Xenharmonic Wiki

8edo: Difference between revisions

← Older edit
VisualWikitext
Wikispaces>alexanderness
**Imported revision 585707903 - Original comment: **
m Cleanup on the temps section
 
(115 intermediate revisions by 35 users not shown)
Line 1: Line 1:
<h2>IMPORTED REVISION FROM WIKISPACES</h2>
{{interwiki
This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br>
| de = 8edo
: This revision was by author [[User:alexanderness|alexanderness]] and made on <tt>2016-06-16 22:31:16 UTC</tt>.<br>
| en = 8edo
: The original revision id was <tt>585707903</tt>.<br>
| es =
: The revision comment was: <tt></tt><br>
| ja = 8平均律
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>
{{Infobox ET}}
<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">&lt;span style="display: block; text-align: right;"&gt;[[８平均律|日本語]]
{{ED intro}}
&lt;/span&gt;
== Theory ==
[[toc|flat]]
[[File:8edo scale.mp3|thumb|A chromatic 8edo scale on C.]]
=Theory=
8-edo forms an odd and even pitch set of two diminished seventh chords, which when used in combination yield dissonance. The system has been described as a "barbaric" harmonic system; even so, it does a good job representing the [[Just intonation subgroups|just intonation subgroup]] 2.11/3.13/5, with good intervals of 13/10 and an excellent version of 11/6.


Another way of looking at 8-EDO is to treat a chord of 0-1-2-3-4 degrees (0-150-300-450-600 cents) as approximating harmonics 10:11:12:13:14 (~0-165-316-454-583 cents), which is not too implausible if you can buy that 12-EDO is a 5-limit temperament. This interpretation would imply that 121/120, 144/143, 169/168, and hence also 36/35 and 66/65, are tempered out.
=== Approximation to JI ===
8edo forms an odd and even pitch set of two diminished seventh chords, which when used in combination yield dissonance. The system has been described as a "barbaric" harmonic system, containing no good approximation of harmonics 3, 5, 7, 11, 13, and 17; even so, it does a good job representing the [[just intonation subgroup]]s 2.11/3.13/5, with good intervals of [[13/10]] and an excellent version of [[11/6]]. Stacking the 450-cent interval can result in some semi-consonant chords such as 0-3-6 degrees, although these still are quite dissonant compared to standard root-3rd-P5 triads, which are unavailable in 8edo.


=Intervals=
Another way of looking at 8edo is to treat a chord of 0-1-2-3-4 degrees (0-150-300-450-600 cents) as approximating harmonics 10:11:12:13:14 (~0-165-316-454-583 cents), which is not too implausible if you can buy that 12edo is a 5-limit temperament. This interpretation would imply that 121/120, 144/143, 169/168, and hence also 36/35 and 66/65, are tempered out.


[[media type="custom" key="24802404"]]
=== Relationship with the father comma ===
When 8edo is treated as a very inaccurate 5-limit system, it ends up tempering out the [[Father]] comma, [[16/15]]. In fact, it is the largest edo that tempers this comma. What this means is that intervals 16/15 apart in 8edo map to the same note, such as [[4/3]] being mapped to the same note as [[5/4]].


[[file:8ed2-001.svg]]
Some other odd equivalencies include:


'''0-2-5''': which can be seen as a minor triad (10:12:15), a sus2 triad (9:8:12), or a major triad in first inversion (5:6:8).


=Scala scale file=
'''0-3-5''': which can be seen as a major triad (4:5:6), a sus4 triad (6:8:9), or a minor chord in second inversion (15:20:24).
For those who use the new tuner Lingot, which accepts scala files, or for anyone else, here is a .scl file of 8 EDO [[file:08-EDO.scl]]


0. 1/1 C Unison
=== Odd harmonics ===
1. 150.000 cents C# (50 cents sharper than C# of 12tet) Neutral 2nd
{{Harmonics in equal|8|intervals=odd}}
2. 300.000 cents D# Minor 3rd (identical to 12-tet)
3. 450.000 cents E Sub-4th, Supermajor 3rd (50 cents sharper than E of 12tet)
4. 600.000 cents F# Tritone (identical to 12-tet)
5. 750.000 cents G Super 5th, Subminor 6th (50 cents sharper than G of 12tet)
6. 900.000 cents A Major 6th (identical to 12-tet)
7. 1050.000 cents A# Neutral 7th (50 cents sharper than A# of 12tet)
8. 2/1 C Octave


=Compositions=  
=== Octave shrinking ===
//[[http://www.h-pi.com/mp3/Fantasia8ET.mp3|Fantasia in 8ET]]// by Aaron Andrew Hunt
8edo's approximation of [[JI]] can be improved via [[octave shrinking]]. Compressing 8edo's octave from 1200 [[cent]]s down to 1188 cents gives the tuning called [[1ed148.5c]].
//[[http://www.h-pi.com/mp3/Fugue8ET.mp3|Fugue in 8ET]]// by Aaron Andrew Hunt
[[http://www.uvnitr.cz/flaoyg/forgotten_works/spendliky.html|Špendlíky]] //[[http://clones.soonlabel.com/public/micro/gene_ward_smith/Others/Gustar/spendliky.mp3|play]]// by Milan Guštar
//[[@http://www.ronsword.com/sounds/ronsword_8edo_improv.mp3|Acoustic Improvisation in 8-edo]]// by Ron Sword (dead link)
//[[http://micro.soonlabel.com/gene_ward_smith/Others/Winchester/07%20-%207.%208%20octave.mp3|Comets Over Flatland 7]]// by [[Randy Winchester]]
//[[@http://ia600607.us.archive.org/3/items/Transcendissonance/10Malebolge-CityOfTheAsleep.mp3|Malebolge]]// Igliashon Jones
//[[@http://www.youtube.com/watch?v=0mpDeL7iybI|News To Me]]// Jake Sherman
//[[@http://www.youtube.com/watch?v=HvDEoZ4LIdc|Tomorrow Night (pop music from 2045)]]// Jake Sherman
//[[http://www.seraph.it/dep/det/FunkEight1.mp3|FunkEight 1]]// by [[Carlo Serafini]] ([[http://www.seraph.it/blog_files/86557ece0348a8d042346d5e1b13e2d9-166.html|blog entry]])
[[file:8edo-pre-improv.ogg]]Preliminary noodling in 8 EDO with ZynAddSubFX synth.(by Cenobyte)
[[file:darkreflections(sketch).ogg]]8EDO Ukulele (cenobyte)
[[file:skiphop(sketch).ogg]]8EDO Ukulele (cenobyte)
[[file:octo-icy-pensive(sketch).ogg]] [[file:octo-icy-pensive-echo(sketch).ogg]]2 versions of the same song, one with echo, one without. (cenobyte)


=Ear Training=
Pure-octaves 8edo approximates only 2 of the first 11 prime harmonics within 15 cents. 1ed148.5c approximates 5 of them.
8 EDO ear-training exercises by Alex Ness available [[@https://drive.google.com/a/playgroundsessions.com/folderview?id=0BwsXD8q2VCYUamtVWEgyRFA5alU&amp;usp=sharing#list|here]].
=See also=
*[[Octatonic scale]] - a scale based on alternating whole and half steps


