7L 1s

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Revision as of 17:21, 20 June 2011 by Wikispaces>xenwolf (**Imported revision 237804969 - Original comment: **)
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There are two notable harmonic entropy minima with this [[MOSScales|MOS]] pattern. The first is [[Porcupine family|porcupine]], in which two generators make a 6/5 and three make a 4/3. The range of porcupine tunings is about 2\15 to 3\22. Less well-known is [[Chromatic pairs|greely]], in which two generators are still 6/5 but three fall quite short of a 4/3, but the scale happens to closely approximate a lot of higher-complexity intervals like 10/7, 11/7, etc.

Scales of this form are always [[Rothenberg propriety|proper]], because there is only one small step.
||||||||||||~ [[Generator]] ||~ [[Cent]]s ||~ Scale in [[EDO]] steps ||~ Comments ||
|| 1\7 ||   ||   ||   ||   ||   || 171.43 ||= 1 1 1 1 1 1 1 0 ||   ||
||   ||   ||   || 4\29 ||   ||   ||   ||= 4 4 4 4 4 4 4 1 ||   ||
||   ||   || 3\22 ||   ||   ||   ||   ||= 3 3 3 3 3 3 3 1 ||   ||
||   ||   ||   || 5\37 ||   ||   ||   ||= 5 5 5 5 5 5 5 2 || Porcupine is in this general region ||
||   ||   ||   ||   || 7\52 ||   ||   ||= 7 7 7 7 7 7 7 3 ||   ||
||   || 2\15 ||   ||   ||   ||   || 160 ||= 2 2 2 2 2 2 2 1 ||   ||
||   ||   || 3\23 ||   ||   ||   ||   ||= 3 3 3 3 3 3 3 2 ||   ||
||   ||   ||   ||   ||   || 10\77 ||   ||= 10 10 10 10 10 10 10 7 || Greely is around here ||
||   ||   ||   ||   || 7\54 ||   ||   ||= 7 7 7 7 7 7 7 5 ||   ||
||   ||   ||   || 4\31 ||   ||   ||   ||= 4 4 4 4 4 4 4 3 ||   ||
|| 1\8 ||   ||   ||   ||   ||   || 150 ||= 1 1 1 1 1 1 1 1 ||   ||

Original HTML content:

<html><head><title>7L 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="/Porcupine%20family">porcupine</a>, in which two generators make a 6/5 and three make a 4/3. The range of porcupine tunings is about 2\15 to 3\22. Less well-known is <a class="wiki_link" href="/Chromatic%20pairs">greely</a>, in which two generators are still 6/5 but three fall quite short of a 4/3, but the scale happens to closely approximate a lot of higher-complexity intervals like 10/7, 11/7, etc.<br />
<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"><a class="wiki_link" href="/Generator">Generator</a><br />
</th>
        <th><a class="wiki_link" href="/Cent">Cent</a>s<br />
</th>
        <th>Scale in <a class="wiki_link" href="/EDO">EDO</a> steps<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;">1 1 1 1 1 1 1 0<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>4\29<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td style="text-align: center;">4 4 4 4 4 4 4 1<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td><br />
</td>
        <td><br />
</td>
        <td>3\22<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td style="text-align: center;">3 3 3 3 3 3 3 1<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>5\37<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td style="text-align: center;">5 5 5 5 5 5 5 2<br />
</td>
        <td>Porcupine is in this general region<br />
</td>
    </tr>
    <tr>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>7\52<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td style="text-align: center;">7 7 7 7 7 7 7 3<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td><br />
</td>
        <td>2\15<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>160<br />
</td>
        <td style="text-align: center;">2 2 2 2 2 2 2 1<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td><br />
</td>
        <td><br />
</td>
        <td>3\23<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td style="text-align: center;">3 3 3 3 3 3 3 2<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>10\77<br />
</td>
        <td><br />
</td>
        <td style="text-align: center;">10 10 10 10 10 10 10 7<br />
</td>
        <td>Greely is around here<br />
</td>
    </tr>
    <tr>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>7\54<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td style="text-align: center;">7 7 7 7 7 7 7 5<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>4\31<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td style="text-align: center;">4 4 4 4 4 4 4 3<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>1\8<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>150<br />
</td>
        <td style="text-align: center;">1 1 1 1 1 1 1 1<br />
</td>
        <td><br />
</td>
    </tr>
</table>

</body></html>
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