ED5: Difference between revisions

Revision as of 18:26, 24 October 2016

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This revision was by author JosephRuhf and made on 2016-10-24 18:26:59 UTC.

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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.<span class="commentBody"> There are (at absolute most) ~4.8 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.

3ed5 [[orwell]] generator (with octaves)
4ed5 [[meantone]] generator (with octaves)
[[5ed5]] [[2L 7s|thuja]] generator (with octaves)
6ed5 [[xenharmonic/Trienstonic clan#Uncle|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]]
[[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]]

Original HTML content:

<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>
 <br />
The fifth harmonic is particularly wide as far as equivalences go.<span class="commentBody"> There are (at absolute most) ~4.8 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 />
<br />
3ed5 <a class="wiki_link" href="/orwell">orwell</a> generator (with octaves)<br />
4ed5 <a class="wiki_link" href="/meantone">meantone</a> generator (with octaves)<br />
<a class="wiki_link" href="/5ed5">5ed5</a> <a class="wiki_link" href="/2L%207s">thuja</a> generator (with octaves)<br />
6ed5 <a class="wiki_link" href="http://xenharmonic.wikispaces.com/Trienstonic%20clan#Uncle">uncle</a> generator (with octaves)<br />
7ed5<br />
<a class="wiki_link" href="/8ed5">8ed5</a><br />
<a class="wiki_link" href="/10ed5">10ed5</a><br />
<a class="wiki_link" href="/11ed5">11ed5</a><br />
12ed5<br />
<a class="wiki_link" href="/13ed5">13ed5</a><br />
14ed5 compare <a class="wiki_link" href="/6edo">6edo</a><br />
<a class="wiki_link" href="/15ed5">15ed5</a><br />
16ed5 compare <a class="wiki_link" href="/7edo">7edo</a><br />
<a class="wiki_link" href="/17ed5">17ed5</a><br />
<a class="wiki_link" href="/18ed5">18ed5</a><br />
19ed5 compare <a class="wiki_link" href="/Bohlen-Pierce">Bohlen-Pierce</a><br />
<a class="wiki_link" href="/20ed5">20ed5</a> (Hieronymus Tuning)<br />
21ed5 compare <a class="wiki_link" href="/9edo">9edo</a><br />
22ed5<br />
23ed5 compare <a class="wiki_link" href="/10edo">10edo</a><br />
<a class="wiki_link" href="/25ed5">25ed5</a> (Stockhausen, McLaren)<br />
26ed5<br />
27ed5<br />
28ed5 compare <a class="wiki_link" href="/12edo">12edo</a><br />
<a class="wiki_link" href="/29ed5">29ed5</a><br />
30ed5 compare <a class="wiki_link" href="/13edo">13edo</a><br />
31ed5<br />
32ed5 compare <a class="wiki_link" href="/14edo">14edo</a><br />
33ed5<br />
34ed5<br />
35ed5 compare <a class="wiki_link" href="/15edo">15edo</a><br />
36ed5<br />
37ed5 compare <a class="wiki_link" href="/16edo">16edo</a><br />
38ed5 compare <a class="wiki_link" href="/26edt">26edt</a><br />
<a class="wiki_link" href="/39ed5">39ed5</a><br />
<br />
<a class="wiki_link" href="/Pentave%20Reduced%20Harmonics">Pentave Reduced Harmonics</a><br />
<a class="wiki_link" href="/Pentave%20Reduced%20Subharmonics">Pentave Reduced Subharmonics</a><br />
<br />
<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>

ED5: Difference between revisions

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IMPORTED REVISION FROM WIKISPACES

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