Jove chords: Difference between revisions

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<h2>IMPORTED REVISION FROM WIKISPACES</h2>
A '''jove chord''' is an [[11-odd-limit]] [[essentially tempered chord]] in [[jove]] temperament. Since [[243/242]] is tempered out, [[rastmic chords]] are also jove chords; since [[441/440]] is tempered out, [[werckismic chords]] are also jove chords; and since [[540/539]] is tempered out, [[swetismic chords]] are also jove chords. Aside from these, there are also essentially jove tempered chords.  
This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br>
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: The original revision id was <tt>286729950</tt>.<br>
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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">A //jove chord// is an 11 odd limit [[Dyadic chord|essentially tempered chords]] chords in [[Breed family#Jove, aka Wonder|jove temperament]]. Since 243/242 is tempered out, [[rastmic chords]] are also jove chords; since 441/440 is tempered out, [[werckismic chords]] are also jove chords; and since 540/539 is tempered out, [[swetismic chords]] are also jove chords. Aside from these, there are also essentially jove tempered chords.  


These are nine tetrads, one palindromic tetrad and four pairs in inverse relationship: 1-11/9-10/7-7/4 with steps 11/9-7/6-11/9-8/7; 1-11/9-3/2-7/4 with steps 11/9-11/9-7/6-8/7 and 1-11/9-3/2-12/7 with steps 11/9-11/9-8/7-7/6; 1-9/8-11/9-7/4 with steps 9/8-12/11-10/7-8/7 and 1-10/7-14/9-7/4 with steps 10/7-12/11-9/8-8/7; 1-9/8-11/7-11/6 with steps 9/8-7/5-7/6-12/11 and 1-9/8-11/9-10/7 and with steps 9/8-12/11-7/6-7/5; 1-9/7-7/5-11/7 with steps 9/7-12/11-9/8-14/11 and 1-9/7-18/11-11/6 with steps 9/7-14/11-9/8-12/11.
These are nine tetrads, one palindromic tetrad and four pairs in inverse relationship:  
* 1–11/9–10/7–7/4 with steps 11/9, 7/6, 11/9, 8/7;  
* 1–11/9–3/2–7/4 with steps 11/9, 11/9, 7/6, 8/7, and its inverse
* 1–11/9–3/2–12/7 with steps 11/9, 11/9, 8/7, 7/6;  
* 1–9/8–11/9–7/4 with steps 9/8, 12/11, 10/7, 8/7, and its inverse
* 1–10/7–14/9–7/4 with steps 10/7, 12/11, 9/8, 8/7;  
* 1–9/8–11/7–11/6 with steps 9/8, 7/5, 7/6, 12/11, and its inverse
* 1–9/8–11/9–10/7 with steps 9/8, 12/11, 7/6, 7/5;  
* 1–9/7–7/5–11/7 with steps 9/7, 12/11, 9/8, 14/11, and its inverse
* 1–9/7–18/11–11/6 with steps 9/7, 14/11, 9/8, 12/11.


