Otones12-24

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Revision as of 14:57, 19 April 2009 by Wikispaces>Andrew_Heathwaite (**Imported revision 68455669 - Original comment: **)
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This revision was by author Andrew_Heathwaite and made on 2009-04-19 14:57:21 UTC.
The original revision id was 68455669.
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Original Wikitext content:

A dedecatonic (12-note) scale borrowed from the overtone series:

12/12, 13/12, 14/12, 15/12, 16/12, 17/12, 18/12, 19/12, 20/12, 21/12, 22/12, 23/12, 24/12

which reduces to:

1/1, 13/12, 7/6, 5/4, 4/3, 17/12, 3/2, 19/12, 5/3, 7/4, 11/6, 23/12, 2/1

in cents:

0, 139, 267, 386, 498, 603, 702, 796, 884, 969, 1049, 1126, 1200

intervals between adjacent steps gradually get smaller, as is usual for overtone chunks like this:

13:12, 14:13, 15:14, 16:15, 17:16, 18:17, 19:18, 21:20, 22:21, 23:22, 24:23
= in cents:
139, 128, 119, 112, 105, 99, 94, 89, 84, 81, 77, 74

==modes== 

For your tuning pleasure, all 12 modes. Note that the names "C", "C#", refer to a keyboard mapping that begins the scale on C. Such a mapping & naming system are, I admit, quite arbitrary.

||   || C-12 || C#-13 || D-14 || D#-15 || E-16 || F-17 || F#-18 || G-19 || G#-20 || A-21 || A#-22 || B-23 ||
|| C-12 ||   ||   ||   ||   ||   ||   ||   ||   ||   ||   ||   ||   ||
|| C#-13 ||   ||   ||   ||   ||   ||   ||   ||   ||   ||   ||   ||   ||
|| D-14 ||   ||   ||   ||   ||   ||   ||   ||   ||   ||   ||   ||   ||
|| D#-15 ||   ||   ||   ||   ||   ||   ||   ||   ||   ||   ||   ||   ||
|| E-16 ||   ||   ||   ||   ||   ||   ||   ||   ||   ||   ||   ||   ||
|| F-17 ||   ||   ||   ||   ||   ||   ||   ||   ||   ||   ||   ||   ||
|| F#-18 ||   ||   ||   ||   ||   ||   ||   ||   ||   ||   ||   ||   ||
|| G-19 ||   ||   ||   ||   ||   ||   ||   ||   ||   ||   ||   ||   ||
|| G#-20 ||   ||   ||   ||   ||   ||   ||   ||   ||   ||   ||   ||   ||
|| A-21 ||   ||   ||   ||   ||   ||   ||   ||   ||   ||   ||   ||   ||
|| A#-22 ||   ||   ||   ||   ||   ||   ||   ||   ||   ||   ||   ||   ||
|| B-23 ||   ||   ||   ||   ||   ||   ||   ||   ||   ||   ||   ||   ||

Original HTML content:

<html><head><title>otones12-24</title></head><body>A dedecatonic (12-note) scale borrowed from the overtone series:<br />
<br />
12/12, 13/12, 14/12, 15/12, 16/12, 17/12, 18/12, 19/12, 20/12, 21/12, 22/12, 23/12, 24/12<br />
<br />
which reduces to:<br />
<br />
1/1, 13/12, 7/6, 5/4, 4/3, 17/12, 3/2, 19/12, 5/3, 7/4, 11/6, 23/12, 2/1<br />
<br />
in cents:<br />
<br />
0, 139, 267, 386, 498, 603, 702, 796, 884, 969, 1049, 1126, 1200<br />
<br />
intervals between adjacent steps gradually get smaller, as is usual for overtone chunks like this:<br />
<br />
13:12, 14:13, 15:14, 16:15, 17:16, 18:17, 19:18, 21:20, 22:21, 23:22, 24:23<br />
= in cents:<br />
139, 128, 119, 112, 105, 99, 94, 89, 84, 81, 77, 74<br />
<br />
<!-- ws:start:WikiTextHeadingRule:0:&lt;h2&gt; --><h2 id="toc0"><a name="x-modes"></a><!-- ws:end:WikiTextHeadingRule:0 -->modes</h2>
 <br />
For your tuning pleasure, all 12 modes. Note that the names &quot;C&quot;, &quot;C#&quot;, refer to a keyboard mapping that begins the scale on C. Such a mapping &amp; naming system are, I admit, quite arbitrary.<br />
<br />


<table class="wiki_table">
    <tr>
        <td><br />
</td>
        <td>C-12<br />
</td>
        <td>C#-13<br />
</td>
        <td>D-14<br />
</td>
        <td>D#-15<br />
</td>
        <td>E-16<br />
</td>
        <td>F-17<br />
</td>
        <td>F#-18<br />
</td>
        <td>G-19<br />
</td>
        <td>G#-20<br />
</td>
        <td>A-21<br />
</td>
        <td>A#-22<br />
</td>
        <td>B-23<br />
</td>
    </tr>
    <tr>
        <td>C-12<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
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</td>
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</td>
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</td>
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</td>
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</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>C#-13<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
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</td>
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</td>
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</td>
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</td>
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</td>
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</td>
    </tr>
    <tr>
        <td>D-14<br />
</td>
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</td>
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</td>
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</td>
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    </tr>
    <tr>
        <td>D#-15<br />
</td>
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    </tr>
    <tr>
        <td>E-16<br />
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    </tr>
    <tr>
        <td>F-17<br />
</td>
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    </tr>
    <tr>
        <td>F#-18<br />
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    </tr>
    <tr>
        <td>G-19<br />
</td>
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    </tr>
    <tr>
        <td>G#-20<br />
</td>
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    </tr>
    <tr>
        <td>A-21<br />
</td>
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    </tr>
    <tr>
        <td>A#-22<br />
</td>
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    </tr>
    <tr>
        <td>B-23<br />
</td>
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    </tr>
</table>

</body></html>
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