OTC 2L 10s - Revision history

Lériendil: Text replacement - "Category:Tempered_scales↵Category:Pages with mostly numerical content" to "Category:Tempered scales Category:Pages with mostly numerical content"

2025-06-24T03:07:33Z

Text replacement - "Category:Tempered_scales↵Category:Pages with mostly numerical content" to "Category:Tempered scales Category:Pages with mostly numerical content"

← Older revision		Revision as of 03:07, 24 June 2025
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	<ul><li>[[Omnitetrachordality\|Omnitetrachordality]]</li><li>[[Gallery_of_omnitetrachordal_scales\|Gallery of omnitetrachordal scales]]</li></ul>		<ul><li>[[Omnitetrachordality\|Omnitetrachordality]]</li><li>[[Gallery_of_omnitetrachordal_scales\|Gallery of omnitetrachordal scales]]</li></ul>
	[[Category:12-tone scales]]		[[Category:12-tone scales]]
	[[Category:~~Tempered_scales~~]]		[[Category:Tempered scales]]
	[[Category:Pages with mostly numerical content]]		[[Category:Pages with mostly numerical content]]
	[[Category:MODMOS]]		[[Category:MODMOS]]
	[[Category:Omnitetrachordal]]		[[Category:Omnitetrachordal]]
	[[Category:Injera]]		[[Category:Injera]]

Lériendil: Text replacement - "Category:Tempered scales↵Category:Pages with mostly numerical content" to "Category:Tempered_scales Category:Pages with mostly numerical content"

2025-06-24T02:41:34Z

Text replacement - "Category:Tempered scales↵Category:Pages with mostly numerical content" to "Category:Tempered_scales Category:Pages with mostly numerical content"

← Older revision		Revision as of 02:41, 24 June 2025
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	<ul><li>[[Omnitetrachordality\|Omnitetrachordality]]</li><li>[[Gallery_of_omnitetrachordal_scales\|Gallery of omnitetrachordal scales]]</li></ul>		<ul><li>[[Omnitetrachordality\|Omnitetrachordality]]</li><li>[[Gallery_of_omnitetrachordal_scales\|Gallery of omnitetrachordal scales]]</li></ul>
	[[Category:12-tone scales]]		[[Category:12-tone scales]]
	[[Category:~~Tempered scales~~]]		[[Category:Tempered_scales]]
	[[Category:Pages with mostly numerical content]]		[[Category:Pages with mostly numerical content]]
	[[Category:MODMOS]]		[[Category:MODMOS]]
	[[Category:Omnitetrachordal]]		[[Category:Omnitetrachordal]]
	[[Category:Injera]]		[[Category:Injera]]

Lériendil: Text replacement - "Category:Tempered scales" to "Category:Tempered scales Category:Pages with mostly numerical content"

2025-06-24T02:35:00Z

Text replacement - "Category:Tempered scales" to "Category:Tempered scales Category:Pages with mostly numerical content"

← Older revision		Revision as of 02:35, 24 June 2025
Line 191:		Line 191:
	[[Category:12-tone scales]]		[[Category:12-tone scales]]
	[[Category:Tempered scales]]		[[Category:Tempered scales]]
			[[Category:Pages with mostly numerical content]]
	[[Category:MODMOS]]		[[Category:MODMOS]]
	[[Category:Omnitetrachordal]]		[[Category:Omnitetrachordal]]
	[[Category:Injera]]		[[Category:Injera]]

BudjarnLambeth: Categorised this uncategorised page

2023-05-02T04:24:55Z

Categorised this uncategorised page

← Older revision		Revision as of 04:24, 2 May 2023
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	===See also===		===See also===
	<ul><li>[[Omnitetrachordality\|Omnitetrachordality]]</li><li>[[Gallery_of_omnitetrachordal_scales\|Gallery of omnitetrachordal scales]]</li></ul>		<ul><li>[[Omnitetrachordality\|Omnitetrachordality]]</li><li>[[Gallery_of_omnitetrachordal_scales\|Gallery of omnitetrachordal scales]]</li></ul>
			[[Category:12-tone scales]]
			[[Category:Tempered scales]]
			[[Category:MODMOS]]
			[[Category:Omnitetrachordal]]
			[[Category:Injera]]