There are sixteen essentially jove pentads, consisting of eight inverse pairs. These are 1-11/9-10/7-11/7-7/4 with steps 11/9-7/6-11/10-10/9-8/7 and 1-7/6-10/7-18/11-20/11 with steps 7/6-11/9-8/7-10/9-11/10; 1-7/6-3/2-18/11-11/6 with steps 7/6-9/7-12/11-9/8-12/11 and 1-9/7-3/2-18/11-11/6 with steps 9/7-7/6-12/11-9/8-12/11; 1-11/9-11/8-3/2-7/4 with steps 11/9-9/8-12/11-7/6-8/7 and 1-12/11-11/9-3/2-12/7 with steps 12/11-9/8-11/9-8/7-7/6; 1-9/8-11/9-3/2-7/4 with steps 9/8-12/11-11/9-7/6-8/7 and 1-9/8-9/7-3/2-11/6 with steps 9/8-8/7-7/6-11/9-12/11; 1-9/8-11/9-10/7-7/4 with steps 9/8-12/11-7/6-11/9-8/7 and 1-11/9-10/7-14/9-7/4 with steps 11/9-7/6-12/11-9/8-8/7; 1-9/8-11/9-10/7-11/7 with steps 9/8-12/11-7/6-11/10-14/11 and 1-9/8-10/7-11/7-11/6 with steps 9/8-14/11-11/10-7/6-12/11; 1-9/8-11/9-11/8-7/4 with steps 9/8-12/11-9/8-14/11-8/7 and 1-14/11-10/7-14/9-7/4 with steps 14/11-9/8-12/11-9/8-8/7; and 1-9/8-11/9-11/7-7/4 with steps 9/8-12/11-9/7-10/9-8/7 and 1-9/7-7/5-11/7-9/5 with steps 9/7-12/11-9/8-8/7-10/9.
There are sixteen essentially jove pentads, consisting of eight inverse pairs. These are  
* 1–11/9–10/7–11/7–7/4 with steps 11/9, 7/6, 11/10, 10/9, 8/7, and its inverse
* 1–7/6–10/7–18/11–20/11 with steps 7/6, 11/9, 8/7, 10/9, 11/10;  
* 1–7/6–3/2–18/11–11/6 with steps 7/6, 9/7, 12/11, 9/8, 12/11, and its inverse
* 1–9/7–3/2–18/11–11/6 with steps 9/7, 7/6, 12/11, 9/8, 12/11;  
* 1–11/9–11/8–3/2–7/4 with steps 11/9, 9/8, 12/11, 7/6, 8/7, and its inverse
* 1–12/11–11/9–3/2–12/7 with steps 12/11, 9/8, 11/9, 8/7, 7/6;  
* 1–9/8–11/9–3/2–7/4 with steps 9/8, 12/11, 11/9, 7/6, 8/7, and its inverse
* 1–9/8–9/7–3/2–11/6 with steps 9/8, 8/7, 7/6, 11/9, 12/11;  
* 1–9/8–11/9–10/7–7/4 with steps 9/8, 12/11, 7/6, 11/9, 8/7, and its inverse
* 1–11/9–10/7–14/9–7/4 with steps 11/9, 7/6, 12/11, 9/8, 8/7;  
* 1–9/8–11/9–10/7–11/7 with steps 9/8, 12/11, 7/6, 11/10, 14/11, and its inverse
* 1–9/8–10/7–11/7–11/6 with steps 9/8, 14/11, 11/10, 7/6, 12/11;  
* 1–9/8–11/9–11/8–7/4 with steps 9/8, 12/11, 9/8, 14/11, 8/7, and its inverse
* 1–14/11–10/7–14/9–7/4 with steps 14/11, 9/8, 12/11, 9/8, 8/7;  
* 1–9/8–11/9–11/7–7/4 with steps 9/8, 12/11, 9/7, 10/9, 8/7, and its inverse
* 1–9/7–7/5–11/7–9/5 with steps 9/7, 12/11, 9/8, 8/7, 10/9.


Finally, there are six essentially jove hexads, two palindromic and two pairs of inversely related chords: 1-9/8-11/9-11/8-11/7-7/4 with steps 9/8-12/11-9/8-8/7-10/9-8/7; 1-7/6-9/7-3/2-18/11-11/6 with steps 7/6-11/10-7/6-12/11-9/8-12/11; 1-9/8-9/7-3/2-18/11-11/6 with steps 9/8-8/7-7/6-12/11-9/8-12/11 and 1-9/8-11/9-11/8-3/2-7/4 with steps 9/8-12/11-9/8-12/11-7/6-8/7; and a pair whose steps are permutations of the JI hexad--1-9/8-9/7-10/7-11/7-11/6 with steps 9/8-8/7-10/9-11/10-7/6-12/11 and 1-9/8-11/9-10/7-11/7-7/4 with steps 9/8-12/11-7/6-11/10-10/9-8/7.
Finally, there are six essentially jove hexads, two palindromic and two pairs of inversely related chords:  
* 1–9/8–11/9–11/8–11/7–7/4 with steps 9/8, 12/11, 9/8, 8/7, 10/9, 8/7;  
* 1–7/6–9/7–3/2–18/11–11/6 with steps 7/6, 11/10, 7/6, 12/11, 9/8, 12/11;  
* 1–9/8–9/7–3/2–18/11–11/6 with steps 9/8, 8/7, 7/6, 12/11, 9/8, 12/11, and its inverse
* 1–9/8–11/9–11/8–3/2–7/4 with steps 9/8, 12/11, 9/8, 12/11, 7/6, 8/7;  
* 1–9/8–9/7–10/7–11/7–11/6 with steps 9/8, 8/7, 10/9, 11/10, 7/6, 12/11, and its inverse
* 1–9/8–11/9–10/7–11/7–7/4 with steps 9/8, 12/11, 7/6, 11/10, 10/9, 8/7.


Equal divisions with jove tetrads include 31, 41, 58, 72, 130, 161, 171 and 202.  </pre></div>
The essentially jove chords number tetrads: 9, pentads: 16, hexads: 6, for a total of 31.
<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;jove chords&lt;/title&gt;&lt;/head&gt;&lt;body&gt;A &lt;em&gt;jove chord&lt;/em&gt; is an 11 odd limit &lt;a class="wiki_link" href="/Dyadic%20chord"&gt;essentially tempered chords&lt;/a&gt; chords in &lt;a class="wiki_link" href="/Breed%20family#Jove, aka Wonder"&gt;jove temperament&lt;/a&gt;. Since 243/242 is tempered out, &lt;a class="wiki_link" href="/rastmic%20chords"&gt;rastmic chords&lt;/a&gt; are also jove chords; since 441/440 is tempered out, &lt;a class="wiki_link" href="/werckismic%20chords"&gt;werckismic chords&lt;/a&gt; are also jove chords; and since 540/539 is tempered out, &lt;a class="wiki_link" href="/swetismic%20chords"&gt;swetismic chords&lt;/a&gt; are also jove chords. Aside from these, there are also essentially jove tempered chords. &lt;br /&gt;
[[Equal temperament]]s with jove tetrads include {{EDOs| 31, 41, 58, 72, 130, 161, 171 and 202 }}.
&lt;br /&gt;
 
