Tablet: 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>2011-10-~~13 02~~:39:27 UTC</tt>.<br>

: This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2011-10-19 15:56:40 UTC</tt>.<br>

: The original revision id was <tt>~~264280030~~</tt>.<br>

: The original revision id was <tt>266534214</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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=The 5-limit 3et tablet=

If we want a way to uniquely denote the octave-equivalent class of a 5-limit major triad, we can simply give the root of the chord, ignoring octaves. In terms of monzos that means a major triad would be denoted ~~<~~* e3 e5|, where the asterisk can be anything. Since the asterisk is not being used to impart information, we can use it to distinguish major from minor triads. So we might decide that ~~<~~r e3 e5| defines a major triad with root given by |* e3 e5> when r is even, and a minor triad when r is odd.

If we want a way to uniquely denote the octave-equivalent class of a 5-limit major triad, we can simply give the root of the chord, ignoring octaves. In terms of monzos that means a major triad would be denoted |* e3 e5>, where the asterisk can be anything. Since the asterisk is not being used to impart information, we can use it to distinguish major from minor triads. So we might decide that [r e3 e5] defines a major triad with root given by |* e3 e5> when r is even, and a minor triad when r is odd.

If r is even, therefore, we will regard the 3-tuple [r e3 e5] as denoting a major triad, and if [n, [r e3 e5]] is the tablet we wish to define, we first calculate u = n - 5e3 - 7e5. Then if r is even, we have

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<br />

<h1 id="toc1"><a name="The 5-limit 3et tablet"></a>The 5-limit 3et tablet</h1>

If we want a way to uniquely denote the octave-equivalent class of a 5-limit major triad, we can simply give the root of the chord, ignoring octaves. In terms of monzos that means a major triad would be denoted &lt;* e3 e5|, where the asterisk can be anything. Since the asterisk is not being used to impart information, we can use it to distinguish major from minor triads. So we might decide that ~~&lt;~~r e3 e5| defines a major triad with root given by |* e3 e5&gt; when r is even, and a minor triad when r is odd.<br />

If we want a way to uniquely denote the octave-equivalent class of a 5-limit major triad, we can simply give the root of the chord, ignoring octaves. In terms of monzos that means a major triad would be denoted |* e3 e5&gt;, where the asterisk can be anything. Since the asterisk is not being used to impart information, we can use it to distinguish major from minor triads. So we might decide that [r e3 e5] defines a major triad with root given by |* e3 e5&gt; when r is even, and a minor triad when r is odd.<br />

<br />

If r is even, therefore, we will regard the 3-tuple [r e3 e5] as denoting a major triad, and if [n, [r e3 e5]] is the tablet we wish to define, we first calculate u = n - 5e3 - 7e5. Then if r is even, we have<br />

@@ 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>2011-10-13 02:39:27 UTC</tt>.<br>
+: This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2011-10-19 15:56:40 UTC</tt>.<br>
-: The original revision id was <tt>264280030</tt>.<br>
+: The original revision id was <tt>266534214</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 14: / Line 14: @@
 =The 5-limit 3et tablet=
-If we want a way to uniquely denote the octave-equivalent class of a 5-limit major triad, we can simply give the root of the chord, ignoring octaves. In terms of monzos that means a major triad would be denoted &lt;* e3 e5|, where the asterisk can be anything. Since the asterisk is not being used to impart information, we can use it to distinguish major from minor triads. So we might decide that &lt;r e3 e5| defines a major triad with root given by |* e3 e5&gt; when r is even, and a minor triad when r is odd.
+If we want a way to uniquely denote the octave-equivalent class of a 5-limit major triad, we can simply give the root of the chord, ignoring octaves. In terms of monzos that means a major triad would be denoted |* e3 e5&gt;, where the asterisk can be anything. Since the asterisk is not being used to impart information, we can use it to distinguish major from minor triads. So we might decide that [r e3 e5] defines a major triad with root given by |* e3 e5&gt; when r is even, and a minor triad when r is odd.
 If r is even, therefore, we will regard the 3-tuple [r e3 e5] as denoting a major triad, and if [n, [r e3 e5]] is the tablet we wish to define, we first calculate u = n - 5e3 - 7e5. Then if r is even, we have
@@ Line 377: / Line 377: @@
 &lt;br /&gt;
 &lt;!-- ws:start:WikiTextHeadingRule:2:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc1"&gt;&lt;a name="The 5-limit 3et tablet"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:2 --&gt;The 5-limit 3et tablet&lt;/h1&gt;
-If we want a way to uniquely denote the octave-equivalent class of a 5-limit major triad, we can simply give the root of the chord, ignoring octaves. In terms of monzos that means a major triad would be denoted &amp;lt;* e3 e5|, where the asterisk can be anything. Since the asterisk is not being used to impart information, we can use it to distinguish major from minor triads. So we might decide that &amp;lt;r e3 e5| defines a major triad with root given by |* e3 e5&amp;gt; when r is even, and a minor triad when r is odd.&lt;br /&gt;
+If we want a way to uniquely denote the octave-equivalent class of a 5-limit major triad, we can simply give the root of the chord, ignoring octaves. In terms of monzos that means a major triad would be denoted |* e3 e5&amp;gt;, where the asterisk can be anything. Since the asterisk is not being used to impart information, we can use it to distinguish major from minor triads. So we might decide that [r e3 e5] defines a major triad with root given by |* e3 e5&amp;gt; when r is even, and a minor triad when r is odd.&lt;br /&gt;
 &lt;br /&gt;
 If r is even, therefore, we will regard the 3-tuple [r e3 e5] as denoting a major triad, and if [n, [r e3 e5]] is the tablet we wish to define, we first calculate u = n - 5e3 - 7e5. Then if r is even, we have&lt;br /&gt;