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<h2>IMPORTED REVISION FROM WIKISPACES</h2>
Otonal 17 is a mode of 17 equal divisions of the octave. It has seven steps, here given in multiples of 17/oct:
This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br>
: This revision was by author [[User:xenjacob|xenjacob]] and made on <tt>2008-09-01 18:09:25 UTC</tt>.<br>
: The original revision id was <tt>36655839</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">Otonal 17 is a mode of 17 equal divisions of the octave. It has seven steps, here given in multiples of 17/oct:


**3 2 3 2 2 2 3**
'''3 2 3 2 2 2 3'''


In pythagorean notation, the scale, beginning on G#: G# A# C D D# F F# G#
In pythagorean notation, the scale, beginning on G#: G# A# C D D# F F# G#
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As understood by the scale archive, it is a rotation of Safi al-Din's maqam Rahawi, but only if you equate 17-equal with 17-pythagorean.
As understood by the scale archive, it is a rotation of Safi al-Din's maqam Rahawi, but only if you equate 17-equal with 17-pythagorean.


As understood by the moment-of-symmetry paradigm, it is obtained by shuffling the [[17edo neutral scale#seven-note|7-note neutral scale]], or by taking a subset of the 10-note neutral scale. The generator is 5/17-oct, its neutral third:
As understood by the moment-of-symmetry paradigm, it is obtained by shuffling the [[17edo_neutral_scale#seven-note|7-note neutral scale]], or by taking a subset of the 10-note neutral scale. The generator is 5/17-oct, its neutral third:


**[0 5 10 15 20 25 30]** wrapped around at 17 yields:
'''[0 5 10 15 20 25 30]''' wrapped around at 17 yields:
**[0 5 10 15 3 8 13]** in ascending order yields:
**[0 3 5 8 10 13 15]** expressed in terms of consecutive intervals:
**[3 2 3 2 3 2 2]**


As you can see, the 3's are all isolated from one another. You have to do two bubble-swaps to get otonal-17. Or, you can start over with a //longer// chain of neutral thirds, but with some holes:
'''[0 5 10 15 3 8 13]''' in ascending order yields:


this time going both directions from zero: **[-20 -15 -10 -5 0 5 10 15 20 25]**
'''[0 3 5 8 10 13 15]''' expressed in terms of consecutive intervals:
now with X's on the omitted notes: **[-20 X X -5 0 5 10 X 20 25]**
wrapped and ordered: **[0 3 5 8 10 12 14]**


A midi file of noodling in this scale - please excuse the pitchbend funniness in the first couple of seconds - it gets better - [[file:17try.mid]]
'''[3 2 3 2 3 2 2]'''
 
As you can see, the 3's are all isolated from one another. You have to do two bubble-swaps to get otonal-17. Or, you can start over with a ''longer'' chain of neutral thirds, but with some holes:
 
this time going both directions from zero: '''[-20 -15 -10 -5 0 5 10 15 20 25]'''
 
now with X's on the omitted notes: '''[-20 X X -5 0 5 10 X 20 25]'''
 
wrapped and ordered: '''[0 3 5 8 10 12 14]'''
 
A midi file of noodling in this scale - please excuse the pitchbend funniness in the first couple of seconds - it gets better - [[:File:17try.mid|17try.mid]]


for an example in a piece of music, see Fonala.
for an example in a piece of music, see Fonala.


