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<h2>IMPORTED REVISION FROM WIKISPACES</h2>
'''Zeus''' is a [[rank-3 temperament|rank-3]] [[regular temperament|temperament]] generated by an [[2/1|octave]], a [[3/2|fifth]], and a neutral second which stands in for both undecimal neutral seconds of [[11/10]] and [[12/11]] as well as the septimal neutral second of [[35/32]], [[tempering out]] [[121/120]], [[176/175]], and [[385/384]]. Notice {{nowrap| 121/120 {{=}} (176/175)⋅(385/384)}}. That makes 11-limit harmony particularly efficient and deeply entangled with 7-limit harmony. This temperament is, in fact, one of the best ways to further temper on top of tempering out 121/120. That said, 121/120 is such a comma that, on tempering out, will neutralize the distinction between many otonal- and utonal-11 chords, so it might not fit those who wish to explore the subtlety of tones in the 11-limit.
This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br>
: This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2013-12-06 21:50:03 UTC</tt>.<br>
: The original revision id was <tt>475389780</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">See[[Porwell family#Zeus|Zeus]]


Gencom: [2 3 11/10; 121/120 176/175 351/350]
It also has an obvious extension to the 13-limit tempering out [[351/350]] and [[352/351]].
Gencom Mapping: [&lt;1 0 1 4 2 7|, &lt;0 1 1 -1 1 -2|, &lt;0 0 -2 3 -1 -1|]
=Spectrum of Zeus Tunings by Eigenmonzos, Assuming Pure 2 and 7/5=
||~ Eigenmonzo ||~ 3/2 ||~ 5/4 ||
|| 12/11 || 685.337 || 384.062 ||
|| 15/11 || 689.089 || 384.813 ||
|| 5/4 || 696.593 || 386.314 ||
|| 11/9 || 697.207 || 386.436 ||
|| 14/13 || 700.880 || 387.171 ||
|| 16/15 || 701.061 || 387.207 ||
|| 15/13 || 701.179 || 387.231 ||
|| 16/13 || 701.237 || 387.243 ||
|| 13/12 || 701.449 || 387.285 ||
|| 18/13 || 701.564 || 387.308 ||
|| 4/3 || 701.955 || 387.386 (7, 9 and 15 limit minimax) ||
|| 10/9 || 702.551 || 387.505 (11 and 13 limit minimax) ||
|| 6/5 || 703.296 || 387.654 ||
|| 13/11 || 703.597 || 387.714 ||
|| 11/8 || 713.034 || 389.602 ||
|| 11/10 || 721.254 || 391.246 ||
</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;Zeus&lt;/title&gt;&lt;/head&gt;&lt;body&gt;See&lt;a class="wiki_link" href="/Porwell%20family#Zeus"&gt;Zeus&lt;/a&gt;&lt;br /&gt;
&lt;br /&gt;
Gencom: [2 3 11/10; 121/120 176/175 351/350]&lt;br /&gt;
Gencom Mapping: [&amp;lt;1 0 1 4 2 7|, &amp;lt;0 1 1 -1 1 -2|, &amp;lt;0 0 -2 3 -1 -1|]&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:0:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc0"&gt;&lt;a name="Spectrum of Zeus Tunings by Eigenmonzos, Assuming Pure 2 and 7/5"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:0 --&gt;Spectrum of Zeus Tunings by Eigenmonzos, Assuming Pure 2 and 7/5&lt;/h1&gt;


See [[Biyatismic clan #Zeus]] for technical data.


&lt;table class="wiki_table"&gt;
== Interval lattice ==
    &lt;tr&gt;
<gallery>
        &lt;th&gt;Eigenmonzo&lt;br /&gt;
File:Lattice Zeus.png|11-limit zeus
&lt;/th&gt;
File:Lattice Zeus13.png|13-limit zeus
        &lt;th&gt;3/2&lt;br /&gt;
</gallery>
&lt;/th&gt;
        &lt;th&gt;5/4&lt;br /&gt;
&lt;/th&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;12/11&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;685.337&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;384.062&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;15/11&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;689.089&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;384.813&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;5/4&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;696.593&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;386.314&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;11/9&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;697.207&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;386.436&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;14/13&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;700.880&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;387.171&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;16/15&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;701.061&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;387.207&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;15/13&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;701.179&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;387.231&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;16/13&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;701.237&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;387.243&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;13/12&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;701.449&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;387.285&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;18/13&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;701.564&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;387.308&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;4/3&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;701.955&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;387.386 (7, 9 and 15 limit minimax)&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;10/9&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;702.551&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;387.505 (11 and 13 limit minimax)&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;6/5&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;703.296&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;387.654&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;13/11&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;703.597&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;387.714&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;11/8&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;713.034&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;389.602&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;11/10&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;721.254&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;391.246&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
&lt;/table&gt;


&lt;/body&gt;&lt;/html&gt;</pre></div>
== Chords ==
Zeus enables [[essentially tempered chord]]s of [[biyatismic chords|biyatismic]], [[valinorsmic chords|valinorsmic]], and [[keenanismic chords|keenanismic]].
 
== Scales ==
* [[Zeus1]]
* [[Zeus2]]
* [[Zeus3]]
* [[Zeus4]]
* [[Zeus5]]
* [[Zeus6]]
* [[Zeus7]]
* [[Zeus7tri]]
* [[Zeus8tri]]
* [[Genus1155zeus]]
 
== Tunings ==
=== Tuning spectrum ===
This spectrum assumes pure 2 and 7/5.
 
{| class="wikitable center-1 center-2 center-3"
|-
! [[Eigenmonzo|Eigenmonzo<br>(Unchanged-interval)]]
! Fifth<br>(¢)
! Major<br>Third (¢)
! Comments
|-
| 12/11
| 685.337
| 384.062
|
|-
| 15/11
| 689.089
| 384.813
|
|-
| 5/4
| 696.593
| 386.314
|
|-
| 11/9
| 697.207
| 386.436
|
|-
| 14/13
| 700.880
| 387.171
|
|-
| 16/15
| 701.061
| 387.207
|
|-
| 15/13
| 701.179
| 387.231
|
|-
| 16/13
| 701.237
| 387.243
|
|-
| 13/12
| 701.449
| 387.285
|
|-
| 18/13
| 701.564
| 387.308
|
|-
| 4/3
| 701.955
| 387.386
| 7-, 9- and 15-odd-limit minimax
|-
| 10/9
| 702.551
| 387.505
| 11- and 13-odd-limit minimax
|-
| 6/5
| 703.296
| 387.654
|
|-
| 13/11
| 703.597
| 387.714
|
|-
| 11/8
| 713.034
| 389.602
|
|-
| 11/10
| 721.254
| 391.246
|
|}
 
== Music ==
; [[Mundoworld]]
* [https://www.youtube.com/watch?v=zo1IYJW43II ''Cloudtop Reverie''] (2021) – in Zeus[7], 99edo tuning
 
[[Category:Zeus| ]] <!-- main article -->
[[Category:Rank-3 temperaments]]
[[Category:Porwell family]]
[[Category:Biyatismic clan]]
[[Category:Valinorsmic clan]]
[[Category:Keenanismic temperaments]]
Retrieved from "https://en.xen.wiki/w/Zeus"