17edt: Difference between revisions

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<h2>IMPORTED REVISION FROM WIKISPACES</h2>

This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br>

: This revision was by author [[User:~~Kosmorsky~~|~~Kosmorsky~~]] and made on <tt>2011-08-~~14 00~~:55:42 UTC</tt>.<br>

: This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2011-09-03 22:45:20 UTC</tt>.<br>

: The original revision id was <tt>~~245831589~~</tt>.<br>

: The original revision id was <tt>250558494</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>

<h4>Original Wikitext 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;white-space: pre-wrap ! important" class="old-revision-html">~~=17 Tone Equal Divided Tritave=~~

<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;white-space: pre-wrap ! important" class="old-revision-html">[[toc|flat]]

=Properties=

17edt divides 3, the tritave, into 17 equal parts of 111.880 cents each. It tempers out 245/243 and 16807/15625 in the 7-limit, 77/75 and 1331/1323 in the 11-limit, and 175/169 and 121/117 in the 13-limit. It supports the no-twos temperament tempering out 245/243 and 77/75, which in terms of tritave patent vals could be written 17&21.

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~~.

=Discussion=

17edt is closely related [[13edt]], the Bohlen-Pierce division, because they share the feature of tempering out 245/243. Both 13edt and 17edt have 4L+5s nonatonic modes, but whereas the ratio of large to small steps in 13edt 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.

If the major chord is defined by degrees 0,8,13 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".

===Intervals===

|| degree of 17edt || cents value || cents value octave reduced ||

|| 0 || 0 || ||

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|| 34 || 3804.0 || 204.0 ||</pre></div>

<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><h1 id="toc0"><a name="~~x17 Tone Equal Divided Tritave~~"></a>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><a href="#Properties">Properties</a> | <a href="#Discussion">Discussion</a>

<br />

<br />

<h1 id="toc0"><a name="Properties"></a>Properties</h1>

17edt divides 3, the tritave, into 17 equal parts of 111.880 cents each. It tempers out 245/243 and 16807/15625 in the 7-limit, 77/75 and 1331/1323 in the 11-limit, and 175/169 and 121/117 in the 13-limit. It supports the no-twos temperament tempering out 245/243 and 77/75, which in terms of tritave patent vals could be written 17&amp;21.<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 />

<h1 id="toc1"><a name="Discussion"></a>Discussion</h1>

17edt is closely related <a class="wiki_link" href="/13edt">13edt</a>, the Bohlen-Pierce division, because they share the feature of tempering out 245/243. Both 13edt and 17edt have 4L+5s nonatonic modes, but whereas the ratio of large to small steps in 13edt 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.<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 />

If the major chord is defined by degrees 0,8,13 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;.<br />

<br />

<h3 id="~~toc1~~"><a name="~~x17 Tone Equal Divided Tritave~~--Intervals"></a>Intervals</h3>

