Val: Difference between revisions

: This revision was by author [[User:clumma|clumma]] and made on <tt>2011-12-27 17:46:26 UTC</tt>.<br>

: The original revision id was <tt>288600522</tt>.<br>

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, &lt;17 27 39], can be called simply, "17". In instances where this may be ambiguous, the letter "h" can be added as a prefix, so that "h17" unambiguously refers to &lt;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 &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.

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 is the third prime number, we add the third letter of the alphabet to the end of the EDO number, to form "17c". If we wanted to use the third-most accurate mapping for 5, &lt;17 27 38], we'd write "17cc".

The general rule is:

* 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.

* If a number representing a val is wartless, it is taken to mean the patent val. This number may be prefixed by the letter "h" to reduce ambiguity; "h17".

  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. For example, the 5-limit patent val for 17-EDO, &amp;lt;17 27 39], can be called simply, &amp;quot;17&amp;quot;. In instances where this may be ambiguous, the letter &amp;quot;h&amp;quot; can be added as a prefix, so that &amp;quot;h17&amp;quot; unambiguously refers to &amp;lt;17 27 39].&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 but may be preferred because it is lower in overall error.&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 is the third prime number, we add the third letter of the alphabet to the end of the EDO number, to form &amp;quot;17c&amp;quot;. If we wanted to use the third-most accurate mapping for 5, &amp;lt;17 27 38], we'd write &amp;quot;17cc&amp;quot;.&lt;br /&gt;