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<h2>IMPORTED REVISION FROM WIKISPACES</h2>
An '''equal division of the 5th harmonic''' ('''ed5''') is a [[tuning]] obtained by dividing the [[5/1|5th harmonic]] in a certain number of [[equal]] steps.
This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br>
: This revision was by author [[User:JosephRuhf|JosephRuhf]] and made on <tt>2016-10-24 18:26:59 UTC</tt>.<br>
: The original revision id was <tt>596758458</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>
<h4>Original Wikitext content:</h4>
<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 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, &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.
The 5th harmonic, quintuple, or pentave, is particularly wide as far as [[equivalence]]s go, as there are at absolute most about 4.8 instances of the 5th harmonic within the [[human hearing range]]. If one does indeed deal with equivalence of the 5th harmonic, this range restriction is a crucial consideration.  


3ed5 [[orwell]] generator (with octaves)
One way to treat 5/1 as an equivalence is by eliminating the [[prime harmonics|primes]] [[2/1|2]] and [[3/1|3]]. The most fundamental chord in this paradigm is [[5:7:11]]. This chord can be approximated in a 5.7.11-subgroup [[regular temperament]] by eliminating the comma 859375/823543, equating a stack of seven [[7/5]] generators with [[11/5]]. Other equivalences that could be used for such no-2's no-3's music include [[ed11/5|equal divisions of 11/5]] and [[ed11/7|equal divisions of 11/7]].
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]]
The quintessential example of a 5th-harmonic based tuning is [[hyperpyth]] (see [[17ed5]]). However, perhaps the more common reason to use these systems 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-5's", full on zeta).
[[Pentave Reduced Subharmonics]]


[[http://www.nonoctave.com/tuning/fifth_harmonic.html]]</pre></div>
== As generator chains for temperaments ==
<h4>Original HTML content:</h4>
One reason for taking the ''n''-th root of 5 include finding temperaments like [[orwell]], [[meantone]], and [[thuja]]. This approach can of course be used indiscriminately. The ed5's serve as generator chains for
<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;
 
&lt;br /&gt;
* [[3ed5]] – [[orwell]] generator
The fifth harmonic is particularly wide as far as equivalences go.&lt;span class="commentBody"&gt; 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, &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;
* [[4ed5]] – [[meantone]] generator
&lt;br /&gt;
* [[5ed5]] – [[thuja]] generator
3ed5 &lt;a class="wiki_link" href="/orwell"&gt;orwell&lt;/a&gt; generator (with octaves)&lt;br /&gt;
* [[6ed5]] – [[uncle]] generator
