Taxicab distance: Difference between revisions
Jump to navigation
Jump to search
Wikispaces>xenjacob **Imported revision 250467730 - Original comment: ** |
Wikispaces>mbattaglia1 **Imported revision 250469074 - 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: | : This revision was by author [[User:mbattaglia1|mbattaglia1]] and made on <tt>2011-09-03 04:43:20 UTC</tt>.<br> | ||
: The original revision id was <tt> | : The original revision id was <tt>250469074</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">One measurement of the complexity of the comma could be the number of prime factors it has, regardless of their magnitude. | <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">One measurement of the complexity of the comma could be the number of prime factors it has, regardless of their magnitude. This corresponds to an interval's unweighted L1 distance on the lattice, as opposed to the more common weighted L1 metric, corresponding to the log of Tenney/Benedetti Height. | ||
To calculate the number of prime factors in a [[monzo]], simply take sum of the absolute values of each coordinate. | To calculate the number of prime factors in a [[monzo]], simply take sum of the absolute values of each coordinate. | ||
| Line 40: | Line 40: | ||
176/169 (11 / 13 / 13)</pre></div> | 176/169 (11 / 13 / 13)</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>commas by taxicab distance</title></head><body>One measurement of the complexity of the comma could be the number of prime factors it has, regardless of their magnitude.<br /> | <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>commas by taxicab distance</title></head><body>One measurement of the complexity of the comma could be the number of prime factors it has, regardless of their magnitude. This corresponds to an interval's unweighted L1 distance on the lattice, as opposed to the more common weighted L1 metric, corresponding to the log of Tenney/Benedetti Height.<br /> | ||
<br /> | <br /> | ||
To calculate the number of prime factors in a <a class="wiki_link" href="/monzo">monzo</a>, simply take sum of the absolute values of each coordinate.<br /> | To calculate the number of prime factors in a <a class="wiki_link" href="/monzo">monzo</a>, simply take sum of the absolute values of each coordinate.<br /> | ||
Revision as of 04:43, 3 September 2011
IMPORTED REVISION FROM WIKISPACES
This is an imported revision from Wikispaces. The revision metadata is included below for reference:
- This revision was by author mbattaglia1 and made on 2011-09-03 04:43:20 UTC.
- The original revision id was 250469074.
- The revision comment was:
The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.
Original Wikitext content:
One measurement of the complexity of the comma could be the number of prime factors it has, regardless of their magnitude. This corresponds to an interval's unweighted L1 distance on the lattice, as opposed to the more common weighted L1 metric, corresponding to the log of Tenney/Benedetti Height. To calculate the number of prime factors in a [[monzo]], simply take sum of the absolute values of each coordinate. For example, 81/80 i.e. |-4 4 1> would have a factor limit of 4+4+1=9, or, with 2's taken for granted, 4+1=5. =Not yet the right name= I want to speak of a limit on the number of instances of prime factors, not the number of different prime factors. For example, 45 has factors 3, 3, and 5; here, we want to count each 3 separately. =With 2's taken for granted= ==2-factor-limit commas== 16/15 ( / 3 / 5) 33/32 (3 * 11) 65/64 (5 * 13) ==3-factor-limit commas== 25/24 (5 * 5 / 3) 128/125 (5 * 5 * 5) 21/20 (3 * 7 / 5) 26/25 (13 / 5 / 5) 49/48 (7 * 7 / 3) 64/63 ( / 3 / 7 / 7) 256/245 ( / 5 / 7 / 7) 80/77 (5 / 7 / 11) 22/21 (11 / 3 / 7) 40/39 (5 / 3 / 13) 96/91 (3 / 7 / 13) 55/52 (5 * 11 / 13) 1024/1001 (7 * 11 * 13) 512/507 (3 * 13 * 13) 169/160 (13 * 13 / 5) 176/169 (11 / 13 / 13)
Original HTML content:
<html><head><title>commas by taxicab distance</title></head><body>One measurement of the complexity of the comma could be the number of prime factors it has, regardless of their magnitude. This corresponds to an interval's unweighted L1 distance on the lattice, as opposed to the more common weighted L1 metric, corresponding to the log of Tenney/Benedetti Height.<br /> <br /> To calculate the number of prime factors in a <a class="wiki_link" href="/monzo">monzo</a>, simply take sum of the absolute values of each coordinate.<br /> <br /> For example, 81/80 i.e. |-4 4 1> would have a factor limit of 4+4+1=9, or, with 2's taken for granted, 4+1=5.<br /> <br /> <!-- ws:start:WikiTextHeadingRule:0:<h1> --><h1 id="toc0"><a name="Not yet the right name"></a><!-- ws:end:WikiTextHeadingRule:0 -->Not yet the right name</h1> I want to speak of a limit on the number of instances of prime factors, not the number of different prime factors. For example, 45 has factors 3, 3, and 5; here, we want to count each 3 separately.<br /> <br /> <!-- ws:start:WikiTextHeadingRule:2:<h1> --><h1 id="toc1"><a name="With 2's taken for granted"></a><!-- ws:end:WikiTextHeadingRule:2 -->With 2's taken for granted</h1> <br /> <!-- ws:start:WikiTextHeadingRule:4:<h2> --><h2 id="toc2"><a name="With 2's taken for granted-2-factor-limit commas"></a><!-- ws:end:WikiTextHeadingRule:4 -->2-factor-limit commas</h2> 16/15 ( / 3 / 5)<br /> 33/32 (3 * 11)<br /> 65/64 (5 * 13)<br /> <br /> <!-- ws:start:WikiTextHeadingRule:6:<h2> --><h2 id="toc3"><a name="With 2's taken for granted-3-factor-limit commas"></a><!-- ws:end:WikiTextHeadingRule:6 -->3-factor-limit commas</h2> 25/24 (5 * 5 / 3)<br /> 128/125 (5 * 5 * 5)<br /> 21/20 (3 * 7 / 5)<br /> 26/25 (13 / 5 / 5)<br /> 49/48 (7 * 7 / 3)<br /> 64/63 ( / 3 / 7 / 7)<br /> 256/245 ( / 5 / 7 / 7)<br /> 80/77 (5 / 7 / 11)<br /> 22/21 (11 / 3 / 7)<br /> 40/39 (5 / 3 / 13)<br /> 96/91 (3 / 7 / 13)<br /> 55/52 (5 * 11 / 13)<br /> 1024/1001 (7 * 11 * 13)<br /> 512/507 (3 * 13 * 13)<br /> 169/160 (13 * 13 / 5)<br /> 176/169 (11 / 13 / 13)</body></html>