Mothwellsmic chords: Difference between revisions

Latest revision as of 10:23, 10 October 2024

Mothwellsmic chords are essentially tempered chords tempered by the mothwellsma, 99/98.

There are one triad, six tetrads and four pentads as 2.3.7.11 subgroup 11-odd-limit essentially tempered chords.

The mothwellsmic triad consists of a stack of two 7/6's and 16/11 closing at the octave:

1–7/6–11/8 with steps 7/6, 7/6, 16/11.

For tetrads, there are two palindromic chords and two pairs of chords in inverse relationship. The palindromic chords are

1–11/8–11/7–7/4 with steps 11/8, 8/7, 9/8, 8/7;
1–7/6–9/7–3/2 with steps 7/6, 12/11, 7/6, 4/3.

The inversely related pairs of chords are

1–7/6–11/8–3/2 with steps 7/6, 7/6, 12/11, 4/3, and its inverse
1–12/11–9/7–3/2 with steps 12/11, 7/6, 7/6, 4/3;
1–9/7–3/2–7/4 with steps 9/7, 7/6, 7/6, 8/7, and its inverse
1–7/6–3/2–12/7 with steps 7/6, 9/7, 8/7, 7/6.

For pentads, there are two palindromic chords and a pair of chords in inverse relationship. The palindromic chords are

1–9/8–9/7–3/2–7/4 with steps 9/8, 8/7, 7/6, 7/6, 8/7;
1–7/6–11/8–3/2–11/6 with steps 7/6, 7/6, 12/11, 11/9, 12/11.

The inversely related pair of chords is

1–7/6–9/7–3/2–7/4 with steps 7/6, 12/11, 7/6, 7/6, 8/7, and its inverse
1–7/6–9/7–3/2–12/7 with steps 7/6, 12/11, 7/6, 8/7, 7/6.

Equal temperaments with mothwellsmic chords include 22, 31, 53, 96, and 127.

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-<h2>IMPORTED REVISION FROM WIKISPACES</h2>
+'''Mothwellsmic chords''' are [[essentially tempered chord]]s tempered by the mothwellsma, [[99/98]].
-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>2011-10-19 02:16:28 UTC</tt>.<br>
+There are one triad, six tetrads and four pentads as 2.3.7.11 subgroup [[11-odd-limit]] essentially tempered chords.
-: The original revision id was <tt>266267912</tt>.<br>
-: The revision comment was: <tt></tt><br>
+The mothwellsmic triad consists of a stack of two [[7/6]]'s and [[16/11]] closing at the octave:
-The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.<br>
+* 1–7/6–11/8 with steps 7/6, 7/6, 16/11.
-<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">The mothwellsmic triad is an [[Dyadic chord|essentially tempered chord]] which is the 99/98 tempering of 1-7/6-11/8, with steps of 7/6-7/6-11/8.</pre></div>
+For tetrads, there are two palindromic chords and two pairs of chords in inverse relationship. The palindromic chords are
-<h4>Original HTML content:</h4>
+* 1–11/8–11/7–7/4 with steps 11/8, 8/7, 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;width:200%;white-space: pre-wrap ! important" class="old-revision-html">&lt;html&gt;&lt;head&gt;&lt;title&gt;mothwellsmic triad&lt;/title&gt;&lt;/head&gt;&lt;body&gt;The mothwellsmic triad is an &lt;a class="wiki_link" href="/Dyadic%20chord"&gt;essentially tempered chord&lt;/a&gt; which is the 99/98 tempering of 1-7/6-11/8, with steps of 7/6-7/6-11/8.&lt;/body&gt;&lt;/html&gt;</pre></div>
+* 1–7/6–9/7–3/2 with steps 7/6, 12/11, 7/6, 4/3.
+The inversely related pairs of chords are
+* 1–7/6–11/8–3/2 with steps 7/6, 7/6, 12/11, 4/3, and its inverse
+* 1–12/11–9/7–3/2 with steps 12/11, 7/6, 7/6, 4/3;
+* 1–9/7–3/2–7/4 with steps 9/7, 7/6, 7/6, 8/7, and its inverse
+* 1–7/6–3/2–12/7 with steps 7/6, 9/7, 8/7, 7/6.
+For pentads, there are two palindromic chords and a pair of chords in inverse relationship. The palindromic chords are
+* 1–9/8–9/7–3/2–7/4 with steps 9/8, 8/7, 7/6, 7/6, 8/7;
+* 1–7/6–11/8–3/2–11/6 with steps 7/6, 7/6, 12/11, 11/9, 12/11.
+The inversely related pair of chords is
+* 1–7/6–9/7–3/2–7/4 with steps 7/6, 12/11, 7/6, 7/6, 8/7, and its inverse
+* 1–7/6–9/7–3/2–12/7 with steps 7/6, 12/11, 7/6, 8/7, 7/6.
+[[Equal temperament]]s with mothwellsmic chords include {{EDOs| 22, 31, 53, 96, and 127 }}.
+[[Category:11-odd-limit chords]]
+[[Category:Essentially tempered chords]]
+[[Category:Triads]]
+[[Category:Tetrads]]
+[[Category:Pentads]]
+[[Category:Mothwellsmic]]

Mothwellsmic chords: Difference between revisions

Latest revision as of 10:23, 10 October 2024

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