4ed5 &lt;a class="wiki_link" href="/meantone"&gt;meantone&lt;/a&gt; generator (with octaves)&lt;br /&gt;
* [[8ed5]] – [[mohajira]] generator
&lt;a class="wiki_link" href="/5ed5"&gt;5ed5&lt;/a&gt; &lt;a class="wiki_link" href="/2L%207s"&gt;thuja&lt;/a&gt; generator (with octaves)&lt;br /&gt;
* [[Hyperpyth]] tuning (e.g. [[17ed5]])
6ed5 &lt;a class="wiki_link" href="http://xenharmonic.wikispaces.com/Trienstonic%20clan#Uncle"&gt;uncle&lt;/a&gt; generator (with octaves)&lt;br /&gt;
* [[20ed5]] – Hieronymus Tuning
7ed5&lt;br /&gt;
* [[25ed5]] – Stockhausen, McLaren
&lt;a class="wiki_link" href="/8ed5"&gt;8ed5&lt;/a&gt;&lt;br /&gt;
 
&lt;a class="wiki_link" href="/10ed5"&gt;10ed5&lt;/a&gt;&lt;br /&gt;
== Individual pages for ed5's ==
&lt;a class="wiki_link" href="/11ed5"&gt;11ed5&lt;/a&gt;&lt;br /&gt;
{| class="wikitable center-all"
12ed5&lt;br /&gt;
|+ style=white-space:nowrap | 0…99
&lt;a class="wiki_link" href="/13ed5"&gt;13ed5&lt;/a&gt;&lt;br /&gt;
| [[0ed5|0]]
14ed5 compare &lt;a class="wiki_link" href="/6edo"&gt;6edo&lt;/a&gt;&lt;br /&gt;
| [[1ed5|1]]
&lt;a class="wiki_link" href="/15ed5"&gt;15ed5&lt;/a&gt;&lt;br /&gt;
| [[2ed5|2]]
16ed5 compare &lt;a class="wiki_link" href="/7edo"&gt;7edo&lt;/a&gt;&lt;br /&gt;
| [[3ed5|3]]
&lt;a class="wiki_link" href="/17ed5"&gt;17ed5&lt;/a&gt;&lt;br /&gt;
| [[4ed5|4]]
&lt;a class="wiki_link" href="/18ed5"&gt;18ed5&lt;/a&gt;&lt;br /&gt;
| [[5ed5|5]]
19ed5 compare &lt;a class="wiki_link" href="/Bohlen-Pierce"&gt;Bohlen-Pierce&lt;/a&gt;&lt;br /&gt;
| [[6ed5|6]]
&lt;a class="wiki_link" href="/20ed5"&gt;20ed5&lt;/a&gt; (Hieronymus Tuning)&lt;br /&gt;
| [[7ed5|7]]
21ed5 compare &lt;a class="wiki_link" href="/9edo"&gt;9edo&lt;/a&gt;&lt;br /&gt;
| [[8ed5|8]]
22ed5&lt;br /&gt;
| [[9ed5|9]]
23ed5 compare &lt;a class="wiki_link" href="/10edo"&gt;10edo&lt;/a&gt;&lt;br /&gt;
|-
&lt;a class="wiki_link" href="/25ed5"&gt;25ed5&lt;/a&gt; (Stockhausen, McLaren)&lt;br /&gt;
| [[10ed5|10]]
26ed5&lt;br /&gt;
| [[11ed5|11]]
27ed5&lt;br /&gt;
| [[12ed5|12]]
28ed5 compare &lt;a class="wiki_link" href="/12edo"&gt;12edo&lt;/a&gt;&lt;br /&gt;
| [[13ed5|13]]
&lt;a class="wiki_link" href="/29ed5"&gt;29ed5&lt;/a&gt;&lt;br /&gt;
| [[14ed5|14]]
30ed5 compare &lt;a class="wiki_link" href="/13edo"&gt;13edo&lt;/a&gt;&lt;br /&gt;
| [[15ed5|15]]
31ed5&lt;br /&gt;
| [[16ed5|16]]
32ed5 compare &lt;a class="wiki_link" href="/14edo"&gt;14edo&lt;/a&gt;&lt;br /&gt;
| [[17ed5|17]]
33ed5&lt;br /&gt;
| [[18ed5|18]]
34ed5&lt;br /&gt;
| [[19ed5|19]]
35ed5 compare &lt;a class="wiki_link" href="/15edo"&gt;15edo&lt;/a&gt;&lt;br /&gt;
|-
36ed5&lt;br /&gt;
| [[20ed5|20]]
37ed5 compare &lt;a class="wiki_link" href="/16edo"&gt;16edo&lt;/a&gt;&lt;br /&gt;
| [[21ed5|21]]
38ed5 compare &lt;a class="wiki_link" href="/26edt"&gt;26edt&lt;/a&gt;&lt;br /&gt;
| [[22ed5|22]]
&lt;a class="wiki_link" href="/39ed5"&gt;39ed5&lt;/a&gt;&lt;br /&gt;