=Commas=
Pure-octaves 8edo approximates only 6 of the first 27 integer harmonics within 20 cents. 1ed148.5c approximates 10 of them.
8 EDO tempers out the following commas. (Note: This assumes val &lt; 8 13 19 22 28 30 |).


||~ Comma ||~ Monzo ||~ Cents ||~ Name 1 ||~ Name 2 ||~ Name 3 ||
In this way, 1ed148.5c (compressed-octaves 8edo) is able to provide a wider and stronger palette of [[consonance]]s compared to pure-octaves 8edo.
||= 648/625 || | 3 4 -4 &gt; ||&gt; 62.57 ||= Major Diesis ||= Diminished Comma ||  ||
||= 250/243 || | 1 -5 3 &gt; ||&gt; 49.17 ||= Maximal Diesis ||= Porcupine Comma ||  ||
||= 78732/78125 || | 2 9 -7 &gt; ||&gt; 13.40 ||= Medium Semicomma ||= Sensipent Comma ||  ||
||= 64/63 || | 6 -2 0 -1 &gt; ||&gt; 27.26 ||= Septimal Comma ||= Archytas' Comma || Leipziger Komma ||
||= 875/864 || | -5 -3 3 1 &gt; ||&gt; 21.90 ||= Keema ||  ||  ||
||= 321489/320000 || | -9 8 -4 2 &gt; ||&gt; 8.04 ||= Varunisma ||  ||  ||
||= 6144/6125 || | 11 1 -3 -2 &gt; ||&gt; 5.36 ||= Porwell ||  ||  ||
||= 100/99 || | 2 -2 2 0 -1 &gt; ||&gt; 17.40 ||= Ptolemisma ||  ||  ||
||= 121/120 || | -3 -1 -1 0 2 &gt; ||&gt; 14.37 ||= Biyatisma ||  ||  ||
||= 176/175 || | 4 0 -2 -1 1 &gt; ||&gt; 9.86 ||= Valinorsma ||  ||  ||
||= 65536/65219 || | 16 0 0 -2 -3 &gt; ||&gt; 8.39 ||= Orgonisma ||  ||  ||
||= 385/384 || | -7 -1 1 1 1 &gt; ||&gt; 4.50 ||= Keenanisma ||  ||  ||
||= 4000/3993 || | 5 -1 3 0 -3 &gt; ||&gt; 3.03 ||= Wizardharry ||  ||  ||</pre></div>
<h4>Original HTML 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;width:200%;white-space: pre-wrap ! important" class="old-revision-html">&lt;html&gt;&lt;head&gt;&lt;title&gt;8edo&lt;/title&gt;&lt;/head&gt;&lt;body&gt;&lt;span style="display: block; text-align: right;"&gt;&lt;a class="wiki_link" href="/%EF%BC%98%E5%B9%B3%E5%9D%87%E5%BE%8B"&gt;日本語&lt;/a&gt;&lt;br /&gt;
&lt;/span&gt;&lt;br /&gt;
&lt;!-- ws:start:WikiTextTocRule:15:&amp;lt;img id=&amp;quot;wikitext@@toc@@flat&amp;quot; class=&amp;quot;WikiMedia WikiMediaTocFlat&amp;quot; title=&amp;quot;Table of Contents&amp;quot; src=&amp;quot;/site/embedthumbnail/toc/flat?w=100&amp;amp;h=16&amp;quot;/&amp;gt; --&gt;&lt;!-- ws:end:WikiTextTocRule:15 --&gt;&lt;!-- ws:start:WikiTextTocRule:16: --&gt;&lt;a href="#Theory"&gt;Theory&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:16 --&gt;&lt;!-- ws:start:WikiTextTocRule:17: --&gt; | &lt;a href="#Intervals"&gt;Intervals&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:17 --&gt;&lt;!-- ws:start:WikiTextTocRule:18: --&gt; | &lt;a href="#Scala scale file"&gt;Scala scale file&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:18 --&gt;&lt;!-- ws:start:WikiTextTocRule:19: --&gt; | &lt;a href="#Compositions"&gt;Compositions&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:19 --&gt;&lt;!-- ws:start:WikiTextTocRule:20: --&gt; | &lt;a href="#Ear Training"&gt;Ear Training&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:20 --&gt;&lt;!-- ws:start:WikiTextTocRule:21: --&gt; | &lt;a href="#See also"&gt;See also&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:21 --&gt;&lt;!-- ws:start:WikiTextTocRule:22: --&gt; | &lt;a href="#Commas"&gt;Commas&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:22 --&gt;&lt;!-- ws:start:WikiTextTocRule:23: --&gt;
&lt;!-- ws:end:WikiTextTocRule:23 --&gt;&lt;!-- ws:start:WikiTextHeadingRule:1:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc0"&gt;&lt;a name="Theory"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:1 --&gt;Theory&lt;/h1&gt;
8-edo forms an odd and even pitch set of two diminished seventh chords, which when used in combination yield dissonance. The system has been described as a &amp;quot;barbaric&amp;quot; harmonic system; even so, it does a good job representing the &lt;a class="wiki_link" href="/Just%20intonation%20subgroups"&gt;just intonation subgroup&lt;/a&gt; 2.11/3.13/5, with good intervals of 13/10 and an excellent version of 11/6.&lt;br /&gt;
&lt;br /&gt;
Another way of looking at 8-EDO is to treat a chord of 0-1-2-3-4 degrees (0-150-300-450-600 cents) as approximating harmonics 10:11:12:13:14 (~0-165-316-454-583 cents), which is not too implausible if you can buy that 12-EDO is a 5-limit temperament. This interpretation would imply that 121/120, 144/143, 169/168, and hence also 36/35 and 66/65, are tempered out.&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:3:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc1"&gt;&lt;a name="Intervals"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:3 --&gt;Intervals&lt;/h1&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextMediaRule:0:&amp;lt;img src=&amp;quot;http://www.wikispaces.com/site/embedthumbnail/custom/24802404?h=0&amp;amp;w=0&amp;quot; class=&amp;quot;WikiMedia WikiMediaCustom&amp;quot; id=&amp;quot;wikitext@@media@@type=&amp;amp;quot;custom&amp;amp;quot; key=&amp;amp;quot;24802404&amp;amp;quot;&amp;quot; title=&amp;quot;Custom Media&amp;quot;/&amp;gt; --&gt;&lt;object id="example" type="image/svg+xml" data="http://xenharmonic.wikispaces.com/file/view/8ed2-001.svg"&gt;alt : Your browser has no SVG support.&lt;/object&gt;&lt;!-- ws:end:WikiTextMediaRule:0 --&gt;&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextFileRule:222:&amp;lt;img src=&amp;quot;http://www.wikispaces.com/site/embedthumbnail/file/8ed2-001.svg?h=52&amp;amp;w=320&amp;quot; class=&amp;quot;WikiFile&amp;quot; id=&amp;quot;wikitext@@file@@8ed2-001.svg&amp;quot; title=&amp;quot;File: 8ed2-001.svg&amp;quot; width=&amp;quot;320&amp;quot; height=&amp;quot;52&amp;quot; /&amp;gt; --&gt;&lt;div class="objectEmbed"&gt;&lt;a href="/file/view/8ed2-001.svg/480698786/8ed2-001.svg" onclick="ws.common.trackFileLink('/file/view/8ed2-001.svg/480698786/8ed2-001.svg');"&gt;&lt;img src="http://www.wikispaces.com/i/mime/32/empty.png" height="32" width="32" alt="8ed2-001.svg" /&gt;&lt;/a&gt;&lt;div&gt;&lt;a href="/file/view/8ed2-001.svg/480698786/8ed2-001.svg" onclick="ws.common.trackFileLink('/file/view/8ed2-001.svg/480698786/8ed2-001.svg');" class="filename" title="8ed2-001.svg"&gt;8ed2-001.svg&lt;/a&gt;&lt;br /&gt;&lt;ul&gt;&lt;li&gt;&lt;a href="/file/detail/8ed2-001.svg"&gt;Details&lt;/a&gt;&lt;/li&gt;&lt;li&gt;&lt;a href="/file/view/8ed2-001.svg/480698786/8ed2-001.svg"&gt;Download&lt;/a&gt;&lt;/li&gt;&lt;li style="color: #666"&gt;12 KB&lt;/li&gt;&lt;/ul&gt;&lt;/div&gt;&lt;/div&gt;&lt;!-- ws:end:WikiTextFileRule:222 --&gt;&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:5:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc2"&gt;&lt;a name="Scala scale file"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:5 --&gt;Scala scale file&lt;/h1&gt;
