Consistency: 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>2011-06-28 16:49:23 UTC</tt>.<br>

: This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2011-06-28 16:51:26 UTC</tt>.<br>

: The original revision id was <tt>~~239203855~~</tt>.<br>

: The original revision id was <tt>239204095</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">If N-edo is an [[edo|equal division of the octave]], and if for any interval r, N(r) is the best N-edo approximation to r, then N is //consistent// with respect to a set of intervals S if for any two intervals a and b in S, N(ab) = N(a) + N(b). Normally this is considered when S is the set of [[Odd limit|q odd limit intervals]], consisting of everything of the form 2^n u/v, where u and v are odd integers less than or equal to q. N is then said to be //q limit consistent//. If each interval in the q-limit is mapped to a unique value by N, then it said to be //uniquely q limit consistent//.

<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">If N-edo is an [[edo|equal division of the octave]], and if for any interval r, N(r) is the best N-edo approximation to r, then N is //consistent// with respect to a set of intervals S if for any two intervals a and b in S where ab is also in S, N(ab) = N(a) + N(b). Normally this is considered when S is the set of [[Odd limit|q odd limit intervals]], consisting of everything of the form 2^n u/v, where u and v are odd integers less than or equal to q. N is then said to be //q limit consistent//. If each interval in the q-limit is mapped to a unique value by N, then it said to be //uniquely q limit consistent//.

An example for a system that is not consistent is [[25edo]]:

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</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>consistent</title></head><body>If N-edo is an <a class="wiki_link" href="/edo">equal division of the octave</a>, and if for any interval r, N(r) is the best N-edo approximation to r, then N is <em>consistent</em> with respect to a set of intervals S if for any two intervals a and b in S, N(ab) = N(a) + N(b). Normally this is considered when S is the set of <a class="wiki_link" href="/Odd%20limit">q odd limit intervals</a>, consisting of everything of the form 2^n u/v, where u and v are odd integers less than or equal to q. N is then said to be <em>q limit consistent</em>. If each interval in the q-limit is mapped to a unique value by N, then it said to be <em>uniquely q limit consistent</em>.<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>consistent</title></head><body>If N-edo is an <a class="wiki_link" href="/edo">equal division of the octave</a>, and if for any interval r, N(r) is the best N-edo approximation to r, then N is <em>consistent</em> with respect to a set of intervals S if for any two intervals a and b in S where ab is also in S, N(ab) = N(a) + N(b). Normally this is considered when S is the set of <a class="wiki_link" href="/Odd%20limit">q odd limit intervals</a>, consisting of everything of the form 2^n u/v, where u and v are odd integers less than or equal to q. N is then said to be <em>q limit consistent</em>. If each interval in the q-limit is mapped to a unique value by N, then it said to be <em>uniquely q limit consistent</em>.<br />

<br />

An example for a system that is not consistent is <a class="wiki_link" href="/25edo">25edo</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:genewardsmith|genewardsmith]] and made on <tt>2011-06-28 16:49:23 UTC</tt>.<br>
+: This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2011-06-28 16:51:26 UTC</tt>.<br>
-: The original revision id was <tt>239203855</tt>.<br>
+: The original revision id was <tt>239204095</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">If N-edo is an [[edo|equal division of the octave]], and if for any interval r, N(r) is the best N-edo approximation to r, then N is //consistent// with respect to a set of intervals S if for any two intervals a and b in S, N(ab) = N(a) + N(b). Normally this is considered when S is the set of [[Odd limit|q odd limit intervals]], consisting of everything of the form 2^n u/v, where u and v are odd integers less than or equal to q. N is then said to be //q limit consistent//. If each interval in the q-limit is mapped to a unique value by N, then it said to be //uniquely q limit consistent//.
+<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">If N-edo is an [[edo|equal division of the octave]], and if for any interval r, N(r) is the best N-edo approximation to r, then N is //consistent// with respect to a set of intervals S if for any two intervals a and b in S where ab is also in S, N(ab) = N(a) + N(b). Normally this is considered when S is the set of [[Odd limit|q odd limit intervals]], consisting of everything of the form 2^n u/v, where u and v are odd integers less than or equal to q. N is then said to be //q limit consistent//. If each interval in the q-limit is mapped to a unique value by N, then it said to be //uniquely q limit consistent//.
 An example for a system that is not consistent is [[25edo]]:
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 </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;consistent&lt;/title&gt;&lt;/head&gt;&lt;body&gt;If N-edo is an &lt;a class="wiki_link" href="/edo"&gt;equal division of the octave&lt;/a&gt;, and if for any interval r, N(r) is the best N-edo approximation to r, then N is &lt;em&gt;consistent&lt;/em&gt; with respect to a set of intervals S if for any two intervals a and b in S, N(ab) = N(a) + N(b). Normally this is considered when S is the set of &lt;a class="wiki_link" href="/Odd%20limit"&gt;q odd limit intervals&lt;/a&gt;, consisting of everything of the form 2^n u/v, where u and v are odd integers less than or equal to q. N is then said to be &lt;em&gt;q limit consistent&lt;/em&gt;. If each interval in the q-limit is mapped to a unique value by N, then it said to be &lt;em&gt;uniquely q limit consistent&lt;/em&gt;.&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;consistent&lt;/title&gt;&lt;/head&gt;&lt;body&gt;If N-edo is an &lt;a class="wiki_link" href="/edo"&gt;equal division of the octave&lt;/a&gt;, and if for any interval r, N(r) is the best N-edo approximation to r, then N is &lt;em&gt;consistent&lt;/em&gt; with respect to a set of intervals S if for any two intervals a and b in S where ab is also in S, N(ab) = N(a) + N(b). Normally this is considered when S is the set of &lt;a class="wiki_link" href="/Odd%20limit"&gt;q odd limit intervals&lt;/a&gt;, consisting of everything of the form 2^n u/v, where u and v are odd integers less than or equal to q. N is then said to be &lt;em&gt;q limit consistent&lt;/em&gt;. If each interval in the q-limit is mapped to a unique value by N, then it said to be &lt;em&gt;uniquely q limit consistent&lt;/em&gt;.&lt;br /&gt;
 &lt;br /&gt;
 An example for a system that is not consistent is &lt;a class="wiki_link" href="/25edo"&gt;25edo&lt;/a&gt;:&lt;br /&gt;