| [[23ed5|23]]
&lt;br /&gt;
| [[24ed5|24]]
&lt;a class="wiki_link" href="/Pentave%20Reduced%20Harmonics"&gt;Pentave Reduced Harmonics&lt;/a&gt;&lt;br /&gt;
| [[25ed5|25]]
&lt;a class="wiki_link" href="/Pentave%20Reduced%20Subharmonics"&gt;Pentave Reduced Subharmonics&lt;/a&gt;&lt;br /&gt;
| [[26ed5|26]]
&lt;br /&gt;
| [[27ed5|27]]
&lt;a class="wiki_link_ext" href="http://www.nonoctave.com/tuning/fifth_harmonic.html" rel="nofollow"&gt;http://www.nonoctave.com/tuning/fifth_harmonic.html&lt;/a&gt;&lt;/body&gt;&lt;/html&gt;</pre></div>
| [[28ed5|28]]
| [[29ed5|29]]
|-
| [[30ed5|30]]
| [[31ed5|31]]
| [[32ed5|32]]
| [[33ed5|33]]
| [[34ed5|34]]
| [[35ed5|35]]
| [[36ed5|36]]
| [[37ed5|37]]
| [[38ed5|38]]
| [[39ed5|39]]
|-
| [[40ed5|40]]
| [[41ed5|41]]
| [[42ed5|42]]
| [[43ed5|43]]
| [[44ed5|44]]
| [[45ed5|45]]
| [[46ed5|46]]
| [[47ed5|47]]
| [[48ed5|48]]
| [[49ed5|49]]
|-
| [[50ed5|50]]
| [[51ed5|51]]
| [[52ed5|52]]
| [[53ed5|53]]
| [[54ed5|54]]
| [[55ed5|55]]
| [[56ed5|56]]
| [[57ed5|57]]
| [[58ed5|58]]
| [[59ed5|59]]
|-
| [[60ed5|60]]
| [[61ed5|61]]
| [[62ed5|62]]
| [[63ed5|63]]
| [[64ed5|64]]
| [[65ed5|65]]
| [[66ed5|66]]
| [[67ed5|67]]
| [[68ed5|68]]
| [[69ed5|69]]
|-
| [[70ed5|70]]
| [[71ed5|71]]
| [[72ed5|72]]
| [[73ed5|73]]
| [[74ed5|74]]
| [[75ed5|75]]
| [[76ed5|76]]
| [[77ed5|77]]
| [[78ed5|78]]
| [[79ed5|79]]
|-
| [[80ed5|80]]
| [[81ed5|81]]
| [[82ed5|82]]
| [[83ed5|83]]
| [[84ed5|84]]
| [[85ed5|85]]
| [[86ed5|86]]
| [[87ed5|87]]
| [[88ed5|88]]
| [[89ed5|89]]
|-
| [[90ed5|90]]
| [[91ed5|91]]
| [[92ed5|92]]
| [[93ed5|93]]
| [[94ed5|94]]
| [[95ed5|95]]
| [[96ed5|96]]
| [[97ed5|97]]
| [[98ed5|98]]
| [[99ed5|99]]
|}
 
; 100 and beyond
* [[116ed5|116]], [[139ed5|139]], [[175ed5|175]], [[256ed5|256]]
 
<!-- Uncomment this when there are more pages
{| class="wikitable center-all mw-collapsible mw-collapsed"
|+ style=white-space:nowrap | 100…199
| [[100ed5|100]]
| [[101ed5|101]]
| [[102ed5|102]]
| [[103ed5|103]]
| [[104ed5|104]]
| [[105ed5|105]]
| [[106ed5|106]]
| [[107ed5|107]]
| [[108ed5|108]]
| [[109ed5|109]]
|-
| [[110ed5|110]]
| [[111ed5|111]]
| [[112ed5|112]]
| [[113ed5|113]]
| [[114ed5|114]]
| [[115ed5|115]]
| [[116ed5|116]]
| [[117ed5|117]]
| [[118ed5|118]]
| [[119ed5|119]]
|-
| [[120ed5|120]]
| [[121ed5|121]]
| [[122ed5|122]]
| [[123ed5|123]]
| [[124ed5|124]]
| [[125ed5|125]]
| [[126ed5|126]]
| [[127ed5|127]]
| [[128ed5|128]]
| [[129ed5|129]]
|-
| [[130ed5|130]]
| [[131ed5|131]]
| [[132ed5|132]]
| [[133ed5|133]]
| [[134ed5|134]]
| [[135ed5|135]]
| [[136ed5|136]]
| [[137ed5|137]]
| [[138ed5|138]]
| [[139ed5|139]]
|-
| [[140ed5|140]]
| [[141ed5|141]]
| [[142ed5|142]]
| [[143ed5|143]]
| [[144ed5|144]]
| [[145ed5|145]]
| [[146ed5|146]]
| [[147ed5|147]]
| [[148ed5|148]]
| [[149ed5|149]]
|-
| [[150ed5|150]]
| [[151ed5|151]]
| [[152ed5|152]]
