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| <h2>IMPORTED REVISION FROM WIKISPACES</h2>
| | =Division of the Fifth Harmonic (5/1) into n equal parts= |
| This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br>
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| : This revision was by author [[User:JosephRuhf|JosephRuhf]] and made on <tt>2016-10-24 18:28:09 UTC</tt>.<br>
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| : The original revision id was <tt>596758518</tt>.<br>
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| : The revision comment was: <tt></tt><br>
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| The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.<br>
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| <h4>Original Wikitext content:</h4>
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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=
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| The fifth harmonic is particularly wide as far as equivalences go.<span class="commentBody"> There are (at absolute most) ~4.8 pentaves within the 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. | | The fifth harmonic is particularly wide as far as equivalences go.<span style=""> There are (at absolute most) ~4.8 pentaves within the 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|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|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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| | 3ed5 [[Orwell|orwell]] generator (with octaves) |
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| | 4ed5 [[Meantone|meantone]] generator (with octaves) |
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| | [[5ed5|5ed5]] [[2L_7s|thuja]] generator (with octaves) |
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| | 6ed5 [[Trienstonic_clan#Uncle|uncle]] generator (with octaves) |
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| 3ed5 [[orwell]] generator (with octaves)
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| 4ed5 [[meantone]] generator (with octaves)
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| [[5ed5]] [[2L 7s|thuja]] generator (with octaves)
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| 6ed5 [[xenharmonic/Trienstonic clan#Uncle|uncle]] generator (with octaves)
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| 7ed5 | | 7ed5 |
| [[8ed5]] | | |
| [[10ed5]] | | [[8ed5|8ed5]] |
| [[11ed5]] | | |
| | [[10ed5|10ed5]] |
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| | [[11ed5|11ed5]] |
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| 12ed5 | | 12ed5 |
| [[13ed5]] | | |
| 14ed5 compare [[6edo]] | | [[13ed5|13ed5]] |
| [[15ed5]] | | |
| 16ed5 compare [[7edo]] | | 14ed5 compare [[6edo|6edo]] |
| [[17ed5]] | | |
| [[18ed5]] | | [[15ed5|15ed5]] |
| 19ed5 compare [[Bohlen-Pierce]] | | |
| [[20ed5]] (Hieronymus Tuning) | | 16ed5 compare [[7edo|7edo]] |
| 21ed5 compare [[9edo]] | | |
| | [[17ed5|17ed5]] |
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| | [[18ed5|18ed5]] |
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| | 19ed5 compare [[Bohlen-Pierce|Bohlen-Pierce]] |
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| | [[20ed5|20ed5]] (Hieronymus Tuning) |
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| | 21ed5 compare [[9edo|9edo]] |
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| 22ed5 | | 22ed5 |
| 23ed5 compare [[10edo]] | | |
| | 23ed5 compare [[10edo|10edo]] |
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| 24ed5 | | 24ed5 |
| [[25ed5]] (Stockhausen, McLaren) | | |
| | [[25ed5|25ed5]] (Stockhausen, McLaren) |
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| 26ed5 | | 26ed5 |
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| 27ed5 | | 27ed5 |
| 28ed5 compare [[12edo]] | | |
| [[29ed5]] | | 28ed5 compare [[12edo|12edo]] |
| 30ed5 compare [[13edo]] | | |
| | [[29ed5|29ed5]] |
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| | 30ed5 compare [[13edo|13edo]] |
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| 31ed5 | | 31ed5 |
| 32ed5 compare [[14edo]] | | |
| | 32ed5 compare [[14edo|14edo]] |
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| 33ed5 | | 33ed5 |
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| 34ed5 | | 34ed5 |
| 35ed5 compare [[15edo]] | | |
| | 35ed5 compare [[15edo|15edo]] |
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| 36ed5 | | 36ed5 |
| 37ed5 compare [[16edo]]
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| 38ed5 compare [[26edt]]
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| [[39ed5]]
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| [[Pentave Reduced Harmonics]] | | 37ed5 compare [[16edo|16edo]] |
| [[Pentave Reduced Subharmonics]] | | |
| | 38ed5 compare [[26edt|26edt]] |
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| | [[39ed5|39ed5]] |
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| | [[Pentave_Reduced_Harmonics|Pentave Reduced Harmonics]] |
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| | [[Pentave_Reduced_Subharmonics|Pentave Reduced Subharmonics]] |
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| [[http://www.nonoctave.com/tuning/fifth_harmonic.html]]</pre></div>
