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| <h2>IMPORTED REVISION FROM WIKISPACES</h2>
| | Otonal 17 is a 7-tone mode of [[17edo]]: '''3 2 3 2 2 2 3''' |
| This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br>
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| : This revision was by author [[User:xenjacob|xenjacob]] and made on <tt>2007-03-26 03:06:57 UTC</tt>.<br>
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| : The original revision id was <tt>3464569</tt>.<br>
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| : The revision comment was: <tt></tt><br>
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| 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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| <h4>Original Wikitext content:</h4>
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| <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:
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| **3 2 3 2 2 2 3**
| | It approximates the chord 8:9:11:12:13 from the [[harmonic series]]. If you equate 17-equal with 17-Pythagorean, it is a rotation of Safi al-Din's ''[[Maqam]] Rahaw''. In Pythagorean notation, it could be written '''G# A# C D D# F F# G#'''. |
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| In pythagorean notation, the scale, beginning on G#: G# A# C D D# F F# G#
| | == Moment of symmetry analysis == |
| | From a [[moment of symmetry]] perspective, Otonal 17 may be 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, its neutral third: |
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| As understood by the harmonic series, an approximate 8:9:11:12:13 sonority is playable if you omit the 3rd note.
| | * '''[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]''' |
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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 you can see, the 3's are all isolated from one another. You have to do two bubble-swaps to get otonal-17. |
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| 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:
| | Or, you can start over with a ''longer'' chain of neutral thirds, but with some holes: |
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| **[0 5 10 15 20 25 30]** wrapped around at 17 yields: | | * this time going both directions from zero: '''[-20 -15 -10 -5 0 5 10 15 20 25]''' |
| **[0 5 10 15 3 8 13]** in ascending order yields:
| | * now with X's on the omitted notes: '''[-20 X X -5 0 5 10 X 20 25]''' |
| **[0 3 5 8 10 13 15]** expressed in terms of consecutive intervals:
| | * wrapped and ordered: '''[0 3 5 8 10 12 14]''' |
| **[3 2 3 2 3 2 2]**
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| 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 understood by the [[MOSNamingScheme]], this scale is a flavor of [[mosh]]. |
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| this time going both directions from zero: **[-20 -15 -10 -5 0 5 10 15 20 25]**
| | == Audio examples == |
| now with X's on the omitted notes: [-20 X X -5 0 5 10 X 20 25]
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| wrapped and ordered: [0 3 5 8 10 13 15]
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| 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]]</pre></div> | | * 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]] |
| <h4>Original HTML content:</h4>
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| <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>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 />
| | * For an example in a piece of music, see ''[[Fonala]]''. |
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| <strong>3 2 3 2 2 2 3</strong><br />
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| In pythagorean notation, the scale, beginning on G#: G# A# C D D# F F# G#<br />
| | [[Category:17edo]] |
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| | [[Category:7-tone scales]] |
| As understood by the harmonic series, an approximate 8:9:11:12:13 sonority is playable if you omit the 3rd note.<br />
| | [[Category:Pythagorean]] |
| <br />
| | [[Category:Maqam]] |
| 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 />
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| <br />
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| 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 />
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| <br />
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| <strong>[0 5 10 15 20 25 30]</strong> wrapped around at 17 yields:<br />
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| <strong>[0 5 10 15 3 8 13]</strong> in ascending order yields:<br />
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| <strong>[0 3 5 8 10 13 15]</strong> expressed in terms of consecutive intervals:<br />
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| <strong>[3 2 3 2 3 2 2]</strong><br />
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| <br />
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| 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 />
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| <br />
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| this time going both directions from zero: <strong>[-20 -15 -10 -5 0 5 10 15 20 25]</strong><br />
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| now with X's on the omitted notes: [-20 X X -5 0 5 10 X 20 25]<br />
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| wrapped and ordered: [0 3 5 8 10 13 15]<br />
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| <br />
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| 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 --></body></html></pre></div>
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Otonal 17 is a 7-tone mode of 17edo: 3 2 3 2 2 2 3
It approximates the chord 8:9:11:12:13 from the harmonic series. If you equate 17-equal with 17-Pythagorean, it is a rotation of Safi al-Din's Maqam Rahaw. In Pythagorean notation, it could be written G# A# C D D# F F# G#.
Moment of symmetry analysis
From a moment of symmetry perspective, Otonal 17 may be obtained by shuffling the 7-note neutral scale, or by taking a subset of the 10-note neutral scale. The generator is 5\17, 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]
As understood by the MOSNamingScheme, this scale is a flavor of mosh.
Audio examples
- A midi file of noodling in this scale - please excuse the pitchbend funniness in the first couple of seconds - it gets better - 17try.mid
- For an example in a piece of music, see Fonala.