For those who use the new tuner Lingot, which accepts scala files, or for anyone else, here is a .scl file of 8 EDO &lt;!-- ws:start:WikiTextFileRule:223:&amp;lt;img src=&amp;quot;http://www.wikispaces.com/site/embedthumbnail/file/08-EDO.scl?h=52&amp;amp;w=320&amp;quot; class=&amp;quot;WikiFile&amp;quot; id=&amp;quot;wikitext@@file@@08-EDO.scl&amp;quot; title=&amp;quot;File: 08-EDO.scl&amp;quot; width=&amp;quot;320&amp;quot; height=&amp;quot;52&amp;quot; /&amp;gt; --&gt;&lt;div class="objectEmbed"&gt;&lt;a href="/file/view/08-EDO.scl/244588383/08-EDO.scl" onclick="ws.common.trackFileLink('/file/view/08-EDO.scl/244588383/08-EDO.scl');"&gt;&lt;img src="http://www.wikispaces.com/i/mime/32/text/plain.png" height="32" width="32" alt="08-EDO.scl" /&gt;&lt;/a&gt;&lt;div&gt;&lt;a href="/file/view/08-EDO.scl/244588383/08-EDO.scl" onclick="ws.common.trackFileLink('/file/view/08-EDO.scl/244588383/08-EDO.scl');" class="filename" title="08-EDO.scl"&gt;08-EDO.scl&lt;/a&gt;&lt;br /&gt;&lt;ul&gt;&lt;li&gt;&lt;a href="/file/detail/08-EDO.scl"&gt;Details&lt;/a&gt;&lt;/li&gt;&lt;li&gt;&lt;a href="/file/view/08-EDO.scl/244588383/08-EDO.scl"&gt;Download&lt;/a&gt;&lt;/li&gt;&lt;li style="color: #666"&gt;1 KB&lt;/li&gt;&lt;/ul&gt;&lt;/div&gt;&lt;/div&gt;&lt;!-- ws:end:WikiTextFileRule:223 --&gt;&lt;br /&gt;
&lt;br /&gt;
0. 1/1 C Unison&lt;br /&gt;
1. 150.000 cents C# (50 cents sharper than C# of 12tet) Neutral 2nd&lt;br /&gt;
2. 300.000 cents D# Minor 3rd (identical to 12-tet)&lt;br /&gt;
3. 450.000 cents E Sub-4th, Supermajor 3rd (50 cents sharper than E of 12tet)&lt;br /&gt;
4. 600.000 cents F# Tritone (identical to 12-tet)&lt;br /&gt;
5. 750.000 cents G Super 5th, Subminor 6th (50 cents sharper than G of 12tet)&lt;br /&gt;
6. 900.000 cents A Major 6th (identical to 12-tet)&lt;br /&gt;
7. 1050.000 cents A# Neutral 7th (50 cents sharper than A# of 12tet)&lt;br /&gt;
8. 2/1 C Octave&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:7:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc3"&gt;&lt;a name="Compositions"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:7 --&gt;Compositions&lt;/h1&gt;
&lt;em&gt;&lt;a class="wiki_link_ext" href="http://www.h-pi.com/mp3/Fantasia8ET.mp3" rel="nofollow"&gt;Fantasia in 8ET&lt;/a&gt;&lt;/em&gt; by Aaron Andrew Hunt&lt;br /&gt;
&lt;em&gt;&lt;a class="wiki_link_ext" href="http://www.h-pi.com/mp3/Fugue8ET.mp3" rel="nofollow"&gt;Fugue in 8ET&lt;/a&gt;&lt;/em&gt; by Aaron Andrew Hunt&lt;br /&gt;
&lt;a class="wiki_link_ext" href="http://www.uvnitr.cz/flaoyg/forgotten_works/spendliky.html" rel="nofollow"&gt;Špendlíky&lt;/a&gt; &lt;em&gt;&lt;a class="wiki_link_ext" href="http://clones.soonlabel.com/public/micro/gene_ward_smith/Others/Gustar/spendliky.mp3" rel="nofollow"&gt;play&lt;/a&gt;&lt;/em&gt; by Milan Guštar&lt;br /&gt;
&lt;em&gt;&lt;a class="wiki_link_ext" href="http://www.ronsword.com/sounds/ronsword_8edo_improv.mp3" rel="nofollow" target="_blank"&gt;Acoustic Improvisation in 8-edo&lt;/a&gt;&lt;/em&gt; by Ron Sword (dead link)&lt;br /&gt;
&lt;em&gt;&lt;a class="wiki_link_ext" href="http://micro.soonlabel.com/gene_ward_smith/Others/Winchester/07%20-%207.%208%20octave.mp3" rel="nofollow"&gt;Comets Over Flatland 7&lt;/a&gt;&lt;/em&gt; by &lt;a class="wiki_link" href="/Randy%20Winchester"&gt;Randy Winchester&lt;/a&gt;&lt;br /&gt;
&lt;em&gt;&lt;a class="wiki_link_ext" href="http://ia600607.us.archive.org/3/items/Transcendissonance/10Malebolge-CityOfTheAsleep.mp3" rel="nofollow" target="_blank"&gt;Malebolge&lt;/a&gt;&lt;/em&gt; Igliashon Jones&lt;br /&gt;
&lt;em&gt;&lt;a class="wiki_link_ext" href="http://www.youtube.com/watch?v=0mpDeL7iybI" rel="nofollow" target="_blank"&gt;News To Me&lt;/a&gt;&lt;/em&gt; Jake Sherman&lt;br /&gt;
&lt;em&gt;&lt;a class="wiki_link_ext" href="http://www.youtube.com/watch?v=HvDEoZ4LIdc" rel="nofollow" target="_blank"&gt;Tomorrow Night (pop music from 2045)&lt;/a&gt;&lt;/em&gt; Jake Sherman&lt;br /&gt;
&lt;em&gt;&lt;a class="wiki_link_ext" href="http://www.seraph.it/dep/det/FunkEight1.mp3" rel="nofollow"&gt;FunkEight 1&lt;/a&gt;&lt;/em&gt; by &lt;a class="wiki_link" href="/Carlo%20Serafini"&gt;Carlo Serafini&lt;/a&gt; (&lt;a class="wiki_link_ext" href="http://www.seraph.it/blog_files/86557ece0348a8d042346d5e1b13e2d9-166.html" rel="nofollow"&gt;blog entry&lt;/a&gt;)&lt;br /&gt;
&lt;!-- ws:start:WikiTextFileRule:224:&amp;lt;img src=&amp;quot;http://www.wikispaces.com/site/embedthumbnail/file/8edo-pre-improv.ogg?h=52&amp;amp;w=320&amp;quot; class=&amp;quot;WikiFile&amp;quot; id=&amp;quot;wikitext@@file@@8edo-pre-improv.ogg&amp;quot; title=&amp;quot;File: 8edo-pre-improv.ogg&amp;quot; width=&amp;quot;320&amp;quot; height=&amp;quot;52&amp;quot; /&amp;gt; --&gt;&lt;div class="objectEmbed"&gt;&lt;a href="/file/view/8edo-pre-improv.ogg/244674815/8edo-pre-improv.ogg" onclick="ws.common.trackFileLink('/file/view/8edo-pre-improv.ogg/244674815/8edo-pre-improv.ogg');"&gt;&lt;img src="http://www.wikispaces.com/i/mime/32/empty.png" height="32" width="32" alt="8edo-pre-improv.ogg" /&gt;&lt;/a&gt;&lt;div&gt;&lt;a href="/file/view/8edo-pre-improv.ogg/244674815/8edo-pre-improv.ogg" onclick="ws.common.trackFileLink('/file/view/8edo-pre-improv.ogg/244674815/8edo-pre-improv.ogg');" class="filename" title="8edo-pre-improv.ogg"&gt;8edo-pre-improv.ogg&lt;/a&gt;&lt;br /&gt;&lt;ul&gt;&lt;li&gt;&lt;a href="/file/detail/8edo-pre-improv.ogg"&gt;Details&lt;/a&gt;&lt;/li&gt;&lt;li&gt;&lt;a href="/file/view/8edo-pre-improv.ogg/244674815/8edo-pre-improv.ogg"&gt;Download&lt;/a&gt;&lt;/li&gt;&lt;li style="color: #666"&gt;1 MB&lt;/li&gt;&lt;/ul&gt;&lt;/div&gt;&lt;/div&gt;&lt;!-- ws:end:WikiTextFileRule:224 --&gt;Preliminary noodling in 8 EDO with ZynAddSubFX synth.(by Cenobyte)&lt;br /&gt;
&lt;!-- ws:start:WikiTextFileRule:225:&amp;lt;img src=&amp;quot;http://www.wikispaces.com/site/embedthumbnail/file/darkreflections%28sketch%29.ogg?h=52&amp;amp;w=320&amp;quot; class=&amp;quot;WikiFile&amp;quot; id=&amp;quot;wikitext@@file@@darkreflections(sketch).ogg&amp;quot; title=&amp;quot;File: darkreflections(sketch).ogg&amp;quot; width=&amp;quot;320&amp;quot; height=&amp;quot;52&amp;quot; /&amp;gt; --&gt;&lt;div class="objectEmbed"&gt;&lt;a href="/file/view/darkreflections%28sketch%29.ogg/246401653/darkreflections%28sketch%29.ogg" onclick="ws.common.trackFileLink('/file/view/darkreflections%28sketch%29.ogg/246401653/darkreflections%28sketch%29.ogg');"&gt;&lt;img src="http://www.wikispaces.com/i/mime/32/empty.png" height="32" width="32" alt="darkreflections(sketch).ogg" /&gt;&lt;/a&gt;&lt;div&gt;&lt;a href="/file/view/darkreflections%28sketch%29.ogg/246401653/darkreflections%28sketch%29.ogg" onclick="ws.common.trackFileLink('/file/view/darkreflections%28sketch%29.ogg/246401653/darkreflections%28sketch%29.ogg');" class="filename" title="darkreflections(sketch).ogg"&gt;darkreflections(sketch).ogg&lt;/a&gt;&lt;br /&gt;&lt;ul&gt;&lt;li&gt;&lt;a href="/file/detail/darkreflections%28sketch%29.ogg"&gt;Details&lt;/a&gt;&lt;/li&gt;&lt;li&gt;&lt;a href="/file/view/darkreflections%28sketch%29.ogg/246401653/darkreflections%28sketch%29.ogg"&gt;Download&lt;/a&gt;&lt;/li&gt;&lt;li style="color: #666"&gt;3 MB&lt;/li&gt;&lt;/ul&gt;&lt;/div&gt;&lt;/div&gt;&lt;!-- ws:end:WikiTextFileRule:225 --&gt;8EDO Ukulele (cenobyte)&lt;br /&gt;
