Prime number: 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:

: This revision was by author [[User:hstraub|hstraub]] and made on <tt>2012-01-26 03:48:44 UTC</tt>.

: This revision was by author [[User:hstraub|hstraub]] and made on <tt>2012-01-26 03:54:12 UTC</tt>.

: The original revision id was <tt>~~295467048~~</tt>.

: The original revision id was <tt>295467536</tt>.

: The revision comment was: <tt></tt>

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A prime edo is useful for avoiding intervals and patterns that are familiar-sounding due to their occurrence in 12edo. Since 12 is 2*2*3, it contains [[2edo]], [[3edo]], [[4edo]] and [[6edo]]. All edos with a 2, 3, 4, or 6 in their factorization will share at least one interval with 12edo, if not a whole chord or subset scale. Of course, if the goal is simply to avoid intervals of 12, then non-prime edos which don't have a 2, 3, 4, or 6 in their factorization, such as [[35edo]], will work just as well for this purpose.

If you like a certain EDO for its intervals or other reasons, but do not like its primality or non-primality, choosing another equivalence interval, such as the [[edt|tritave (3/1)]] instead of the octave, can be an option. For example, [[27edt]] is a non-prime system very similar to [[17edo]], while [[19edt|19edt (Stopper tuning)]] is a prime system very similar to the ubiquitous [[12edo]]. Anyway, for every prime EDO system there is a non-prime [[ED4]] system with identical step sizes.

If you like a certain EDO for its intervals or other reasons, but do not like its primality or non-primality, choosing another equivalence interval, such as the [[edt|tritave (3/1)]] instead of the octave, can be an option. For example, [[27edt]] is a non-prime system very similar to [[17edo]], while [[19edt|19edt (Stopper tuning)]] is a prime system very similar to the ubiquitous [[12edo]]. (See [[edt#EDO-EDT%20correspondence|EDO-EDT correspondence]] for more of these.) Anyway, for every prime EDO system there is a non-prime [[ED4]] system with identical step sizes.

The larger //n// is, the less these points matter, since the difference between an //absolutely// uniform scale and an approximated, //nearly// uniform scale eventually become inaudible.

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A prime edo is useful for avoiding intervals and patterns that are familiar-sounding due to their occurrence in 12edo. Since 12 is 2*2*3, it contains <a class="wiki_link" href="/2edo">2edo</a>, <a class="wiki_link" href="/3edo">3edo</a>, <a class="wiki_link" href="/4edo">4edo</a> and <a class="wiki_link" href="/6edo">6edo</a>. All edos with a 2, 3, 4, or 6 in their factorization will share at least one interval with 12edo, if not a whole chord or subset scale. Of course, if the goal is simply to avoid intervals of 12, then non-prime edos which don't have a 2, 3, 4, or 6 in their factorization, such as <a class="wiki_link" href="/35edo">35edo</a>, will work just as well for this purpose.

If you like a certain EDO for its intervals or other reasons, but do not like its primality or non-primality, choosing another equivalence interval, such as the <a class="wiki_link" href="/edt">tritave (3/1)</a> instead of the octave, can be an option. For example, <a class="wiki_link" href="/27edt">27edt</a> is a non-prime system very similar to <a class="wiki_link" href="/17edo">17edo</a>, while <a class="wiki_link" href="/19edt">19edt (Stopper tuning)</a> is a prime system very similar to the ubiquitous <a class="wiki_link" href="/12edo">12edo</a>. Anyway, for every prime EDO system there is a non-prime <a class="wiki_link" href="/ED4">ED4</a> system with identical step sizes.

If you like a certain EDO for its intervals or other reasons, but do not like its primality or non-primality, choosing another equivalence interval, such as the <a class="wiki_link" href="/edt">tritave (3/1)</a> instead of the octave, can be an option. For example, <a class="wiki_link" href="/27edt">27edt</a> is a non-prime system very similar to <a class="wiki_link" href="/17edo">17edo</a>, while <a class="wiki_link" href="/19edt">19edt (Stopper tuning)</a> is a prime system very similar to the ubiquitous <a class="wiki_link" href="/12edo">12edo</a>. (See <a class="wiki_link" href="/edt#EDO-EDT%20correspondence">EDO-EDT correspondence</a> for more of these.) Anyway, for every prime EDO system there is a non-prime <a class="wiki_link" href="/ED4">ED4</a> system with identical step sizes.

The larger n is, the less these points matter, since the difference between an absolutely uniform scale and an approximated, nearly uniform scale eventually become inaudible.

