Val: 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:mbattaglia1|mbattaglia1]] and made on <tt>2011-09-~~28 13~~:23:14 UTC</tt>.<br>

: This revision was by author [[User:mbattaglia1|mbattaglia1]] and made on <tt>2011-12-27 06:59:15 UTC</tt>.<br>

: The original revision id was <tt>~~259162186~~</tt>.<br>

: The original revision id was <tt>288554698</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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If for some strange reason you'd instead like to say that 900 cents is 7/4, then that would be represented by the <12 19 28 33] val, and if you'd like to say that 123000 cents is 7/4, that would be represented by the <12 19 28 1254] val.

=Shorthand Notation=

Given an explicit or assumed limit, any [[patent val]] can simply be represented by stating its first coefficient - the digit representing how many generators map to 2/1 - plus the character "p". So for example, <12 19 28] can be represented by the phrase "12p." This "p" is sometimes referred to as a **wart**.

The patent val for any EDO will use the most accurate mapping for each individual prime. However, it may often be the case that one wants to refer to vals other than the patent val. For example, the 5-limit val <17 27 40], which maps the 5/4 to the 424 cent interval rather than the 353 cent interval, is NOT the patent val for 17-EDO. One reason to prefer the use of this val in certain circumstances is that it is lower in error.

Non-patent vals are specified by adding a "wart" to the end of their name which specifies their deviation from the patent val. In this case, we want to specify that the 5/1 has been changed to use its second-most accurate mapping. Since 5/1 is the third prime, we add the third corresponding letter from the alphabet to the end of the EDO, to form "17c." If we instead wanted to use the third-most accurate mapping for 5, we'd denote that by the "cc" wart, so that 17cc is <17 27 38].

In general, the rule is:

* For each wart, the letter specifies which prime is being deviated from, so that the nth letter of the alphabet refers to the nth prime.

* A letter which appears m times refers to the (m+1)th most accurate mapping for that prime.

If a number representing a val should appear at all without any corresponding wart, it is taken to mean the patent val. So the 5-limit val "12" is taken to be identical to 12p.

See also: [[Monzos and Interval Space]], [[Patent val]], [[Vals and Tuning Space]]</pre></div>

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<br />

If for some strange reason you'd instead like to say that 900 cents is 7/4, then that would be represented by the &lt;12 19 28 33] val, and if you'd like to say that 123000 cents is 7/4, that would be represented by the &lt;12 19 28 1254] val.<br />

<br />

<h1 id="toc2"><a name="Shorthand Notation"></a>Shorthand Notation</h1>

Given an explicit or assumed limit, any <a class="wiki_link" href="/patent%20val">patent val</a> can simply be represented by stating its first coefficient - the digit representing how many generators map to 2/1 - plus the character &quot;p&quot;. So for example, &lt;12 19 28] can be represented by the phrase &quot;12p.&quot; This &quot;p&quot; is sometimes referred to as a <strong>wart</strong>.<br />

<br />

The patent val for any EDO will use the most accurate mapping for each individual prime. However, it may often be the case that one wants to refer to vals other than the patent val. For example, the 5-limit val &lt;17 27 40], which maps the 5/4 to the 424 cent interval rather than the 353 cent interval, is NOT the patent val for 17-EDO. One reason to prefer the use of this val in certain circumstances is that it is lower in error.<br />

<br />

Non-patent vals are specified by adding a &quot;wart&quot; to the end of their name which specifies their deviation from the patent val. In this case, we want to specify that the 5/1 has been changed to use its second-most accurate mapping. Since 5/1 is the third prime, we add the third corresponding letter from the alphabet to the end of the EDO, to form &quot;17c.&quot; If we instead wanted to use the third-most accurate mapping for 5, we'd denote that by the &quot;cc&quot; wart, so that 17cc is &lt;17 27 38].<br />

<br />

In general, the rule is:<br />

<ul><li>For each wart, the letter specifies which prime is being deviated from, so that the nth letter of the alphabet refers to the nth prime.</li><li>A letter which appears m times refers to the (m+1)th most accurate mapping for that prime.</li></ul><br />

If a number representing a val should appear at all without any corresponding wart, it is taken to mean the patent val. So the 5-limit val &quot;12&quot; is taken to be identical to 12p.<br />

<br />

See also: <a class="wiki_link" href="/Monzos%20and%20Interval%20Space">Monzos and Interval Space</a>, <a class="wiki_link" href="/Patent%20val">Patent val</a>, <a class="wiki_link" href="/Vals%20and%20Tuning%20Space">Vals and Tuning Space</a></body></html></pre></div>

