SeventeenTheory - Revision history

BudjarnLambeth: Added links to dead end pg

2024-01-09T06:39:01Z

Added links to dead end pg

← Older revision		Revision as of 06:39, 9 January 2024
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	\| ja = 17音理論		\| ja = 17音理論
	}}		}}
	17-tone equal tuning has fifths very close to just-intonation (and 12-equal) fifths. Consequently we use the usual circle-of-fifths on a five-line-staff notation, with a twist of new enharmonic equivalents, caused by the accumulation of the difference in the size of the fifth. To figure out the enharmonic names of any closed circle of fifths, write out a portion of it, like:		[[17edo\|17-tone equal tuning]] has fifths very close to [[just intonation\|just-intonation]] (and [[12edo\|12-equal]]) fifths. Consequently we use the usual [[Circle of fifths\|circle-of-fifths]] on a five-line-staff [[notation]], with a twist of new [[enharmonic]] equivalents, caused by the accumulation of the difference in the size of the fifth. To figure out the enharmonic names of any closed circle of fifths, write out a portion of it, like:

	Cb Gb Db Ab Eb Bb F C G D A E B F# C# G# D# A# E#		Cb Gb Db Ab Eb Bb F C G D A E B F# C# G# D# A# E#
Line 13:		Line 13:
	[[File:17fifths-withext.jpg\|alt=17fifths\|17fifths]]		[[File:17fifths-withext.jpg\|alt=17fifths\|17fifths]]

	The lines across indicate five fourths = "minor second" = 1/17 of an octave. (We know this because 17's perfect fourth is 7/17 of an octave, and 7*5 modulo 17 = 1.)		The lines across indicate five fourths = "minor second" = 1/17 of an octave. (We know this because 17's perfect fourth is 7/17 of an [[octave]], and 7*5 modulo 17 = 1.)

	So if we re-wrap the circle according to these lines, we should get the 17 notes of the scale in ascending/descending order (I moved A to the top just because):		So if we re-wrap the circle according to these lines, we should get the 17 notes of the scale in ascending/descending order (I moved A to the top just because):
Line 19:		Line 19:
	[[File:17versus12names-withext.jpg\|alt=17versus12names\|17versus12names]]		[[File:17versus12names-withext.jpg\|alt=17versus12names\|17versus12names]]

	Note that C# is HIGHER than Db; note that none of the intervals save the octave/unison are exactly the same as in 12. Note that The "half step"/"minor second" in 17 is twice as small as the "augmented unison"/"sharp"/"flat." Two sharp/flats add up to a minor third. Two "neutral thirds" add up to a "perfect fifth." 17 shares this last property with the quartertone scale (24-EDO).		Note that C# is HIGHER than Db; note that none of the intervals save the octave/unison are exactly the same as in 12. Note that The "half step"/"minor second" in 17 is twice as small as the "augmented unison"/"sharp"/"flat." Two sharp/flats add up to a minor third. Two "neutral thirds" add up to a "perfect fifth." 17 shares this last property with the quartertone scale ([[24-EDO]]).

	If the old notation is bothering you, here it is in cents (hundredths of a 12-equal half step):		If the old notation is bothering you, here it is in [[cents]] (hundredths of a 12-equal half step):

	[[File:17versus12cents-withext.jpg\|alt=17versus12cents\|17versus12cents]]		[[File:17versus12cents-withext.jpg\|alt=17versus12cents\|17versus12cents]]

Fredg999: Add interwiki

2023-09-13T04:00:55Z

Add interwiki

← Older revision		Revision as of 04:00, 13 September 2023
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	~~<span style~~=~~"display: block; text-align: right;">[[~~17音理論~~\|日本語]]</span>~~		{{interwiki
			\| de =
			\| en = SeventeenTheory
			\| es =
			\| ja = 17音理論
			}}
	17-tone equal tuning has fifths very close to just-intonation (and 12-equal) fifths. Consequently we use the usual circle-of-fifths on a five-line-staff notation, with a twist of new enharmonic equivalents, caused by the accumulation of the difference in the size of the fifth. To figure out the enharmonic names of any closed circle of fifths, write out a portion of it, like:		17-tone equal tuning has fifths very close to just-intonation (and 12-equal) fifths. Consequently we use the usual circle-of-fifths on a five-line-staff notation, with a twist of new enharmonic equivalents, caused by the accumulation of the difference in the size of the fifth. To figure out the enharmonic names of any closed circle of fifths, write out a portion of it, like:

BudjarnLambeth: Moved from category "theory" to "EDO theory pages"

2023-04-26T09:26:12Z

Moved from category "theory" to "EDO theory pages"

← Older revision		Revision as of 09:26, 26 April 2023
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	[[File:17versus12pcs-withext.jpg\|alt=17versus12pcs\|17versus12pcs]]		[[File:17versus12pcs-withext.jpg\|alt=17versus12pcs\|17versus12pcs]]
	[[Category:17edo]]		[[Category:17edo]]
	[[Category:~~Theory~~]]		[[Category:EDO theory pages]]

BudjarnLambeth: Categorised this uncategorised page

2023-04-26T00:59:42Z

Categorised this uncategorised page

← Older revision		Revision as of 00:59, 26 April 2023
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	[[File:17versus12pcs-withext.jpg\|alt=17versus12pcs\|17versus12pcs]]		[[File:17versus12pcs-withext.jpg\|alt=17versus12pcs\|17versus12pcs]]
			[[Category:17edo]]
			[[Category:Theory]]

PreImportHandFixes>Battaglia01: Mike - added jpg extension to imported images

2018-08-19T18:35:01Z

Mike - added jpg extension to imported images

← Older revision		Revision as of 18:35, 19 August 2018
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	and then wrap it into a circle of the desired size. If you do this with 17, you will notice that Cb = A#...that's how big the value of "flat/sharp" is in 17. The closer two notes are in the circle, the more familiar to us their harmonic function.		and then wrap it into a circle of the desired size. If you do this with 17, you will notice that Cb = A#...that's how big the value of "flat/sharp" is in 17. The closer two notes are in the circle, the more familiar to us their harmonic function.

	[[File:17fifths\|alt=17fifths\|17fifths]]		[[File:17fifths-withext.jpg\|alt=17fifths\|17fifths]]

	The lines across indicate five fourths = "minor second" = 1/17 of an octave. (We know this because 17's perfect fourth is 7/17 of an octave, and 7*5 modulo 17 = 1.)		The lines across indicate five fourths = "minor second" = 1/17 of an octave. (We know this because 17's perfect fourth is 7/17 of an octave, and 7*5 modulo 17 = 1.)
Line 13:		Line 13:
	So if we re-wrap the circle according to these lines, we should get the 17 notes of the scale in ascending/descending order (I moved A to the top just because):		So if we re-wrap the circle according to these lines, we should get the 17 notes of the scale in ascending/descending order (I moved A to the top just because):

	[[File:17versus12names~~\|alt=17versus12names\|1x1px\|17versus12names]][[File:17versus12names~~\|alt=17versus12names\|17versus12names]]		[[File:17versus12names-withext.jpg\|alt=17versus12names\|17versus12names]]

	Note that C# is HIGHER than Db; note that none of the intervals save the octave/unison are exactly the same as in 12. Note that The "half step"/"minor second" in 17 is twice as small as the "augmented unison"/"sharp"/"flat." Two sharp/flats add up to a minor third. Two "neutral thirds" add up to a "perfect fifth." 17 shares this last property with the quartertone scale (24-EDO).		Note that C# is HIGHER than Db; note that none of the intervals save the octave/unison are exactly the same as in 12. Note that The "half step"/"minor second" in 17 is twice as small as the "augmented unison"/"sharp"/"flat." Two sharp/flats add up to a minor third. Two "neutral thirds" add up to a "perfect fifth." 17 shares this last property with the quartertone scale (24-EDO).
Line 19:		Line 19:
	If the old notation is bothering you, here it is in cents (hundredths of a 12-equal half step):		If the old notation is bothering you, here it is in cents (hundredths of a 12-equal half step):