| [[153ed5|153]]
| [[154ed5|154]]
| [[155ed5|155]]
| [[156ed5|156]]
| [[157ed5|157]]
| [[158ed5|158]]
| [[159ed5|159]]
|-
| [[160ed5|160]]
| [[161ed5|161]]
| [[162ed5|162]]
| [[163ed5|163]]
| [[164ed5|164]]
| [[165ed5|165]]
| [[166ed5|166]]
| [[167ed5|167]]
| [[168ed5|168]]
| [[169ed5|169]]
|-
| [[170ed5|170]]
| [[171ed5|171]]
| [[172ed5|172]]
| [[173ed5|173]]
| [[174ed5|174]]
| [[175ed5|175]]
| [[176ed5|176]]
| [[177ed5|177]]
| [[178ed5|178]]
| [[179ed5|179]]
|-
| [[180ed5|180]]
| [[181ed5|181]]
| [[182ed5|182]]
| [[183ed5|183]]
| [[184ed5|184]]
| [[185ed5|185]]
| [[186ed5|186]]
| [[187ed5|187]]
| [[188ed5|188]]
| [[189ed5|189]]
|-
| [[190ed5|190]]
| [[191ed5|191]]
| [[192ed5|192]]
| [[193ed5|193]]
| [[194ed5|194]]
| [[195ed5|195]]
| [[196ed5|196]]
| [[197ed5|197]]
| [[198ed5|198]]
| [[199ed5|199]]
|}
{| class="wikitable center-all mw-collapsible mw-collapsed"
|+ style=white-space:nowrap | 200…299
| [[200ed5|200]]
| [[201ed5|201]]
| [[202ed5|202]]
| [[203ed5|203]]
| [[204ed5|204]]
| [[205ed5|205]]
| [[206ed5|206]]
| [[207ed5|207]]
| [[208ed5|208]]
| [[209ed5|209]]
|-
| [[210ed5|210]]
| [[211ed5|211]]
| [[212ed5|212]]
| [[213ed5|213]]
| [[214ed5|214]]
| [[215ed5|215]]
| [[216ed5|216]]
| [[217ed5|217]]
| [[218ed5|218]]
| [[219ed5|219]]
|-
| [[220ed5|220]]
| [[221ed5|221]]
| [[222ed5|222]]
| [[223ed5|223]]
| [[224ed5|224]]
| [[225ed5|225]]
| [[226ed5|226]]
| [[227ed5|227]]
| [[228ed5|228]]
| [[229ed5|229]]
|-
| [[230ed5|230]]
| [[231ed5|231]]
| [[232ed5|232]]
| [[233ed5|233]]
| [[234ed5|234]]
| [[235ed5|235]]
| [[236ed5|236]]
| [[237ed5|237]]
| [[238ed5|238]]
| [[239ed5|239]]
|-
| [[240ed5|240]]
| [[241ed5|241]]
| [[242ed5|242]]
| [[243ed5|243]]
| [[244ed5|244]]
| [[245ed5|245]]
| [[246ed5|246]]
| [[247ed5|247]]
| [[248ed5|248]]
| [[249ed5|249]]
|-
| [[250ed5|250]]
| [[251ed5|251]]
| [[252ed5|252]]
| [[253ed5|253]]
| [[254ed5|254]]
| [[255ed5|255]]
| [[256ed5|256]]
| [[257ed5|257]]
| [[258ed5|258]]
| [[259ed5|259]]
|-
| [[260ed5|260]]
| [[261ed5|261]]
| [[262ed5|262]]
| [[263ed5|263]]
| [[264ed5|264]]
| [[265ed5|265]]
| [[266ed5|266]]
| [[267ed5|267]]
| [[268ed5|268]]
| [[269ed5|269]]
|-
| [[270ed5|270]]
| [[271ed5|271]]
| [[272ed5|272]]
| [[273ed5|273]]
| [[274ed5|274]]
| [[275ed5|275]]
| [[276ed5|276]]
| [[277ed5|277]]
| [[278ed5|278]]
| [[279ed5|279]]
|-
| [[280ed5|280]]
| [[281ed5|281]]
| [[282ed5|282]]
| [[283ed5|283]]
| [[284ed5|284]]
| [[285ed5|285]]
| [[286ed5|286]]
| [[287ed5|287]]
| [[288ed5|288]]
| [[289ed5|289]]
|-
| [[290ed5|290]]
| [[291ed5|291]]
| [[292ed5|292]]
| [[293ed5|293]]
| [[294ed5|294]]
| [[295ed5|295]]
| [[296ed5|296]]
| [[297ed5|297]]
| [[298ed5|298]]
| [[299ed5|299]]
|}
-->
 
== Ed5–edo correspondence ==
Following ed5's (up to 339) contain good correspondences to edo tunings<ref>Edo with relative error of 5th harmonic below 1/3</ref>.