...As understood by the [[MOSNamingScheme]], this scale is a flavor of mosh!</pre></div>
...As understood by the [[MOSNamingScheme|MOSNamingScheme]], this scale is a flavor of mosh!
<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;Otonal 17&lt;/title&gt;&lt;/head&gt;&lt;body&gt;Otonal 17 is a mode of 17 equal divisions of the octave. It has seven steps, here given in multiples of 17/oct:&lt;br /&gt;
&lt;br /&gt;
&lt;strong&gt;3 2 3 2 2 2 3&lt;/strong&gt;&lt;br /&gt;
&lt;br /&gt;
In pythagorean notation, the scale, beginning on G#: G# A# C D D# F F# G#&lt;br /&gt;
&lt;br /&gt;
As understood by the harmonic series, an approximate 8:9:11:12:13 sonority is playable if you omit the 3rd note.&lt;br /&gt;
&lt;br /&gt;
As understood by the scale archive, it is a rotation of Safi al-Din's maqam Rahawi, but only if you equate 17-equal with 17-pythagorean.&lt;br /&gt;
&lt;br /&gt;
As understood by the moment-of-symmetry paradigm, it is obtained by shuffling the &lt;a class="wiki_link" href="/17edo%20neutral%20scale#seven-note"&gt;7-note neutral scale&lt;/a&gt;, or by taking a subset of the 10-note neutral scale. The generator is 5/17-oct, its neutral third:&lt;br /&gt;
&lt;br /&gt;
&lt;strong&gt;[0 5 10 15 20 25 30]&lt;/strong&gt; wrapped around at 17 yields:&lt;br /&gt;
&lt;strong&gt;[0 5 10 15 3 8 13]&lt;/strong&gt; in ascending order yields:&lt;br /&gt;
&lt;strong&gt;[0 3 5 8 10 13 15]&lt;/strong&gt; expressed in terms of consecutive intervals:&lt;br /&gt;
&lt;strong&gt;[3 2 3 2 3 2 2]&lt;/strong&gt;&lt;br /&gt;
&lt;br /&gt;
As you can see, the 3's are all isolated from one another. You have to do two bubble-swaps to get otonal-17. Or, you can start over with a &lt;em&gt;longer&lt;/em&gt; chain of neutral thirds, but with some holes:&lt;br /&gt;
&lt;br /&gt;
this time going both directions from zero: &lt;strong&gt;[-20 -15 -10 -5 0 5 10 15 20 25]&lt;/strong&gt;&lt;br /&gt;
now with X's on the omitted notes: &lt;strong&gt;[-20 X X -5 0 5 10 X 20 25]&lt;/strong&gt;&lt;br /&gt;
wrapped and ordered: &lt;strong&gt;[0 3 5 8 10 12 14]&lt;/strong&gt;&lt;br /&gt;
&lt;br /&gt;
A midi file of noodling in this scale - please excuse the pitchbend funniness in the first couple of seconds - it gets better - &lt;!-- ws:start:WikiTextFileRule:0:&amp;lt;img src=&amp;quot;http://www.wikispaces.com/site/embedthumbnail/file/17try.mid?h=52&amp;amp;w=320&amp;quot; class=&amp;quot;WikiFile&amp;quot; id=&amp;quot;wikitext@@file@@17try.mid&amp;quot; title=&amp;quot;File: 17try.mid&amp;quot; width=&amp;quot;320&amp;quot; height=&amp;quot;52&amp;quot; /&amp;gt; --&gt;&lt;div class="objectEmbed"&gt;&lt;a href="/file/view/17try.mid/30481740/17try.mid" onclick="ws.common.trackFileLink('/file/view/17try.mid/30481740/17try.mid');"&gt;&lt;img src="http://c1.wikicdn.com/i/mime/32/audio/mid.png" height="32" width="32" alt="17try.mid" /&gt;&lt;/a&gt;&lt;div&gt;&lt;a href="/file/view/17try.mid/30481740/17try.mid" onclick="ws.common.trackFileLink('/file/view/17try.mid/30481740/17try.mid');" class="filename" title="17try.mid"&gt;17try.mid&lt;/a&gt;&lt;br /&gt;&lt;ul&gt;&lt;li&gt;&lt;a href="/file/detail/17try.mid"&gt;Details&lt;/a&gt;&lt;/li&gt;&lt;li&gt;&lt;a href="/file/view/17try.mid/30481740/17try.mid"&gt;Download&lt;/a&gt;&lt;/li&gt;&lt;li style="color: #666"&gt;11 KB&lt;/li&gt;&lt;/ul&gt;&lt;/div&gt;&lt;/div&gt;&lt;!-- ws:end:WikiTextFileRule:0 --&gt;&lt;br /&gt;
&lt;br /&gt;
for an example in a piece of music, see Fonala.&lt;br /&gt;
&lt;br /&gt;
...As understood by the &lt;a class="wiki_link" href="/MOSNamingScheme"&gt;MOSNamingScheme&lt;/a&gt;, this scale is a flavor of mosh!&lt;/body&gt;&lt;/html&gt;</pre></div>
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