	[[File:17versus12cents\|alt=17versus12cents\|17versus12cents]]		[[File:17versus12cents-withext.jpg\|alt=17versus12cents\|17versus12cents]]

	and in pitch/interval classes:		and in pitch/interval classes:

	[[File:17versus12pcs\|alt=17versus12pcs~~\|17versus12pcs]][[File:17versus12pcs\|alt=17versus12pcs\|1x1px~~\|17versus12pcs]]		[[File:17versus12pcs-withext.jpg\|alt=17versus12pcs\|17versus12pcs]]

Wikispaces>FREEZE at 00:00, 17 July 2018

2018-07-17T00:00:00Z

← Older revision		Revision as of 00:00, 17 July 2018
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	<~~h2>IMPORTED REVISION FROM WIKISPACES</h2>~~		<span style="display: block; text-align: right;">[[17音理論\|日本語]]</span>
	~~This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br>~~
	~~: This revision was by author [[User:hstraub\|hstraub]] and made on <tt>2015-08-10 05:57:43 UTC</tt>.<br>~~
	~~: The original revision id was <tt>556417609</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"><span style="display: block; text-align: right;"~~>~~[[17音理論\|日本語]]
	~~<~~/span~~>~~
	17-tone equal tuning has fifths very close to just-intonation (and 12-equal) fifths. Consequently we use the usual circle-of-fifths on a five-line-staff notation, with a twist of new enharmonic equivalents, caused by the accumulation of the difference in the size of the fifth. To figure out the enharmonic names of any closed circle of fifths, write out a portion of it, like:		17-tone equal tuning has fifths very close to just-intonation (and 12-equal) fifths. Consequently we use the usual circle-of-fifths on a five-line-staff notation, with a twist of new enharmonic equivalents, caused by the accumulation of the difference in the size of the fifth. To figure out the enharmonic names of any closed circle of fifths, write out a portion of it, like:

Line 14:		Line 7:
	and then wrap it into a circle of the desired size. If you do this with 17, you will notice that Cb = A#...that's how big the value of "flat/sharp" is in 17. The closer two notes are in the circle, the more familiar to us their harmonic function.		and then wrap it into a circle of the desired size. If you do this with 17, you will notice that Cb = A#...that's how big the value of "flat/sharp" is in 17. The closer two notes are in the circle, the more familiar to us their harmonic function.

	[[~~image~~:17fifths]]		[[File:17fifths\|alt=17fifths\|17fifths]]

	The lines across indicate five fourths = "minor second" = 1/17 of an octave. (We know this because 17's perfect fourth is 7/17 of an octave, and 7*5 modulo 17 = 1.)		The lines across indicate five fourths = "minor second" = 1/17 of an octave. (We know this because 17's perfect fourth is 7/17 of an octave, and 7*5 modulo 17 = 1.)

	So if we re-wrap the circle according to these lines, we should get the 17 notes of the scale in ascending/descending order (I moved A to the top just because):		So if we re-wrap the circle according to these lines, we should get the 17 notes of the scale in ascending/descending order (I moved A to the top just because):

	[[~~image~~:17versus12names ~~width~~=~~"1" height="1"~~]][[~~image~~:17versus12names]]		[[File:17versus12names\|alt=17versus12names\|1x1px\|17versus12names]][[File:17versus12names\|alt=17versus12names\|17versus12names]]

	Note that C# is HIGHER than Db; note that none of the intervals save the octave/unison are exactly the same as in 12. Note that The "half step"/"minor second" in 17 is twice as small as the "augmented unison"/"sharp"/"flat." Two sharp/flats add up to a minor third. Two "neutral thirds" add up to a "perfect fifth." 17 shares this last property with the quartertone scale (24-EDO).		Note that C# is HIGHER than Db; note that none of the intervals save the octave/unison are exactly the same as in 12. Note that The "half step"/"minor second" in 17 is twice as small as the "augmented unison"/"sharp"/"flat." Two sharp/flats add up to a minor third. Two "neutral thirds" add up to a "perfect fifth." 17 shares this last property with the quartertone scale (24-EDO).
Line 25:		Line 19:
	If the old notation is bothering you, here it is in cents (hundredths of a 12-equal half step):		If the old notation is bothering you, here it is in cents (hundredths of a 12-equal half step):