 
{| class="wikitable center-1 center-2"
|-
! Ed5
! Edo
! Comments
|-
| [[7ed5]]
| [[3edo]]
| 7ed5 is 3edo with ~5.9 cent compressed octaves. Equivalently, 3edo is 7ed5 with pentaves stretched by ~13.7 cents. Patent vals match through the 67-limit.
|-
| [[9ed5]]
| [[4edo]]
| Very rough correspondence (~38 cent octave stretch), but patent vals agree through the 7-limit.
|-
| [[14ed5]]
| [[6edo]]
| Same 5.9 cent octave compression as 7ed5~3edo. Patent vals agree through the 17-limit.
|-
| [[16ed5]]
| [[7edo]]
|  Only rough correspondence (~19 cent octave stretch). Patent vals differ in the 7-limit.
|-
| [[21ed5]]
| [[9edo]]
| Same 5.9 cent octave compression as 7ed5~3edo. Patent vals agree through the 59-limit.
|-
| [[23ed5]]
| [[10edo]]
|  23ed5 is 10edo with ~11 cent stretched octaves. Patent vals match through the 23-limit, with the exception of 11 and 17.
|-
| [[28ed5]]
| [[12edo]]
| Same 5.9 cent octave compression as 7ed5~3edo. Patent vals match through the 19-limit, with the exception of 13 (as expected).
|-
| [[30ed5]]
| [[13edo]]
| 30ed5 is 13edo with ~7.4 cent stretched octaves. Patent vals match through the 19-limit, with the exception of 3 (which neither represents well).
|-
| [[35ed5]]
| [[15edo]]
| Same 5.9 cent octave compression as 7ed5~3edo. Patent vals agree through the 13-limit.
|-
| [[37ed5]]
| [[16edo]]
| 37ed5 is 16edo with ~4.9 cent stretched octaves. Patent vals match through the 23-limit.
|-
| [[42ed5]]
| [[18edo]]
| Same 5.9 cent octave compression as 7ed5~3edo. Patent vals match through the 17-limit, with the exception of 11.
|-
| [[44ed5]]
| [[19edo]]
| 44ed5 is 19edo with ~3.2 cent stretched octaves. Patent vals match through the 13-limit.
|-
| [[49ed5]]
| [[21edo]]
| Same 5.9 cent octave compression as 7ed5~3edo. Patent vals agree through the 17-limit.
|-
| [[51ed5]]
| [[22edo]]
| 51ed5 is 22edo with ~1.9 cent stretched octaves. Patent vals match through the 19-limit.
|-
|  [[56ed5]]
|  [[24edo]]
|  This is a rough correspondence, as the (7n)ed5 ~ (3n)edo sequence begins to break down. Patent vals match through the 13-limit, with the exception of 7.
|-
| [[58ed5]]
| [[25edo]]
| 58ed5 is 25edo with ~1.0 cent stretched octaves. Patent vals match through the 73-limit, with the exception of 13.
|-
| [[63ed5]]
| [[27edo]]
| This is a rough correspondence, but the (7n)ed5 ~ (3n)edo sequence is momentarily fixed. Patent vals match through the 13-limit.
|-
| [[65ed5]]
| [[28edo]]
| 65ed5 is 28edo with ~0.26 cent stretched octaves. Patent vals match through the 43-limit.
|-
| [[72ed5]]
| [[31edo]]
| 72ed5 is 31edo with ~0.34 cent compressed octaves. Patent vals match through the 31-limit.
|-
| [[74ed5]]
| [[32edo]]
| Same 4.9 cent octave stretch as 37ed5~16edo. Patent vals match through the 13-limit with the exception of 7 and 11.
|-
| [[79ed5]]
| [[34edo]]
| 79ed5 is 34edo with ~0.83 cent compressed octaves. Patent vals match through the 17-limit, with the exception of 7 (which neither represents well).
|-
| [[81ed5]]
| [[35edo]]
| 81ed5 is 35edo with ~4.0 cent stretched octaves. Patent vals match through the 11-limit.
|-
| [[84ed5]]
| [[36edo]]
| Same 5.9 cent octave compression as 7ed5~3edo. Patent vals match through the 11-limit, with the exception of 7.
|-
| [[86ed5]]
| [[37edo]]
| 86ed5 is 37edo with ~1.2 cent compressed octaves. Patent vals match through the 19-limit.
