Bohpier/Chords: Difference between revisions

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<h2>IMPORTED REVISION FROM WIKISPACES</h2>

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-~~28 16~~:18:41 UTC</tt>.<br>

: This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2012-01-05 19:13:42 UTC</tt>.<br>

: The original revision id was <tt>~~288679822~~</tt>.<br>

: The original revision id was <tt>289920621</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>

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<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">Below are listed the [[Dyadic chord|dyadic chords]] of 11-limit [[Sensamagic clan#Bohpier|bohpier temperament]]. The essentially just chords are typed as otonal, utonal, or ambitonal. Those requiring tempering only by 540/539 are swetismic, by 245/243 sensamagic, by 100/99 ptolemismic, and by 1344/1331 hemimin. Chords requiring any two of 540/539, 245/243 or 100/99 are labeled octarod.

Bohpier has MOS of size 8, 9, 17, 25, 33, 41 and 49, and it may be seen that even the eight-note MOS comes equipped with some triads and tetrads. It should also be noted that the generator chain of ~~bohpier~~ is the [[Bohlen-Pierce]] scale. Hence, every chord listed below has a voicing which makes it a chord of Bohlen-Pierce, showing Bohlen-Pierce contains many essentially tempered chords. The listed transversals my be converted to Bohlen-Pierce transversals by adjusting up an octave past 9/5~20/11, so that 7/6 becomes 7/3, 14/11 becomes 28/11, 11/8 becomes 11/4, 3/2 becomes 3, 18/11 becomes 36/11, 5/4 becomes 5, 7/4 becomes 7, and 9/8 becomes 9. It should also be noted that 13-limit bohpier, and hence 13-limit Bohlen-Pierce, has many more 13-limit essentially tempered chords.

Bohpier has MOS of size 8, 9, 17, 25, 33, 41 and 49, and it may be seen that even the eight-note MOS comes equipped with some triads and tetrads. It should also be noted that the generator chain of 7-limitbohpier is the [[Bohlen-Pierce]] scale, and the same is true of 11-limit bohpier if we do not regard 11/4 as a forbidden interval because the denominator is an even number. Hence, every chord listed below has a voicing which makes it a chord of Bohlen-Pierce, showing Bohlen-Pierce contains many essentially tempered chords. The listed transversals my be converted to Bohlen-Pierce transversals by adjusting up an octave past 9/5~20/11, so that 7/6 becomes 7/3, 14/11 becomes 28/11, 11/8 becomes 11/4, 3/2 becomes 3, 18/11 becomes 36/11, 5/4 becomes 5, 7/4 becomes 7, and 9/8 becomes 9. It should also be noted that 13-limit bohpier, and hence 13-limit Bohlen-Pierce, has many more 13-limit essentially tempered chords.

=Triads=

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<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"><html><head><title>Chords of bohpier</title></head><body>Below are listed the <a class="wiki_link" href="/Dyadic%20chord">dyadic chords</a> of 11-limit <a class="wiki_link" href="/Sensamagic%20clan#Bohpier">bohpier temperament</a>. The essentially just chords are typed as otonal, utonal, or ambitonal. Those requiring tempering only by 540/539 are swetismic, by 245/243 sensamagic, by 100/99 ptolemismic, and by 1344/1331 hemimin. Chords requiring any two of 540/539, 245/243 or 100/99 are labeled octarod.<br />

<br />

Bohpier has MOS of size 8, 9, 17, 25, 33, 41 and 49, and it may be seen that even the eight-note MOS comes equipped with some triads and tetrads. It should also be noted that the generator chain of ~~bohpier~~ is the <a class="wiki_link" href="/Bohlen-Pierce">Bohlen-Pierce</a> scale. Hence, every chord listed below has a voicing which makes it a chord of Bohlen-Pierce, showing Bohlen-Pierce contains many essentially tempered chords. The listed transversals my be converted to Bohlen-Pierce transversals by adjusting up an octave past 9/5~20/11, so that 7/6 becomes 7/3, 14/11 becomes 28/11, 11/8 becomes 11/4, 3/2 becomes 3, 18/11 becomes 36/11, 5/4 becomes 5, 7/4 becomes 7, and 9/8 becomes 9. It should also be noted that 13-limit bohpier, and hence 13-limit Bohlen-Pierce, has many more 13-limit essentially tempered chords.<br />

Bohpier has MOS of size 8, 9, 17, 25, 33, 41 and 49, and it may be seen that even the eight-note MOS comes equipped with some triads and tetrads. It should also be noted that the generator chain of 7-limitbohpier is the <a class="wiki_link" href="/Bohlen-Pierce">Bohlen-Pierce</a> scale, and the same is true of 11-limit bohpier if we do not regard 11/4 as a forbidden interval because the denominator is an even number. Hence, every chord listed below has a voicing which makes it a chord of Bohlen-Pierce, showing Bohlen-Pierce contains many essentially tempered chords. The listed transversals my be converted to Bohlen-Pierce transversals by adjusting up an octave past 9/5~20/11, so that 7/6 becomes 7/3, 14/11 becomes 28/11, 11/8 becomes 11/4, 3/2 becomes 3, 18/11 becomes 36/11, 5/4 becomes 5, 7/4 becomes 7, and 9/8 becomes 9. It should also be noted that 13-limit bohpier, and hence 13-limit Bohlen-Pierce, has many more 13-limit essentially tempered chords.<br />