<h3 id="toc2"><a name="Discussion--Intervals"></a>Intervals</h3>

~~<br />~~

@@ Line 1: / Line 1: @@
 <h2>IMPORTED REVISION FROM WIKISPACES</h2>
 This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br>
-: This revision was by author [[User:Kosmorsky|Kosmorsky]] and made on <tt>2011-08-14 00:55:42 UTC</tt>.<br>
+: This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2011-09-03 22:45:20 UTC</tt>.<br>
-: The original revision id was <tt>245831589</tt>.<br>
+: The original revision id was <tt>250558494</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>
 <h4>Original Wikitext 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;white-space: pre-wrap ! important" class="old-revision-html">=17 Tone Equal Divided Tritave=
+<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;white-space: pre-wrap ! important" class="old-revision-html">[[toc|flat]]
+=Properties=
+edt divides 3, the tritave, into 17 equal parts of 111.880 cents each. It tempers out 245/243 and 16807/15625 in the 7-limit, 77/75 and 1331/1323 in the 11-limit, and 175/169 and 121/117 in the 13-limit. It supports the no-twos temperament tempering out 245/243 and 77/75, which in terms of tritave patent vals could be written 17&amp;21.
-edt 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.
+=Discussion=
+edt is closely related [[13edt]], the Bohlen-Pierce division, because they share the feature of tempering out 245/243. Both 13edt and 17edt have 4L+5s nonatonic modes, but whereas the ratio of large to small steps in 13edt 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.
+If the major chord is defined by degrees 0,8,13 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".
 ===Intervals===
 || degree of 17edt || cents value || cents value octave reduced ||
 || 0 || 0 ||   ||
@@ Line 52: / Line 55: @@
 || 34 || 3804.0 || 204.0 ||</pre></div>
 <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">&lt;html&gt;&lt;head&gt;&lt;title&gt;17edt&lt;/title&gt;&lt;/head&gt;&lt;body&gt;&lt;!-- ws:start:WikiTextHeadingRule:0:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc0"&gt;&lt;a name="x17 Tone Equal Divided Tritave"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:0 --&gt;17 Tone Equal Divided Tritave&lt;/h1&gt;
+<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">&lt;html&gt;&lt;head&gt;&lt;title&gt;17edt&lt;/title&gt;&lt;/head&gt;&lt;body&gt;&lt;!-- ws:start:WikiTextTocRule:6:&amp;lt;img id=&amp;quot;wikitext@@toc@@flat&amp;quot; class=&amp;quot;WikiMedia WikiMediaTocFlat&amp;quot; title=&amp;quot;Table of Contents&amp;quot; src=&amp;quot;/site/embedthumbnail/toc/flat?w=100&amp;amp;h=16&amp;quot;/&amp;gt; --&gt;&lt;!-- ws:end:WikiTextTocRule:6 --&gt;&lt;!-- ws:start:WikiTextTocRule:7: --&gt;&lt;a href="#Properties"&gt;Properties&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:7 --&gt;&lt;!-- ws:start:WikiTextTocRule:8: --&gt; | &lt;a href="#Discussion"&gt;Discussion&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:8 --&gt;&lt;!-- ws:start:WikiTextTocRule:9: --&gt;&lt;!-- ws:end:WikiTextTocRule:9 --&gt;&lt;!-- ws:start:WikiTextTocRule:10: --&gt;
- &lt;br /&gt;
+&lt;!-- ws:end:WikiTextTocRule:10 --&gt;&lt;br /&gt;
+&lt;!-- ws:start:WikiTextHeadingRule:0:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc0"&gt;&lt;a name="Properties"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:0 --&gt;Properties&lt;/h1&gt;
+edt divides 3, the tritave, into 17 equal parts of 111.880 cents each. It tempers out 245/243 and 16807/15625 in the 7-limit, 77/75 and 1331/1323 in the 11-limit, and 175/169 and 121/117 in the 13-limit. It supports the no-twos temperament tempering out 245/243 and 77/75, which in terms of tritave patent vals could be written 17&amp;amp;21.&lt;br /&gt;
+&lt;br /&gt;
 &lt;br /&gt;
-edt 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?&lt;br /&gt;
+&lt;!-- ws:start:WikiTextHeadingRule:2:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc1"&gt;&lt;a name="Discussion"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:2 --&gt;Discussion&lt;/h1&gt;
+edt is closely related &lt;a class="wiki_link" href="/13edt"&gt;13edt&lt;/a&gt;, the Bohlen-Pierce division, because they share the feature of tempering out 245/243. Both 13edt and 17edt have 4L+5s nonatonic modes, but whereas the ratio of large to small steps in 13edt 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.&lt;br /&gt;
 &lt;br /&gt;
-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 &amp;quot;Moll I&amp;quot; or &amp;quot;Delta&amp;quot;, if I'm not mistaken.&lt;br /&gt;
+If the major chord is defined by degrees 0,8,13 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 &amp;quot;Moll I&amp;quot; or &amp;quot;Delta&amp;quot;.&lt;br /&gt;
 &lt;br /&gt;
-&lt;!-- ws:start:WikiTextHeadingRule:2:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc1"&gt;&lt;a name="x17 Tone Equal Divided Tritave--Intervals"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:2 --&gt;Intervals&lt;/h3&gt;
+&lt;!-- ws:start:WikiTextHeadingRule:4:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc2"&gt;&lt;a name="Discussion--Intervals"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:4 --&gt;Intervals&lt;/h3&gt;
-  &lt;br /&gt;
 &lt;table class="wiki_table"&gt;