&lt;!-- ws:start:WikiTextFileRule:226:&amp;lt;img src=&amp;quot;http://www.wikispaces.com/site/embedthumbnail/file/skiphop%28sketch%29.ogg?h=52&amp;amp;w=320&amp;quot; class=&amp;quot;WikiFile&amp;quot; id=&amp;quot;wikitext@@file@@skiphop(sketch).ogg&amp;quot; title=&amp;quot;File: skiphop(sketch).ogg&amp;quot; width=&amp;quot;320&amp;quot; height=&amp;quot;52&amp;quot; /&amp;gt; --&gt;&lt;div class="objectEmbed"&gt;&lt;a href="/file/view/skiphop%28sketch%29.ogg/246401869/skiphop%28sketch%29.ogg" onclick="ws.common.trackFileLink('/file/view/skiphop%28sketch%29.ogg/246401869/skiphop%28sketch%29.ogg');"&gt;&lt;img src="http://www.wikispaces.com/i/mime/32/empty.png" height="32" width="32" alt="skiphop(sketch).ogg" /&gt;&lt;/a&gt;&lt;div&gt;&lt;a href="/file/view/skiphop%28sketch%29.ogg/246401869/skiphop%28sketch%29.ogg" onclick="ws.common.trackFileLink('/file/view/skiphop%28sketch%29.ogg/246401869/skiphop%28sketch%29.ogg');" class="filename" title="skiphop(sketch).ogg"&gt;skiphop(sketch).ogg&lt;/a&gt;&lt;br /&gt;&lt;ul&gt;&lt;li&gt;&lt;a href="/file/detail/skiphop%28sketch%29.ogg"&gt;Details&lt;/a&gt;&lt;/li&gt;&lt;li&gt;&lt;a href="/file/view/skiphop%28sketch%29.ogg/246401869/skiphop%28sketch%29.ogg"&gt;Download&lt;/a&gt;&lt;/li&gt;&lt;li style="color: #666"&gt;3 MB&lt;/li&gt;&lt;/ul&gt;&lt;/div&gt;&lt;/div&gt;&lt;!-- ws:end:WikiTextFileRule:226 --&gt;8EDO Ukulele (cenobyte)&lt;br /&gt;
&lt;!-- ws:start:WikiTextFileRule:227:&amp;lt;img src=&amp;quot;http://www.wikispaces.com/site/embedthumbnail/file/octo-icy-pensive%28sketch%29.ogg?h=52&amp;amp;w=320&amp;quot; class=&amp;quot;WikiFile&amp;quot; id=&amp;quot;wikitext@@file@@octo-icy-pensive(sketch).ogg&amp;quot; title=&amp;quot;File: octo-icy-pensive(sketch).ogg&amp;quot; width=&amp;quot;320&amp;quot; height=&amp;quot;52&amp;quot; /&amp;gt; --&gt;&lt;div class="objectEmbed"&gt;&lt;a href="/file/view/octo-icy-pensive%28sketch%29.ogg/246402077/octo-icy-pensive%28sketch%29.ogg" onclick="ws.common.trackFileLink('/file/view/octo-icy-pensive%28sketch%29.ogg/246402077/octo-icy-pensive%28sketch%29.ogg');"&gt;&lt;img src="http://www.wikispaces.com/i/mime/32/empty.png" height="32" width="32" alt="octo-icy-pensive(sketch).ogg" /&gt;&lt;/a&gt;&lt;div&gt;&lt;a href="/file/view/octo-icy-pensive%28sketch%29.ogg/246402077/octo-icy-pensive%28sketch%29.ogg" onclick="ws.common.trackFileLink('/file/view/octo-icy-pensive%28sketch%29.ogg/246402077/octo-icy-pensive%28sketch%29.ogg');" class="filename" title="octo-icy-pensive(sketch).ogg"&gt;octo-icy-pensive(sketch).ogg&lt;/a&gt;&lt;br /&gt;&lt;ul&gt;&lt;li&gt;&lt;a href="/file/detail/octo-icy-pensive%28sketch%29.ogg"&gt;Details&lt;/a&gt;&lt;/li&gt;&lt;li&gt;&lt;a href="/file/view/octo-icy-pensive%28sketch%29.ogg/246402077/octo-icy-pensive%28sketch%29.ogg"&gt;Download&lt;/a&gt;&lt;/li&gt;&lt;li style="color: #666"&gt;2 MB&lt;/li&gt;&lt;/ul&gt;&lt;/div&gt;&lt;/div&gt;&lt;!-- ws:end:WikiTextFileRule:227 --&gt; &lt;!-- ws:start:WikiTextFileRule:228:&amp;lt;img src=&amp;quot;http://www.wikispaces.com/site/embedthumbnail/file/octo-icy-pensive-echo%28sketch%29.ogg?h=52&amp;amp;w=320&amp;quot; class=&amp;quot;WikiFile&amp;quot; id=&amp;quot;wikitext@@file@@octo-icy-pensive-echo(sketch).ogg&amp;quot; title=&amp;quot;File: octo-icy-pensive-echo(sketch).ogg&amp;quot; width=&amp;quot;320&amp;quot; height=&amp;quot;52&amp;quot; /&amp;gt; --&gt;&lt;div class="objectEmbed"&gt;&lt;a href="/file/view/octo-icy-pensive-echo%28sketch%29.ogg/246402235/octo-icy-pensive-echo%28sketch%29.ogg" onclick="ws.common.trackFileLink('/file/view/octo-icy-pensive-echo%28sketch%29.ogg/246402235/octo-icy-pensive-echo%28sketch%29.ogg');"&gt;&lt;img src="http://www.wikispaces.com/i/mime/32/empty.png" height="32" width="32" alt="octo-icy-pensive-echo(sketch).ogg" /&gt;&lt;/a&gt;&lt;div&gt;&lt;a href="/file/view/octo-icy-pensive-echo%28sketch%29.ogg/246402235/octo-icy-pensive-echo%28sketch%29.ogg" onclick="ws.common.trackFileLink('/file/view/octo-icy-pensive-echo%28sketch%29.ogg/246402235/octo-icy-pensive-echo%28sketch%29.ogg');" class="filename" title="octo-icy-pensive-echo(sketch).ogg"&gt;octo-icy-pensive-echo(sketch).ogg&lt;/a&gt;&lt;br /&gt;&lt;ul&gt;&lt;li&gt;&lt;a href="/file/detail/octo-icy-pensive-echo%28sketch%29.ogg"&gt;Details&lt;/a&gt;&lt;/li&gt;&lt;li&gt;&lt;a href="/file/view/octo-icy-pensive-echo%28sketch%29.ogg/246402235/octo-icy-pensive-echo%28sketch%29.ogg"&gt;Download&lt;/a&gt;&lt;/li&gt;&lt;li style="color: #666"&gt;2 MB&lt;/li&gt;&lt;/ul&gt;&lt;/div&gt;&lt;/div&gt;&lt;!-- ws:end:WikiTextFileRule:228 --&gt;2 versions of the same song, one with echo, one without. (cenobyte)&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:9:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc4"&gt;&lt;a name="Ear Training"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:9 --&gt;Ear Training&lt;/h1&gt;
8 EDO ear-training exercises by Alex Ness available &lt;a class="wiki_link_ext" href="https://drive.google.com/a/playgroundsessions.com/folderview?id=0BwsXD8q2VCYUamtVWEgyRFA5alU&amp;amp;usp=sharing#list" rel="nofollow" target="_blank"&gt;here&lt;/a&gt;.&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:11:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc5"&gt;&lt;a name="See also"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:11 --&gt;See also&lt;/h1&gt;
*&lt;a class="wiki_link" href="/Octatonic%20scale"&gt;Octatonic scale&lt;/a&gt; - a scale based on alternating whole and half steps&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:13:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc6"&gt;&lt;a name="Commas"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:13 --&gt;Commas&lt;/h1&gt;
8 EDO tempers out the following commas. (Note: This assumes val &amp;lt; 8 13 19 22 28 30 |).&lt;br /&gt;
&lt;br /&gt;


