Otonal 17
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- This revision was by author xenjacob and made on 2007-03-26 22:33:13 UTC.
- The original revision id was 3482995.
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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 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 it. Which is equivalent to a //longer// chain of neutral thirds, but with some omitted: 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 it. Which is equivalent to a <em>longer</em> chain of neutral thirds, but with some omitted:<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: [-20 X X -5 0 5 10 X 20 25]<br />
wrapped and ordered: [0 3 5 8 10 13 15]<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 />
...As understood by the <a class="wiki_link" href="/MOSNamingScheme">MOSNamingScheme</a>, this scale is a flavor of mosh!</body></html>