	[[~~image~~:17versus12cents]]		[[File:17versus12cents\|alt=17versus12cents\|17versus12cents]]

	and in pitch/interval classes:		and in pitch/interval classes:

	[[~~image~~:17versus12pcs]][[~~image~~:17versus12pcs ~~width="1" height="1"]]</pre></div>~~		[[File:17versus12pcs\|alt=17versus12pcs\|17versus12pcs]][[File:17versus12pcs\|alt=17versus12pcs\|1x1px\|17versus12pcs]]
	~~<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>SeventeenTheory</title></head><body><span style="display: block; text-align: right;"><a class="wiki_link" href="/17%E9%9F%B3%E7%90%86%E8%AB%96">日本語</a><br />
	~~</span><br />~~
	17-tone equal tuning has fifths very close to just-intonation (and 12-equal) fifths. Consequently we use the usual circle-of-fifths on a five-line-staff notation, with a twist of new enharmonic equivalents, caused by the accumulation of the difference in the size of the fifth. To figure out the enharmonic names of any closed circle of fifths, write out a portion of it, like:<br />
	~~<br />~~
	~~Cb Gb Db Ab Eb Bb F C G D A E B F# C# G# D# A# E#<br />~~
	~~<br />~~
	and then wrap it into a circle of the desired size. If you do this with 17, you will notice that Cb = A#...that's how big the value of &quot;flat/sharp&quot; is in 17. The closer two notes are in the circle, the more familiar to us their harmonic function.<br />
	~~<br />~~
	~~<!-- ws:start:WikiTextLocalImageRule:0:&lt;img src=&quot;/file/view/17fifths/30122064/17fifths&quot;~~ alt=&quot;&quot; title=&quot;&quot; /&gt; --><img src="/file/view/17fifths/30122064/17fifths" alt="17fifths" title="17fifths" /><!-- ws:end:WikiTextLocalImageRule:0 --><br />
	~~The lines across indicate five fourths = &quot;minor second&quot; = 1/17 of an octave. (We know this because 17's perfect fourth is 7/17 of an octave, and 7*5 modulo 17 = 1.)<br />~~
	~~<br />~~
	~~So if we re-wrap the circle according to these lines, we should get the 17 notes of the scale in ascending/descending order (I moved A to the top just because):<br />~~
	~~<br />~~
	<!-- ws:start:WikiTextLocalImageRule:1:&lt;img src=&quot;/file/view/17versus12names/30122065/1x1/17versus12names&quot; alt=&quot;&quot; title=&quot;&quot; style=&quot;height: 1px; width: 1px;&quot; /&gt; --><img src="/file/view/17versus12names/30122065/1x1/17versus12names" alt="17versus12names" title="17versus12names" style="height: 1px; width: 1px;" /><!-- ws:end:WikiTextLocalImageRule:1 --><!-- ws:start:WikiTextLocalImageRule:2:&lt;img src=&quot;/file/view/17versus12names/30122065/17versus12names&quot; alt=&quot;&quot; title=&quot;&quot; /&gt; --><img src="/file/view/17versus12names/30122065/17versus12names" alt="17versus12names" title="17versus12names" /><!-- ws:end:WikiTextLocalImageRule:2 --><br />
	~~<br />~~
	Note that C# is HIGHER than Db; note that none of the intervals save the octave/unison are exactly the same as in 12. Note that The &quot;half step&quot;/&quot;minor second&quot; in 17 is twice as small as the &quot;augmented unison&quot;/&quot;sharp&quot;/&quot;flat.&quot; Two sharp/flats add up to a minor third. Two &quot;neutral thirds&quot; add up to a &quot;perfect fifth.&quot; 17 shares this last property with the quartertone scale (24-EDO).<br />
	~~<br />~~
	~~If the old notation is bothering you, here it is in cents (hundredths of a 12-equal half step):<br />~~
	~~<br />~~
	<!-- ws:start:WikiTextLocalImageRule:3:&lt;img src=&quot;/file/view/17versus12cents/30122071/17versus12cents&quot; alt=&quot;&quot; title=&quot;&quot; /&gt; --><img src="/file/view/17versus12cents/30122071/17versus12cents" alt="17versus12cents" title="17versus12cents" /><!-- ws:end:WikiTextLocalImageRule:3 --><br />
	~~and in pitch/interval classes:<br />~~
	~~<br />~~
	~~<!-- ws:start:WikiTextLocalImageRule:4:&lt;img src=&quot;/file/view/~~17versus12pcs~~/30122074/~~17versus12pcs&quot; alt=&quot;&quot; title=&quot;&quot; /&gt; --><img src="/file/view/17versus12pcs/30122074/17versus12pcs" alt="17versus12pcs" title="17versus12pcs" /><!-- ws:end:WikiTextLocalImageRule:4 --><!-- ws:start:WikiTextLocalImageRule:5:&lt;img src=&quot;/file/view/17versus12pcs/30122074/1x1/17versus12pcs&quot; alt=&quot;&quot; title=&quot;&quot; style=&quot;height: 1px; width: 1px;&quot; /&gt; --><img src="/file/view/17versus12pcs/30122074/1x1/17versus12pcs" alt="17versus12pcs" title="17versus12pcs" style="height: 1px; width: 1px;" /><!-- ws:end:WikiTextLocalImageRule:5 --></body></html></pre></div>