Wikispaces>FREEZE at 00:00, 17 July 2018

2018-07-17T00:00:00Z

Show changes

Wikispaces>spt3125: Imported revision 591038810 - Original comment:

2016-09-04T15:23:12Z

**Imported revision 591038810 - Original comment: **

← Older revision		Revision as of 15:23, 4 September 2016
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:spt3125\|spt3125]] and made on <tt>2016-08-~~28 21~~:12~~:26~~ UTC</tt>.<br>		: This revision was by author [[User:spt3125\|spt3125]] and made on <tt>2016-09-04 15:23:12 UTC</tt>.<br>
	: The original revision id was <tt>~~590308376~~</tt>.<br>		: The original revision id was <tt>591038810</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 64:		Line 64:
	Only works at high values of L/s.		Only works at high values of L/s.

			Q<span style="vertical-align: sub;">2</span> ``=`` 3.8274237885 (4/3 = L+3.5s)
	P = 6.7698983847		P = 6.7698983847
	Q = 9.7123729809 (4/3 = L+2.5s)		Q<span style="vertical-align: sub;">1</span> ``=`` 9.7123729809 (4/3 = L+2.5s)

	L = 100.00 to 600.00 cents (345.11 cents @ P, 396.09 cents @ Q)		L = 100.00 to 600.00 cents (260.15 cents @ Q<span style="vertical-align: sub;">2</span>, 345.11 cents @ P, 396.09 cents @ Q<span style="vertical-align: sub;">1</span>)
	s = 0.00 to 100.00 cents (50.98 cents @ P, 40.78 cents @ Q)		s = 0.00 to 100.00 cents (67.97 cents @ Q<span style="vertical-align: sub;">2</span>, 50.98 cents @ P, 40.78 cents @ Q<span style="vertical-align: sub;">1</span>)