There are [[zeta peak index]] tunings nearby 8edo as well, however they damage the octave by over 20 cents, rendering them unrecognisable as stretched or compressed 8edo and more like entirely new scales in their own right.


&lt;table class="wiki_table"&gt;
=== Subsets and supersets ===
    &lt;tr&gt;
8edo contains [[2edo]] and [[4edo]] as subsets. Among its supersets are [[16edo]], [[24edo]], [[32edo]], ….
        &lt;th&gt;Comma&lt;br /&gt;
&lt;/th&gt;
        &lt;th&gt;Monzo&lt;br /&gt;
&lt;/th&gt;
        &lt;th&gt;Cents&lt;br /&gt;
&lt;/th&gt;
        &lt;th&gt;Name 1&lt;br /&gt;
&lt;/th&gt;
        &lt;th&gt;Name 2&lt;br /&gt;
&lt;/th&gt;
        &lt;th&gt;Name 3&lt;br /&gt;
&lt;/th&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td style="text-align: center;"&gt;648/625&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;| 3 4 -4 &amp;gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: right;"&gt;62.57&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;Major Diesis&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;Diminished Comma&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td style="text-align: center;"&gt;250/243&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;| 1 -5 3 &amp;gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: right;"&gt;49.17&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;Maximal Diesis&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;Porcupine Comma&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td style="text-align: center;"&gt;78732/78125&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;| 2 9 -7 &amp;gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: right;"&gt;13.40&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;Medium Semicomma&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;Sensipent Comma&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td style="text-align: center;"&gt;64/63&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;| 6 -2 0 -1 &amp;gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: right;"&gt;27.26&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;Septimal Comma&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;Archytas' Comma&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;Leipziger Komma&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td style="text-align: center;"&gt;875/864&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;| -5 -3 3 1 &amp;gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: right;"&gt;21.90&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;Keema&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td style="text-align: center;"&gt;321489/320000&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;| -9 8 -4 2 &amp;gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: right;"&gt;8.04&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;Varunisma&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td style="text-align: center;"&gt;6144/6125&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;| 11 1 -3 -2 &amp;gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: right;"&gt;5.36&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;Porwell&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td style="text-align: center;"&gt;100/99&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;| 2 -2 2 0 -1 &amp;gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: right;"&gt;17.40&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;Ptolemisma&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td style="text-align: center;"&gt;121/120&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;| -3 -1 -1 0 2 &amp;gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: right;"&gt;14.37&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;Biyatisma&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td style="text-align: center;"&gt;176/175&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;| 4 0 -2 -1 1 &amp;gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: right;"&gt;9.86&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;Valinorsma&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td style="text-align: center;"&gt;65536/65219&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;| 16 0 0 -2 -3 &amp;gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: right;"&gt;8.39&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;Orgonisma&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td style="text-align: center;"&gt;385/384&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;| -7 -1 1 1 1 &amp;gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: right;"&gt;4.50&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;Keenanisma&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td style="text-align: center;"&gt;4000/3993&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;| 5 -1 3 0 -3 &amp;gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: right;"&gt;3.03&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;Wizardharry&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
&lt;/table&gt;


