Patent val: Difference between revisions
Wikispaces>hstraub **Imported revision 556616753 - Original comment: ** |
Wikispaces>hstraub **Imported revision 556616767 - Original comment: ** |
||
| Line 1: | Line 1: | ||
<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:hstraub|hstraub]] and made on <tt>2015-08-13 07: | : This revision was by author [[User:hstraub|hstraub]] and made on <tt>2015-08-13 07:26:26 UTC</tt>.<br> | ||
: The original revision id was <tt> | : The original revision id was <tt>556616767</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> | ||
<h4>Original Wikitext content:</h4> | <h4>Original Wikitext content:</h4> | ||
<div style="width:100%; max-height:400pt; overflow:auto; background-color:#f8f9fa; border: 1px solid #eaecf0; padding:0em"><pre style="margin:0px;border:none;background:none;word-wrap:break-word;white-space: pre-wrap ! important" class="old-revision-html"><span style="display: block; text-align: right;">[[特徴的なヴァル|日本語]][[toc|flat]] | <div style="width:100%; max-height:400pt; overflow:auto; background-color:#f8f9fa; border: 1px solid #eaecf0; padding:0em"><pre style="margin:0px;border:none;background:none;word-wrap:break-word;white-space: pre-wrap ! important" class="old-revision-html"><span style="display: block; text-align: right;">[[特徴的なヴァル|日本語]]</span> | ||
[[toc|flat]] | |||
---- | ---- | ||
=Introduction= | =Introduction= | ||
| Line 103: | Line 104: | ||
Instead of assuming the patent val for N-edo comes from an integer N, we could define a patent val for X-edo, where X is any real number, in just the same way. For instance, the [[The Riemann Zeta Function and Tuning#The%20Z%20function|Z-function]] maximum at 48.9451 leads to a 13-limit X-edo val of <49 78 114 137 169 181|, whereas the minimum at 49.1412 leads to an X-edo val of <49 78 114 138 170 182|. Meanwhile, the patent val, which is the X-edo val for X=49.0000 exactly, is <49 78 114 138 170 181|.</pre></div> | Instead of assuming the patent val for N-edo comes from an integer N, we could define a patent val for X-edo, where X is any real number, in just the same way. For instance, the [[The Riemann Zeta Function and Tuning#The%20Z%20function|Z-function]] maximum at 48.9451 leads to a 13-limit X-edo val of <49 78 114 137 169 181|, whereas the minimum at 49.1412 leads to an X-edo val of <49 78 114 138 170 182|. Meanwhile, the patent val, which is the X-edo val for X=49.0000 exactly, is <49 78 114 138 170 181|.</pre></div> | ||
<h4>Original HTML content:</h4> | <h4>Original HTML content:</h4> | ||
<div style="width:100%; max-height:400pt; overflow:auto; background-color:#f8f9fa; border: 1px solid #eaecf0; padding:0em"><pre style="margin:0px;border:none;background:none;word-wrap:break-word;width:200%;white-space: pre-wrap ! important" class="old-revision-html"><html><head><title>Patent val</title></head><body><span style="display: block; text-align: right;"><a class="wiki_link" href="/%E7%89%B9%E5%BE%B4%E7%9A%84%E3%81%AA%E3%83%B4%E3%82%A1%E3%83%AB">日本語</a><!-- ws:start:WikiTextTocRule:14:&lt;img id=&quot;wikitext@@toc@@flat&quot; class=&quot;WikiMedia WikiMediaTocFlat&quot; title=&quot;Table of Contents&quot; src=&quot;/site/embedthumbnail/toc/flat?w=100&amp;h=16&quot;/&gt; --><!-- ws:end:WikiTextTocRule:14 --><!