|-
| [[88ed5]]
| [[38edo]]
| Same 3.2 cent octave stretch as 44ed5~19edo. Patent vals differ in the 7-limit.
|-
| [[93ed5]]
| [[40edo]]
| 93ed5 is 40edo with ~1.6 cent compressed octaves. Patent vals match through the 7-limit.
|-
| [[95ed5]]
| [[41edo]]
| 95ed5 is 41edo with ~2.5 cent stretched octaves. Patent vals match through the 11-limit.
|-
| [[100ed5]]
| [[43edo]]
| 100ed5 is 43edo with ~1.9 cent compressed octaves. Patent vals match through the 37-limit.
|-
| [[102ed5]]
| [[44edo]]
| Same 1.9 cent octave stretch as 51ed5~22edo. Patent vals match through the 23-limit, with the exception of 7.
|-
| [[107ed5]]
| [[46edo]]
| 107ed5 is 46edo with ~2.1 cent compressed octaves. Patent vals match through the 11-limit.
|-
| [[109ed5]]
| [[47edo]]
| 109ed5 is 47edo with ~1.4 cent stretched octaves. Patent vals match through the 17-limit, with the exception of 11.
|-
| [[114ed5]]
| [[49edo]]
| 114ed5 is 49edo with ~2.4 cent compressed octaves. Patent vals match through the 11-limit.
|-
| [[116ed5]]
| [[50edo]]
| Same 1.0 cent octave stretch as 58ed5~25edo. Patent vals agree through the 43-limit.
|-
| [[121ed5]]
| [[52edo]]
| 121ed5 is 52edo with ~2.6 cent compressed octaves, but the correspondence is rough. Patent vals match through the 11-limit, with the exception of 3 (which neither represents well).
|-
| [[123ed5]]
|  [[53edo]]
| 123ed5 is 53edo with ~0.61 cent stretched octaves. Patent vals match through the 29-limit.
|-
| [[128ed5]]
| [[55edo]]
| 128ed5 is 55edo with ~2.8 cent compressed octaves, but the correspondence is rough. Patent vals differ in the 7-limit.
|-
| [[130ed5]]
| [[56edo]]
| Same 0.26 cent octave stretch as 65ed5~28edo. Patent vals agree through the 103-limit.
|-
| [[135ed5]]
| [[58edo]]
| 135ed5 is 58edo with ~2.9 cent compressed octaves. Patent vals match through the 13-limit.
|-
| [[137ed5]]
| [[59edo]]
| 137ed5 is 59edo with ~0.05 cent compressed octaves. Patent vals match through the 179-limit.
|-
| [[139ed5]]
| [[60edo]]
| 139ed5 is 60edo with ~2.7 cent stretched octaves. Pantent vals match through the 31-limit with the exception of 11.
|-
| [[144ed5]]
| [[62edo]]
| Same 0.34 cent octave compression as 72ed5~31edo. Patent vals match through the 19-limit, with the exception of 11.
|-
| [[146ed5]]
| [[63edo]]
| 146ed5 is 63edo with ~2.3 cent stretched octaves. Patent vals match through the 13-limit.
|-
| [[151ed5]]
| [[65edo]]
| 151ed5 is 65edo with ~0.59 cent compressed octaves. Patent vals match through the 53-limit, with the exception of 7 (as expected).
|-
| [[153ed5]]
| [[66edo]]
| Same 1.9 cent octave stretch as 51ed5~22edo. Patent vals match through the 13-limit, with the exception of 3.
|-
| [[158ed5]]
| [[68edo]]
| Same 0.83 cent octave compression as 79ed5~34edo. Patent vals agree through the 23-limit.
|-
| [[160ed5]]
| [[69edo]]
| 160ed5 is 69edo with ~1.6 cent stretched octaves. Patent vals differ in the 7-limit.
|-
| [[165ed5]]
| [[71edo]]
| 165ed5 is 71edo with ~1.0 cent compressed octaves. Patent vals match through the 37-limit.
|-
| [[167ed5]]
| [[72edo]]
| 167ed5 is 72edo with ~1.3 cent stretched octaves. Patent vals agree through the 19-limit.
|-
| [[172ed5]]
| [[74edo]]
| Same 1.2 cent octave compression as 86ed5~37edo. Patent vals agree through the 13-limit.
|-
| [[174ed5]]
| [[75edo]]
| Same 1.0 cent octave stretch as 58ed5~25edo. Patent vals differ in the 7-limit.
