Val: Difference between revisions
Wikispaces>clumma **Imported revision 288600522 - Original comment: ** |
Wikispaces>mbattaglia1 **Imported revision 288624394 - 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: | : This revision was by author [[User:mbattaglia1|mbattaglia1]] and made on <tt>2011-12-28 02:01:00 UTC</tt>.<br> | ||
: The original revision id was <tt> | : The original revision id was <tt>288624394</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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=Shorthand Notation= | =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. For example, the 5-limit patent val for 17-EDO, <17 27 39], can be called simply, "17". In instances where this may be ambiguous, the letter " | 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. For example, the 5-limit patent val for 17-EDO, <17 27 39], can be called simply, "17". In instances where this may be ambiguous, the letter "p" can be added as a suffix, so that "17p" unambiguously refers to <17 27 39]. | ||
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 but may be preferred because it is lower in overall error. | 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 but may be preferred because it is lower in overall error. | ||
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* For each wart, the letter specifies which prime approximation is being altered, so that the nth letter of the alphabet refers to the nth prime. | * For each wart, the letter specifies which prime approximation is being altered, 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. | * A letter which appears m times refers to the (m+1)th most accurate mapping for that prime. | ||
* If a number representing a val is wartless, it is taken to mean the patent val. This number may be | * If a number representing a val is wartless, it is taken to mean the patent val. This number may be suffixed by the letter "p" to reduce ambiguity; "h17p". | ||
See also: [[Monzos and Interval Space]], [[Patent val]], [[Vals and Tuning Space]]</pre></div> | See also: [[Monzos and Interval Space]], [[Patent val]], [[Vals and Tuning Space]]</pre></div> | ||
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<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule:4:&lt;h1&gt; --><h1 id="toc2"><a name="Shorthand Notation"></a><!-- ws:end:WikiTextHeadingRule:4 -->Shorthand Notation</h1> | <!-- ws:start:WikiTextHeadingRule:4:&lt;h1&gt; --><h1 id="toc2"><a name="Shorthand Notation"></a><!-- ws:end:WikiTextHeadingRule:4 -->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. For example, the 5-limit patent val for 17-EDO, &lt;17 27 39], can be called simply, &quot;17&quot;. In instances where this may be ambiguous, the letter &quot; | 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. For example, the 5-limit patent val for 17-EDO, &lt;17 27 39], can be called simply, &quot;17&quot;. In instances where this may be ambiguous, the letter &quot;p&quot; can be added as a suffix, so that &quot;17p&quot; unambiguously refers to &lt;17 27 39].<br /> | ||
<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 but may be preferred because it is lower in overall error.<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 but may be preferred because it is lower in overall error.<br /> | ||
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<br /> | <br /> | ||
The general rule is:<br /> | The general rule is:<br /> | ||
<ul><li>For each wart, the letter specifies which prime approximation is being altered, 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><li>If a number representing a val is wartless, it is taken to mean the patent val. This number may be | <ul><li>For each wart, the letter specifies which prime approximation is being altered, 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><li>If a number representing a val is wartless, it is taken to mean the patent val. This number may be suffixed by the letter &quot;p&quot; to reduce ambiguity; &quot;h17p&quot;.</li></ul><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> | 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> | ||