Sensamagic chords: Difference between revisions

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<h2>IMPORTED REVISION FROM WIKISPACES</h2>
A '''sensamagic chord''' is an [[essentially tempered dyadic chord]] tempered by the sensamagic comma, [[245/243]].  
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>2011-12-11 17:13:25 UTC</tt>.<br>
: The original revision id was <tt>284765720</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 //sensamagic chord// is an [[Dyadic chord#Essentially tempered dyadic chords|essentially tempered dyadic chord]] tempered by the sensamagic comma, 245/243. The sensamagic triad is a sensamagic chord with three notes when reduced to the octave, which in close position consists of two supermajor thirds, approximately 9/7, and a minor third, approximately 6/5, or in other words a 9/7-9/7-6/5 chord, which closes at the octave because the sensamagic comma, 245/243, is tempered out. It can also be described as a sensamagic-tempered version of 1-9/7-5/3. The other sensamagic triads are the chord 1-7/6-9/7, with steps of 7/6-10/9-14/9, and its inversion 1-7/6-9/5, with steps 7/6-14/9-10/9.


For sensamagic tetrads there are 1-7/6-9/7-3/2, with steps 7/6-10/9-7/6-4/3; 1-7/6-3/2-9/5 with steps 7/6-9/7-6/5-10/9 and its inversion 1-9/7-3/2-5/3 with steps 9/7-7/6-10/9-6/5; 1-7/6-7/5-9/5 with steps 7/6-6/5-9/7-10/9 and its inversion 1-7/6-9/7-5/3 with steps 7/6-10/9-9/7-6/5; and 1-7/6-9/7-9/5 with steps 7/6-10/9-7/5-10/9. For pentads there are 1-7/6-9/7-3/2-5/3 with steps 7/6-10/9-7/6-10/9-6/5 and its inversion, 1-7/6-9/7-3/2-9/5 with steps 7/6-10/9-7/6-6/5-10/9. Equal temperaments with sensamagic chords include 19, 22, 27, 41, 46, 65, 68, 87, 128, 196, 283, 324d, 411bd, 607bd and 694bd.</pre></div>
The [[9-odd-limit]] sensamagic chords are of [[Dyadic chord/Pattern of essentially tempered chords|pattern 1a]], meaning that there are 3 triads, 6 tetrads and 2 pentads, for a total of 11 distinct chord structures. In this article, voicing with the [[perfect fifth]] is prioritized.  
<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;sensamagic chords&lt;/title&gt;&lt;/head&gt;&lt;body&gt;A &lt;em&gt;sensamagic chord&lt;/em&gt; is an &lt;a class="wiki_link" href="/Dyadic%20chord#Essentially tempered dyadic chords"&gt;essentially tempered dyadic chord&lt;/a&gt; tempered by the sensamagic comma, 245/243. The sensamagic triad is a sensamagic chord with three notes when reduced to the octave, which in close position consists of two supermajor thirds, approximately 9/7, and a minor third, approximately 6/5, or in other words a 9/7-9/7-6/5 chord, which closes at the octave because the sensamagic comma, 245/243, is tempered out. It can also be described as a sensamagic-tempered version of 1-9/7-5/3. The other sensamagic triads are the chord 1-7/6-9/7, with steps of 7/6-10/9-14/9, and its inversion 1-7/6-9/5, with steps 7/6-14/9-10/9.&lt;br /&gt;
The sensamagic triad is a sensamagic chord with three notes when reduced to the octave. One of the sensamagic triads in close position consists of two supermajor thirds, approximately [[9/7]], and a minor third, approximately [[6/5]], which closes at the octave because the sensamagic comma, 245/243, is tempered out:
&lt;br /&gt;
* 1–9/7–5/3 with steps of 9/7, 9/7, 6/5.  
For sensamagic tetrads there are 1-7/6-9/7-3/2, with steps 7/6-10/9-7/6-4/3; 1-7/6-3/2-9/5 with steps 7/6-9/7-6/5-10/9 and its inversion 1-9/7-3/2-5/3 with steps 9/7-7/6-10/9-6/5; 1-7/6-7/5-9/5 with steps 7/6-6/5-9/7-10/9 and its inversion 1-7/6-9/7-5/3 with steps 7/6-10/9-9/7-6/5; and 1-7/6-9/7-9/5 with steps 7/6-10/9-7/5-10/9. For pentads there are 1-7/6-9/7-3/2-5/3 with steps 7/6-10/9-7/6-10/9-6/5 and its inversion, 1-7/6-9/7-3/2-9/5 with steps 7/6-10/9-7/6-6/5-10/9. Equal temperaments with sensamagic chords include 19, 22, 27, 41, 46, 65, 68, 87, 128, 196, 283, 324d, 411bd, 607bd and 694bd.&lt;/body&gt;&lt;/html&gt;</pre></div>
 
