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>
: This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2011-12-15 22:25:11 UTC</tt>.<br>
: The original revision id was <tt>286729950</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">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>

Latest revision as of 12:51, 17 October 2024

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.

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 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 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.

The essentially jove chords number tetrads: 9, pentads: 16, hexads: 6, for a total of 31.

Equal temperaments with jove tetrads include 31, 41, 58, 72, 130, 161, 171 and 202.

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