a class="wiki_link" href="/12_7"&gt;12/7&lt;/a&gt; and &lt;a class="wiki_link" href="/7_4"&gt;7/4&lt;/a&gt;. There are four interseptimal regions given below, with approximate cents ranges from Schulter's article &lt;a class="wiki_link_ext" href="http://www.bestii.com/%7Emschulter/IntervalSpectrumRegions.txt" rel="nofollow"&gt;Regions of the Interval Spectrum&lt;/a&gt;:&lt;br /&gt;
 &lt;ol&gt;&lt;li&gt;Maj2-min3 -- intermediate between 8/7 and 7/6 -- 240¢-260¢&lt;/li&gt;&lt;li&gt;Maj3-4 -- intermediate between &lt;a class="wiki_link" href="/9_7"&gt;9/7&lt;/a&gt; and &lt;a class="wiki_link" href="/21_16"&gt;21/16&lt;/a&gt; -- 440¢-468¢&lt;/li&gt;&lt;li&gt;5-min6 -- intermediate between &lt;a class="wiki_link" href="/32_21"&gt;32/21&lt;/a&gt; and &lt;a class="wiki_link" href="/14_9"&gt;14/9&lt;/a&gt; -- 732¢-760¢&lt;/li&gt;&lt;li&gt;Maj6-min7 -- intermediate between 12/7 and 7/4 -- 940¢-960¢&lt;/li&gt;&lt;/ol&gt;&lt;br /&gt;
-Interseptimal intervals are well-represented in &lt;a class="wiki_link" href="/24edo"&gt;24edo&lt;/a&gt; at 250¢, 450¢, 750¢ and 950¢. As they fall in ambiguous zones between simpler categories, they are inevitably xenharmonic.&lt;br /&gt;
+Interseptimal intervals are well-represented in &lt;a class="wiki_link" href="/24edo"&gt;24edo&lt;/a&gt; at 250¢, 450¢, 750¢ and 950¢. They also appear in &lt;a class="wiki_link" href="/19edo"&gt;19edo&lt;/a&gt; and &lt;a class="wiki_link" href="/29edo"&gt;29edo&lt;/a&gt;.&lt;br /&gt;
+&lt;br /&gt;
+As they fall in ambiguous zones between simpler categories, they are inevitably xenharmonic. This also makes them difficult to name: do we classify a 250-cent interval as a second, a third, both, or neither? One option is to give each region a distinct name (analogous to using the word &lt;em&gt;tritone&lt;/em&gt; rather than diminished fifth or augmented fourth). Possible names that could be used are:&lt;br /&gt;
+&lt;br /&gt;
+&lt;ol&gt;&lt;li&gt;240¢-260¢ -- semifourth -- an interval of this size is around half the size of a perfect fourth.&lt;/li&gt;&lt;li&gt;440¢-468¢ -- semisixth -- an interval of this size is around half the size of a major sixth.&lt;/li&gt;&lt;li&gt;732¢-760¢ -- semitenth -- an interval of this size is around half the size of a major tenth (i. e., compound major third). Another possible name is sesquifourth (since this is also about one and a half times the size of a perfect fourth).&lt;/li&gt;&lt;li&gt;940¢-960¢ -- semitwelfth -- an interval of this size is around half the size of a perfect twelfth (i e., a compound perfect fifth, or tritave). All even &lt;a class="wiki_link" href="/edt"&gt;edts&lt;/a&gt; have a semitwelfth of approximately 951 cents, analogous to the 600 cent tritone shared by all even edos.&lt;/li&gt;&lt;/ol&gt;&lt;br /&gt;
+This makes notating these intervals very easy as long as we have an agreed-upon symbol for &amp;quot;semi&amp;quot;.&lt;br /&gt;
+&lt;br /&gt;
+By analogy the tritone could also be called a semioctave, although the term tritone is so well-established that seems is little reason to change it now.&lt;br /&gt;
+&lt;br /&gt;
 &lt;br /&gt;
 &lt;!-- ws:start:WikiTextHeadingRule:0:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc0"&gt;&lt;a name="x-Examples"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:0 --&gt;Examples&lt;/h2&gt;