|-
| [[179ed5]]
| [[77edo]]
| 179ed5 is 77edo with ~1.4 cent compressed octaves. Patent vals match through the 19-limit, with the exception of 11.
|-
| [[181ed5]]
| [[78edo]]
| 181ed5 is 78edo with ~0.73 cent stretched octaves. Patent vals match through the 59-limit, with the exception of 13.
|-
| [[186ed5]]
| [[80edo]]
| Same 1.6 cent octave compression as 93ed5~40edo. Patent vals agree through the 29-limit.
|-
| [[188ed5]]
| [[81edo]]
| 188ed5 is 81edo with ~0.49 cent stretched octaves. Patent vals match through the 41-limit.
|-
| [[193ed5]]
| [[83edo]]
|  193ed5 is 83edo with ~1.7 cent compressed octaves. Patent vals match through the 7-limit.
|-
| [[195ed5]]
| [[84edo]]
|  Same 0.26 cent octave stretch as 65ed5~28edo. Patent vals agree through the 31-limit.
|-
| [[200ed5]]
| [[86edo]]
|  Same 1.9 cent octeave compression as 100ed5~43edo. Patent vals match alternate primes through the 17-limit.
|-
| [[202ed5]]
| [[87edo]]
| 202ed5 is 87edo with ~0.05 cent stretched octaves. Patent vals match through the 71-limit.
|-
| [[204ed5]]
| [[88edo]]
| Same 1.9 cent octave stretch as 51ed5~22edo. Patent vals match through the 7-limit.
|-
| [[209ed5]]
| [[90edo]]
| 209ed5 is 90edo with ~0.15 cent compressed octaves. Patent vals match through the 53-limit.
|-
| [[211ed5]]
| [[91edo]]
| 211ed5 is 91edo with ~1.7 cent stretched octaves. Patent vals match through the 7-limit.
|-
| [[216ed5]]
| [[93edo]]
| Same 0.34 cent octave compression as 72ed5~31edo. Patent vals agree through the 31-limit.
|-
| [[218ed5]]
| [[94edo]]
| Same 1.4 cent octave stretch as 109ed5~47edo. Patent vals match through the 23-limit, with the exception of 13.
|-
| [[223ed5]]
| [[96edo]]
|  223ed5 is 96edo with ~0.51 cent compressed octaves. Patent vals match through the 13-limit.
|-
| [[225ed5]]
| [[97edo]]
| 225ed5 is 97edo with ~1.2 cent stretched octaves. Patent vals match through the 19-limit, with the exception of 11.
|-
| [[230ed5]]
| [[99edo]]
| 230ed5 is 99edo with ~0.67 cent compressed octaves. Patent vals match through the 7-limit.
|-
| [[232ed5]]
| [[100edo]]
| Same 1.0 cent octave stretch as 58ed5~25edo. Patent vals match through the 13-limit.
|-
| [[237ed5]]
| [[102edo]]
| Same 0.83 cent octave compression as 79ed5~34edo. Patent vals differ in the 7-limit.
|-
| [[239ed5]]
| [[103edo]]
| 239ed5 is 103edo with ~0.80 cent stretched octaves. Patent vals match through the 17-limit.
|-
| [[244ed5]]
| [[105edo]]
| 244ed5 is 105edo with ~0.97 cent compressed octaves. Patent vals disagree in the 5-limit and higher prime limit.
|-
| [[246ed5]]
| [[106edo]]
| Same 0.61 cent octave stretch as 123ed5~53edo. Patent vals match through the 43-limit, with the exception of 7.
|-
| [[251ed5]]
| [[108edo]]
| 251ed5 is 108edo with ~1.1 cent compressed octaves. Patent vals match through the 13-limit.
|-
| [[253ed5]]
| [[109edo]]
| 253ed5 is 109edo with ~0.43 cent stretched octaves. Patent vals match through the 13-limit.
|-
| [[258ed5]]
| [[111edo]]
| Same 1.2 cent octave compression as 86ed5~37edo. Patent vals agree through the 19-limit.
|-
| [[260ed5]]
| [[112edo]]
| Same 0.26 cent octave stretch as 65ed5~28edo. Patent vals match through the 47-limit, with the exception of 3.
|-
| [[265ed5]]
| [[114edo]]
| 265ed5 is 114edo with ~2.2 cent compressed octaves. Patent vals match through the 43-limit, with the exception of 11, 19 and 37.