<br />

<h1 id="toc0"><a name="Triads"></a>Triads</h1>

@@ Line 1: / Line 1: @@
 <h2>IMPORTED REVISION FROM WIKISPACES</h2>
 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>2011-12-28 16:18:41 UTC</tt>.<br>
+: This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2012-01-05 19:13:42 UTC</tt>.<br>
-: The original revision id was <tt>288679822</tt>.<br>
+: The original revision id was <tt>289920621</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>
@@ Line 8: / Line 8: @@
 <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">Below are listed the [[Dyadic chord|dyadic chords]] of 11-limit [[Sensamagic clan#Bohpier|bohpier temperament]]. The essentially just chords are typed as otonal, utonal, or ambitonal. Those requiring tempering only by 540/539 are swetismic, by 245/243 sensamagic, by 100/99 ptolemismic, and by 1344/1331 hemimin. Chords requiring any two of 540/539, 245/243 or 100/99 are labeled octarod.
-Bohpier has MOS of size 8, 9, 17, 25, 33, 41 and 49, and it may be seen that even the eight-note MOS comes equipped with some triads and tetrads. It should also be noted that the generator chain of bohpier is the [[Bohlen-Pierce]] scale. Hence, every chord listed below has a voicing which makes it a chord of Bohlen-Pierce, showing Bohlen-Pierce contains many essentially tempered chords. The listed transversals my be converted to Bohlen-Pierce transversals by adjusting up an octave past 9/5~20/11, so that 7/6 becomes 7/3, 14/11 becomes 28/11, 11/8 becomes 11/4, 3/2 becomes 3, 18/11 becomes 36/11, 5/4 becomes 5, 7/4 becomes 7, and 9/8 becomes 9. It should also be noted that 13-limit bohpier, and hence 13-limit Bohlen-Pierce, has many more 13-limit essentially tempered chords.
+Bohpier has MOS of size 8, 9, 17, 25, 33, 41 and 49, and it may be seen that even the eight-note MOS comes equipped with some triads and tetrads. It should also be noted that the generator chain of 7-limitbohpier is the [[Bohlen-Pierce]] scale, and the same is true of 11-limit bohpier if we do not regard 11/4 as a forbidden interval because the denominator is an even number. Hence, every chord listed below has a voicing which makes it a chord of Bohlen-Pierce, showing Bohlen-Pierce contains many essentially tempered chords. The listed transversals my be converted to Bohlen-Pierce transversals by adjusting up an octave past 9/5~20/11, so that 7/6 becomes 7/3, 14/11 becomes 28/11, 11/8 becomes 11/4, 3/2 becomes 3, 18/11 becomes 36/11, 5/4 becomes 5, 7/4 becomes 7, and 9/8 becomes 9. It should also be noted that 13-limit bohpier, and hence 13-limit Bohlen-Pierce, has many more 13-limit essentially tempered chords.
 =Triads=
@@ Line 180: / Line 180: @@
 <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;Chords of bohpier&lt;/title&gt;&lt;/head&gt;&lt;body&gt;Below are listed the &lt;a class="wiki_link" href="/Dyadic%20chord"&gt;dyadic chords&lt;/a&gt; of 11-limit &lt;a class="wiki_link" href="/Sensamagic%20clan#Bohpier"&gt;bohpier temperament&lt;/a&gt;. The essentially just chords are typed as otonal, utonal, or ambitonal. Those requiring tempering only by 540/539 are swetismic, by 245/243 sensamagic, by 100/99 ptolemismic, and by 1344/1331 hemimin. Chords requiring any two of 540/539, 245/243 or 100/99 are labeled octarod.&lt;br /&gt;
 &lt;br /&gt;
-Bohpier has MOS of size 8, 9, 17, 25, 33, 41 and 49, and it may be seen that even the eight-note MOS comes equipped with some triads and tetrads. It should also be noted that the generator chain of bohpier is the &lt;a class="wiki_link" href="/Bohlen-Pierce"&gt;Bohlen-Pierce&lt;/a&gt; scale. Hence, every chord listed below has a voicing which makes it a chord of Bohlen-Pierce, showing Bohlen-Pierce contains many essentially tempered chords. The listed transversals my be converted to Bohlen-Pierce transversals by adjusting up an octave past 9/5~20/11, so that 7/6 becomes 7/3, 14/11 becomes 28/11, 11/8 becomes 11/4, 3/2 becomes 3, 18/11 becomes 36/11, 5/4 becomes 5, 7/4 becomes 7, and 9/8 becomes 9. It should also be noted that 13-limit bohpier, and hence 13-limit Bohlen-Pierce, has many more 13-limit essentially tempered chords.&lt;br /&gt;
+Bohpier has MOS of size 8, 9, 17, 25, 33, 41 and 49, and it may be seen that even the eight-note MOS comes equipped with some triads and tetrads. It should also be noted that the generator chain of 7-limitbohpier is the &lt;a class="wiki_link" href="/Bohlen-Pierce"&gt;Bohlen-Pierce&lt;/a&gt; scale, and the same is true of 11-limit bohpier if we do not regard 11/4 as a forbidden interval because the denominator is an even number. Hence, every chord listed below has a voicing which makes it a chord of Bohlen-Pierce, showing Bohlen-Pierce contains many essentially tempered chords. The listed transversals my be converted to Bohlen-Pierce transversals by adjusting up an octave past 9/5~20/11, so that 7/6 becomes 7/3, 14/11 becomes 28/11, 11/8 becomes 11/4, 3/2 becomes 3, 18/11 becomes 36/11, 5/4 becomes 5, 7/4 becomes 7, and 9/8 becomes 9. It should also be noted that 13-limit bohpier, and hence 13-limit Bohlen-Pierce, has many more 13-limit essentially tempered chords.&lt;br /&gt;
 &lt;br /&gt;
 &lt;!-- ws:start:WikiTextHeadingRule:0:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc0"&gt;&lt;a name="Triads"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:0 --&gt;Triads&lt;/h1&gt;