List of anomalous saturated suspensions: Difference between revisions
Wikispaces>clumma **Imported revision 588951856 - Original comment: ** |
Wikispaces>clumma **Imported revision 588951872 - Original comment: ** |
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<h2>IMPORTED REVISION FROM WIKISPACES</h2> | <h2>IMPORTED REVISION FROM WIKISPACES</h2> | ||
This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br> | This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br> | ||
: This revision was by author [[User:clumma|clumma]] and made on <tt>2016-08-09 00: | : This revision was by author [[User:clumma|clumma]] and made on <tt>2016-08-09 01:00:44 UTC</tt>.<br> | ||
: The original revision id was <tt> | : The original revision id was <tt>588951872</tt>.<br> | ||
: The revision comment was: <tt></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> | 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 is a complete list of [[http://x31eq.com/ass.htm|Anomalous Saturated Suspensions]] through the 23-limit. Each chord listed is either ambitonal or has a [[Otonality and utonality|o/utonal]] inverse that is also an ASS. | <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 is a complete list of [[http://x31eq.com/ass.htm|Anomalous Saturated Suspensions]] through the 23-limit. Each chord listed is either ambitonal or has a [[Otonality and utonality|o/utonal]] inverse that is also an ASS. | ||
== | ==Formal names== | ||
For each odd limit we can list ambitonal chords in lexicographic order by harmonic series representation, along with o/utonal chord pairs according to the harmonic series representation of the otonal chord in the pair. Each chord is then designated by a capital "A" whose subscript is a tuple, where the first value is its odd limit and the second value is its index in the list for that odd limit. This is followed by an "a," "o," or "u" depending on whether the chord is ambitonal, otonal, or utonal. | For each odd limit we can list ambitonal chords in lexicographic order by harmonic series representation, along with o/utonal chord pairs according to the harmonic series representation of the otonal chord in the pair. Each chord is then designated by a capital "A" whose subscript is a tuple, where the first value is its odd limit and the second value is its index in the list for that odd limit. This is followed by an "a," "o," or "u" depending on whether the chord is ambitonal, otonal, or utonal. | ||
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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>Anomalous Saturated Suspensions</title></head><body>Below is a complete list of <a class="wiki_link_ext" href="http://x31eq.com/ass.htm" rel="nofollow">Anomalous Saturated Suspensions</a> through the 23-limit. Each chord listed is either ambitonal or has a <a class="wiki_link" href="/Otonality%20and%20utonality">o/utonal</a> inverse that is also an ASS.<br /> | <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>Anomalous Saturated Suspensions</title></head><body>Below is a complete list of <a class="wiki_link_ext" href="http://x31eq.com/ass.htm" rel="nofollow">Anomalous Saturated Suspensions</a> through the 23-limit. Each chord listed is either ambitonal or has a <a class="wiki_link" href="/Otonality%20and%20utonality">o/utonal</a> inverse that is also an ASS.<br /> | ||
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<!-- ws:start:WikiTextHeadingRule:0:&lt;h2&gt; --><h2 id="toc0"><a name="x- | <!-- ws:start:WikiTextHeadingRule:0:&lt;h2&gt; --><h2 id="toc0"><a name="x-Formal names"></a><!-- ws:end:WikiTextHeadingRule:0 -->Formal names</h2> | ||
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For each odd limit we can list ambitonal chords in lexicographic order by harmonic series representation, along with o/utonal chord pairs according to the harmonic series representation of the otonal chord in the pair. Each chord is then designated by a capital &quot;A&quot; whose subscript is a tuple, where the first value is its odd limit and the second value is its index in the list for that odd limit. This is followed by an &quot;a,&quot; &quot;o,&quot; or &quot;u&quot; depending on whether the chord is ambitonal, otonal, or utonal.<br /> | For each odd limit we can list ambitonal chords in lexicographic order by harmonic series representation, along with o/utonal chord pairs according to the harmonic series representation of the otonal chord in the pair. Each chord is then designated by a capital &quot;A&quot; whose subscript is a tuple, where the first value is its odd limit and the second value is its index in the list for that odd limit. This is followed by an &quot;a,&quot; &quot;o,&quot; or &quot;u&quot; depending on whether the chord is ambitonal, otonal, or utonal.<br /> | ||