ED5: 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:Kosmorsky|Kosmorsky]] and made on <tt>2011-10-25 14:43:09 UTC</tt>.<br>

: This revision was by author [[User:Kosmorsky|Kosmorsky]] and made on <tt>2011-10-25 14:45:58 UTC</tt>.<br>

: The original revision id was <tt>~~268456870~~</tt>.<br>

: The original revision id was <tt>268458094</tt>.<br>

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

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<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">=Division of the Fifth Harmonic (5/1) into n equal parts=

The fifth harmonic is particularly wide as far as equivalences go.<span class="commentBody"> There are (at most) ~4.3 pentaves within human hearing range; imagine if that were the case with octaves. If one does indeed deal with pentave equivalence </span>this fact shapes one's musical approach dramatically. However, perhaps the more common reason to use these scales is in approximation ~~to scales~~ with lower ~~harmonics~~ than ~~the fifth~~. This approach is highlighted by Hieronymus ([[20ed5]]) which itself is a zeta peak tuning. Other reasons for taking the nth root of 5 include finding temperaments like orwell, meantone, and thuja. This approach can of course be used indiscriminately.

The fifth harmonic is particularly wide as far as equivalences go.<span class="commentBody"> There are (at most) ~4.3 pentaves within human hearing range; imagine if that were the case with octaves. If one does indeed deal with pentave equivalence, </span>this fact shapes one's musical approach dramatically. Following this, the quintessential example of a pentave based tuning is hyperpyth (see [[17ed5]]). However, perhaps the more common reason to use these scales is in approximation with lower harmonic factors than 5. This approach is highlighted by Hieronymus ([[20ed5]]) which itself is a zeta peak tuning (not "no-fives", full on zeta). Other reasons for taking the nth root of 5 include finding temperaments like orwell, meantone, and thuja. This approach can of course be used indiscriminately.

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<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>ed5</title></head><body><h1 id="toc0"><a name="Division of the Fifth Harmonic (5/1) into n equal parts"></a>Division of the Fifth Harmonic (5/1) into n equal parts</h1>

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The fifth harmonic is particularly wide as far as equivalences go.<span class="commentBody"> There are (at most) ~4.3 pentaves within human hearing range; imagine if that were the case with octaves. If one does indeed deal with pentave equivalence </span>this fact shapes one's musical approach dramatically. However, perhaps the more common reason to use these scales is in approximation ~~to scales~~ with lower ~~harmonics~~ than ~~the fifth~~. This approach is highlighted by Hieronymus (<a class="wiki_link" href="/20ed5">20ed5</a>) which itself is a zeta peak tuning. Other reasons for taking the nth root of 5 include finding temperaments like orwell, meantone, and thuja. This approach can of course be used indiscriminately.<br />

The fifth harmonic is particularly wide as far as equivalences go.<span class="commentBody"> There are (at most) ~4.3 pentaves within human hearing range; imagine if that were the case with octaves. If one does indeed deal with pentave equivalence, </span>this fact shapes one's musical approach dramatically. Following this, the quintessential example of a pentave based tuning is hyperpyth (see <a class="wiki_link" href="/17ed5">17ed5</a>). However, perhaps the more common reason to use these scales is in approximation with lower harmonic factors than 5. This approach is highlighted by Hieronymus (<a class="wiki_link" href="/20ed5">20ed5</a>) which itself is a zeta peak tuning (not &quot;no-fives&quot;, full on zeta). Other reasons for taking the nth root of 5 include finding temperaments like orwell, meantone, and thuja. This approach can of course be used indiscriminately.<br />

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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:Kosmorsky|Kosmorsky]] and made on <tt>2011-10-25 14:43:09 UTC</tt>.<br>
+: This revision was by author [[User:Kosmorsky|Kosmorsky]] and made on <tt>2011-10-25 14:45:58 UTC</tt>.<br>
-: The original revision id was <tt>268456870</tt>.<br>
+: The original revision id was <tt>268458094</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 8: / Line 8: @@
 <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">=Division of the Fifth Harmonic (5/1) into n equal parts=
-The fifth harmonic is particularly wide as far as equivalences go.&lt;span class="commentBody"&gt; There are (at most) ~4.3 pentaves within human hearing range; imagine if that were the case with octaves. If one does indeed deal with pentave equivalence &lt;/span&gt;this fact shapes one's musical approach dramatically. However, perhaps the more common reason to use these scales is in approximation to scales with lower harmonics than the fifth. This approach is highlighted by Hieronymus ([[20ed5]]) which itself is a zeta peak tuning. Other reasons for taking the nth root of 5 include finding temperaments like orwell, meantone, and thuja. This approach can of course be used indiscriminately.
+The fifth harmonic is particularly wide as far as equivalences go.&lt;span class="commentBody"&gt; There are (at most) ~4.3 pentaves within human hearing range; imagine if that were the case with octaves. If one does indeed deal with pentave equivalence, &lt;/span&gt;this fact shapes one's musical approach dramatically. Following this, the quintessential example of a pentave based tuning is hyperpyth (see [[17ed5]]). However, perhaps the more common reason to use these scales is in approximation with lower harmonic factors than 5. This approach is highlighted by Hieronymus ([[20ed5]]) which itself is a zeta peak tuning (not "no-fives", full on zeta). Other reasons for taking the nth root of 5 include finding temperaments like orwell, meantone, and thuja. This approach can of course be used indiscriminately.
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 <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;ed5&lt;/title&gt;&lt;/head&gt;&lt;body&gt;&lt;!-- ws:start:WikiTextHeadingRule:0:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc0"&gt;&lt;a name="Division of the Fifth Harmonic (5/1) into n equal parts"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:0 --&gt;Division of the Fifth Harmonic (5/1) into n equal parts&lt;/h1&gt;
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-The fifth harmonic is particularly wide as far as equivalences go.&lt;span class="commentBody"&gt; There are (at most) ~4.3 pentaves within human hearing range; imagine if that were the case with octaves. If one does indeed deal with pentave equivalence &lt;/span&gt;this fact shapes one's musical approach dramatically. However, perhaps the more common reason to use these scales is in approximation to scales with lower harmonics than the fifth. This approach is highlighted by Hieronymus (&lt;a class="wiki_link" href="/20ed5"&gt;20ed5&lt;/a&gt;) which itself is a zeta peak tuning. Other reasons for taking the nth root of 5 include finding temperaments like orwell, meantone, and thuja. This approach can of course be used indiscriminately.&lt;br /&gt;
+The fifth harmonic is particularly wide as far as equivalences go.&lt;span class="commentBody"&gt; There are (at most) ~4.3 pentaves within human hearing range; imagine if that were the case with octaves. If one does indeed deal with pentave equivalence, &lt;/span&gt;this fact shapes one's musical approach dramatically. Following this, the quintessential example of a pentave based tuning is hyperpyth (see &lt;a class="wiki_link" href="/17ed5"&gt;17ed5&lt;/a&gt;). However, perhaps the more common reason to use these scales is in approximation with lower harmonic factors than 5. This approach is highlighted by Hieronymus (&lt;a class="wiki_link" href="/20ed5"&gt;20ed5&lt;/a&gt;) which itself is a zeta peak tuning (not &amp;quot;no-fives&amp;quot;, full on zeta). Other reasons for taking the nth root of 5 include finding temperaments like orwell, meantone, and thuja. This approach can of course be used indiscriminately.&lt;br /&gt;
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