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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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| 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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Division of the Fifth Harmonic (5/1) into n equal parts
The fifth harmonic is particularly wide as far as equivalences go. 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, 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.
3ed5 orwell generator (with octaves)
4ed5 meantone generator (with octaves)
5ed5 thuja generator (with octaves)
6ed5 uncle generator (with octaves)
7ed5
8ed5
10ed5
11ed5
12ed5
13ed5
14ed5 compare 6edo
15ed5
16ed5 compare 7edo
17ed5
18ed5
19ed5 compare Bohlen-Pierce
20ed5 (Hieronymus Tuning)
21ed5 compare 9edo
22ed5
23ed5 compare 10edo
24ed5
25ed5 (Stockhausen, McLaren)
26ed5
27ed5
28ed5 compare 12edo
29ed5
30ed5 compare 13edo
31ed5
32ed5 compare 14edo
33ed5
34ed5
35ed5 compare 15edo
36ed5
37ed5 compare 16edo
38ed5 compare 26edt
39ed5
Pentave Reduced Harmonics
Pentave Reduced Subharmonics
http://www.nonoctave.com/tuning/fifth_harmonic.html