@@ 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:hstraub|hstraub]] and made on <tt>2012-01-26 03:48:44 UTC</tt>.<br>
+: This revision was by author [[User:hstraub|hstraub]] and made on <tt>2012-01-26 03:54:12 UTC</tt>.<br>
-: The original revision id was <tt>295467048</tt>.<br>
+: The original revision id was <tt>295467536</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>
@@ Line 21: / Line 21: @@
 A prime edo is useful for avoiding intervals and patterns that are familiar-sounding due to their occurrence in 12edo. Since 12 is 2*2*3, it contains [[2edo]], [[3edo]], [[4edo]] and [[6edo]]. All edos with a 2, 3, 4, or 6 in their factorization will share at least one interval with 12edo, if not a whole chord or subset scale. Of course, if the goal is simply to avoid intervals of 12, then non-prime edos which don't have a 2, 3, 4, or 6 in their factorization, such as [[35edo]], will work just as well for this purpose.
-If you like a certain EDO for its intervals or other reasons, but do not like its primality or non-primality, choosing another equivalence interval, such as the [[edt|tritave (3/1)]] instead of the octave, can be an option. For example, [[27edt]] is a non-prime system very similar to [[17edo]], while [[19edt|19edt (Stopper tuning)]] is a prime system very similar to the ubiquitous [[12edo]]. Anyway, for every prime EDO system there is a non-prime [[ED4]] system with identical step sizes.
+If you like a certain EDO for its intervals or other reasons, but do not like its primality or non-primality, choosing another equivalence interval, such as the [[edt|tritave (3/1)]] instead of the octave, can be an option. For example, [[27edt]] is a non-prime system very similar to [[17edo]], while [[19edt|19edt (Stopper tuning)]] is a prime system very similar to the ubiquitous [[12edo]]. (See [[edt#EDO-EDT%20correspondence|EDO-EDT correspondence]] for more of these.) Anyway, for every prime EDO system there is a non-prime [[ED4]] system with identical step sizes.
 The larger //n// is, the less these points matter, since the difference between an //absolutely// uniform scale and an approximated, //nearly// uniform scale eventually become inaudible.
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 A prime edo is useful for avoiding intervals and patterns that are familiar-sounding due to their occurrence in 12edo. Since 12 is 2*2*3, it contains &lt;a class="wiki_link" href="/2edo"&gt;2edo&lt;/a&gt;, &lt;a class="wiki_link" href="/3edo"&gt;3edo&lt;/a&gt;, &lt;a class="wiki_link" href="/4edo"&gt;4edo&lt;/a&gt; and &lt;a class="wiki_link" href="/6edo"&gt;6edo&lt;/a&gt;. All edos with a 2, 3, 4, or 6 in their factorization will share at least one interval with 12edo, if not a whole chord or subset scale. Of course, if the goal is simply to avoid intervals of 12, then non-prime edos which don't have a 2, 3, 4, or 6 in their factorization, such as &lt;a class="wiki_link" href="/35edo"&gt;35edo&lt;/a&gt;, will work just as well for this purpose.&lt;br /&gt;
 &lt;br /&gt;
-If you like a certain EDO for its intervals or other reasons, but do not like its primality or non-primality, choosing another equivalence interval, such as the &lt;a class="wiki_link" href="/edt"&gt;tritave (3/1)&lt;/a&gt; instead of the octave, can be an option. For example, &lt;a class="wiki_link" href="/27edt"&gt;27edt&lt;/a&gt; is a non-prime system very similar to &lt;a class="wiki_link" href="/17edo"&gt;17edo&lt;/a&gt;, while &lt;a class="wiki_link" href="/19edt"&gt;19edt (Stopper tuning)&lt;/a&gt; is a prime system very similar to the ubiquitous &lt;a class="wiki_link" href="/12edo"&gt;12edo&lt;/a&gt;. Anyway, for every prime EDO system there is a non-prime &lt;a class="wiki_link" href="/ED4"&gt;ED4&lt;/a&gt; system with identical step sizes.&lt;br /&gt;
+If you like a certain EDO for its intervals or other reasons, but do not like its primality or non-primality, choosing another equivalence interval, such as the &lt;a class="wiki_link" href="/edt"&gt;tritave (3/1)&lt;/a&gt; instead of the octave, can be an option. For example, &lt;a class="wiki_link" href="/27edt"&gt;27edt&lt;/a&gt; is a non-prime system very similar to &lt;a class="wiki_link" href="/17edo"&gt;17edo&lt;/a&gt;, while &lt;a class="wiki_link" href="/19edt"&gt;19edt (Stopper tuning)&lt;/a&gt; is a prime system very similar to the ubiquitous &lt;a class="wiki_link" href="/12edo"&gt;12edo&lt;/a&gt;. (See &lt;a class="wiki_link" href="/edt#EDO-EDT%20correspondence"&gt;EDO-EDT correspondence&lt;/a&gt; for more of these.) Anyway, for every prime EDO system there is a non-prime &lt;a class="wiki_link" href="/ED4"&gt;ED4&lt;/a&gt; system with identical step sizes.&lt;br /&gt;
 &lt;br /&gt;
 The larger &lt;em&gt;n&lt;/em&gt; is, the less these points matter, since the difference between an &lt;em&gt;absolutely&lt;/em&gt; uniform scale and an approximated, &lt;em&gt;nearly&lt;/em&gt; uniform scale eventually become inaudible.&lt;br /&gt;