	9/8 = 4s (0.00 to 400.00 cents)		9/8 = 4s (0.00 to 400.00 cents)
Line 111:		Line 112:
	<hr />		<hr />
	<br />		<br />
	<!-- ws:start:WikiTextHeadingRule:0:&lt;h3&gt; --><h3 id="toc0"><a name="x--Class 1"></a><!-- ws:end:WikiTextHeadingRule:0 -->Class 1</h3>		<!-- ws:start:WikiTextHeadingRule:2:&lt;h3&gt; --><h3 id="toc0"><a name="x--Class 1"></a><!-- ws:end:WikiTextHeadingRule:2 -->Class 1</h3>
	12 tones (5+2+5)<br />		12 tones (5+2+5)<br />
	<br />		<br />
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	<br />		<br />
	<!-- ws:start:WikiTextLocalImageRule:~~211~~:&lt;img src=&quot;/file/view/12_02_10_ssLss_ss_ssLss.png/589273820/12_02_10_ssLss_ss_ssLss.png&quot; alt=&quot;&quot; title=&quot;&quot; /&gt; --><img src="/file/view/12_02_10_ssLss_ss_ssLss.png/589273820/12_02_10_ssLss_ss_ssLss.png" alt="12_02_10_ssLss_ss_ssLss.png" title="12_02_10_ssLss_ss_ssLss.png" /><!-- ws:end:WikiTextLocalImageRule:~~211~~ --><br />		<!-- ws:start:WikiTextLocalImageRule:213:&lt;img src=&quot;/file/view/12_02_10_ssLss_ss_ssLss.png/589273820/12_02_10_ssLss_ss_ssLss.png&quot; alt=&quot;&quot; title=&quot;&quot; /&gt; --><img src="/file/view/12_02_10_ssLss_ss_ssLss.png/589273820/12_02_10_ssLss_ss_ssLss.png" alt="12_02_10_ssLss_ss_ssLss.png" title="12_02_10_ssLss_ss_ssLss.png" /><!-- ws:end:WikiTextLocalImageRule:213 --><br />
	<br />		<br />
	<hr />		<hr />
	<br />		<br />
	<!-- ws:start:WikiTextHeadingRule:2:&lt;h3&gt; --><h3 id="toc1"><a name="x--Class 2"></a><!-- ws:end:WikiTextHeadingRule:2 -->Class 2</h3>		<!-- ws:start:WikiTextHeadingRule:4:&lt;h3&gt; --><h3 id="toc1"><a name="x--Class 2"></a><!-- ws:end:WikiTextHeadingRule:4 -->Class 2</h3>
	12 tones (4+4+4)<br />		12 tones (4+4+4)<br />
	<br />		<br />
	Only works at high values of L/s.<br />		Only works at high values of L/s.<br />
	<br />		<br />
			Q<span style="vertical-align: sub;">2</span> <!-- ws:start:WikiTextRawRule:00:``=`` -->=<!-- ws:end:WikiTextRawRule:00 --> 3.8274237885 (4/3 = L+3.5s)<br />
	P = 6.7698983847<br />		P = 6.7698983847<br />
	Q = 9.7123729809 (4/3 = L+2.5s)<br />		Q<span style="vertical-align: sub;">1</span> <!-- ws:start:WikiTextRawRule:01:``=`` -->=<!-- ws:end:WikiTextRawRule:01 --> 9.7123729809 (4/3 = L+2.5s)<br />
	<br />		<br />
	L = 100.00 to 600.00 cents (345.11 cents @ P, 396.09 cents @ Q)<br />		L = 100.00 to 600.00 cents (260.15 cents @ Q<span style="vertical-align: sub;">2</span>, 345.11 cents @ P, 396.09 cents @ Q<span style="vertical-align: sub;">1</span>)<br />
	s = 0.00 to 100.00 cents (50.98 cents @ P, 40.78 cents @ Q)<br />		s = 0.00 to 100.00 cents (67.97 cents @ Q<span style="vertical-align: sub;">2</span>, 50.98 cents @ P, 40.78 cents @ Q<span style="vertical-align: sub;">1</span>)<br />
	<br />		<br />
	9/8 = 4s (0.00 to 400.00 cents)<br />		9/8 = 4s (0.00 to 400.00 cents)<br />
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	<hr />		<hr />
	<br />		<br />
	<!-- ws:start:WikiTextHeadingRule:4:&lt;h3&gt; --><h3 id="toc2"><a name="x--See also"></a><!-- ws:end:WikiTextHeadingRule:4 -->See also</h3>		<!-- ws:start:WikiTextHeadingRule:6:&lt;h3&gt; --><h3 id="toc2"><a name="x--See also"></a><!-- ws:end:WikiTextHeadingRule:6 -->See also</h3>
	<ul><li><a class="wiki_link" href="/Omnitetrachordality">Omnitetrachordality</a></li><li><a class="wiki_link" href="/Gallery%20of%20omnitetrachordal%20scales">Gallery of omnitetrachordal scales</a></li></ul></body></html></pre></div>		<ul><li><a class="wiki_link" href="/Omnitetrachordality">Omnitetrachordality</a></li><li><a class="wiki_link" href="/Gallery%20of%20omnitetrachordal%20scales">Gallery of omnitetrachordal scales</a></li></ul></body></html></pre></div>

Wikispaces>spt3125: Imported revision 590308376 - Original comment:

2016-08-28T21:12:26Z

**Imported revision 590308376 - 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: 
: This revision was by author [[User:spt3125|spt3125]] and made on <tt>2016-08-28 21:12:26 UTC</tt>. 
: The original revision id was <tt>590308376</tt>. 
: The revision comment was: <tt></tt> 
The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it. 
<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">Omnitetrachordal MODMOS scales
[[2L 10s|2L+10s]]

This OTC scale pattern has two classes (with different tetrachordal divisions). Only a few other scales of the form [[OTC 2L ns|2L+ns]] are known to have this property.

temperaments: [[injera]] ?

----

===Class 1===
12 tones (5+2+5)

[[Gallery of omnitetrachordal scales#dual|Dual]] of [[OTC 10L 2s|OTC 10L+2s]]. Probably only useful for small values of L/s.

