Pretty Pictures: 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:JosephRuhf|JosephRuhf]] and made on <tt>2012-11-24 23:01:34 UTC</tt>.<br>

: This revision was by author [[User:JosephRuhf|JosephRuhf]] and made on <tt>2012-11-24 23:03:57 UTC</tt>.<br>

: The original revision id was <tt>~~385637072~~</tt>.<br>

: The original revision id was <tt>385637366</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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=Aids to understanding=

===The rulers metaphor for microtonality===

Imagine a ruler with 12 inches on it. Now imagine one where, in the space of 12 inches, 13 equally spaced lines are drawn. Although these new lines are each only a little less than an inch apart from each other, they are clearly not "inches" and it would be silly to use them as such. If you used these 13ths of a foot to measure and estimate lengths frequently, you would soon find yourself rounding to this new set of lengths which before you would have rounded to inches. You might soon find yourself rounding something exactly inches long to ~~either~~ 6 ~~or 7~~ of these. My, what a crazy you must be!

Imagine a ruler with 12 inches on it. Now imagine one where, in the space of 12 inches, 13 equally spaced lines are drawn. Although these new lines are each only a little less than an inch apart from each other, they are clearly not "inches" and it would be silly to use them as such. If you used these 13ths of a foot to measure and estimate lengths frequently, you would soon find yourself rounding to this new set of lengths which before you would have rounded to inches. You might soon find yourself rounding something exactly 7 inches long to 7.6 of these. My, what a crazy you must be!

===The colors metaphor for microtonality===

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<h1 id="toc6"><a name="Aids to understanding"></a>Aids to understanding</h1>

<h3 id="toc7"><a name="Aids to understanding--The rulers metaphor for microtonality"></a>The rulers metaphor for microtonality</h3>

Imagine a ruler with 12 inches on it. Now imagine one where, in the space of 12 inches, 13 equally spaced lines are drawn. Although these new lines are each only a little less than an inch apart from each other, they are clearly not &quot;inches&quot; and it would be silly to use them as such. If you used these 13ths of a foot to measure and estimate lengths frequently, you would soon find yourself rounding to this new set of lengths which before you would have rounded to inches. You might soon find yourself rounding something exactly inches long to ~~either~~ 6 ~~or 7~~ of these. My, what a crazy you must be!<br />

Imagine a ruler with 12 inches on it. Now imagine one where, in the space of 12 inches, 13 equally spaced lines are drawn. Although these new lines are each only a little less than an inch apart from each other, they are clearly not &quot;inches&quot; and it would be silly to use them as such. If you used these 13ths of a foot to measure and estimate lengths frequently, you would soon find yourself rounding to this new set of lengths which before you would have rounded to inches. You might soon find yourself rounding something exactly 7 inches long to 7.6 of these. My, what a crazy you must be!<br />

<br />

<h3 id="toc8"><a name="Aids to understanding--The colors metaphor for microtonality"></a>The colors metaphor for microtonality</h3>

@@ 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:JosephRuhf|JosephRuhf]] and made on <tt>2012-11-24 23:01:34 UTC</tt>.<br>
+: This revision was by author [[User:JosephRuhf|JosephRuhf]] and made on <tt>2012-11-24 23:03:57 UTC</tt>.<br>
-: The original revision id was <tt>385637072</tt>.<br>
+: The original revision id was <tt>385637366</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 23: / Line 23: @@
 =Aids to understanding=
 ===The rulers metaphor for microtonality===
-Imagine a ruler with 12 inches on it. Now imagine one where, in the space of 12 inches, 13 equally spaced lines are drawn. Although these new lines are each only a little less than an inch apart from each other, they are clearly not "inches" and it would be silly to use them as such. If you used these 13ths of a foot to measure and estimate lengths frequently, you would soon find yourself rounding to this new set of lengths which before you would have rounded to inches. You might soon find yourself rounding something exactly  inches long to either 6 or 7 of these. My, what a crazy you must be!
+Imagine a ruler with 12 inches on it. Now imagine one where, in the space of 12 inches, 13 equally spaced lines are drawn. Although these new lines are each only a little less than an inch apart from each other, they are clearly not "inches" and it would be silly to use them as such. If you used these 13ths of a foot to measure and estimate lengths frequently, you would soon find yourself rounding to this new set of lengths which before you would have rounded to inches. You might soon find yourself rounding something exactly 7 inches long to 7.6 of these. My, what a crazy you must be!
 ===The colors metaphor for microtonality===
@@ Line 52: / Line 52: @@
   &lt;!-- ws:start:WikiTextHeadingRule:12:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc6"&gt;&lt;a name="Aids to understanding"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:12 --&gt;Aids to understanding&lt;/h1&gt;
   &lt;!-- ws:start:WikiTextHeadingRule:14:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc7"&gt;&lt;a name="Aids to understanding--The rulers metaphor for microtonality"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:14 --&gt;The rulers metaphor for microtonality&lt;/h3&gt;
-  Imagine a ruler with 12 inches on it. Now imagine one where, in the space of 12 inches, 13 equally spaced lines are drawn. Although these new lines are each only a little less than an inch apart from each other, they are clearly not &amp;quot;inches&amp;quot; and it would be silly to use them as such. If you used these 13ths of a foot to measure and estimate lengths frequently, you would soon find yourself rounding to this new set of lengths which before you would have rounded to inches. You might soon find yourself rounding something exactly  inches long to either 6 or 7 of these. My, what a crazy you must be!&lt;br /&gt;
+  Imagine a ruler with 12 inches on it. Now imagine one where, in the space of 12 inches, 13 equally spaced lines are drawn. Although these new lines are each only a little less than an inch apart from each other, they are clearly not &amp;quot;inches&amp;quot; and it would be silly to use them as such. If you used these 13ths of a foot to measure and estimate lengths frequently, you would soon find yourself rounding to this new set of lengths which before you would have rounded to inches. You might soon find yourself rounding something exactly 7 inches long to 7.6 of these. My, what a crazy you must be!&lt;br /&gt;
 &lt;br /&gt;
 &lt;!-- ws:start:WikiTextHeadingRule:16:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc8"&gt;&lt;a name="Aids to understanding--The colors metaphor for microtonality"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:16 --&gt;The colors metaphor for microtonality&lt;/h3&gt;