This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br>
| en = Prime number
: This revision was by author [[User:xenwolf|xenwolf]] and made on <tt>2011-06-29 09:21:47 UTC</tt>.<br>
| de = Primzahlen
: The original revision id was <tt>239309681</tt>.<br>
| es =
: The revision comment was: <tt></tt><br>
| ja = 素数
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| ro = numere prime
<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">todo: add something useful about prime numbers for musicians, composers, microtonalists, xenharmonicians, theorists here.
{{Wikipedia}}
== The first "Prime edos" ==
A '''prime number''' is an integer (whole number) greater than one that is divisible only by itself and one. There are an infinite number of prime numbers, the first few of which are 2, 3, 5, 7, 11, 13, ….
Prime [[edo]]s inherit most of its properties to its multiple edos. The children can often more, but they lose in handiness compared to their parents.
By the {{w|fundamental theorem of arithmetic}}, any [[ratio]] can be uniquely represented by a product of prime numbers through prime factorization. It enables the notation of ratios as [[monzo]]s.
A prime equal division is an [[equal-step tuning]] that divides a given [[interval]] into a prime number of pitches. They are notable because of many interesting properties.
== Coprime numbers ==
{{Wikipedia|Coprime integers}}
Two integers are '''coprime''' if they have no divisor in common except 1.
== See also ==
== See also ==
* [[The Prime Harmonic Series]]
* [[Prime harmonic series]]
* [[Monzo]] - an alternative notation for interval ratios
* [[Harmonic limit]]
* [[prime limit]] or [[Harmonic Limit]]
* [[List of integer factorizations]]
== External links ==
* [http://www.arndt-bruenner.de/mathe/scripts/primzahlen.htm Die Primzahlseite] (German) by Arndt Brünner (helpful tools for prime factorization and ~test)
== Links ==
[[Category:Prime| ]] <!-- main article -->
* [[http://www.arndt-bruenner.de/mathe/scripts/primzahlen.htm|Die Primzahlseite]] (German) by Arndt Brünner (helpful tools for prime factorization and ~test)
[[Category:Elementary math]]
* [[http://en.wikipedia.org/wiki/Prime_number|Prime number]] the Wikipedia article</pre></div>
[[Category:Terms]]
<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>prime numbers</title></head><body>todo: add something useful about prime numbers for musicians, composers, microtonalists, xenharmonicians, theorists here.<br />
<br />
<!-- ws:start:WikiTextHeadingRule:0:&lt;h2&gt; --><h2 id="toc0"><a name="x-The first &quot;Prime edos&quot;"></a><!-- ws:end:WikiTextHeadingRule:0 --> The first &quot;Prime edos&quot; </h2>
Prime <a class="wiki_link" href="/edo">edo</a>s inherit most of its properties to its multiple edos. The children can often more, but they lose in handiness compared to their parents.<br />
<!-- ws:start:WikiTextHeadingRule:2:&lt;h2&gt; --><h2 id="toc1"><a name="x-See also"></a><!-- ws:end:WikiTextHeadingRule:2 --> See also </h2>
<ul><li><a class="wiki_link" href="/The%20Prime%20Harmonic%20Series">The Prime Harmonic Series</a></li><li><a class="wiki_link" href="/Monzo">Monzo</a> - an alternative notation for interval ratios</li><li><a class="wiki_link" href="/prime%20limit">prime limit</a> or <a class="wiki_link" href="/Harmonic%20Limit">Harmonic Limit</a></li></ul><br />
<ul><li><a class="wiki_link_ext" href="http://www.arndt-bruenner.de/mathe/scripts/primzahlen.htm" rel="nofollow">Die Primzahlseite</a> (German) by Arndt Brünner (helpful tools for prime factorization and ~test)</li><li><a class="wiki_link_ext" href="http://en.wikipedia.org/wiki/Prime_number" rel="nofollow">Prime number</a> the Wikipedia article</li></ul></body></html></pre></div>
A prime number is an integer (whole number) greater than one that is divisible only by itself and one. There are an infinite number of prime numbers, the first few of which are 2, 3, 5, 7, 11, 13, ….
By the fundamental theorem of arithmetic, any ratio can be uniquely represented by a product of prime numbers through prime factorization. It enables the notation of ratios as monzos.
A prime equal division is an equal-step tuning that divides a given interval into a prime number of pitches. They are notable because of many interesting properties.