&lt;/body&gt;&lt;/html&gt;</pre></div>
== Intervals ==
{| class="wikitable"
|-
! rowspan="2" | Steps
! rowspan="2" | Cents
! colspan="3" | JI approximation
!Other
|-
! 2.11/3.13/5.19*
! 2.5/3.11/3.13/5*
! 10:11:12:13:14*
!Patent val ⟨8 13 19]
|-
| 0
| 0
| 1/1
| 1/1
| 1/1
|1/1, 16/15
|-
| 1
| 150
| 12/11
| 12/11
| 12/11, 11/10
|10/9, 25/24
|-
| 2
| 300
| 19/16
| 6/5
| 6/5
|6/5, 9/8
|-
| 3
| 450
| 13/10
| 13/10
| 13/10
|4/3, 5/4
|-
| 4
| 600
|
|
| 7/5, 10/7
|27/20, 25/18, 36/25
|-
| 5
| 750
| 20/13
| 20/13
| 20/13
|3/2, 8/5
|-
| 6
| 900
| 32/19
| 5/3
| 5/3
|5/3, 16/9
|-
| 7
| 1050
| 11/6
| 11/6
| 20/11, 11/6
|9/5, 48/50
|-
| 8
| 1200
| 2/1
| 2/1
| 2/1
|2/1, 15/8
|}
<nowiki />* Allows [[inversion]] by 2/1; other interpretations also possible
 
== Notation ==
=== Ups and downs notation ===
8edo can be notated as a subset of 24edo, using [[Ups and downs notation|ups and downs]]. It can also be notated as a subset of 16edo, but this is a less intuitive notation.
 
{| class="wikitable center-all"
|-
! Edostep
! [[Cent]]s
! colspan="2" | 24edo subset notation<br />([[Enharmonic unisons in ups and downs notation|EUs:]] vvA1 and d2)
! colspan="2" | 16edo subset notation<br />(major narrower than minor)
! colspan="2" | 16edo subset notation<br />(major wider than minor)
! [[3L&nbsp;2s]] notation<br />({{nowrap|J {{=}} 1/1}})
! Audio
|-
| 0
| 0¢
| P1
| D
| P1
| D
| P1
| D
| J
| [[File:0-0 unison.mp3|frameless]]
|-
| 1
| 150
| ~2
| vE
| M2
| E
| m2
| E
| K
| [[File:0-150 (8-EDO).mp3|frameless]]
|-
| 2
| 300
| m3
| F
| M3
| F#
| m3
| Fb
| K#, Lb
| [[File:0-300 (12-EDO).mp3|frameless]]
|-
| 3
| 450
| ^M3 / v4
| ^F# / vG
| d3 / A4
| Fb / G#
| A3, D4
| F#, Gb
| L
| [[File:0-450 (8-EDO).mp3|frameless]]
|-
| 4
| 600
| A4, d5
| G#, Ab
| d4, A5
| Gb, A#
| A4, D5
| G#, Ab
| M
| [[File:0-600 (12-EDO).mp3|frameless]]
|-
| 5
| 750
| ^5, vm6
| ^A, vBb
| d5, A6
| Ab, B#
| A5, d6
| A#, Bb
| M#, Nb
| [[File:0-750 (8-EDO).mp3|frameless]]
|-
| 6
| 900
| M6
| B
| m6
| Bb
| M6
| B#
| N
| [[File:0-900 (12-EDO).mp3|frameless]]
|-
| 7
| 1050
| ~7
| ^C
| m7
| C
| M7
| C
| N#, Jb
| [[File:0-1050 (8-EDO).mp3|frameless]]
|-
| 8
| 1200
| P8
| D
| P8
| D
| P8
| D
| J
| [[File:0-1200 octave.mp3|frameless]]
|}
 
This is a heptatonic notation generated by 5ths (5th meaning 3/2). Alternative notations include pentatonic 5th-generated, octatonic, and heptatonic 2nd-generated.
 
