6L 1s

Revision as of 14:47, 21 July 2011 by Wikispaces>guest (**Imported revision 242305375 - Original comment: **)

IMPORTED REVISION FROM WIKISPACES

This is an imported revision from Wikispaces. The revision metadata is included below for reference:

This revision was by author guest and made on 2011-07-21 14:47:01 UTC.
The original revision id was 242305375.
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:

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 roulette [[Chromatic pair]]. (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 ||   ||
||   || 2\13 ||   ||   ||   ||   || 184.62 ||   ||
||   ||   || 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 roulette <a class="wiki_link" href="/Chromatic%20pair">Chromatic pair</a>. (Other temperaments like &quot;luna&quot;, &quot;hemithird&quot;, and &quot;hemiwürschmidt&quot; 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><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><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>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><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><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><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><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><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>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><br />
</td>
    </tr>
</table>

</body></html>