Monzos and interval space: Difference between revisions
Wikispaces>xenwolf **Imported revision 146156308 - Original comment: ** |
Wikispaces>xenwolf **Imported revision 146156350 - 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>2010-06-01 02:56: | : This revision was by author [[User:xenwolf|xenwolf]] and made on <tt>2010-06-01 02:56:40 UTC</tt>.<br> | ||
: The original revision id was <tt> | : The original revision id was <tt>146156350</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">A [[Harmonic Limit|p-limit]] rational number q can by definition be factored into primes of size less than or equal to p, giving q = 2^e2 3^e3 ... p^ep, where the exponents are integers (positive, negative, or zero.) This is often written in [[http://mathworld.wolfram.com/Ket.html|ket vector]]([[http://en.wikipedia.org/wiki/Bra-ket_notation|wp]]) notation as |e2 e3 ... ep>, in which case it is called a **monzo**, where the name refers to the enthusiastic advocacy of [[Joe Monzo]]. | <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">A [[Harmonic Limit|p-limit]] rational number q can by definition be factored into primes of size less than or equal to p, giving q = 2^e2 3^e3 ... p^ep, where the exponents are integers (positive, negative, or zero.) This is often written in [[http://mathworld.wolfram.com/Ket.html|ket vector]] ([[http://en.wikipedia.org/wiki/Bra-ket_notation|wp]]) notation as |e2 e3 ... ep>, in which case it is called a **monzo**, where the name refers to the enthusiastic advocacy of [[Joe Monzo]]. | ||
The [[Tenney Height|Tenney height]] of this monzo is given by | The [[Tenney Height|Tenney height]] of this monzo is given by | ||
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and if the coordinates are the standard interval space coordinates, then the Euclidean norm is the [[http://mathworld.wolfram.com/L2-Norm.html|standard Euclidean, or L2, norm]].</pre></div> | and if the coordinates are the standard interval space coordinates, then the Euclidean norm is the [[http://mathworld.wolfram.com/L2-Norm.html|standard Euclidean, or L2, norm]].</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>Monzos and Interval Space</title></head><body>A <a class="wiki_link" href="/Harmonic%20Limit">p-limit</a> rational number q can by definition be factored into primes of size less than or equal to p, giving q = 2^e2 3^e3 ... p^ep, where the exponents are integers (positive, negative, or zero.) This is often written in <a class="wiki_link_ext" href="http://mathworld.wolfram.com/Ket.html" rel="nofollow">ket vector</a>(<a class="wiki_link_ext" href="http://en.wikipedia.org/wiki/Bra-ket_notation" rel="nofollow">wp</a>) notation as |e2 e3 ... ep&gt;, in which case it is called a <strong>monzo</strong>, where the name refers to the enthusiastic advocacy of <a class="wiki_link" href="/Joe%20Monzo">Joe Monzo</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>Monzos and Interval Space</title></head><body>A <a class="wiki_link" href="/Harmonic%20Limit">p-limit</a> rational number q can by definition be factored into primes of size less than or equal to p, giving q = 2^e2 3^e3 ... p^ep, where the exponents are integers (positive, negative, or zero.) This is often written in <a class="wiki_link_ext" href="http://mathworld.wolfram.com/Ket.html" rel="nofollow">ket vector</a> (<a class="wiki_link_ext" href="http://en.wikipedia.org/wiki/Bra-ket_notation" rel="nofollow">wp</a>) notation as |e2 e3 ... ep&gt;, in which case it is called a <strong>monzo</strong>, where the name refers to the enthusiastic advocacy of <a class="wiki_link" href="/Joe%20Monzo">Joe Monzo</a>.<br /> | ||
<br /> | <br /> | ||
The <a class="wiki_link" href="/Tenney%20Height">Tenney height</a> of this monzo is given by<br /> | The <a class="wiki_link" href="/Tenney%20Height">Tenney height</a> of this monzo is given by<br /> | ||