Wikispaces>hstraub: Imported revision 556417609 - Original comment:

2015-08-10T05:57:43Z

**Imported revision 556417609 - Original comment: **

Wikispaces>hstraub: Imported revision 556417579 - Original comment:

2015-08-10T05:56:44Z

**Imported revision 556417579 - Original comment: **

← Older revision		Revision as of 05:56, 10 August 2015
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>~~2009~~-03-~~01 14~~:59:17 UTC</tt>.<br>		: This revision was by author [[User:hstraub\|hstraub]] and made on <tt>2015-08-10 05:56:44 UTC</tt>.<br>
	: The original revision id was <tt>~~60217352~~</tt>.<br>		: The original revision id was <tt>556417579</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>
	<h4>Original Wikitext content:</h4>		<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">17-tone equal tuning has fifths very close to just-intonation (and 12-equal) fifths. Consequently we use the usual circle-of-fifths on a five-line-staff notation, with a twist of new enharmonic equivalents, caused by the accumulation of the difference in the size of the fifth. To figure out the enharmonic names of any closed circle of fifths, write out a portion of it, like:		<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"><span style="display: block; text-align: right;">[[17音理論\|English]]
			</span>
			17-tone equal tuning has fifths very close to just-intonation (and 12-equal) fifths. Consequently we use the usual circle-of-fifths on a five-line-staff notation, with a twist of new enharmonic equivalents, caused by the accumulation of the difference in the size of the fifth. To figure out the enharmonic names of any closed circle of fifths, write out a portion of it, like:

	Cb Gb Db Ab Eb Bb F C G D A E B F# C# G# D# A# E#		Cb Gb Db Ab Eb Bb F C G D A E B F# C# G# D# A# E#
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	[[image:17versus12pcs]][[image:17versus12pcs width="1" height="1"]]</pre></div>		[[image:17versus12pcs]][[image:17versus12pcs width="1" height="1"]]</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>SeventeenTheory</title></head><body>17-tone equal tuning has fifths very close to just-intonation (and 12-equal) fifths. Consequently we use the usual circle-of-fifths on a five-line-staff notation, with a twist of new enharmonic equivalents, caused by the accumulation of the difference in the size of the fifth. To figure out the enharmonic names of any closed circle of fifths, write out a portion of it, like:<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>SeventeenTheory</title></head><body><span style="display: block; text-align: right;"><a class="wiki_link" href="/17%E9%9F%B3%E7%90%86%E8%AB%96">English</a><br />
			</span><br />
			17-tone equal tuning has fifths very close to just-intonation (and 12-equal) fifths. Consequently we use the usual circle-of-fifths on a five-line-staff notation, with a twist of new enharmonic equivalents, caused by the accumulation of the difference in the size of the fifth. To figure out the enharmonic names of any closed circle of fifths, write out a portion of it, like:<br />
	<br />		<br />
	Cb Gb Db Ab Eb Bb F C G D A E B F# C# G# D# A# E#<br />		Cb Gb Db Ab Eb Bb F C G D A E B F# C# G# D# A# E#<br />

