ED5
IMPORTED REVISION FROM WIKISPACES
This is an imported revision from Wikispaces. The revision metadata is included below for reference:
- This revision was by author JosephRuhf and made on 2016-10-24 18:27:45 UTC.
- The original revision id was 596758498.
- The revision comment was:
The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.
Original Wikitext content:
=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]] 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]]
Original HTML content:
<html><head><title>ed5</title></head><body><!-- ws:start:WikiTextHeadingRule:0:<h1> --><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 "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.<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 /> 24ed5<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>