|-
| [[267ed5]]
| [[115edo]]
| 267ed5 is 115edo with ~0.10 cent stretched octaves. Patent vals match through the 17-limit.
|-
| [[274ed5]]
| [[118edo]]
| Same 0.05 cent octave compression as 137ed5~59edo. Patent vals agree through the 103-limit.
|-
| [[276ed5]]
| [[119edo]]
| 276ed5 is 119edo with ~1.35 cent stretched octaves. Patent vals match through the 23-limit with the exception of 13 and 19.
|-
| [[281ed5]]
| [[121edo]]
| 281ed5 is 121edo with ~0.20 cent compressed octaves. Patent vals match through the 29-limit.
|-
| [[283ed5]]
| [[122edo]]
| 283ed5 is 122edo with ~1.2 cent stretched octaves. Patent vals match through the 13-limit.
|-
| [[288ed5]]
| [[124edo]]
| Same 0.34 cent octave compression as 72ed5~31edo. Patent vals agree through the 23-limit.
|-
| [[290ed5]]
| [[125edo]]
| Same 1.0 cent octave stretch as 58ed5~25edo. Patent vals match through the 37-limit, with the exception of 13.
|-
| [[295ed5]]
| [[127edo]]
| 295ed5 is 127edo with ~0.47 cent compressed octaves. Patent vals match through the 17-limit, with the exception of 11.
|-
| [[297ed5]]
| [[128edo]]
| 297ed5 is 128edo with ~0.84 cent stretched octaves. Patent vals match through the 7-limit.
|-
| [[302ed5]]
| [[130edo]]
| Same 0.59 cent octave compression as 151ed5~65edo. Patent vals match through the 41-limit, with the exception of 11, 19 and 23.
|-
| [[304ed5]]
| [[131edo]]
| 304ed5 is 131edo with ~0.68 cent stretched octaves. Patent vals match through the 41-limit, with the exception of 13 and 23.
|-
| [[309ed5]]
| [[133edo]]
| 309ed5 is 133edo with ~0.73 cent compressed octaves. Patent vals match through the 71-limit, with the exception of 7 and 59.
|-
| [[311ed5]]
| [[134edo]]
| 311ed5 is 134edo with ~0.53 cent stretched octaves. Patent vals match through the 59-limit, with the exception of 11, 19 and 53.
|-
| [[316ed5]]
| [[136edo]]
| Same 0.83 cent octave compression as 79ed5~34edo. Patent vals match through the 41-limit, with the exception of 13 and 23.
|-
| [[318ed5]]
| [[137edo]]
| 318ed5 is 137edo with ~0.39 cent stretched octaves. Patent vals match through the 23-limit, with the exception of 7.
|-
| [[323ed5]]
| [[139edo]]
| 323ed5 is 139edo with ~0.94 cent compressed compressed octaves. Patent vals match alternating primes through the 11-limit.
|-
| [[325ed5]]
| [[140edo]]
|  Same 0.26 cent octave stretch as 65ed5~28edo. Patent vals match through the 73-limit, with the exception of 31 and 67.
|-
| [[330ed5]]
| [[142edo]]
| Same 1.0 cent octave compression as 165ed5~71edo. Patent vals match through the 13-limit, with the exception of 11.
|-
| [[332ed5]]
| [[143edo]]
| 32ed5 is 143edo with ~0.13 cent stretched octaves. Patent vals match through the 29-limit, with the exception of 7, 17 and 19.
|-
| [[337ed5]]
| [[145edo]]
| 337ed5 is 145edo with ~1.1 cent compressed octaves. Patent vals match through the 17-limit, with the exception of 7.
|-
| [[339ed5]]
| [[146edo]]
| 339ed5 is practically identical to 146edo, with a slight octave stretch (~0.0053 cents). Patent vals match through the 827-limit.
|}
<references />
 
== See also ==
* [[Pentave Reduced Harmonics]]
* [[Pentave Reduced Subharmonics]]
* [[Relative errors of small ED5s]]
 
== External links ==
* [http://www.nonoctave.com/tuning/fifth_harmonic.html| Nonoctave.com: tuning: equal division of the fifth harmonic]
 
[[Category:Ed5's| ]]
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[[Category:Lists of scales]]
[[Category:Pentave]]
 
{{Todo|add sound example}}
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