These are nine tetrads, one palindromic tetrad and four pairs in inverse relationship: 1-11/9-10/7-7/4 with steps 11/9-7/6-11/9-8/7; 1-11/9-3/2-7/4 with steps 11/9-11/9-7/6-8/7 and 1-11/9-3/2-12/7 with steps 11/9-11/9-8/7-7/6; 1-9/8-11/9-7/4 with steps 9/8-12/11-10/7-8/7 and 1-10/7-14/9-7/4 with steps 10/7-12/11-9/8-8/7; 1-9/8-11/7-11/6 with steps 9/8-7/5-7/6-12/11 and 1-9/8-11/9-10/7 and with steps 9/8-12/11-7/6-7/5; 1-9/7-7/5-11/7 with steps 9/7-12/11-9/8-14/11 and 1-9/7-18/11-11/6 with steps 9/7-14/11-9/8-12/11.&lt;br /&gt;
[[Category:11-odd-limit chords]]
&lt;br /&gt;
[[Category:Essentially tempered chords]]
There are sixteen essentially jove pentads, consisting of eight inverse pairs. These are 1-11/9-10/7-11/7-7/4 with steps 11/9-7/6-11/10-10/9-8/7 and 1-7/6-10/7-18/11-20/11 with steps 7/6-11/9-8/7-10/9-11/10; 1-7/6-3/2-18/11-11/6 with steps 7/6-9/7-12/11-9/8-12/11 and 1-9/7-3/2-18/11-11/6 with steps 9/7-7/6-12/11-9/8-12/11; 1-11/9-11/8-3/2-7/4 with steps 11/9-9/8-12/11-7/6-8/7 and 1-12/11-11/9-3/2-12/7 with steps 12/11-9/8-11/9-8/7-7/6; 1-9/8-11/9-3/2-7/4 with steps 9/8-12/11-11/9-7/6-8/7 and 1-9/8-9/7-3/2-11/6 with steps 9/8-8/7-7/6-11/9-12/11; 1-9/8-11/9-10/7-7/4 with steps 9/8-12/11-7/6-11/9-8/7 and 1-11/9-10/7-14/9-7/4 with steps 11/9-7/6-12/11-9/8-8/7; 1-9/8-11/9-10/7-11/7 with steps 9/8-12/11-7/6-11/10-14/11 and 1-9/8-10/7-11/7-11/6 with steps 9/8-14/11-11/10-7/6-12/11; 1-9/8-11/9-11/8-7/4 with steps 9/8-12/11-9/8-14/11-8/7 and 1-14/11-10/7-14/9-7/4 with steps 14/11-9/8-12/11-9/8-8/7; and 1-9/8-11/9-11/7-7/4 with steps 9/8-12/11-9/7-10/9-8/7 and 1-9/7-7/5-11/7-9/5 with steps 9/7-12/11-9/8-8/7-10/9.&lt;br /&gt;
[[Category:Tetrads]]
&lt;br /&gt;
[[Category:Pentads]]
Finally, there are six essentially jove hexads, two palindromic and two pairs of inversely related chords: 1-9/8-11/9-11/8-11/7-7/4 with steps 9/8-12/11-9/8-8/7-10/9-8/7; 1-7/6-9/7-3/2-18/11-11/6 with steps 7/6-11/10-7/6-12/11-9/8-12/11; 1-9/8-9/7-3/2-18/11-11/6 with steps 9/8-8/7-7/6-12/11-9/8-12/11 and 1-9/8-11/9-11/8-3/2-7/4 with steps 9/8-12/11-9/8-12/11-7/6-8/7; and a pair whose steps are permutations of the JI hexad--1-9/8-9/7-10/7-11/7-11/6 with steps 9/8-8/7-10/9-11/10-7/6-12/11 and 1-9/8-11/9-10/7-11/7-7/4 with steps 9/8-12/11-7/6-11/10-10/9-8/7.&lt;br /&gt;
[[Category:Hexads]]
&lt;br /&gt;
[[Category:Jove]]
Equal divisions with jove tetrads include 31, 41, 58, 72, 130, 161, 171 and 202.&lt;/body&gt;&lt;/html&gt;</pre></div>