Tonality diamond: Difference between revisions
Wikispaces>xenwolf **Imported revision 575043915 - Original comment: ** |
Wikispaces>xenwolf **Imported revision 575157565 - Original comment: ** |
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<h2>IMPORTED REVISION FROM WIKISPACES</h2> | <h2>IMPORTED REVISION FROM WIKISPACES</h2> | ||
This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br> | 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- | : This revision was by author [[User:xenwolf|xenwolf]] and made on <tt>2016-02-18 08:47:51 UTC</tt>.<br> | ||
: The original revision id was <tt> | : The original revision id was <tt>575157565</tt>.<br> | ||
: The revision comment was: <tt></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> | 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> | <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">The q-odd-limit tonality diamond is the [[Diamonds|diamond]] function applied to the odd numbers from 1 to q: diamond({1, 3, 5, ..., q}). Another way of defining it is in terms of the most common number theoretic height function on rational numbers: H(N/M) = max(|M|, |N|); as all rational numbers which are the quotient of two positive odd integers N/M with H(N/M) ≤ q, reduced to 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">The q-odd-limit tonality diamond is the [[Diamonds|diamond]] function applied to the odd numbers from 1 to q: diamond({1, 3, 5, ..., q}). Another way of defining it is in terms of the most common number theoretic height function on rational numbers: H(N/M) = max(|M|, |N|); as all rational numbers which are the quotient of two positive odd integers N/M with H(N/M) ≤ q, [[octave-reduce|reduced to the octave]]. | ||
* [[http://en.wikipedia.org/wiki/Tonality_diamond|Wikipedia article on the tonality diamond]] | * [[http://en.wikipedia.org/wiki/Tonality_diamond|Wikipedia article on the tonality diamond]] | ||
* [[http://www.tonalsoft.com/enc/t/tonality-diamond.aspx|tonality diamond - arrangement of musical frequency ratios showing the dual identity of each ratio]]</pre></div> | * [[http://www.tonalsoft.com/enc/t/tonality-diamond.aspx|tonality diamond - arrangement of musical frequency ratios showing the dual identity of each ratio]]</pre></div> | ||
<h4>Original HTML content:</h4> | <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>Tonality diamond</title></head><body>The q-odd-limit tonality diamond is the <a class="wiki_link" href="/Diamonds">diamond</a> function applied to the odd numbers from 1 to q: diamond({1, 3, 5, ..., q}). Another way of defining it is in terms of the most common number theoretic height function on rational numbers: H(N/M) = max(|M|, |N|); as all rational numbers which are the quotient of two positive odd integers N/M with H(N/M) ≤ q, reduced to the octave.<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>Tonality diamond</title></head><body>The q-odd-limit tonality diamond is the <a class="wiki_link" href="/Diamonds">diamond</a> function applied to the odd numbers from 1 to q: diamond({1, 3, 5, ..., q}). Another way of defining it is in terms of the most common number theoretic height function on rational numbers: H(N/M) = max(|M|, |N|); as all rational numbers which are the quotient of two positive odd integers N/M with H(N/M) ≤ q, <a class="wiki_link" href="/octave-reduce">reduced to the octave</a>.<br /> | ||
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<ul><li><a class="wiki_link_ext" href="http://en.wikipedia.org/wiki/Tonality_diamond" rel="nofollow">Wikipedia article on the tonality diamond</a></li><li><a class="wiki_link_ext" href="http://www.tonalsoft.com/enc/t/tonality-diamond.aspx" rel="nofollow">tonality diamond - arrangement of musical frequency ratios showing the dual identity of each ratio</a></li></ul></body></html></pre></div> | <ul><li><a class="wiki_link_ext" href="http://en.wikipedia.org/wiki/Tonality_diamond" rel="nofollow">Wikipedia article on the tonality diamond</a></li><li><a class="wiki_link_ext" href="http://www.tonalsoft.com/enc/t/tonality-diamond.aspx" rel="nofollow">tonality diamond - arrangement of musical frequency ratios showing the dual identity of each ratio</a></li></ul></body></html></pre></div> | ||