-- ws:start:WikiTextTocRule:15: --><a href="#Introduction">Introduction</a><!-- ws:end:WikiTextTocRule:15 --><!-- ws:start:WikiTextTocRule:16: --> | <a href="#Further explanation">Further explanation</a><!-- ws:end:WikiTextTocRule:16 --><!-- ws:start:WikiTextTocRule:17: --> | <a href="#A 12 EDO Example">A 12 EDO Example</a><!-- ws:end:WikiTextTocRule:17 --><!-- ws:start:WikiTextTocRule:18: --> | <a href="#An alternate and expanded example for 31 EDO">An alternate and expanded example for 31 EDO</a><!-- ws:end:WikiTextTocRule:18 --><!-- ws:start:WikiTextTocRule:19: --> | <a href="#How this defines a rank 1 temperament">How this defines a rank 1 temperament</a><!-- ws:end:WikiTextTocRule:19 --><!-- ws:start:WikiTextTocRule:20: --> | <a href="#How this relates to commas">How this relates to commas</a><!-- ws:end:WikiTextTocRule:20 --><!-- ws:start:WikiTextTocRule:21: --> | <a href="#Patent vals from real numbers (Generalized patent vals)">Patent vals from real numbers (Generalized patent vals)</a><!-- ws:end:WikiTextTocRule:21 --><!-- ws:start:WikiTextTocRule:22: --> | <div style="width:100%; max-height:400pt; overflow:auto; background-color:#f8f9fa; border: 1px solid #eaecf0; padding:0em"><pre style="margin:0px;border:none;background:none;word-wrap:break-word;width:200%;white-space: pre-wrap ! important" class="old-revision-html"><html><head><title>Patent val</title></head><body><span style="display: block; text-align: right;"><a class="wiki_link" href="/%E7%89%B9%E5%BE%B4%E7%9A%84%E3%81%AA%E3%83%B4%E3%82%A1%E3%83%AB">日本語</a></span><br /> | ||
<!-- ws:start:WikiTextTocRule:14:&lt;img id=&quot;wikitext@@toc@@flat&quot; class=&quot;WikiMedia WikiMediaTocFlat&quot; title=&quot;Table of Contents&quot; src=&quot;/site/embedthumbnail/toc/flat?w=100&amp;h=16&quot;/&gt; --><!-- ws:end:WikiTextTocRule:14 --><!-- ws:start:WikiTextTocRule:15: --><a href="#Introduction">Introduction</a><!-- ws:end:WikiTextTocRule:15 --><!-- ws:start:WikiTextTocRule:16: --> | <a href="#Further explanation">Further explanation</a><!-- ws:end:WikiTextTocRule:16 --><!-- ws:start:WikiTextTocRule:17: --> | <a href="#A 12 EDO Example">A 12 EDO Example</a><!-- ws:end:WikiTextTocRule:17 --><!-- ws:start:WikiTextTocRule:18: --> | <a href="#An alternate and expanded example for 31 EDO">An alternate and expanded example for 31 EDO</a><!-- ws:end:WikiTextTocRule:18 --><!-- ws:start:WikiTextTocRule:19: --> | <a href="#How this defines a rank 1 temperament">How this defines a rank 1 temperament</a><!-- ws:end:WikiTextTocRule:19 --><!-- ws:start:WikiTextTocRule:20: --> | <a href="#How this relates to commas">How this relates to commas</a><!-- ws:end:WikiTextTocRule:20 --><!-- ws:start:WikiTextTocRule:21: --> | <a href="#Patent vals from real numbers (Generalized patent vals)">Patent vals from real numbers (Generalized patent vals)</a><!-- ws:end:WikiTextTocRule:21 --><!-- ws:start:WikiTextTocRule:22: --> | |||
<!-- ws:end:WikiTextTocRule:22 --><br /> | <!-- ws:end:WikiTextTocRule:22 --><br /> | ||
<hr /> | <hr /> | ||
<!-- ws:start:WikiTextHeadingRule:0:&lt;h1&gt; --><h1 id="toc0"><a name="Introduction"></a><!-- ws:end:WikiTextHeadingRule:0 -->Introduction</h1> | <!-- ws:start:WikiTextHeadingRule:0:&lt;h1&gt; --><h1 id="toc0"><a name="Introduction"></a><!-- ws:end:WikiTextHeadingRule:0 -->Introduction</h1> | ||