17edt: Difference between revisions

Revision as of 19:18, 11 August 2011

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=17 Tone Equal Divided Tritave= 


17edt is closely related to the Bohlen-Pierce scale, and I might go as far as calling it an 11-limit version of it. Both have 4L+5s nonatonic modes, but whereas the ratio of large to small steps in BP is a calm 2:1, in 17edt it is a hard 3:1. Thus, the approximation of 5/3 and 7/3 suffers slightly, in return for a very good approximation of 11/9, which is in fact the size of the large step! Nifty right?

If the major chord is defined by degrees 0,8,13 (fibonacci numbers, coincidence?), and a major chord is built atop the two chord tones, an hexatonic set of 0,4,8,9,13,16,17 results. Excluding #16 produces a LLsLL pentatonic scale. Continuing the trend by building major chords on the three new chord tones (4, 9, and 16) gives you a set of the notes 0,3,4,7,8,9,12,13,15,16,17. Excluding #15 produces a LsLssLsLs moment of symmetry, which is called "Moll I" or "Delta", if I'm not mistaken.

===Intervals=== 

|| degree of 17edt || cents value || cents value octave reduced ||
|| 0 || 0 ||   ||
|| 1 || 111.9 ||   ||
|| 2 || 223.8 ||   ||
|| 3 || 335.6 ||   ||
|| 4 || 447.5 ||   ||
|| 5 || 559.4 ||   ||
|| 6 || 671.3 ||   ||
|| 7 || 783.2 ||   ||
|| 8 || 895.1 ||   ||
|| 9 || 1006.9 ||   ||
|| 10 || 1118.8 ||   ||
|| 11 || 1230.7 || 30.7 ||
|| 12 || 1342.6 || 142.6 ||
|| 13 || 1454.5 || 254.5 ||
|| 14 || 1566.3 || 366.3 ||
|| 15 || 1678.2 || 478.2 ||
|| 16 || 1790.1 || 590.1 ||
|| 17 || 1902.0 || 702.0 ||
|| 18 || 2013.9 || 813.9 ||
|| 19 || 2125.8 || 925.8 ||
|| 20 || 2237.6 || 1037.6 ||
|| 21 || 2349..5 || 1149.5 ||
|| 22 || 2461.4 || 61.4 ||
|| 23 || 2573.2 || 173.2 ||
|| 24 || 2685.2 || 285.2 ||
|| 25 || 2797.1 || 397.1 ||
|| 26 || 2908.9 || 508.9 ||
|| 27 || 3020.8 || 620.8 ||
|| 28 || 3132.7 || 732.7 ||
|| 29 || 3244.6 || 844.6 ||
|| 30 || 3356.5 || 956.5 ||
|| 31 || 3468.3 || 1068.3 ||
|| 32 || 3580.2 || 1180.2 ||
|| 33 || 3692.1 || 92.1 ||
|| 34 || 3804.0 || 204.0 ||

Original HTML content:

<html><head><title>17edt</title></head><body><!-- ws:start:WikiTextHeadingRule:0:&lt;h1&gt; --><h1 id="toc0"><a name="x17 Tone Equal Divided Tritave"></a><!-- ws:end:WikiTextHeadingRule:0 -->17 Tone Equal Divided Tritave</h1>
 <br />
<br />
17edt is closely related to the Bohlen-Pierce scale, and I might go as far as calling it an 11-limit version of it. Both have 4L+5s nonatonic modes, but whereas the ratio of large to small steps in BP is a calm 2:1, in 17edt it is a hard 3:1. Thus, the approximation of 5/3 and 7/3 suffers slightly, in return for a very good approximation of 11/9, which is in fact the size of the large step! Nifty right?<br />
<br />
If the major chord is defined by degrees 0,8,13 (fibonacci numbers, coincidence?), and a major chord is built atop the two chord tones, an hexatonic set of 0,4,8,9,13,16,17 results. Excluding #16 produces a LLsLL pentatonic scale. Continuing the trend by building major chords on the three new chord tones (4, 9, and 16) gives you a set of the notes 0,3,4,7,8,9,12,13,15,16,17. Excluding #15 produces a LsLssLsLs moment of symmetry, which is called &quot;Moll I&quot; or &quot;Delta&quot;, if I'm not mistaken.<br />
<br />
<!-- ws:start:WikiTextHeadingRule:2:&lt;h3&gt; --><h3 id="toc1"><a name="x17 Tone Equal Divided Tritave--Intervals"></a><!-- ws:end:WikiTextHeadingRule:2 -->Intervals</h3>
 <br />