'''<u>Pentatonic 5th-generated</u>: D * E G * A C * D'''  (generator = 5\8 = perfect 5thoid)
 
D - D#/Eb - E - G - G#/Ab - A - C - C#/Db - D
 
P1 - A1/ms3 - Ms3 - P4d - A4d/d5d - P5d - ms7 - Ms7/d8d - P8d  (s = sub-, d = -oid, see [[5edo#Alternative notations|5edo]] notation)
 
pentatonic genchain of 5ths: ...Cb - Gb - Db - Ab - Eb - C - G - D - A - E - C# - G# - D# - A# - E#...
 
pentatonic genchain of 5ths: ...d8d - d5d - ms3 - ms7 - P4d - P1 - P5d - Ms3 - Ms7 - A4d - A1... (s = sub-, d = -oid)
 
[[Enharmonic unison]]: ds3
 
'''<u>Octatonic:</u>''' '''A B C D E F G H A'''  (every interval is a generator)
 
P1 - P2 - P3 - P4 - P5 - P6 - P7 - P8 - P9
 
Enharmonic unison: none
 
'''<u>Heptatonic 2nd-generated</u>: D E F G * A B C D'''  (generator = 1\8 = perfect 2nd = 150¢)
 
D - E - F - G - G#/Ab - A -B - C - D
 
P1 - P2 - m3 - M3/m4 - M4/m5 - M5/m6 - M6 - P7 - P8
 
genchain of 2nds: ...D# - E# - F# - G# - A - B - C - D - E - F - G - Ab - Bb - Cb - Db...
 
genchain of 2nds: ...A1 - A2 - M3 - M4 - M5 - M6 - P7 - P1 - P2 - m3 - m4 - m5 - m6 - d7 - d8...
 
Enharmonic unison: d2
 
===Sagittal notation===
This notation is a subset of the notations for EDOs [[24edo#Sagittal notation|24]], [[48edo#Sagittal notation|48]], and [[72edo#Sagittal notation|72]].
====Evo flavor====
 
<imagemap>
File:8-EDO_Evo_Sagittal.svg
desc none
rect 80 0 300 50 [[Sagittal_notation]]
rect 392 0 552 80 [https://sagittal.org#periodic-table Periodic table of EDOs with sagittal notation]
rect 20 80 392 106 [[24-EDO#Sagittal_notation | 24-EDO notation]]
default [[File:8-EDO_Evo_Sagittal.svg]]
</imagemap>
 
====Revo flavor====
 
<imagemap>
File:8-EDO_Revo_Sagittal.svg
desc none
rect 80 0 300 50 [[Sagittal_notation]]
rect 400 0 560 80 [https://sagittal.org#periodic-table Periodic table of EDOs with sagittal notation]
rect 20 80 400 106 [[24-EDO#Sagittal_notation | 24-EDO notation]]
default [[File:8-EDO_Revo_Sagittal.svg]]
</imagemap>
 
====Evo-SZ flavor====
 
<imagemap>
File:8-EDO_Evo-SZ_Sagittal.svg
desc none
rect 80 0 300 50 [[Sagittal_notation]]
rect 376 0 536 80 [https://sagittal.org#periodic-table Periodic table of EDOs with sagittal notation]
rect 20 80 376 106 [[24-EDO#Sagittal_notation | 24-EDO notation]]
default [[File:8-EDO_Evo-SZ_Sagittal.svg]]
</imagemap>
 
Because it contains no Sagittal symbols, this Evo-SZ Sagittal notation is also a Stein-Zimmerman notation.
 
== Chord names ==
[[Ups and downs notation #Chords and Chord Progressions|Ups and downs]] can name any 8edo chord. Alterations are always enclosed in parentheses, additions never are. An up, down or mid immediately after the chord root affects the 3rd, 6th, 7th, and/or the 11th (every other note of a stacked-3rds chord 6-1-3-5-7-9-11-13).
 
8edo chords are very ambiguous, with many chord homonyms. Even the major and minor triads are [[Chord homonym|homonyms]]. Chord components usually default to M2, M3, P4, P5, M6, m7, M9, P11 and M13. Thus D7 has a M3, P5 and m7. 8-edo chord names using 24edo subset names are greatly simplified by using different defaults: instead of the conventional M2, M3, P4, P5, M6, m7, M9, P11 and M13, we have  ~2, ^M3, v4, ^5, M6, ~7, ~9, v11 and M13. Thus D7 becomes ^M3, ^5 and ~7.
 
{| class="wikitable"
|-
! Chord edosteps
! Chord notes
! Full name
! Abbreviated name
! Homonyms
|-
| 0 – 3 – 5
| D ^F♯ ^A
| D^(^5)
| D
| ^F♯m or vGm
|-
| 0 – 2 – 5
| D F ^A
| Dm(^5)
| Dm
| ^A or vB♭
|-
| 0 – 3 – 5 – 7
| D ^F♯ ^A ^C
| D^7(^5)
| D7
| ^F♯m♯11 or vGm♯11
|-
| 0 – 3 – 5 – 6
| D ^F♯ ^A B
| D6(^3,^5)
| D6
| Bm7 and vG,♯9
|-
| 0 – 2 – 5 – 7
| D F ^A ^C
| Dm,~7(^5)
| Dm7
| F6 and vB♭,♯9
|-
| 0 – 2 – 5 – 6
| D F ^A B
| Dm6(^5)
| Dm6
| Bm7(♭5)
|-
| 0 – 2 – 4 – 7
| D F A♭ ^C
| Ddim,~7
| Dm7(♭5)
| Fm6
|}
 
== Approximation to JI ==
[[File:8ed2-001.svg]]
 
== Regular temperament properties ==
=== Uniform maps ===
{{Uniform map|edo=8}}
 
=== Commas ===
8et [[tempering out|tempers out]] the following [[comma]]s. This assumes [[val]] {{val| 8 13 19 22 28 30 }}.
 
{| class="commatable wikitable center-all left-3 right-4 left-6"
! [[Harmonic limit|Prime<br />limit]]
! [[Ratio]]<ref>Ratios longer than 10 digits are presented by placeholders with informative hints</ref>
! [[Monzo]]
! [[Cent]]s
! [[Color name]]
! Name(s)
|-
| 3
| [[8192/6561]]
| {{monzo| 13 -8 }}
| 384.35
| sawa 4th
| Pythagorean diminished fourth
|-
| 5
| [[16/15]]
| {{monzo| 4 -1 -1 }}
| 111.73
| gu 2nd
| Father comma, classic limma
|-
| 5
| [[648/625]]
| {{monzo| 3 4 -4 }}
| 62.57
| Quadgu
| Diminished comma, major diesis
|-
| 5
| [[250/243]]
| {{monzo| 1 -5 3 }}
| 49.17
| Triyo
| Porcupine comma, maximal diesis
|-
| 5
| [[78732/78125]]
| {{monzo| 2 9 -7 }}
| 13.40
| Sepgu
| Sensipent comma, medium semicomma
|-
| 7
| [[64/63]]
| {{monzo| 6 -2 0 -1 }}
| 27.26
| Ru
| Septimal comma, Archytas' comma, Leipziger Komma
|-
| 7
| [[875/864]]
| {{monzo| -5 -3 3 1 }}
| 21.90
| Zotriyo
| Keema
|-
| 7
| <abbr title="321489/320000">(12 digits)</abbr>
| {{monzo| -9 8 -4 2 }}
| 8.04
| Labizogugu
| [[Varunisma]]
|-
| 7
| [[6144/6125]]
| {{monzo| 11 1 -3 -2 }}
| 5.36
| Sarurutrigu
| Porwell comma
|-
| 11
| [[100/99]]
| {{monzo| 2 -2 2 0 -1 }}
| 17.40
| Luyoyo
| Ptolemisma
|-
| 11
| [[121/120]]
| {{monzo| -3 -1 -1 0 2 }}
| 14.37
| Lologu
| Biyatisma
|-
| 11
| [[176/175]]
| {{monzo| 4 0 -2 -1 1 }}
| 9.86
| Lorugugu
| Valinorsma
|-
| 11
| [[65536/65219]]
| {{monzo| 16 0 0 -2 -3 }}
| 8.39
| Satrilu-aruru
| Orgonisma
|-
| 11
| [[385/384]]
| {{monzo| -7 -1 1 1 1 }}
| 4.50
| Lozoyo
| Keenanisma
|-
| 11
| [[4000/3993]]
| {{monzo| 5 -1 3 0 -3 }}
| 3.03
| Triluyo
| Wizardharry comma
|-
| 13
| [[40/39]]
| {{monzo| 3 -1 1 0 0 -1 }}
| 43.83
| Thuyo unison
| Tridecimal minor diesis
|}
<references/>
 
