Octave-reduce: 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:xenwolf|xenwolf]] and made on <tt>2011-06-29 04:45:17 UTC</tt>.<br>

: This revision was by author [[User:xenwolf|xenwolf]] and made on <tt>2011-06-29 04:57:19 UTC</tt>.<br>

: The original revision id was <tt>~~239287393~~</tt>.<br>

: The original revision id was <tt>239288307</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">**Octave-reducing** ~~an interval makes~~ it fit into the range from 1/1 (or 1, the [[unisone]]) up to (excluding) 2/1 (the [[octave]]).

<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">**Octave-reducing** a fraction means to make it fit into the range from 1 (or 1/1 the [[unisone]]) to (excluding) 2/1 (the [[octave]]).

~~Intervals higher~~ than 2~~/1 have~~ to be divided by 2, ~~intervals~~ less than 1/1 ~~have to be multiplied by~~ 2.

A fraction r greater than 2 has to be divided by 2, or multiplied by 2 if it is less than 1, until it satisfies the inequality

[[math]]

1 \le r < 2

[[math]]

== Examples ==

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* 2/1 gets 1/1 (or simply 1)</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>octave-reduce</title></head><body><strong>Octave-reducing</strong> ~~an interval makes~~ it fit into the range from 1/1 (or 1, the <a class="wiki_link" href="/unisone">unisone</a>) up to (excluding) 2/1 (the <a class="wiki_link" href="/octave">octave</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>octave-reduce</title></head><body><strong>Octave-reducing</strong> a fraction means to make it fit into the range from 1 (or 1/1 the <a class="wiki_link" href="/unisone">unisone</a>) to (excluding) 2/1 (the <a class="wiki_link" href="/octave">octave</a>).<br />

~~Intervals higher~~ than 2~~/1 have~~ to be divided by 2, ~~intervals~~ less than 1/1 ~~have to be multiplied by~~ 2.<br />

A fraction r greater than 2 has to be divided by 2, or multiplied by 2 if it is less than 1, until it satisfies the inequality <br />

<!-- ws:start:WikiTextMathRule:0:

[[math]]&lt;br/&gt;

1 \le r &lt; 2&lt;br/&gt;[[math]]

--><script type="math/tex">1 \le r < 2</script><br />

<br />

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

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

<ul><li>3/4 gets <a class="wiki_link" href="/3_2">3/2</a></li><li>7/2 gets <a class="wiki_link" href="/7_4">7/4</a></li><li>2/1 gets 1/1 (or simply 1)</li></ul></body></html></pre></div>

@@ 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>2011-06-29 04:45:17 UTC</tt>.<br>
+: This revision was by author [[User:xenwolf|xenwolf]] and made on <tt>2011-06-29 04:57:19 UTC</tt>.<br>
-: The original revision id was <tt>239287393</tt>.<br>
+: The original revision id was <tt>239288307</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">**Octave-reducing** an interval makes it fit into the range from 1/1 (or 1, the [[unisone]]) up to (excluding) 2/1 (the [[octave]]).
+<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">**Octave-reducing** a fraction means to make it fit into the range from 1 (or 1/1 the [[unisone]]) to (excluding) 2/1 (the [[octave]]).
-Intervals higher than 2/1 have to be divided by 2, intervals less than 1/1 have to be multiplied by 2.
+A fraction r greater than 2 has to be divided by 2, or multiplied by 2 if it is less than 1, until it satisfies the inequality
+[[math]]
+\le r &lt; 2
+[[math]]
 == Examples ==
@@ Line 14: / Line 17: @@
 * 2/1 gets 1/1 (or simply 1)</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;octave-reduce&lt;/title&gt;&lt;/head&gt;&lt;body&gt;&lt;strong&gt;Octave-reducing&lt;/strong&gt; an interval makes it fit into the range from 1/1 (or 1, the &lt;a class="wiki_link" href="/unisone"&gt;unisone&lt;/a&gt;) up to (excluding) 2/1 (the &lt;a class="wiki_link" href="/octave"&gt;octave&lt;/a&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;octave-reduce&lt;/title&gt;&lt;/head&gt;&lt;body&gt;&lt;strong&gt;Octave-reducing&lt;/strong&gt; a fraction means to make it fit into the range from 1 (or 1/1 the &lt;a class="wiki_link" href="/unisone"&gt;unisone&lt;/a&gt;) to (excluding) 2/1 (the &lt;a class="wiki_link" href="/octave"&gt;octave&lt;/a&gt;).&lt;br /&gt;
-Intervals higher than 2/1 have to be divided by 2, intervals less than 1/1 have to be multiplied by 2.&lt;br /&gt;
+A fraction r greater than 2 has to be divided by 2, or multiplied by 2 if it is less than 1, until it satisfies the inequality &lt;br /&gt;
+&lt;!-- ws:start:WikiTextMathRule:0:
+[[math]]&amp;lt;br/&amp;gt;
+\le r &amp;lt; 2&amp;lt;br/&amp;gt;[[math]]
+ --&gt;&lt;script type="math/tex"&gt;1 \le r &lt; 2&lt;/script&gt;&lt;!-- ws:end:WikiTextMathRule:0 --&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;
+&lt;!-- ws:start:WikiTextHeadingRule:1:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc0"&gt;&lt;a name="x-Examples"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:1 --&gt; Examples &lt;/h2&gt;
 &lt;ul&gt;&lt;li&gt;3/4 gets &lt;a class="wiki_link" href="/3_2"&gt;3/2&lt;/a&gt;&lt;/li&gt;&lt;li&gt;7/2 gets &lt;a class="wiki_link" href="/7_4"&gt;7/4&lt;/a&gt;&lt;/li&gt;&lt;li&gt;2/1 gets 1/1 (or simply 1)&lt;/li&gt;&lt;/ul&gt;&lt;/body&gt;&lt;/html&gt;</pre></div>