Meet and join: Difference between revisions

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<h2>IMPORTED REVISION FROM WIKISPACES</h2>

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: This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2014-12-23 23:45:52 UTC</tt>.<br>

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There is a partial order on the temperaments of G, given by A≤B iff A⋏B = A and A≤B iff A⋎B = B. Since A⋎G = G, G is the maximal temperament, and since A⋏G^ = G^, G^ is the minimal temperament. In the temperament defined by G, everything is tempered out, and we may also call it <JI>; and in the temperament defined by G^, nothing is tempered out, and we may also call it <1>. A≤B may be expressed by "A is supported by B".

In mathematical order theory, meet and join are denoted by ∨ and ∧. We avoid doing that for two reasons; the first is to avoid confusion with the interior and ~~wedgects~~ of multivals. The second is that meet and join are operations on abstract temperaments; ordering by increasing size of the group of commas and decreasing size of the group of vals is regarded and notated as the same.

In mathematical order theory, meet and join are denoted by ∨ and ∧. We avoid doing that for two reasons; the first is to avoid confusion with the interior and wedge products of multivals. The second is that meet and join are operations on abstract temperaments; ordering by increasing size of the group of commas and decreasing size of the group of vals is regarded and notated as the same.

=Examples=

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There is a partial order on the temperaments of G, given by A≤B iff A⋏B = A and A≤B iff A⋎B = B. Since A⋎G = G, G is the maximal temperament, and since A⋏G^ = G^, G^ is the minimal temperament. In the temperament defined by G, everything is tempered out, and we may also call it &lt;JI&gt;; and in the temperament defined by G^, nothing is tempered out, and we may also call it &lt;1&gt;. A≤B may be expressed by &quot;A is supported by B&quot;.<br />

<br />

In mathematical order theory, meet and join are denoted by ∨ and ∧. We avoid doing that for two reasons; the first is to avoid confusion with the interior and ~~wedgects~~ of multivals. The second is that meet and join are operations on abstract temperaments; ordering by increasing size of the group of commas and decreasing size of the group of vals is regarded and notated as the same.<br />

In mathematical order theory, meet and join are denoted by ∨ and ∧. We avoid doing that for two reasons; the first is to avoid confusion with the interior and wedge products of multivals. The second is that meet and join are operations on abstract temperaments; ordering by increasing size of the group of commas and decreasing size of the group of vals is regarded and notated as the same.<br />

<br />

<h1 id="toc2"><a name="Examples"></a>Examples</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>2014-12-23 23:45:52 UTC</tt>.<br>
+: This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2014-12-23 23:48:01 UTC</tt>.<br>
-: The original revision id was <tt>535876738</tt>.<br>
+: The original revision id was <tt>535876780</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 16: / Line 16: @@
 There is a partial order on the temperaments of G, given by A≤B iff A⋏B = A and A≤B iff A⋎B = B. Since A⋎G = G, G is the maximal temperament, and since A⋏G^ = G^, G^ is the minimal temperament. In the temperament defined by G, everything is tempered out, and we may also call it &lt;JI&gt;; and in the temperament defined by G^, nothing is tempered out, and we may also call it &lt;1&gt;. A≤B may be expressed by "A is supported by B".
-In mathematical order theory, meet and join are denoted by ∨ and ∧. We avoid doing that for two reasons; the first is to avoid confusion with the interior and wedgects of multivals. The second is that meet and join are operations on abstract temperaments; ordering by increasing size of the group of commas and decreasing size of the group of vals is regarded and notated as the same.
+In mathematical order theory, meet and join are denoted by ∨ and ∧. We avoid doing that for two reasons; the first is to avoid confusion with the interior and wedge products of multivals. The second is that meet and join are operations on abstract temperaments; ordering by increasing size of the group of commas and decreasing size of the group of vals is regarded and notated as the same.
 =Examples=
@@ Line 47: / Line 47: @@
 There is a partial order on the temperaments of G, given by A≤B iff A⋏B = A and A≤B iff A⋎B = B. Since A⋎G = G, G is the maximal temperament, and since A⋏G^ = G^, G^ is the minimal temperament. In the temperament defined by G, everything is tempered out, and we may also call it &amp;lt;JI&amp;gt;; and in the temperament defined by G^, nothing is tempered out, and we may also call it &amp;lt;1&amp;gt;. A≤B may be expressed by &amp;quot;A is supported by B&amp;quot;.&lt;br /&gt;
 &lt;br /&gt;
-In mathematical order theory, meet and join are denoted by ∨ and ∧. We avoid doing that for two reasons; the first is to avoid confusion with the interior and wedgects of multivals. The second is that meet and join are operations on abstract temperaments; ordering by increasing size of the group of commas and decreasing size of the group of vals is regarded and notated as the same.&lt;br /&gt;
+In mathematical order theory, meet and join are denoted by ∨ and ∧. We avoid doing that for two reasons; the first is to avoid confusion with the interior and wedge products of multivals. The second is that meet and join are operations on abstract temperaments; ordering by increasing size of the group of commas and decreasing size of the group of vals is regarded and notated as the same.&lt;br /&gt;
 &lt;br /&gt;
 &lt;!-- ws:start:WikiTextHeadingRule:4:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc2"&gt;&lt;a name="Examples"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:4 --&gt;Examples&lt;/h1&gt;