5L 5s: Difference between revisions
Wikispaces>keenanpepper **Imported revision 227938282 - Original comment: ** |
Wikispaces>keenanpepper **Imported revision 228043956 - 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:keenanpepper|keenanpepper]] and made on <tt>2011-05-12 | : This revision was by author [[User:keenanpepper|keenanpepper]] and made on <tt>2011-05-12 19:39:44 UTC</tt>.<br> | ||
: The original revision id was <tt> | : The original revision id was <tt>228043956</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"> | <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">There is only one significant harmonic entropy minimum with this MOS pattern: [[Archytas clan|blackwood]], in which intervals of the prime numbers 3 and 7 are all represented using steps of [[5edo]], and the generator gets you to intervals of 5 like 6/5, 5/4, or 7/5. | ||
| | The true MOS, LsLsLsLsLs, is always proper because there is only one small step per period, but because there are 5 periods in an octave, there are a wealth of near-MOSes in which multiples of the period (that is, intervals of an even number of steps) are the only generic intervals that come in more than two different flavors. Specifically, there are 6 others: LLssLsLsLs, LLssLLssLs, LLsLssLsLs, LLsLssLLss, LLsLsLssLs, LLsLsLsLss. In the blackwood temperament, these are right on the boundary of being [[Rothenberg propriety|proper]] (because 1\15 is in the middle of the range of good blackwood generators). | ||
|| || || || || | ||||||~ Generator ||~ Cents ||~ Comments || | ||
|| || || || || | || 0\5 || || || 0 || || | ||
|| || || || || | || || || 1\20 || 60 || || | ||
|| || || || || | || || 1\15 || || 80 || Blackwood is around here || | ||
|| || || || || | || || || 2\25 || 96 || || | ||
|| || || || || || | || 1\10 || || || 120 || ||</pre></div> | ||
</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>5L 5s</title></head><body><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>5L 5s</title></head><body>There is only one significant harmonic entropy minimum with this MOS pattern: <a class="wiki_link" href="/Archytas%20clan">blackwood</a>, in which intervals of the prime numbers 3 and 7 are all represented using steps of <a class="wiki_link" href="/5edo">5edo</a>, and the generator gets you to intervals of 5 like 6/5, 5/4, or 7/5.<br /> | ||
<br /> | |||
The true MOS, LsLsLsLsLs, is always proper because there is only one small step per period, but because there are 5 periods in an octave, there are a wealth of near-MOSes in which multiples of the period (that is, intervals of an even number of steps) are the only generic intervals that come in more than two different flavors. Specifically, there are 6 others: LLssLsLsLs, LLssLLssLs, LLsLssLsLs, LLsLssLLss, LLsLsLssLs, LLsLsLsLss. In the blackwood temperament, these are right on the boundary of being <a class="wiki_link" href="/Rothenberg%20propriety">proper</a> (because 1\15 is in the middle of the range of good blackwood generators).<br /> | |||
<table class="wiki_table"> | <table class="wiki_table"> | ||
<tr> | <tr> | ||
< | <th colspan="3">Generator<br /> | ||
</ | </th> | ||
< | <th>Cents<br /> | ||
</ | </th> | ||
< | <th>Comments<br /> | ||
</ | </th> | ||
</tr> | </tr> | ||
<tr> | <tr> | ||
<td> | <td>0\5<br /> | ||
</td> | </td> | ||
<td><br /> | <td><br /> | ||
| Line 88: | Line 37: | ||
<td><br /> | <td><br /> | ||
</td> | </td> | ||
<td><br /> | <td>0<br /> | ||
</td> | </td> | ||
<td><br /> | <td><br /> | ||
| Line 98: | Line 47: | ||
<td><br /> | <td><br /> | ||
</td> | </td> | ||
<td> | <td>1\20<br /> | ||
</td> | </td> | ||
<td><br /> | <td>60<br /> | ||
</td> | </td> | ||
<td><br /> | <td><br /> | ||
| Line 114: | Line 57: | ||
<td><br /> | <td><br /> | ||
</td> | </td> | ||
<td><br /> | <td>1\15<br /> | ||
</td> | </td> | ||
<td><br /> | <td><br /> | ||
</td> | </td> | ||
<td><br /> | <td>80<br /> | ||
</td> | </td> | ||
<td> | <td>Blackwood is around here<br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
| Line 134: | Line 71: | ||
<td><br /> | <td><br /> | ||
</td> | </td> | ||
<td> | <td>2\25<br /> | ||
</td> | </td> | ||
<td> | <td>96<br /> | ||
</td> | </td> | ||
<td><br /> | <td><br /> | ||
| Line 148: | Line 79: | ||
</tr> | </tr> | ||
<tr> | <tr> | ||
<td><br /> | <td>1\10<br /> | ||
</td> | </td> | ||
<td><br /> | <td><br /> | ||
| Line 154: | Line 85: | ||
<td><br /> | <td><br /> | ||
</td> | </td> | ||
<td> | <td>120<br /> | ||
</td> | </td> | ||
<td><br /> | <td><br /> | ||