Otonal 17 - Revision history

BudjarnLambeth: Cleaned up the page

2023-04-26T07:34:40Z

Cleaned up the page

← Older revision		Revision as of 07:34, 26 April 2023
Line 1:		Line 1:
	Otonal 17 is a mode of ~~17 equal divisions of the octave. It has seven steps, here given in multiples of 17/oct~~:		Otonal 17 is a 7-tone mode of [[17edo]]: '''3 2 3 2 2 2 3'''

	'''~~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#'''.

	~~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:

	~~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]'''

	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.

	~~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~~:		Or, you can start over with a ''longer'' chain of neutral thirds, but with some holes:

	'''[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]'''
			* 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]'''

	~~'''~~[~~0 5 10 15 3 8 13~~]~~''' in ascending order yields:~~		As understood by the [[MOSNamingScheme]], this scale is a flavor of [[mosh]].

	~~'''[0 3 5 8 10 13 15]''' expressed in terms of consecutive intervals:~~		== Audio examples ==

	~~'''~~[~~3 2 3 2 3 2 2~~]~~'''~~		* 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]]

	~~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:~~		* For an example in a piece of music, see ''[[Fonala]]''.

	~~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.~~

	~~...As understood by the [[MOSNamingScheme\|MOSNamingScheme]], this scale is a flavor of mosh!~~
	~~[[Category:Todo:cleanup]]~~
	[[Category:17edo]]		[[Category:17edo]]
	[[Category:7-tone scales]]		[[Category:7-tone scales]]
			[[Category:Pythagorean]]
			[[Category:Maqam]]

BudjarnLambeth: Categorised this uncategorised page

2023-04-26T01:04:25Z

Categorised this uncategorised page

← Older revision		Revision as of 01:04, 26 April 2023
Line 32:		Line 32:

	...As understood by the [[MOSNamingScheme\|MOSNamingScheme]], this scale is a flavor of mosh!		...As understood by the [[MOSNamingScheme\|MOSNamingScheme]], this scale is a flavor of mosh!
			[[Category:Todo:cleanup]]
			[[Category:17edo]]
			[[Category:7-tone scales]]

Wikispaces>FREEZE at 00:00, 17 July 2018

2018-07-17T00:00:00Z

@@ Line 1: / Line 1: @@
-<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:
-**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#
@@ Line 16: / Line 9: @@
 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:
-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:
-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]'''
 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!

Wikispaces>xenjacob: Imported revision 36655839 - Original comment:

2008-09-01T18:09:25Z

**Imported revision 36655839 - Original comment: **

← Older revision		Revision as of 18:09, 1 September 2008
Line 1:		Line 1:
	<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>2008-09-01 18:07:56 UTC</tt>.<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>~~36655723~~</tt>.<br>		: The original revision id was <tt>36655839</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>
Line 16:		Line 16:
	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:
Line 45:		Line 45:
	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 <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 />		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 />
Line 58:		Line 58:
	wrapped and ordered: <strong>[0 3 5 8 10 12 14]</strong><br />		wrapped and ordered: <strong>[0 3 5 8 10 12 14]</strong><br />
	<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 />		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://c1.wikicdn.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 />		<br />
	for an example in a piece of music, see Fonala.<br />		for an example in a piece of music, see Fonala.<br />
	<br />		<br />
	...As understood by the <a class="wiki_link" href="/MOSNamingScheme">MOSNamingScheme</a>, this scale is a flavor of mosh!</body></html></pre></div>		...As understood by the <a class="wiki_link" href="/MOSNamingScheme">MOSNamingScheme</a>, this scale is a flavor of mosh!</body></html></pre></div>

Wikispaces>xenjacob: Imported revision 36655723 - Original comment:

2008-09-01T18:07:56Z

**Imported revision 36655723 - Original comment: **

Wikispaces>xenjacob: Imported revision 4444523 - Original comment:

2007-05-16T19:03:12Z

**Imported revision 4444523 - Original comment: **

← Older revision		Revision as of 19:03, 16 May 2007
Line 1:		Line 1:
	<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>2007-03-~~26 22~~:34:36 UTC</tt>.<br>		: This revision was by author [[User:xenjacob\|xenjacob]] and made on <tt>2007-05-16 19:03:12 UTC</tt>.<br>
	: The original revision id was <tt>~~3483018~~</tt>.<br>		: The original revision id was <tt>4444523</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>
Line 27:		Line 27:
	this time going both directions from zero: [-20 -15 -10 -5 0 5 10 15 20 25]		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 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]]		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!</pre></div>		...As understood by the [[MOSNamingScheme]], this scale is a flavor of mosh!</pre></div>
Line 54:		Line 56:
	this time going both directions from zero: <strong>[-20 -15 -10 -5 0 5 10 15 20 25]</strong><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 />		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 />		wrapped and ordered: <strong>[0 3 5 8 10 12 14]</strong><br />
	<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 />		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 />
			for an example in a piece of music, see Fonala.<br />
	<br />		<br />
	...As understood by the <a class="wiki_link" href="/MOSNamingScheme">MOSNamingScheme</a>, this scale is a flavor of mosh!</body></html></pre></div>		...As understood by the <a class="wiki_link" href="/MOSNamingScheme">MOSNamingScheme</a>, this scale is a flavor of mosh!</body></html></pre></div>

Wikispaces>xenjacob: Imported revision 3483018 - Original comment:

2007-03-26T22:34:36Z

**Imported revision 3483018 - Original comment: **

← Older revision		Revision as of 22:34, 26 March 2007
Line 1:		Line 1:
	<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>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 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>
Line 23:		Line 23:
	[3 2 3 2 3 2 2]		[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]		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]]		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:
	<strong>[3 2 3 2 3 2 2]</strong><br />		<strong>[3 2 3 2 3 2 2]</strong><br />
	<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 />		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 />		<br />
	this time going both directions from zero: <strong>[-20 -15 -10 -5 0 5 10 15 20 25]</strong><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 />		now with X's on the omitted notes: <strong>[-20 X X -5 0 5 10 X 20 25]</strong><br />
	wrapped and ordered: [0 3 5 8 10 13 15]<br />		wrapped and ordered: <strong>[0 3 5 8 10 13 15]</strong><br />
	<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 />		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 />		<br />
	...As understood by the <a class="wiki_link" href="/MOSNamingScheme">MOSNamingScheme</a>, this scale is a flavor of mosh!</body></html></pre></div>		...As understood by the <a class="wiki_link" href="/MOSNamingScheme">MOSNamingScheme</a>, this scale is a flavor of mosh!</body></html></pre></div>

Wikispaces>xenjacob: Imported revision 3482995 - Original comment:

2007-03-26T22:33:13Z

**Imported revision 3482995 - Original comment: **

← Older revision		Revision as of 22:33, 26 March 2007
Line 1:		Line 1:
	<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>2007-03-26 03:06:57 UTC</tt>.<br>		: This revision was by author [[User:xenjacob\|xenjacob]] and made on <tt>2007-03-26 22:33:13 UTC</tt>.<br>
	: The original revision id was <tt>~~3464569~~</tt>.<br>		: The original revision id was <tt>3482995</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>
Line 29:		Line 29:
	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]]</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]]

			...As understood by the [[MOSNamingScheme]], this scale is a flavor of mosh!</pre></div>
	<h4>Original HTML content:</h4>		<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"><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 />		<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 />
Line 54:		Line 56:
	wrapped and ordered: [0 3 5 8 10 13 15]<br />		wrapped and ordered: [0 3 5 8 10 13 15]<br />
	<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 --></body></html></pre></div>		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></pre></div>

Wikispaces>xenjacob: Imported revision 3464569 - Original comment:

2007-03-26T03:06:57Z

**Imported revision 3464569 - Original comment: **

New page

<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 03:06:57 UTC</tt>.<br>
: The original revision id was <tt>3464569</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**

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]]</pre></div>
<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"><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 - <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></body></html></pre></div>

← Older revision		Revision as of 18:07, 1 September 2008
Line 1:		Line 1:
	<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>~~2007~~-05-~~16 19~~:03:12 UTC</tt>.<br>		: 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>~~4444523~~</tt>.<br>		: 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>
Line 16:		Line 16:
	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:
Line 45:		Line 45:
	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 />

Otonal 17 - Revision history

BudjarnLambeth: Cleaned up the page

BudjarnLambeth: Categorised this uncategorised page

Wikispaces>FREEZE at 00:00, 17 July 2018

Wikispaces>xenjacob: **Imported revision 36655839 - Original comment: **

Wikispaces>xenjacob: **Imported revision 36655723 - Original comment: **

Wikispaces>xenjacob: **Imported revision 4444523 - Original comment: **

Wikispaces>xenjacob: **Imported revision 3483018 - Original comment: **