Meantone intervals: Difference between revisions

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<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:keenanpepper|keenanpepper]] and made on <tt>2011-10-31 19:51:10 UTC</tt>.<br>

: This revision was by author [[User:keenanpepper|keenanpepper]] and made on <tt>2011-10-31 20:02:32 UTC</tt>.<br>

: The original revision id was <tt>~~270458208~~</tt>.<br>

: The original revision id was <tt>270460686</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>

<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">||~ Name ||~ Size* ||~ Ratios ||

<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">This table shows all the simple intervals of [[Meantone family#Septimal%20meantone|septimal meantone]], which includes the entire 7-limit tonality diamond.

In [[12edo]] the diminished second vanishes, so this cornucopia of intervals collapses to a mere 12. None of the intervals is inherently septimal in 12edo, because they all have simpler 5-limit descriptions.

In [[19edo]], in contrast, the *double* diminished second vanishes, so the equivalences are A1~d2, A2~d3, A3~d4, A4~dd5, AA4~d5, A5~d6, A6~d7, and A7~d8. Thus some intervals are undeniably septimal, but ambiguously so because 49/48 vanishes.

See also [[http://en.wikipedia.org/wiki/List_of_meantone_intervals|Wikipedia's list of meantone intervals]]

||~ Name ||~ Size* ||~ Ratios ||

||||||~ Unisons ||

|| Perfect unison (P1) || 0 || 1/1 ||

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|| Perfect octave (P8) || 1200.0 || 2/1 ||

|| Augmented octave (A8) || 1275.5 || 25/12~21/20 ||

``*`` In POTE septimal meantone

``*`` In POTE septimal meantone</pre></div>

</pre></div>

<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>Meantone intervals</title></head><body>

<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>Meantone intervals</title></head><body>This table shows all the simple intervals of <a class="wiki_link" href="/Meantone%20family#Septimal%20meantone">septimal meantone</a>, which includes the entire 7-limit tonality diamond.<br />

<br />

In <a class="wiki_link" href="/12edo">12edo</a> the diminished second vanishes, so this cornucopia of intervals collapses to a mere 12. None of the intervals is inherently septimal in 12edo, because they all have simpler 5-limit descriptions.<br />

<br />

In <a class="wiki_link" href="/19edo">19edo</a>, in contrast, the *double* diminished second vanishes, so the equivalences are A1~d2, A2~d3, A3~d4, A4~dd5, AA4~d5, A5~d6, A6~d7, and A7~d8. Thus some intervals are undeniably septimal, but ambiguously so because 49/48 vanishes.<br />

<br />

See also <a class="wiki_link_ext" href="http://en.wikipedia.org/wiki/List_of_meantone_intervals" rel="nofollow">Wikipedia's list of meantone intervals</a><br />

@@ 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:keenanpepper|keenanpepper]] and made on <tt>2011-10-31 19:51:10 UTC</tt>.<br>
+: This revision was by author [[User:keenanpepper|keenanpepper]] and made on <tt>2011-10-31 20:02:32 UTC</tt>.<br>
-: The original revision id was <tt>270458208</tt>.<br>
+: The original revision id was <tt>270460686</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>
 <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">||~ Name ||~ Size* ||~ Ratios ||
+<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">This table shows all the simple intervals of [[Meantone family#Septimal%20meantone|septimal meantone]], which includes the entire 7-limit tonality diamond.
+In [[12edo]] the diminished second vanishes, so this cornucopia of intervals collapses to a mere 12. None of the intervals is inherently septimal in 12edo, because they all have simpler 5-limit descriptions.
+In [[19edo]], in contrast, the *double* diminished second vanishes, so the equivalences are A1~d2, A2~d3, A3~d4, A4~dd5, AA4~d5, A5~d6, A6~d7, and A7~d8. Thus some intervals are undeniably septimal, but ambiguously so because 49/48 vanishes.
+See also [[http://en.wikipedia.org/wiki/List_of_meantone_intervals|Wikipedia's list of meantone intervals]]
+||~ Name ||~ Size* ||~ Ratios ||
 ||||||~ Unisons ||
 || Perfect unison (P1) || 0 || 1/1 ||
@@ Line 44: / Line 51: @@
 || Perfect octave (P8) || 1200.0 || 2/1 ||
 || Augmented octave (A8) || 1275.5 || 25/12~21/20 ||
-``*`` In POTE septimal meantone
+``*`` In POTE septimal meantone</pre></div>
-</pre></div>
 <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">&lt;html&gt;&lt;head&gt;&lt;title&gt;Meantone intervals&lt;/title&gt;&lt;/head&gt;&lt;body&gt;
+<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;Meantone intervals&lt;/title&gt;&lt;/head&gt;&lt;body&gt;This table shows all the simple intervals of &lt;a class="wiki_link" href="/Meantone%20family#Septimal%20meantone"&gt;septimal meantone&lt;/a&gt;, which includes the entire 7-limit tonality diamond.&lt;br /&gt;
+&lt;br /&gt;
+In &lt;a class="wiki_link" href="/12edo"&gt;12edo&lt;/a&gt; the diminished second vanishes, so this cornucopia of intervals collapses to a mere 12. None of the intervals is inherently septimal in 12edo, because they all have simpler 5-limit descriptions.&lt;br /&gt;
+&lt;br /&gt;
+In &lt;a class="wiki_link" href="/19edo"&gt;19edo&lt;/a&gt;, in contrast, the *double* diminished second vanishes, so the equivalences are A1~d2, A2~d3, A3~d4, A4~dd5, AA4~d5, A5~d6, A6~d7, and A7~d8. Thus some intervals are undeniably septimal, but ambiguously so because 49/48 vanishes.&lt;br /&gt;
+&lt;br /&gt;
+See also &lt;a class="wiki_link_ext" href="http://en.wikipedia.org/wiki/List_of_meantone_intervals" rel="nofollow"&gt;Wikipedia's list of meantone intervals&lt;/a&gt;&lt;br /&gt;
 &lt;table class="wiki_table"&gt;