Otonal 17: Difference between revisions

Revision as of 22:34, 26 March 2007

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This revision was by author xenjacob and made on 2007-03-26 22:34:36 UTC.

The original revision id was 3483018.

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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**

In pythagorean notation, the scale, beginning on G#: G# A# C D D# F F# G#

As understood by the harmonic series, an approximate 8:9:11:12:13 sonority is playable if you omit the 3rd note.

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 7-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 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:

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 13 15]**

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]]

...As understood by the [[MOSNamingScheme]], this scale is a flavor of mosh!

Original HTML content:

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

@@ 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:xenjacob|xenjacob]] and made on <tt>2007-03-26 22:33:13 UTC</tt>.<br>
+: This revision was by author [[User:xenjacob|xenjacob]] and made on <tt>2007-03-26 22:34:36 UTC</tt>.<br>
-: The original revision id was <tt>3482995</tt>.<br>
+: The original revision id was <tt>3483018</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>
@@ Line 23: / Line 23: @@
 **[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 it. Which is equivalent to a //longer// chain of neutral thirds, but with some omitted:
+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]
+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 13 15]
+wrapped and ordered: **[0 3 5 8 10 13 15]**
 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]]
@@ Line 50: / Line 50: @@
 &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 it. Which is equivalent to a &lt;em&gt;longer&lt;/em&gt; chain of neutral thirds, but with some omitted:&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: [-20 X X -5 0 5 10 X 20 25]&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: [0 3 5 8 10 13 15]&lt;br /&gt;
+wrapped and ordered: &lt;strong&gt;[0 3 5 8 10 13 15]&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://www.wikispaces.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;
 ...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>

Otonal 17: Difference between revisions

Revision as of 22:34, 26 March 2007

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