6L 1s
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- This revision was by author keenanpepper and made on 2011-11-25 21:15:38 UTC.
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Original Wikitext content:
There are two notable harmonic entropy minima with this [[MOSScales|MOS]] pattern. The first is [[Tetracot family|tetracot]], in which four generators make a 3/2, and the second is known as [[roulette7]], the seven note albitonic scale for the 2.5.7.11.13 subgroup temperament [[Chromatic pairs#Roulette|roulette]]. (Other temperaments like "luna", "hemithird", and "hemiwürschmidt" have very similar 7-note MOSes.) The 6L+1s pattern also houses a temperament of the 11th and 13th harmonics, for example L=7 s=4 (46 edo) is such a scale. Scales of this form are always [[Rothenberg propriety|proper]], because there is only one small step. ||||||||||||~ Generator ||~ Cents ||~ Comments || || 1\7 || || || || || || 171.43 ||= || || || || || || || 6\41 || 175.61 ||= || || || || || || 5\34 || || 176.47 ||= Tetracot is around here || || || || || 4\27 || || || 177.78 ||= || || || || 3\20 || || || || 180 ||= || || || || || || 8\53 || || 181.13 ||= || || || || || || || || 1200/(5+phi) ||= Unnamed golden temperament (discussed in [[http://launch.groups.yahoo.com/group/tuning/message/100254|this thread]]) || || || || || 5\33 || || || 181.82 ||= || || || 2\13 || || || || || 184.62 ||= Optimum rank range glacial (L/s=2/1) || || || || 3\19 || || || || 189.47 ||= || || || || || 4\25 || || || 192 ||= || || || || || || 5\31 || || 193.55 ||= Luna/hemithird/roulette is around here || || 1\6 || || || || || || 200 ||= ||
Original HTML content:
<html><head><title>6L 1s</title></head><body>There are two notable harmonic entropy minima with this <a class="wiki_link" href="/MOSScales">MOS</a> pattern. The first is <a class="wiki_link" href="/Tetracot%20family">tetracot</a>, in which four generators make a 3/2, and the second is known as <a class="wiki_link" href="/roulette7">roulette7</a>, the seven note albitonic scale for the 2.5.7.11.13 subgroup temperament <a class="wiki_link" href="/Chromatic%20pairs#Roulette">roulette</a>. (Other temperaments like "luna", "hemithird", and "hemiwürschmidt" have very similar 7-note MOSes.)<br />
<br />
The 6L+1s pattern also houses a temperament of the 11th and 13th harmonics, for example L=7 s=4 (46 edo) is such a scale.<br />
Scales of this form are always <a class="wiki_link" href="/Rothenberg%20propriety">proper</a>, because there is only one small step.<br />
<table class="wiki_table">
<tr>
<th colspan="6">Generator<br />
</th>
<th>Cents<br />
</th>
<th>Comments<br />
</th>
</tr>
<tr>
<td>1\7<br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td>171.43<br />
</td>
<td style="text-align: center;"><br />
</td>
</tr>
<tr>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td>6\41<br />
</td>
<td>175.61<br />
</td>
<td style="text-align: center;"><br />
</td>
</tr>
<tr>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td>5\34<br />
</td>
<td><br />
</td>
<td>176.47<br />
</td>
<td style="text-align: center;">Tetracot is around here<br />
</td>
</tr>
<tr>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td>4\27<br />
</td>
<td><br />
</td>
<td><br />
</td>
<td>177.78<br />
</td>
<td style="text-align: center;"><br />
</td>
</tr>
<tr>
<td><br />
</td>
<td><br />
</td>
<td>3\20<br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td>180<br />
</td>
<td style="text-align: center;"><br />
</td>
</tr>
<tr>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td>8\53<br />
</td>
<td><br />
</td>
<td>181.13<br />
</td>
<td style="text-align: center;"><br />
</td>
</tr>
<tr>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td>1200/(5+phi)<br />
</td>
<td style="text-align: center;">Unnamed golden temperament (discussed in <a class="wiki_link_ext" href="http://launch.groups.yahoo.com/group/tuning/message/100254" rel="nofollow">this thread</a>)<br />
</td>
</tr>
<tr>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td>5\33<br />
</td>
<td><br />
</td>
<td><br />
</td>
<td>181.82<br />
</td>
<td style="text-align: center;"><br />
</td>
</tr>
<tr>
<td><br />
</td>
<td>2\13<br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td>184.62<br />
</td>
<td style="text-align: center;">Optimum rank range glacial (L/s=2/1)<br />
</td>
</tr>
<tr>
<td><br />
</td>
<td><br />
</td>
<td>3\19<br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td>189.47<br />
</td>
<td style="text-align: center;"><br />
</td>
</tr>
<tr>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td>4\25<br />
</td>
<td><br />
</td>
<td><br />
</td>
<td>192<br />
</td>
<td style="text-align: center;"><br />
</td>
</tr>
<tr>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td>5\31<br />
</td>
<td><br />
</td>
<td>193.55<br />
</td>
<td style="text-align: center;">Luna/hemithird/roulette is around here<br />
</td>
</tr>
<tr>
<td>1\6<br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td>200<br />
</td>
<td style="text-align: center;"><br />
</td>
</tr>
</table>
</body></html>