Map of rank-2 temperaments: 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:~~genewardsmith~~|~~genewardsmith~~]] and made on <tt>2012-04-~~14 14~~:38:36 UTC</tt>.<br>

: This revision was by author [[User:keenanpepper|keenanpepper]] and made on <tt>2012-05-01 23:27:43 UTC</tt>.<br>

: The original revision id was <tt>~~320479278~~</tt>.<br>

: The original revision id was <tt>328353680</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">This is intended to be a map of all interesting ~~linear (~~rank-2) temperaments that are compatible with octave equivalence. The only linear temperaments not appearing here should be ones like [[Bohlen-Pierce]] that completely lack octaves.

<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 is intended to be a map of all interesting rank-2 temperaments that are compatible with octave equivalence. The only linear temperaments not appearing here should be ones like [[Bohlen-Pierce]] that completely lack octaves.

Please make sure each fraction of an octave is always the [[mediant]] of the ones directly above and below.

==One period per octave==

Since this is the largest subset, it has its own page: [[Map of ~~period-1~~ temperaments]].

Since this is the largest subset, it has its own page: [[Map of linear temperaments]].

==Two periods per octave==

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* [[Atomic]] - Does not temper out the schisma, so 3/2 is one schisma sharp of its 12edo value. In atomic, since twelve fifths are sharp of seven octaves by twelve schismas, the Pythagorean comma is twelve schismas, and hence 81/80, the Didymus comma, is eleven schismas. In fact eleven schismas is sharp of 81/80, and twelve schismas of the Pythaorean comma, by the microscopic interval of the atom, which atomic tempers out. Extremely accurate.</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>Map of rank-2 temperaments</title></head><body>This is intended to be a map of all interesting ~~linear (~~rank-2) temperaments that are compatible with octave equivalence. The only linear temperaments not appearing here should be ones like <a class="wiki_link" href="/Bohlen-Pierce">Bohlen-Pierce</a> that completely lack octaves.<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>Map of rank-2 temperaments</title></head><body>This is intended to be a map of all interesting rank-2 temperaments that are compatible with octave equivalence. The only linear temperaments not appearing here should be ones like <a class="wiki_link" href="/Bohlen-Pierce">Bohlen-Pierce</a> that completely lack octaves.<br />

Please make sure each fraction of an octave is always the <a class="wiki_link" href="/mediant">mediant</a> of the ones directly above and below.<br />

<br />

<h2 id="toc0"><a name="x-One period per octave"></a>One period per octave</h2>

Since this is the largest subset, it has its own page: <a class="wiki_link" href="/Map%20of%~~20period-1~~%20temperaments">Map of ~~period-1~~ temperaments</a>.<br />

Since this is the largest subset, it has its own page: <a class="wiki_link" href="/Map%20of%20linear%20temperaments">Map of linear temperaments</a>.<br />

<br />

<h2 id="toc1"><a name="x-Two periods per octave"></a>Two periods per octave</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:genewardsmith|genewardsmith]] and made on <tt>2012-04-14 14:38:36 UTC</tt>.<br>
+: This revision was by author [[User:keenanpepper|keenanpepper]] and made on <tt>2012-05-01 23:27:43 UTC</tt>.<br>
-: The original revision id was <tt>320479278</tt>.<br>
+: The original revision id was <tt>328353680</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">This is intended to be a map of all interesting linear (rank-2) temperaments that are compatible with octave equivalence. The only linear temperaments not appearing here should be ones like [[Bohlen-Pierce]] that completely lack octaves.
+<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 is intended to be a map of all interesting rank-2 temperaments that are compatible with octave equivalence. The only linear temperaments not appearing here should be ones like [[Bohlen-Pierce]] that completely lack octaves.
 Please make sure each fraction of an octave is always the [[mediant]] of the ones directly above and below.
 ==One period per octave==
-Since this is the largest subset, it has its own page: [[Map of period-1 temperaments]].
+Since this is the largest subset, it has its own page: [[Map of linear temperaments]].
 ==Two periods per octave==
@@ Line 137: / Line 137: @@
 * [[Atomic]] - Does not temper out the schisma, so 3/2 is one schisma sharp of its 12edo value. In atomic, since twelve fifths are sharp of seven octaves by twelve schismas, the Pythagorean comma is twelve schismas, and hence 81/80, the Didymus comma, is eleven schismas. In fact eleven schismas is sharp of 81/80, and twelve schismas of the Pythaorean comma, by the microscopic interval of the atom, which atomic tempers out. Extremely accurate.</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;Map of rank-2 temperaments&lt;/title&gt;&lt;/head&gt;&lt;body&gt;This is intended to be a map of all interesting linear (rank-2) temperaments that are compatible with octave equivalence. The only linear temperaments not appearing here should be ones like &lt;a class="wiki_link" href="/Bohlen-Pierce"&gt;Bohlen-Pierce&lt;/a&gt; that completely lack octaves.&lt;br /&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;Map of rank-2 temperaments&lt;/title&gt;&lt;/head&gt;&lt;body&gt;This is intended to be a map of all interesting rank-2 temperaments that are compatible with octave equivalence. The only linear temperaments not appearing here should be ones like &lt;a class="wiki_link" href="/Bohlen-Pierce"&gt;Bohlen-Pierce&lt;/a&gt; that completely lack octaves.&lt;br /&gt;
 Please make sure each fraction of an octave is always the &lt;a class="wiki_link" href="/mediant"&gt;mediant&lt;/a&gt; of the ones directly above and below.&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-One period per octave"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:0 --&gt;One period per octave&lt;/h2&gt;
-  Since this is the largest subset, it has its own page: &lt;a class="wiki_link" href="/Map%20of%20period-1%20temperaments"&gt;Map of period-1 temperaments&lt;/a&gt;.&lt;br /&gt;
+  Since this is the largest subset, it has its own page: &lt;a class="wiki_link" href="/Map%20of%20linear%20temperaments"&gt;Map of linear temperaments&lt;/a&gt;.&lt;br /&gt;
 &lt;br /&gt;
 &lt;!-- ws:start:WikiTextHeadingRule:2:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc1"&gt;&lt;a name="x-Two periods per octave"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:2 --&gt;Two periods per octave&lt;/h2&gt;