Wikispaces>xenjacob: Imported revision 60217352 - Original comment:

2009-03-01T14:59:17Z

**Imported revision 60217352 - Original comment: **

Wikispaces>xenjacob: Imported revision 21038807 - Original comment:

2008-04-06T03:37:42Z

**Imported revision 21038807 - Original comment: **

← Older revision		Revision as of 03:37, 6 April 2008
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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>~~2006~~-07-~~27 12~~:27:42 UTC</tt>.<br>		: This revision was by author [[User:xenjacob\|xenjacob]] and made on <tt>2008-04-06 03:37:42 UTC</tt>.<br>
	: The original revision id was <tt>~~937751~~</tt>.<br>		: The original revision id was <tt>21038807</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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	[[image:17fifths]]		[[image:17fifths]]
	The lines across indicate five ~~fifths (~~"minor second") (1/17 of an octave).		The lines across indicate five fourths = "minor second" = 1/17 of an octave. (We know this because 17's perfect fourth is 7/17 of an octave, and 7*5 modulo 17 = 1.)

	So if we re-wrap the circle according to these lines, we should get the 17 notes of the scale in ascending/descending order (I moved A to the top just because):		So if we re-wrap the circle according to these lines, we should get the 17 notes of the scale in ascending/descending order (I moved A to the top just because):
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	<br />		<br />
	<!-- ws:start:WikiTextLocalImageRule:0:&lt;img src=&quot;/file/view/17fifths/30122064/17fifths&quot; alt=&quot;&quot; title=&quot;&quot; /&gt; --><img src="/file/view/17fifths/30122064/17fifths" alt="17fifths" title="17fifths" /><!-- ws:end:WikiTextLocalImageRule:0 --><br />		<!-- ws:start:WikiTextLocalImageRule:0:&lt;img src=&quot;/file/view/17fifths/30122064/17fifths&quot; alt=&quot;&quot; title=&quot;&quot; /&gt; --><img src="/file/view/17fifths/30122064/17fifths" alt="17fifths" title="17fifths" /><!-- ws:end:WikiTextLocalImageRule:0 --><br />
	The lines across indicate five ~~fifths (~~&quot;minor second&quot;) (1/17 of an octave).<br />		The lines across indicate five fourths = &quot;minor second&quot; = 1/17 of an octave. (We know this because 17's perfect fourth is 7/17 of an octave, and 7*5 modulo 17 = 1.)<br />
	<br />		<br />
	So if we re-wrap the circle according to these lines, we should get the 17 notes of the scale in ascending/descending order (I moved A to the top just because):<br />		So if we re-wrap the circle according to these lines, we should get the 17 notes of the scale in ascending/descending order (I moved A to the top just because):<br />

