Valentine/Chords: Difference between revisions

<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 [[Starling temperaments#Valentine%20temperament-11-limit|valentine temperament]]. Typing the chords requires consideration of the fact that valentine conflates 12/11 and 11/10 and so also 11/6 and 20/11. If a transversal can be found which shows the chord to be essentially just, that transversal is listed along with a typing as otonal, utonal, or ambitonal. If the chord is essentially tempered, it is analyzed in terms of the transversal which employs 11/10 and 20/11.

Valentine has MOS of size 15, 16, 31 and 46. It is readily observed from the list below that even the smallest of these is well-supplied with chords. Because [[Carlos Alpha]] is the generator chain of valentine in the tuning with pure 3/2's, the list below is also a list of chords of Carlos Alpha, so long as the transversals are adjusted so that the notes are in the correct octave. This means that a number in a chord listed under "chord" less than 16 corresponds to a note in the transversal which should be left unaltered, whereas the notes from 16 to 21 correspond to transversal notes which should be adjusted up an octave. Hence, tetrad 8, the 0-2-5-9 chord with transversal 1-6/5-11/8-3/2, is an essentially zeus chord of Carlos Alpha as well as valentine. On the other hand, tetrad 76, 0-10-13-18 with transversal 1-11/7-9/5-9/8, corresponds to the werckismic 1-11/7-9/5-9/4 chord of Carlos Alpha.

