Patent val: Difference between revisions
Wikispaces>jdfreivald **Imported revision 246412585 - Original comment: ** |
Wikispaces>jdfreivald **Imported revision 246416533 - 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:jdfreivald|jdfreivald]] and made on <tt>2011-08-17 00: | : This revision was by author [[User:jdfreivald|jdfreivald]] and made on <tt>2011-08-17 01:00:15 UTC</tt>.<br> | ||
: The original revision id was <tt> | : The original revision id was <tt>246416533</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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==Example for 31 EDO== | ==Example for 31 EDO== | ||
Paraphrased from the Tuning list: | Paraphrased from the Tuning list: | ||
The scalar multiplication described above is mathematically correct, but I (Jake) found this method to be more intuitive. | |||
The val contains the number of steps it takes to get to a given prime number, in prime number order: | The val contains the number of steps it takes to get to a given prime number, in prime number order: | ||
< [2/1] [3/1] [5/1] [7/1] [etc.] | | < [2/1] [3/1] [5/1] [7/1] [etc.] | | ||
By definition, for any EDO, the number of steps to 2/1 is the EDO division: 31 for 31 EDO. The 2-limit patent val is < 31 |. | By definition, for any EDO, the number of steps to 2/1 is the EDO division: 31 for 31 EDO. The 2-limit patent val is < 31 |. | ||
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To do the whole thing one more time, let's do it for the 19-limit. | To do the whole thing one more time, let's do it for the 19-limit. | ||
19/1 = 5097.51 cents, 5097.51 / 38.70967742 cents/step = 131.6857529 steps. Round to get 132. | 19/1 = 5097.51 cents, 5097.51 / 38.70967742 cents/step = 131.6857529 steps. Round to get 132. | ||
The 19-limit patent val is | The 19-limit patent val is | ||
< 31 49 72 87 107 115 127 132 |</pre></div> | < 31 49 72 87 107 115 127 132 |</pre></div> | ||
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<!-- ws:start:WikiTextHeadingRule:2:&lt;h2&gt; --><h2 id="toc1"><a name="x-Example for 31 EDO"></a><!-- ws:end:WikiTextHeadingRule:2 -->Example for 31 EDO</h2> | <!-- ws:start:WikiTextHeadingRule:2:&lt;h2&gt; --><h2 id="toc1"><a name="x-Example for 31 EDO"></a><!-- ws:end:WikiTextHeadingRule:2 -->Example for 31 EDO</h2> | ||
Paraphrased from the Tuning list:<br /> | Paraphrased from the Tuning list:<br /> | ||
The scalar multiplication described above is mathematically correct, but I (Jake) found this method to be more intuitive.<br /> | |||
<br /> | <br /> | ||
The val contains the number of steps it takes to get to a given prime number, in prime number order:<br /> | The val contains the number of steps it takes to get to a given prime number, in prime number order:<br /> | ||
&lt; [2/1] [3/1] [5/1] [7/1] [etc.] |<br /> | &lt; [2/1] [3/1] [5/1] [7/1] [etc.] |<br /> | ||
By definition, for any EDO, the number of steps to 2/1 is the EDO division: 31 for 31 EDO. The 2-limit patent val is &lt; 31 |.<br /> | By definition, for any EDO, the number of steps to 2/1 is the EDO division: 31 for 31 EDO. The 2-limit patent val is &lt; 31 |.<br /> | ||
<br /> | <br /> | ||
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<br /> | <br /> | ||
To do the whole thing one more time, let's do it for the 19-limit.<br /> | To do the whole thing one more time, let's do it for the 19-limit.<br /> | ||
19/1 = 5097.51 cents, 5097.51 / 38.70967742 cents/step = 131.6857529 steps. Round to get 132. <br /> | 19/1 = 5097.51 cents, 5097.51 / 38.70967742 cents/step = 131.6857529 steps. Round to get 132.<br /> | ||
The 19-limit patent val is<br /> | The 19-limit patent val is<br /> | ||
&lt; 31 49 72 87 107 115 127 132 |</body></html></pre></div> | &lt; 31 49 72 87 107 115 127 132 |</body></html></pre></div> | ||