17edt: Difference between revisions
Wikispaces>Kosmorsky **Imported revision 245287801 - Original comment: ** |
Wikispaces>guest **Imported revision 245526861 - Original comment: ** |
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<h2>IMPORTED REVISION FROM WIKISPACES</h2> | <h2>IMPORTED REVISION FROM WIKISPACES</h2> | ||
This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br> | This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br> | ||
: This revision was by author [[User: | : This revision was by author [[User:guest|guest]] and made on <tt>2011-08-11 19:18:45 UTC</tt>.<br> | ||
: The original revision id was <tt> | : The original revision id was <tt>245526861</tt>.<br> | ||
: The revision comment was: <tt></tt><br> | : The revision comment was: <tt></tt><br> | ||
The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.<br> | The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.<br> | ||
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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? | 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.</pre></div> | 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 ||</pre></div> | |||
<h4>Original HTML content:</h4> | <h4>Original HTML content:</h4> | ||
<div style="width:100%; max-height:400pt; overflow:auto; background-color:#f8f9fa; border: 1px solid #eaecf0; padding:0em"><pre style="margin:0px;border:none;background:none;word-wrap:break-word;width:200%;white-space: pre-wrap ! important" class="old-revision-html"><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> | <div style="width:100%; max-height:400pt; overflow:auto; background-color:#f8f9fa; border: 1px solid #eaecf0; padding:0em"><pre style="margin:0px;border:none;background:none;word-wrap:break-word;width:200%;white-space: pre-wrap ! important" class="old-revision-html"><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> | ||
| Line 18: | Line 57: | ||
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 /> | 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 /> | <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.</body></html></pre></div> | 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></pre></div> | |||