Otonal 17: Difference between revisions
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Wikispaces>xenjacob **Imported revision 4444523 - Original comment: ** |
Wikispaces>xenjacob **Imported revision 36655723 - 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:xenjacob|xenjacob]] and made on <tt> | : This revision was by author [[User:xenjacob|xenjacob]] and made on <tt>2008-09-01 18:07:56 UTC</tt>.<br> | ||
: The original revision id was <tt> | : The original revision id was <tt>36655723</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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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 7-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: | ||
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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.<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 /> | <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 /> | As understood by the moment-of-symmetry paradigm, it is obtained by shuffling the <a class="wiki_link" href="/17edo%20neutral%20scale#seven-note">7-note neutral scale</a> , or by taking a subset of the 10-note neutral scale. The generator is 5/17-oct, its neutral third:<br /> | ||
<br /> | <br /> | ||
<strong>[0 5 10 15 20 25 30]</strong> wrapped around at 17 yields:<br /> | <strong>[0 5 10 15 20 25 30]</strong> wrapped around at 17 yields:<br /> | ||
Revision as of 18:07, 1 September 2008
IMPORTED REVISION FROM WIKISPACES
This is an imported revision from Wikispaces. The revision metadata is included below for reference:
- This revision was by author xenjacob and made on 2008-09-01 18:07:56 UTC.
- The original revision id was 36655723.
- The revision comment was:
The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.
Original Wikitext content:
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 [[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 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 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]] for an example in a piece of music, see Fonala. ...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 <a class="wiki_link" href="/17edo%20neutral%20scale#seven-note">7-note neutral scale</a> , or by taking a subset of the 10-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 12 14]</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:<img src="http://www.wikispaces.com/site/embedthumbnail/file/17try.mid?h=52&w=320" class="WikiFile" id="wikitext@@file@@17try.mid" title="File: 17try.mid" width="320" height="52" /> --><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 />
for an example in a piece of music, see Fonala.<br />
<br />
...As understood by the <a class="wiki_link" href="/MOSNamingScheme">MOSNamingScheme</a>, this scale is a flavor of mosh!</body></html>