Miracle chords: Difference between revisions

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<h2>IMPORTED REVISION FROM WIKISPACES</h2>
A '''miracle chord''' is an [[essentially tempered chord]] of the [[miracle]] temperament; they are included among those listed as [[chords of miracle]]. Aside from the [[swetismic chords|swetismic]], [[werckismic chords|werckismic]], [[keenanismic chords|keenanismic]], [[rastmic chords|rastmic]], [[marvel chords|marvel]], [[undecimal marvel chords|unimarvel]], [[jove chords|jove]] and [[prodigy chords|prodigy]] chords listed there, there are ten further essentially miracle chords. These are the inversely related pair of tetrads:
This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br>
* 1–10/7–8/5–7/4 with steps 10/7, 9/8, 12/11, 8/7, and its inverse
: This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2011-12-19 21:16:05 UTC</tt>.<br>
* 1–9/8–8/5–11/6 with steps 9/8, 10/7, 8/7, 12/11;  
: The original revision id was <tt>287543704</tt>.<br>
 
: The revision comment was: <tt></tt><br>
The three pairs of pentads:
The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.<br>
* 1–5/4–10/7–8/5–7/4 with steps 5/4, 8/7, 9/8, 12/11, 8/7, and its inverse
<h4>Original Wikitext content:</h4>
* 1–5/4–10/7–14/9–7/4 with steps 5/4, 8/7, 12/11, 9/8, 8/7;  
<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 //miracle chord// is an [[Dyadic chord#Essentially tempered dyadic chord]] of miracle temperament; they are included among those listed as [[chords of miracle]]. Aside from the swetismic, werckismic, keenanismic, rastmic, marvel, unimarvel, jove and prodigy chords listed there, there are ten further essentially miracle chords. These are the inversely related pair of tetrads 1-10/7-8/5-7/4 with steps 10/7-9/8-12/11-8/7 and 1-9/8-8/5-11/6 with steps 9/8-10/7-8/7-12/11; the three pairs of pentads 1-5/4-10/7-8/5-7/4 with steps 5/4-8/7-9/8-12/11-8/7 and 1-5/4-10/7-14/9-7/4 with steps 5/4-8/7-12/11-9/8-8/7; 1-11/9-11/8-3/2-12/7 with steps 11/9-9/8-12/11-8/7-7/6 and 1-12/11-11/9-3/2-7/4 with steps 12/11-9/8-11/9-7/6-8/7; 1-9/8-10/7-8/5-7/4 with steps 9/8-14/11-9/8-12/11-8/7 and 1-9/8-10/7-8/5-11/6 with steps 9/8-14/11-9/8-8/7-12/11; and the pair of hexads 1-9/8-5/4-10/7-8/5-7/4 with steps 9/8-10/9-8/7-9/8-12/11-8/7 and 1-10/9-5/4-10/7-14/9-7/4 with steps 10/9-9/8-8/7-12/11-9/8-8/7. </pre></div>
* 1–11/9–11/8–3/2–12/7 with steps 11/9, 9/8, 12/11, 8/7, 7/6, and its inverse
<h4>Original HTML content:</h4>
* 1–12/11–11/9–3/2–7/4 with steps 12/11, 9/8, 11/9, 7/6, 8/7;  
<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;miracle chords&lt;/title&gt;&lt;/head&gt;&lt;body&gt;A &lt;em&gt;miracle chord&lt;/em&gt; is an &lt;a class="wiki_link" href="/Dyadic%20chord#Essentially tempered dyadic chord"&gt;Dyadic chord&lt;/a&gt; of miracle temperament; they are included among those listed as &lt;a class="wiki_link" href="/chords%20of%20miracle"&gt;chords of miracle&lt;/a&gt;. Aside from the swetismic, werckismic, keenanismic, rastmic, marvel, unimarvel, jove and prodigy chords listed there, there are ten further essentially miracle chords. These are the inversely related pair of tetrads 1-10/7-8/5-7/4 with steps 10/7-9/8-12/11-8/7 and 1-9/8-8/5-11/6 with steps 9/8-10/7-8/7-12/11; the three pairs of pentads 1-5/4-10/7-8/5-7/4 with steps 5/4-8/7-9/8-12/11-8/7 and 1-5/4-10/7-14/9-7/4 with steps 5/4-8/7-12/11-9/8-8/7;  1-11/9-11/8-3/2-12/7 with steps 11/9-9/8-12/11-8/7-7/6 and 1-12/11-11/9-3/2-7/4 with steps 12/11-9/8-11/9-7/6-8/7; 1-9/8-10/7-8/5-7/4 with steps 9/8-14/11-9/8-12/11-8/7 and 1-9/8-10/7-8/5-11/6 with steps 9/8-14/11-9/8-8/7-12/11; and the pair of hexads 1-9/8-5/4-10/7-8/5-7/4 with steps 9/8-10/9-8/7-9/8-12/11-8/7 and 1-10/9-5/4-10/7-14/9-7/4 with steps 10/9-9/8-8/7-12/11-9/8-8/7.&lt;/body&gt;&lt;/html&gt;</pre></div>
* 1–9/8–10/7–8/5–7/4 with steps 9/8, 14/11, 9/8, 12/11, 8/7, and its inverse
* 1–9/8–10/7–8/5–11/6 with steps 9/8, 14/11, 9/8, 8/7, 12/11;  
 