@@ 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:mbattaglia1|mbattaglia1]] and made on <tt>2011-09-28 13:23:14 UTC</tt>.<br>
+: This revision was by author [[User:mbattaglia1|mbattaglia1]] and made on <tt>2011-12-27 06:59:15 UTC</tt>.<br>
-: The original revision id was <tt>259162186</tt>.<br>
+: The original revision id was <tt>288554698</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 25: / Line 25: @@
 If for some strange reason you'd instead like to say that 900 cents is 7/4, then that would be represented by the &lt;12 19 28 33] val, and if you'd like to say that 123000 cents is 7/4, that would be represented by the &lt;12 19 28 1254] val.
+=Shorthand Notation=
+Given an explicit or assumed limit, any [[patent val]] can simply be represented by stating its first coefficient - the digit representing how many generators map to 2/1 - plus the character "p". So for example, &lt;12 19 28] can be represented by the phrase "12p." This "p" is sometimes referred to as a **wart**.
+The patent val for any EDO will use the most accurate mapping for each individual prime. However, it may often be the case that one wants to refer to vals other than the patent val. For example, the 5-limit val &lt;17 27 40], which maps the 5/4 to the 424 cent interval rather than the 353 cent interval, is NOT the patent val for 17-EDO. One reason to prefer the use of this val in certain circumstances is that it is lower in error.
+Non-patent vals are specified by adding a "wart" to the end of their name which specifies their deviation from the patent val. In this case, we want to specify that the 5/1 has been changed to use its second-most accurate mapping. Since 5/1 is the third prime, we add the third corresponding letter from the alphabet to the end of the EDO, to form "17c." If we instead wanted to use the third-most accurate mapping for 5, we'd denote that by the "cc" wart, so that 17cc is &lt;17 27 38].
+In general, the rule is:
+* For each wart, the letter specifies which prime is being deviated from, so that the nth letter of the alphabet refers to the nth prime.
+* A letter which appears m times refers to the (m+1)th most accurate mapping for that prime.
+If a number representing a val should appear at all without any corresponding wart, it is taken to mean the patent val. So the 5-limit val "12" is taken to be identical to 12p.
 See also: [[Monzos and Interval Space]], [[Patent val]], [[Vals and Tuning Space]]</pre></div>
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 &lt;br /&gt;
 If for some strange reason you'd instead like to say that 900 cents is 7/4, then that would be represented by the &amp;lt;12 19 28 33] val, and if you'd like to say that 123000 cents is 7/4, that would be represented by the &amp;lt;12 19 28 1254] val.&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="Shorthand Notation"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:4 --&gt;Shorthand Notation&lt;/h1&gt;
+ Given an explicit or assumed limit, any &lt;a class="wiki_link" href="/patent%20val"&gt;patent val&lt;/a&gt; can simply be represented by stating its first coefficient - the digit representing how many generators map to 2/1 - plus the character &amp;quot;p&amp;quot;. So for example, &amp;lt;12 19 28] can be represented by the phrase &amp;quot;12p.&amp;quot; This &amp;quot;p&amp;quot; is sometimes referred to as a &lt;strong&gt;wart&lt;/strong&gt;.&lt;br /&gt;
+&lt;br /&gt;
+The patent val for any EDO will use the most accurate mapping for each individual prime. However, it may often be the case that one wants to refer to vals other than the patent val. For example, the 5-limit val &amp;lt;17 27 40], which maps the 5/4 to the 424 cent interval rather than the 353 cent interval, is NOT the patent val for 17-EDO. One reason to prefer the use of this val in certain circumstances is that it is lower in error.&lt;br /&gt;
+&lt;br /&gt;
+Non-patent vals are specified by adding a &amp;quot;wart&amp;quot; to the end of their name which specifies their deviation from the patent val. In this case, we want to specify that the 5/1 has been changed to use its second-most accurate mapping. Since 5/1 is the third prime, we add the third corresponding letter from the alphabet to the end of the EDO, to form &amp;quot;17c.&amp;quot; If we instead wanted to use the third-most accurate mapping for 5, we'd denote that by the &amp;quot;cc&amp;quot; wart, so that 17cc is &amp;lt;17 27 38].&lt;br /&gt;
+&lt;br /&gt;
+In general, the rule is:&lt;br /&gt;
+&lt;ul&gt;&lt;li&gt;For each wart, the letter specifies which prime is being deviated from, so that the nth letter of the alphabet refers to the nth prime.&lt;/li&gt;&lt;li&gt;A letter which appears m times refers to the (m+1)th most accurate mapping for that prime.&lt;/li&gt;&lt;/ul&gt;&lt;br /&gt;
+If a number representing a val should appear at all without any corresponding wart, it is taken to mean the patent val. So the 5-limit val &amp;quot;12&amp;quot; is taken to be identical to 12p.&lt;br /&gt;
 &lt;br /&gt;
 See also: &lt;a class="wiki_link" href="/Monzos%20and%20Interval%20Space"&gt;Monzos and Interval Space&lt;/a&gt;, &lt;a class="wiki_link" href="/Patent%20val"&gt;Patent val&lt;/a&gt;, &lt;a class="wiki_link" href="/Vals%20and%20Tuning%20Space"&gt;Vals and Tuning Space&lt;/a&gt;&lt;/body&gt;&lt;/html&gt;</pre></div>