Xenharmonic Wiki

1L 10s

Revision as of 16:34, 23 May 2015 by Wikispaces>JosephRuhf (**Imported revision 551974672 - Original comment: **)

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This revision was by author JosephRuhf and made on 2015-05-23 16:34:03 UTC.
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Original Wikitext content:

This MOS, generated by any interval up to a diatonic semitone of 1/11edo (109 1/9 cents), achieves its simplest harmonic entropy minimum where two generators equal 9/8. The temperament which occupies this harmonic entropy minimum is called Ripple, but there are several lower (and more complex) harmonic entropy minima of note including (in descending order of generator height): Passion (6/5=+3 generators), Octacot (3/2=+8 generators), Nautilus (3/2=-6 generators) and Valentine (7/4=-3 generators).
|| 0/1 ||   ||   ||   ||   || 0 ||
||   ||   ||   ||   || 1/15 || 80 ||
||   ||   ||   || 1/14 ||   || 85 5/7 ||
||   ||   ||   ||   || 2/27 || 88 8/9 ||
||   ||   ||   ||   ||   || 1200/(10+pi) ||
||   ||   || 1/13 ||   ||   || 92 4/13 ||
||   ||   ||   ||   ||   || 1200/(10+e) ||
||   ||   ||   ||   || 3/38 || 94.736842 ||
||   ||   ||   || 2/25 ||   || 96 ||
||   ||   ||   ||   || 3/37 || 97 11/37 ||
||   || 1/12 ||   ||   ||   || 100 ||
||   ||   ||   ||   || 4/47 || 102.12766 ||
||   ||   ||   || 3/35 ||   || 102 6/7 ||
||   ||   ||   ||   || 5/58 || 103.448276 ||
||   ||   || 2/23 ||   ||   || 104.347826 ||
||   ||   ||   ||   || 5/57 || 105.263158 ||
||   ||   ||   || 3/34 ||   || 105.882353 ||
||   ||   ||   ||   || 4/45 || 106 2/3 ||
|| 1/11 ||   ||   ||   ||   || 109 1/11 ||

Original HTML content:

<html><head><title>1L 10s</title></head><body>This MOS, generated by any interval up to a diatonic semitone of 1/11edo (109 1/9 cents), achieves its simplest harmonic entropy minimum where two generators equal 9/8. The temperament which occupies this harmonic entropy minimum is called Ripple, but there are several lower (and more complex) harmonic entropy minima of note including (in descending order of generator height): Passion (6/5=+3 generators), Octacot (3/2=+8 generators), Nautilus (3/2=-6 generators) and Valentine (7/4=-3 generators).<br />


<table class="wiki_table">
    <tr>
        <td>0/1<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>0<br />
</td>
    </tr>
    <tr>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>1/15<br />
</td>
        <td>80<br />
</td>
    </tr>
    <tr>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>1/14<br />
</td>
        <td><br />
</td>
        <td>85 5/7<br />
</td>
    </tr>
    <tr>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>2/27<br />
</td>
        <td>88 8/9<br />
</td>
    </tr>
    <tr>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>1200/(10+pi)<br />
</td>
    </tr>
    <tr>
        <td><br />
</td>
        <td><br />
</td>
        <td>1/13<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>92 4/13<br />
</td>
    </tr>
    <tr>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>1200/(10+e)<br />
</td>
    </tr>
    <tr>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>3/38<br />
</td>
        <td>94.736842<br />
</td>
    </tr>
    <tr>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>2/25<br />
</td>
        <td><br />
</td>
        <td>96<br />
</td>
    </tr>
    <tr>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>3/37<br />
</td>
        <td>97 11/37<br />
</td>
    </tr>
    <tr>
        <td><br />
</td>
        <td>1/12<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>100<br />
</td>
    </tr>
    <tr>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>4/47<br />
</td>
        <td>102.12766<br />
</td>
    </tr>
    <tr>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>3/35<br />
</td>
        <td><br />
</td>
        <td>102 6/7<br />
</td>
    </tr>
    <tr>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>5/58<br />
</td>
        <td>103.448276<br />
</td>
    </tr>
    <tr>
        <td><br />
</td>
        <td><br />
</td>
        <td>2/23<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>104.347826<br />
</td>
    </tr>
    <tr>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>5/57<br />
</td>
        <td>105.263158<br />
</td>
    </tr>
    <tr>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>3/34<br />
</td>
        <td><br />
</td>
        <td>105.882353<br />
</td>
    </tr>
    <tr>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>4/45<br />
</td>
        <td>106 2/3<br />
</td>
    </tr>
    <tr>
        <td>1/11<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>109 1/11<br />
</td>
    </tr>
</table>

</body></html>
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