And the pair of hexads:
* 1–9/8–5/4–10/7–8/5–7/4 with steps 9/8, 10/9, 8/7, 9/8, 12/11, 8/7, and its inverse
* 1–10/9–5/4–10/7–14/9–7/4 with steps 10/9, 9/8, 8/7, 12/11, 9/8, 8/7.  
 
The count of miracle chords is therefore tetrads: 2, pentads: 6, and hexads: 2.
 
[[Equal temperament]]s allowing miracle chords include {{EDOs| 31, 41, 72, 103, 175, 216c, 247c, 319bcde, 391bcde and 463bcde }}.
 
[[Category:11-odd-limit chords]]
[[Category:Essentially tempered chords]]
[[Category:Tetrads]]
[[Category:Pentads]]
[[Category:Hexads]]
[[Category:Miracle]]

Latest revision as of 12:55, 17 October 2024

A miracle chord is an essentially tempered chord of the miracle temperament; they are included among those listed as chords of miracle. Aside from the swetismic, werckismic, keenanismic, rastmic, marvel, unimarvel, jove and prodigy chords listed there, there are ten further essentially miracle chords. These are the inversely related pair of tetrads:

  • 1–10/7–8/5–7/4 with steps 10/7, 9/8, 12/11, 8/7, and its inverse
  • 1–9/8–8/5–11/6 with steps 9/8, 10/7, 8/7, 12/11;

The three pairs of pentads:

  • 1–5/4–10/7–8/5–7/4 with steps 5/4, 8/7, 9/8, 12/11, 8/7, and its inverse
  • 1–5/4–10/7–14/9–7/4 with steps 5/4, 8/7, 12/11, 9/8, 8/7;
  • 1–11/9–11/8–3/2–12/7 with steps 11/9, 9/8, 12/11, 8/7, 7/6, and its inverse
  • 1–12/11–11/9–3/2–7/4 with steps 12/11, 9/8, 11/9, 7/6, 8/7;
  • 1–9/8–10/7–8/5–7/4 with steps 9/8, 14/11, 9/8, 12/11, 8/7, and its inverse
  • 1–9/8–10/7–8/5–11/6 with steps 9/8, 14/11, 9/8, 8/7, 12/11;

And the pair of hexads:

  • 1–9/8–5/4–10/7–8/5–7/4 with steps 9/8, 10/9, 8/7, 9/8, 12/11, 8/7, and its inverse
  • 1–10/9–5/4–10/7–14/9–7/4 with steps 10/9, 9/8, 8/7, 12/11, 9/8, 8/7.

The count of miracle chords is therefore tetrads: 2, pentads: 6, and hexads: 2.

Equal temperaments allowing miracle chords include 31, 41, 72, 103, 175, 216c, 247c, 319bcde, 391bcde and 463bcde.

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