== Scales ==
=== Scala file ===
Here is a .scl file of 8edo: [[:File:08-EDO.scl|08-edo.scl]]
 
<pre>
! 08-EDO.scl
!
8 EDO
8
!
150.00
300.00
450.00
600.00
750.00
900.00
1050.00
2/1
</pre>
 
=== Temperaments ===
8edo is fairly composite, so the only step that generates a [[mos]] scale that covers every interval other than the 1 is the 3, producing scales of 332 and [[3L 2s|21212]]. In terms of temperaments, in the 5-limit this is best interpreted as [[father]], as 8edo is the highest edo that tempers out the diatonic semitone in it's [[patent val]], merging 5/4 and 4/3 into a single interval, which is also the generator. This means major and minor chords are rotations of each other, making them inaccurate but very simple, with even the 5 note mos having 3 of both and providing a functional skeleton of 5-limit harmony, albeit with some very strange enharmonic equivalences. In terms of 7-limit extensions things get even more inaccurate, as the patent val supports [[mother]], but the ideal tuning for that is much closer to [[5edo]]. The 8d val supports septimal father and [[pater]], and is much closer to the ideal tuning for both, as the extremely sharp 7 works better with the {{nowrap| 3 & 5 }}. In terms of multi-period temperaments, it makes for a near perfect [[walid]] or a much less accurate [[diminished (temperament)|diminished]] scale.
 
== Instruments ==
A [[Lumatone mapping for 8edo]] is available.
 
== Music ==
; [[Abnormality]]
* [https://www.youtube.com/watch?v=tqgRYQxsA9U ''mushroom''] (2024)
 
; [[Cenobyte]]
* [[:File:8edo-pre-improv.ogg|8edo-pre-improv]] (2011)
* [[:File:darkreflections(sketch).ogg|darkreflections(sketch)]] (2011)
* [[:File:skiphop(sketch).ogg|skiphop(sketch)]] (2011)
* [[:File:octo-icy-pensive(sketch).ogg|octo-icy-pensive(sketch)]], [[:File:octo-icy-pensive-echo(sketch).ogg|octo-icy-pensive-echo(sketch)]] (2011)
 
; [[City of the Asleep]]
* [http://ia600607.us.archive.org/3/items/Transcendissonance/10Malebolge-CityOfTheAsleep.mp3 "Malebolge"], from [https://cityoftheasleep.bandcamp.com/album/transcendissonance ''Transcendissonance''] (2011)
 
; [[Milan Guštar]]
* [http://www.uvnitr.cz/flaoyg/forgotten_works/spendliky.html ''Špendlíky''] (1988-2005)
 
; [[Hideya]]
* [https://www.youtube.com/watch?v=dxjBt4Umbw4 ''Like yamashiro''] (2021)
* [https://www.youtube.com/watch?v=h75K1KOb5is ''Like Ensor's paintings''] (2023)
 
; [[Nathan Ho]]
* [https://www.youtube.com/watch?v=DR1SSW-kQqs ''8edo minimal techno in SuperCollider''] (2023)
 
; [[Aaron Andrew Hunt]]
* [https://aaronandrewhunt.bandcamp.com/track/fantasia-fugue-a4-in-8et "Fantasia & Fugue a4 in 8ET"], from [https://aaronandrewhunt.bandcamp.com/album/the-equal-tempered-keyboard ''The Equal-Tempered Keyboard''] (1999-2022)
 
; [[NullPointerException Music]]
* [https://www.youtube.com/watch?v=CryT-HTzrZE "Disorient"], from [https://www.youtube.com/playlist?list=PLg1YtcJbLxnwTJkG4m0BWZWxIHj7ScdNn ''Edolian''] (2020)
* [https://www.youtube.com/watch?v=AErBW21bljk ''Towards Dissolution''] (2020)
 
; [[User:Phanomium|Phanomium]]
* [https://www.youtube.com/watch?v=22OKO6e6nGk ''Octahedron''] (2024)
 
; [[Carlo Serafini]]
* ''FunkEight 1'' (2013) – [http://www.seraph.it/blog_files/86557ece0348a8d042346d5e1b13e2d9-166.html blog] | [http://www.seraph.it/dep/det/FunkEight1.mp3 play]
 
; [[Sevish]]
* [https://youtu.be/1fpYEVEdcaE ''Reckoner''] (2025)
 
; [[Jake Sherman]]
* [https://www.youtube.com/watch?v=0mpDeL7iybI ''News To Me''] (2011)
* [https://www.youtube.com/watch?v=HvDEoZ4LIdc ''Tomorrow Night (pop music from 2045)''] (2011)
 
; [[Ron Sword]]
* [http://www.ronsword.com/sounds/ronsword_8edo_improv.mp3 ''Acoustic Improvisation in 8EDO'']{{dead link}}
 
; [[Stephen Weigel]]
* [https://soundcloud.com/overtoneshock/tenacious-chorale-9-edo-and-8-edo-live ''Tenacious Chorale'': Movement 2] (2016)
 
; [[Randy Winchester]]
* [https://archive.org/details/jamendo-005173/07.mp3 "7. 8 / octave"], from ''[[Comets Over Flatland]]'' (2007)
 
; [[User:Fitzgerald_Lee|Fitzgerald Lee]]
* [https://youtu.be/zwRDfjLzXkU Jonky Jazz] (2025)
 
== Ear training ==
8edo ear-training exercises by Alex Ness available [https://drive.google.com/a/playgroundsessions.com/folderview?id=0BwsXD8q2VCYUamtVWEgyRFA5alU&usp=sharing#list here].
 
== See also ==
* [[Octatonic scale]] - a scale based on alternating whole and half steps
* [[Fendo family]] - temperaments closely related to 8edo
 
[[Category:8-tone scales]]
[[Category:Listen]]
Retrieved from "https://en.xen.wiki/w/8edo"