3L 5s

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Revision as of 12:31, 11 February 2015 by Wikispaces>JosephRuhf (**Imported revision 540622250 - Original comment: **)
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This revision was by author JosephRuhf and made on 2015-02-11 12:31:37 UTC.
The original revision id was 540622250.
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Original Wikitext content:

There are two significant harmonic entropy minima with this MOS pattern. [[Sensipent family|Sensi]], in which the generator is 9/7, two of them make 5/3, and seven of them make 6/1, is the proper one. [[Meantone family#Squares|Squares]], in which the generator is also 9/7, but two of them make 18/11 and five of them make 8/3, is improper.
||||||||||||~ Generator ||~ Cents ||~ Comments ||
|| 1\3 ||   ||   ||   ||   ||   || 400 ||=   ||
||   ||   ||   || 6\17 ||   ||   || 423.53 ||= L/s = 4 ||
||   ||   ||   ||   ||   || 17\48 || 425 ||= Squares is around here ||
||   ||   ||   ||   || 11\31 ||   || 425.81 ||=   ||
||   ||   ||   ||   ||   ||   || 428.40 ||= <span style="display: block; text-align: center;">L/s = 3*2^(1/75)</span> ||
||   ||   || 5\14 ||   ||   ||   || 428.57 ||= L/s = 3 ||
||   ||   ||   ||   ||   ||   || 428.74 ||= <span style="display: block; text-align: center;">L/s = 3/2^(1/75)</span> ||
||   || 4\11 ||   ||   ||   ||   || 436.36 ||= Boundary of propriety:
generators larger than this are proper ||
||   ||   ||   || 11\30 ||   ||   || 440 ||=   ||
||   ||   ||   ||   ||   || 29\79 || 440.51 ||= Unnamed golden temperament ||
||   ||   ||   ||   || 18\49 ||   || 440.82 ||=   ||
||   ||   || 7\19 ||   ||   ||   || 442.11 ||= Optimum rank range (L/s=3/2) sensi ||
||   ||   ||   ||   || 17\46 ||   || 443.48 ||= Sensi is around here ||
||   ||   ||   || 10\27 ||   ||   || 444.44 ||=   ||
|| 3\8 ||   ||   ||   ||   ||   || 450 ||=   ||

Original HTML content:

<html><head><title>3L 5s</title></head><body>There are two significant harmonic entropy minima with this MOS pattern. <a class="wiki_link" href="/Sensipent%20family">Sensi</a>, in which the generator is 9/7, two of them make 5/3, and seven of them make 6/1, is the proper one. <a class="wiki_link" href="/Meantone%20family#Squares">Squares</a>, in which the generator is also 9/7, but two of them make 18/11 and five of them make 8/3, is improper.<br />


<table class="wiki_table">
    <tr>
        <th colspan="6">Generator<br />
</th>
        <th>Cents<br />
</th>
        <th>Comments<br />
</th>
    </tr>
    <tr>
        <td>1\3<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>400<br />
</td>
        <td style="text-align: center;"><br />
</td>
    </tr>
    <tr>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>6\17<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>423.53<br />
</td>
        <td style="text-align: center;">L/s = 4<br />
</td>
    </tr>
    <tr>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>17\48<br />
</td>
        <td>425<br />
</td>
        <td style="text-align: center;">Squares is around here<br />
</td>
    </tr>
    <tr>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>11\31<br />
</td>
        <td><br />
</td>
        <td>425.81<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>428.40<br />
</td>
        <td style="text-align: center;"><span style="display: block; text-align: center;">L/s = 3*2^(1/75)</span><br />
</td>
    </tr>
    <tr>
        <td><br />
</td>
        <td><br />
</td>
        <td>5\14<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>428.57<br />
</td>
        <td style="text-align: center;">L/s = 3<br />
</td>
    </tr>
    <tr>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>428.74<br />
</td>
        <td style="text-align: center;"><span style="display: block; text-align: center;">L/s = 3/2^(1/75)</span><br />
</td>
    </tr>
    <tr>
        <td><br />
</td>
        <td>4\11<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>436.36<br />
</td>
        <td style="text-align: center;">Boundary of propriety:<br />
generators larger than this are proper<br />
</td>
    </tr>
    <tr>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>11\30<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>440<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>29\79<br />
</td>
        <td>440.51<br />
</td>
        <td style="text-align: center;">Unnamed golden temperament<br />
</td>
    </tr>
    <tr>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>18\49<br />
</td>
        <td><br />
</td>
        <td>440.82<br />
</td>
        <td style="text-align: center;"><br />
</td>
    </tr>
    <tr>
        <td><br />
</td>
        <td><br />
</td>
        <td>7\19<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>442.11<br />
</td>
        <td style="text-align: center;">Optimum rank range (L/s=3/2) sensi<br />
</td>
    </tr>
    <tr>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>17\46<br />
</td>
        <td><br />
</td>
        <td>443.48<br />
</td>
        <td style="text-align: center;">Sensi is around here<br />
</td>
    </tr>
    <tr>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>10\27<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>444.44<br />
</td>
        <td style="text-align: center;"><br />
</td>
    </tr>
    <tr>
        <td>3\8<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>450<br />
</td>
        <td style="text-align: center;"><br />
</td>
    </tr>
</table>

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