| | [http://www.nonoctave.com/tuning/fifth_harmonic.html http://www.nonoctave.com/tuning/fifth_harmonic.html] [[Category:ed5]] |
| <h4>Original HTML content:</h4>
| | [[Category:equal]] |
| <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><!-- ws:start:WikiTextHeadingRule:0:&lt;h1&gt; --><h1 id="toc0"><a name="Division of the Fifth Harmonic (5/1) into n equal parts"></a><!-- ws:end:WikiTextHeadingRule:0 -->Division of the Fifth Harmonic (5/1) into n equal parts</h1>
| | [[Category:overview]] |
| <br />
| | [[Category:todo:add_sound_examples]] |
| The fifth harmonic is particularly wide as far as equivalences go.<span class="commentBody"> There are (at absolute most) ~4.8 pentaves within the 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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| <br />
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| 3ed5 <a class="wiki_link" href="/orwell">orwell</a> generator (with octaves)<br />
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| 4ed5 <a class="wiki_link" href="/meantone">meantone</a> generator (with octaves)<br />
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| <a class="wiki_link" href="/5ed5">5ed5</a> <a class="wiki_link" href="/2L%207s">thuja</a> generator (with octaves)<br />
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| 6ed5 <a class="wiki_link" href="http://xenharmonic.wikispaces.com/Trienstonic%20clan#Uncle">uncle</a> generator (with octaves)<br />
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| 7ed5<br />
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| <a class="wiki_link" href="/8ed5">8ed5</a><br />
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| <a class="wiki_link" href="/10ed5">10ed5</a><br />
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| <a class="wiki_link" href="/11ed5">11ed5</a><br />
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| 12ed5<br />
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| <a class="wiki_link" href="/13ed5">13ed5</a><br />
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| 14ed5 compare <a class="wiki_link" href="/6edo">6edo</a><br />
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| <a class="wiki_link" href="/15ed5">15ed5</a><br />
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| 16ed5 compare <a class="wiki_link" href="/7edo">7edo</a><br />
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| <a class="wiki_link" href="/17ed5">17ed5</a><br />
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| <a class="wiki_link" href="/18ed5">18ed5</a><br />
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| 19ed5 compare <a class="wiki_link" href="/Bohlen-Pierce">Bohlen-Pierce</a><br />
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| <a class="wiki_link" href="/20ed5">20ed5</a> (Hieronymus Tuning)<br />
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| 21ed5 compare <a class="wiki_link" href="/9edo">9edo</a><br />
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| 22ed5<br />
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| 23ed5 compare <a class="wiki_link" href="/10edo">10edo</a><br />
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| 24ed5<br />
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| <a class="wiki_link" href="/25ed5">25ed5</a> (Stockhausen, McLaren)<br />
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| 26ed5<br />
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| 27ed5<br />
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| 28ed5 compare <a class="wiki_link" href="/12edo">12edo</a><br />
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| <a class="wiki_link" href="/29ed5">29ed5</a><br />
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| 30ed5 compare <a class="wiki_link" href="/13edo">13edo</a><br />
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| 31ed5<br />
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| 32ed5 compare <a class="wiki_link" href="/14edo">14edo</a><br />
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| 33ed5<br />
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| 34ed5<br />
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| 35ed5 compare <a class="wiki_link" href="/15edo">15edo</a><br />
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| 36ed5<br />
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| 37ed5 compare <a class="wiki_link" href="/16edo">16edo</a><br />
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| 38ed5 compare <a class="wiki_link" href="/26edt">26edt</a><br />
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| <a class="wiki_link" href="/39ed5">39ed5</a><br />
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| <br />
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| <a class="wiki_link" href="/Pentave%20Reduced%20Harmonics">Pentave Reduced Harmonics</a><br />
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| <a class="wiki_link" href="/Pentave%20Reduced%20Subharmonics">Pentave Reduced Subharmonics</a><br />
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| <br />
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| <a class="wiki_link_ext" href="http://www.nonoctave.com/tuning/fifth_harmonic.html" rel="nofollow">http://www.nonoctave.com/tuning/fifth_harmonic.html</a></body></html></pre></div>
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