← Older revision		Revision as of 05:57, 10 August 2015
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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:hstraub\|hstraub]] and made on <tt>2015-08-10 05:56:44 UTC</tt>.<br>		: This revision was by author [[User:hstraub\|hstraub]] and made on <tt>2015-08-10 05:57:43 UTC</tt>.<br>
	: The original revision id was <tt>~~556417579~~</tt>.<br>		: The original revision id was <tt>556417609</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>
	<h4>Original Wikitext content:</h4>		<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"><span style="display: block; text-align: right;">[[17音理論\|~~English~~]]		<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"><span style="display: block; text-align: right;">[[17音理論\|日本語]]
	</span>		</span>
	17-tone equal tuning has fifths very close to just-intonation (and 12-equal) fifths. Consequently we use the usual circle-of-fifths on a five-line-staff notation, with a twist of new enharmonic equivalents, caused by the accumulation of the difference in the size of the fifth. To figure out the enharmonic names of any closed circle of fifths, write out a portion of it, like:		17-tone equal tuning has fifths very close to just-intonation (and 12-equal) fifths. Consequently we use the usual circle-of-fifths on a five-line-staff notation, with a twist of new enharmonic equivalents, caused by the accumulation of the difference in the size of the fifth. To figure out the enharmonic names of any closed circle of fifths, write out a portion of it, like:
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	[[image:17versus12pcs]][[image:17versus12pcs width="1" height="1"]]</pre></div>		[[image:17versus12pcs]][[image:17versus12pcs width="1" height="1"]]</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>SeventeenTheory</title></head><body><span style="display: block; text-align: right;"><a class="wiki_link" href="/17%E9%9F%B3%E7%90%86%E8%AB%96">~~English~~</a><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>SeventeenTheory</title></head><body><span style="display: block; text-align: right;"><a class="wiki_link" href="/17%E9%9F%B3%E7%90%86%E8%AB%96">日本語</a><br />
	</span><br />		</span><br />
	17-tone equal tuning has fifths very close to just-intonation (and 12-equal) fifths. Consequently we use the usual circle-of-fifths on a five-line-staff notation, with a twist of new enharmonic equivalents, caused by the accumulation of the difference in the size of the fifth. To figure out the enharmonic names of any closed circle of fifths, write out a portion of it, like:<br />		17-tone equal tuning has fifths very close to just-intonation (and 12-equal) fifths. Consequently we use the usual circle-of-fifths on a five-line-staff notation, with a twist of new enharmonic equivalents, caused by the accumulation of the difference in the size of the fifth. To figure out the enharmonic names of any closed circle of fifths, write out a portion of it, like:<br />

← Older revision		Revision as of 14:59, 1 March 2009
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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>~~2008~~-04-~~06 03~~:37:42 UTC</tt>.<br>		: This revision was by author [[User:xenjacob\|xenjacob]] and made on <tt>2009-03-01 14:59:17 UTC</tt>.<br>
	: The original revision id was <tt>~~21038807~~</tt>.<br>		: The original revision id was <tt>60217352</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>
	<h4>Original Wikitext content:</h4>		<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">17-tone equal tuning has fifths very close to just-intonation (and 12-equal) fifths. Consequently we use the usual circle-of-fifths on a five-line-staff notation, with a twist of new ~~enharmonics~~, caused by the accumulation of the difference in the size of the fifth. To figure out the enharmonic names of any closed circle of fifths, write out a portion of it, like:		<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">17-tone equal tuning has fifths very close to just-intonation (and 12-equal) fifths. Consequently we use the usual circle-of-fifths on a five-line-staff notation, with a twist of new enharmonic equivalents, caused by the accumulation of the difference in the size of the fifth. To figure out the enharmonic names of any closed circle of fifths, write out a portion of it, like:

	Cb Gb Db Ab Eb Bb F C G D A E B F# C# G# D# A# E#		Cb Gb Db Ab Eb Bb F C G D A E B F# C# G# D# A# E#
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	[[image:17versus12pcs]][[image:17versus12pcs width="1" height="1"]]</pre></div>		[[image:17versus12pcs]][[image:17versus12pcs width="1" height="1"]]</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>SeventeenTheory</title></head><body>17-tone equal tuning has fifths very close to just-intonation (and 12-equal) fifths. Consequently we use the usual circle-of-fifths on a five-line-staff notation, with a twist of new ~~enharmonics~~, caused by the accumulation of the difference in the size of the fifth. To figure out the enharmonic names of any closed circle of fifths, write out a portion of it, like:<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>SeventeenTheory</title></head><body>17-tone equal tuning has fifths very close to just-intonation (and 12-equal) fifths. Consequently we use the usual circle-of-fifths on a five-line-staff notation, with a twist of new enharmonic equivalents, caused by the accumulation of the difference in the size of the fifth. To figure out the enharmonic names of any closed circle of fifths, write out a portion of it, like:<br />
	<br />		<br />
	Cb Gb Db Ab Eb Bb F C G D A E B F# C# G# D# A# E#<br />		Cb Gb Db Ab Eb Bb F C G D A E B F# C# G# D# A# E#<br />