[[File:sensamagic.jpg|alt=sensamagic.jpg|thumb|Sensamagic triad]]
 
The other sensamagic triads are
* 1–7/6–9/7, with steps 7/6, 10/9, 14/9, and its inversion
* 1–7/6–9/5, with steps 7/6, 14/9, 10/9.
 
For sensamagic tetrads there are the following palindromes:
* 1–7/6–9/7–3/2, with steps 7/6, 10/9, 7/6, 4/3;  
* 1–7/6–9/7–9/5 with steps 7/6, 10/9, 7/5, 10/9.
 
And the following inversely related pairs:
* 1–7/6–3/2–9/5 with steps 7/6, 9/7, 6/5, 10/9 and its inversion  
* 1–9/7–3/2–5/3 with steps 9/7, 7/6, 10/9, 6/5;  
* 1–7/6–7/5–9/5 with steps 7/6, 6/5, 9/7, 10/9 and its inversion  
* 1–7/6–9/7–5/3 with steps 7/6, 10/9, 9/7, 6/5.  
 
For pentads there are
* 1–7/6–9/7–3/2–5/3 with steps 7/6, 10/9, 7/6, 10/9, 6/5 and its inversion,  
* 1–7/6–9/7–3/2–9/5 with steps 7/6, 10/9, 7/6, 6/5, 10/9.  
 
[[Equal temperament]]s with sensamagic chords include {{EDOs| 19, 22, 27, 41, 46, 65, 68, 87, 128, 196, 283 }}, with 283edo giving the [[optimal patent val]].  
 
== See also ==
* [[Undecimal sensamagic chords]]
 
[[Category:9-odd-limit chords]]
[[Category:Essentially tempered chords]]
[[Category:Triads]]
[[Category:Tetrads]]
[[Category:Pentads]]
[[Category:Sensamagic]]

Latest revision as of 10:12, 9 October 2024

A sensamagic chord is an essentially tempered dyadic chord tempered by the sensamagic comma, 245/243.

The 9-odd-limit sensamagic chords are of pattern 1a, meaning that there are 3 triads, 6 tetrads and 2 pentads, for a total of 11 distinct chord structures. In this article, voicing with the perfect fifth is prioritized.

The sensamagic triad is a sensamagic chord with three notes when reduced to the octave. One of the sensamagic triads in close position consists of two supermajor thirds, approximately 9/7, and a minor third, approximately 6/5, which closes at the octave because the sensamagic comma, 245/243, is tempered out:

  • 1–9/7–5/3 with steps of 9/7, 9/7, 6/5.
sensamagic.jpg
Sensamagic triad

The other sensamagic triads are

  • 1–7/6–9/7, with steps 7/6, 10/9, 14/9, and its inversion
  • 1–7/6–9/5, with steps 7/6, 14/9, 10/9.

For sensamagic tetrads there are the following palindromes:

  • 1–7/6–9/7–3/2, with steps 7/6, 10/9, 7/6, 4/3;
  • 1–7/6–9/7–9/5 with steps 7/6, 10/9, 7/5, 10/9.

And the following inversely related pairs:

  • 1–7/6–3/2–9/5 with steps 7/6, 9/7, 6/5, 10/9 and its inversion
  • 1–9/7–3/2–5/3 with steps 9/7, 7/6, 10/9, 6/5;
  • 1–7/6–7/5–9/5 with steps 7/6, 6/5, 9/7, 10/9 and its inversion
  • 1–7/6–9/7–5/3 with steps 7/6, 10/9, 9/7, 6/5.

For pentads there are

  • 1–7/6–9/7–3/2–5/3 with steps 7/6, 10/9, 7/6, 10/9, 6/5 and its inversion,
  • 1–7/6–9/7–3/2–9/5 with steps 7/6, 10/9, 7/6, 6/5, 10/9.

Equal temperaments with sensamagic chords include 19, 22, 27, 41, 46, 65, 68, 87, 128, 196, 283, with 283edo giving the optimal patent val.

See also

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