=Triads=  

=Tetrads=

|| Number || Chord || Transversal || Type ||

|| 1 || 0-2-4-7 || 1-11/10-6/5-11/8 || zeus ||

|| 2 || 0-2-5-7 || 1-11/10-5/4-11/8 || valinorsmic ||

|| 3 || 0-3-5-7 || 1-8/7-5/4-11/8 || zeus ||

|| 4 || 0-3-5-8 || 1-8/7-5/4-10/7 || valinorsmic ||

|| 5 || 0-2-4-9 || 1-12/11-6/5-3/2 || utonal ||

|| 6 || 0-2-5-9 || 1-11/10-5/4-3/2 || zeus ||

|| 7 || 0-2-7-9 || 1-11/10-11/8-3/2 || biyatismic ||

|| 8 || 0-4-7-9 || 1-6/5-11/8-3/2 || zeus ||

|| 9 || 0-5-7-9 || 1-5/4-11/8-3/2 || otonal ||

|| 10 || 0-2-5-10 || 1-11/10-5/4-11/7 || valinorsmic ||

|| 11 || 0-3-5-10 || 1-8/7-5/4-11/7 || valinorsmic ||

|| 12 || 0-2-7-10 || 1-11/10-11/8-11/7 || utonal ||

|| 13 || 0-3-7-10 || 1-8/7-11/8-11/7 || keenanismic ||

|| 14 || 0-5-7-10 || 1-5/4-11/8-11/7 || valinorsmic ||

|| 15 || 0-3-8-10 || 1-8/7-10/7-11/7 || otonal ||

|| 16 || 0-5-8-10 || 1-5/4-10/7-11/7 || valinorsmic ||

|| 17 || 0-2-4-11 || 1-11/10-6/5-18/11 || biyatismic ||

|| 18 || 0-2-7-11 || 1-11/10-11/8-18/11 || biyatismic ||

|| 19 || 0-3-7-11 || 1-8/7-11/8-18/11 || valentine ||

|| 20 || 0-4-7-11 || 1-6/5-11/8-18/11 || zeus ||

|| 21 || 0-3-8-11 || 1-8/7-10/7-18/11 || werckismic ||

|| 22 || 0-4-8-11 || 1-6/5-10/7-18/11 || valentine ||

|| 23 || 0-2-9-11 || 1-12/11-3/2-18/11 || ambitonal ||

|| 24 || 0-4-9-11 || 1-6/5-3/2-18/11 || biyatismic ||

|| 25 || 0-7-9-11 || 1-11/8-3/2-18/11 || biyatismic ||

|| 26 || 0-2-4-12 || 1-12/11-6/5-12/7 || utonal ||

|| 27 || 0-2-5-12 || 1-11/10-5/4-12/7 || zeus ||

|| 28 || 0-3-5-12 || 1-8/7-5/4-12/7 || zeus ||

|| 29 || 0-2-7-12 || 1-11/10-11/8-12/7 || zeus ||

|| 30 || 0-3-7-12 || 1-8/7-11/8-12/7 || keenanismic ||

|| 31 || 0-4-7-12 || 1-6/5-11/8-12/7 || keenanismic ||

|| 32 || 0-5-7-12 || 1-5/4-11/8-12/7 || keenanismic ||

|| 33 || 0-3-8-12 || 1-8/7-10/7-12/7 || otonal ||

|| 34 || 0-4-8-12 || 1-6/5-10/7-12/7 || starling ||

|| 35 || 0-5-8-12 || 1-5/4-10/7-12/7 || keenanismic ||

|| 36 || 0-2-9-12 || 1-12/11-3/2-12/7 || utonal ||

|| 37 || 0-4-9-12 || 1-6/5-3/2-12/7 || utonal ||

|| 38 || 0-5-9-12 || 1-5/4-3/2-12/7 || keenanismic ||

|| 39 || 0-7-9-12 || 1-11/8-3/2-12/7 || zeus ||

|| 40 || 0-2-10-12 || 1-11/10-11/7-12/7 || biyatismic ||

|| 41 || 0-3-10-12 || 1-8/7-11/7-12/7 || otonal ||

|| 42 || 0-5-10-12 || 1-5/4-11/7-12/7 || zeus ||

|| 43 || 0-7-10-12 || 1-11/8-11/7-12/7 || zeus ||

|| 44 || 0-8-10-12 || 1-10/7-11/7-12/7 || otonal ||

|| 45 || 0-2-4-13 || 1-11/10-6/5-9/5 || otonal ||

|| 46 || 0-2-5-13 || 1-11/10-5/4-9/5 || thrush ||

|| 47 || 0-3-5-13 || 1-8/7-5/4-9/5 || thrush ||

|| 48 || 0-3-8-13 || 1-8/7-10/7-9/5 || thrush ||

|| 49 || 0-4-8-13 || 1-6/5-10/7-9/5 || starling ||

|| 50 || 0-5-8-13 || 1-5/4-10/7-9/5 || starling ||

|| 51 || 0-2-9-13 || 1-11/10-3/2-9/5 || biyatismic ||

|| 52 || 0-4-9-13 || 1-6/5-3/2-9/5 || ambitonal ||

|| 53 || 0-5-9-13 || 1-5/4-3/2-9/5 || starling ||

|| 54 || 0-2-10-13 || 1-11/10-11/7-9/5 || werckismic ||

|| 55 || 0-3-10-13 || 1-8/7-11/7-9/5 || werckismic ||

|| 56 || 0-5-10-13 || 1-5/4-11/7-9/5 || thrush ||

|| 96 || 0-11-18-21 || 1-18/11-9/8-9/7 || utonal ||

|| 97 || 0-13-18-21 || 1-9/5-9/8-9/7 || utonal ||

=Pentads=  

=Hexads=

|| Number || Chord || Transversal || Type ||

|| 1 || 0-2-4-7-9-11 || 1-11/10-6/5-11/8-3/2-18/11 || zeus ||

|| 2 || 0-2-4-7-9-12 || 1-11/10-6/5-11/8-3/2-12/7 || zeus ||

|| 3 || 0-2-5-7-9-12 || 1-11/10-5/4-11/8-3/2-12/7 || zeus ||

|| 4 || 0-2-5-7-10-12 || 1-11/10-5/4-11/8-11/7-12/7 || zeus ||

|| 5 || 0-3-5-7-10-12 || 1-8/7-5/4-11/8-11/7-12/7 || zeus ||

|| 6 || 0-3-5-8-10-12 || 1-8/7-5/4-10/7-11/7-12/7 || zeus ||

|| 7 || 0-3-5-8-10-13 || 1-8/7-5/4-10/7-11/7-9/5 || thrush ||

|| 8 || 0-2-4-9-11-13 || 1-11/10-6/5-3/2-18/11-9/5 || biyatismic ||

|| 9 || 0-5-8-10-13-18 || 1-5/4-10/7-11/7-9/5-9/8 || thrush ||

|| 10 || 0-3-8-10-12-21 || 1-8/7-10/7-11/7-12/7-9/7 || otonal ||

|| 11 || 0-3-8-10-13-21 || 1-8/7-10/7-11/7-9/5-9/7 || thrush ||

|| 12 || 0-3-8-11-13-21 || 1-8/7-10/7-18/11-9/5-9/7 || thrush ||

|| 13 || 0-8-10-13-18-21 || 1-10/7-11/7-9/5-9/8-9/7 || thrush ||

|| 14 || 0-8-11-13-18-21 || 1-10/7-18/11-9/5-9/8-9/7 || thrush ||

|| 15 || 0-9-11-13-18-21 || 1-3/2-18/11-9/5-9/8-9/7 || utonal ||</pre></div>

<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 valentine&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="/Starling%20temperaments#Valentine%20temperament-11-limit"&gt;valentine temperament&lt;/a&gt;. Typing the chords requires consideration of the fact that valentine conflates 12/11 and 11/10 and so also 11/6 and 20/11. If a transversal can be found which shows the chord to be essentially just, that transversal is listed along with a typing as otonal, utonal, or ambitonal. If the chord is essentially tempered, it is analyzed in terms of the transversal which employs 11/10 and 20/11.&lt;br /&gt;

Valentine has MOS of size 15, 16, 31 and 46. It is readily observed from the list below that even the smallest of these is well-supplied with chords. Because &lt;a class="wiki_link" href="/Carlos%20Alpha"&gt;Carlos Alpha&lt;/a&gt; is the generator chain of valentine in the tuning with pure 3/2's, the list below is also a list of chords of Carlos Alpha, so long as the transversals are adjusted so that the notes are in the correct octave. This means that a number in a chord listed under &amp;quot;chord&amp;quot; less than 16 corresponds to a note in the transversal which should be left unaltered, whereas the notes from 16 to 21 correspond to transversal notes which should be adjusted up an octave. Hence, tetrad 8, the 0-2-5-9 chord with transversal 1-6/5-11/8-3/2, is an essentially zeus chord of Carlos Alpha as well as valentine. On the other hand, tetrad 76, 0-10-13-18 with transversal 1-11/7-9/5-9/8, corresponds to the werckismic 1-11/7-9/5-9/4 chord of Carlos Alpha.&lt;br /&gt;

In other words, each chord here has an unlimited number of &amp;quot;voicings&amp;quot; in valentine temperament, but exactly one voicing in Carlos Alpha, because there are no octaves.&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;

&lt;table class="wiki_table"&gt;