<table class="wiki_table">
    <tr>
        <td>degree of 17edt<br />
</td>
        <td>cents value<br />
</td>
        <td>cents value octave reduced<br />
</td>
    </tr>
    <tr>
        <td>0<br />
</td>
        <td>0<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>1<br />
</td>
        <td>111.9<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>2<br />
</td>
        <td>223.8<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>3<br />
</td>
        <td>335.6<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>4<br />
</td>
        <td>447.5<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>5<br />
</td>
        <td>559.4<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>6<br />
</td>
        <td>671.3<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>7<br />
</td>
        <td>783.2<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>8<br />
</td>
        <td>895.1<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>9<br />
</td>
        <td>1006.9<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>10<br />
</td>
        <td>1118.8<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>11<br />
</td>
        <td>1230.7<br />
</td>
        <td>30.7<br />
</td>
    </tr>
    <tr>
        <td>12<br />
</td>
        <td>1342.6<br />
</td>
        <td>142.6<br />
</td>
    </tr>
    <tr>
        <td>13<br />
</td>
        <td>1454.5<br />
</td>
        <td>254.5<br />
</td>
    </tr>
    <tr>
        <td>14<br />
</td>
        <td>1566.3<br />
</td>
        <td>366.3<br />
</td>
    </tr>
    <tr>
        <td>15<br />
</td>
        <td>1678.2<br />
</td>
        <td>478.2<br />
</td>
    </tr>
    <tr>
        <td>16<br />
</td>
        <td>1790.1<br />
</td>
        <td>590.1<br />
</td>
    </tr>
    <tr>
        <td>17<br />
</td>
        <td>1902.0<br />
</td>
        <td>702.0<br />
</td>
    </tr>
    <tr>
        <td>18<br />
</td>
        <td>2013.9<br />
</td>
        <td>813.9<br />
</td>
    </tr>
    <tr>
        <td>19<br />
</td>
        <td>2125.8<br />
</td>
        <td>925.8<br />
</td>
    </tr>
    <tr>
        <td>20<br />
</td>
        <td>2237.6<br />
</td>
        <td>1037.6<br />
</td>
    </tr>
    <tr>
        <td>21<br />
</td>
        <td>2349..5<br />
</td>
        <td>1149.5<br />
</td>
    </tr>
    <tr>
        <td>22<br />
</td>
        <td>2461.4<br />
</td>
        <td>61.4<br />
</td>
    </tr>
    <tr>
        <td>23<br />
</td>
        <td>2573.2<br />
</td>
        <td>173.2<br />
</td>
    </tr>
    <tr>
        <td>24<br />
</td>
        <td>2685.2<br />
</td>
        <td>285.2<br />
</td>
    </tr>
    <tr>
        <td>25<br />
</td>
        <td>2797.1<br />
</td>
        <td>397.1<br />
</td>
    </tr>
    <tr>
        <td>26<br />
</td>
        <td>2908.9<br />
</td>
        <td>508.9<br />
</td>
    </tr>
    <tr>
        <td>27<br />
</td>
        <td>3020.8<br />
</td>
        <td>620.8<br />
</td>
    </tr>
    <tr>
        <td>28<br />
</td>
        <td>3132.7<br />
</td>
        <td>732.7<br />
</td>
    </tr>
    <tr>
        <td>29<br />
</td>
        <td>3244.6<br />
</td>
        <td>844.6<br />
</td>
    </tr>
    <tr>
        <td>30<br />
</td>
        <td>3356.5<br />
</td>
        <td>956.5<br />
</td>
    </tr>
    <tr>
        <td>31<br />
</td>
        <td>3468.3<br />
</td>
        <td>1068.3<br />
</td>
    </tr>
    <tr>
        <td>32<br />
</td>
        <td>3580.2<br />
</td>
        <td>1180.2<br />
</td>
    </tr>
    <tr>
        <td>33<br />
</td>
        <td>3692.1<br />
</td>
        <td>92.1<br />
</td>
    </tr>
    <tr>
        <td>34<br />
</td>
        <td>3804.0<br />
</td>
        <td>204.0<br />
</td>
    </tr>
</table>

</body></html>

17edt: Difference between revisions

Revision as of 19:18, 11 August 2011

IMPORTED REVISION FROM WIKISPACES

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