[[Gallery of omnitetrachordal scales#perfect|P]] = 0.8849491924
[[Gallery of omnitetrachordal scales#Q|Q]] = 3.8274237885 (4/3 = L+3.5s)

L = 100.00 to 600.00 cents (260.15 cents @ Q)
s = 0.00 to 100.00 cents (67.97 cents @ Q)

9/8 = 2s (0.00 to 200.00 cents)
4/3 = L+4s (500.00 to 600.00 cents)
MOS generator = s (0.00 to 100.00 cents)
MOS period = 1/2 octave (600.00 cents)

notable EDOs: 14, 16, 26, 38

{{ LsssssLsssss }} (MOS, not OTC)
{{ || }}
{{ LssssLssssss }} (OTC MODMOS) - gen chains 7,5

symmetric modes:
{{ sssLssssLsss }}
{{ ssLssssssLss }}

all modes:
|| || {{ ssLss ss ssLss }} || ||
|| || {{ sLsss ss sLsss }} || ||
|| || {{ Lssss ss Lssss }} || ||
|| {{ ss ssssL ssssL }} || || ||
|| {{ ss sssLs sssLs }} || || ||
|| {{ ss ssLss ssLss }} || || {{ ssssL ssssL ss }} ||
|| {{ ss sLsss sLsss }} || || {{ sssLs sssLs ss }} ||
|| {{ ss Lssss Lssss }} || || {{ ssLss ssLss ss }} ||
|| || || {{ sLsss sLsss ss }} ||
|| || || {{ Lssss Lssss ss }} ||
|| || {{ ssssL ss ssssL }} || ||
|| || {{ sssLs ss sssLs }} || ||

[[image:12_02_10_ssLss_ss_ssLss.png]]

----

===Class 2===
12 tones (4+4+4)

Only works at high values of L/s.

P = 6.7698983847
Q = 9.7123729809 (4/3 = L+2.5s)

L = 100.00 to 600.00 cents (345.11 cents @ P, 396.09 cents @ Q)
s = 0.00 to 100.00 cents (50.98 cents @ P, 40.78 cents @ Q)

9/8 = 4s (0.00 to 400.00 cents)
4/3 = L+3s (400.00 to 600.00 cents)
MOS generator = s (0.00 to 100.00 cents)
MOS period = 1/2 octave (600.00 cents)

notable EDOs: 20, 22, 24

{{ LsssssLsssss }} (MOS, not OTC)
{{ | | }}
{{ LsssLsssssss }} (OTC MODMOS) - gen chains 8,4

all modes:
|| || || {{ Lsss Lsss ssss }} ||
|| || {{ sssL ssss sssL }} || ||
|| || {{ ssLs ssss ssLs }} || ||
|| || {{ sLss ssss sLss }} || ||
|| || {{ Lsss ssss Lsss }} || ||
|| {{ ssss sssL sssL }} || || ||
|| {{ ssss ssLs ssLs }} || || ||
|| {{ ssss sLss sLss }} || || ||
|| {{ ssss Lsss Lsss }} || || ||
|| || || {{ sssL sssL ssss }} ||
|| || || {{ ssLs ssLs ssss }} ||
|| || || {{ sLss sLss ssss }} ||

----

===See also===
* [[Omnitetrachordality]]
* [[Gallery of omnitetrachordal scales]]
</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>OTC 2L 10s</title></head><body>Omnitetrachordal MODMOS scales 
<a class="wiki_link" href="/2L%2010s">2L+10s</a> 
 
This OTC scale pattern has two classes (with different tetrachordal divisions). Only a few other scales of the form <a class="wiki_link" href="/OTC%202L%20ns">2L+ns</a> are known to have this property. 
 
temperaments: <a class="wiki_link" href="/injera">injera</a> ? 
 
<hr />
 
<h3 id="toc0"><a name="x--Class 1"></a>Class 1</h3>
12 tones (5+2+5) 
 
<a class="wiki_link" href="/Gallery%20of%20omnitetrachordal%20scales#dual">Dual</a> of <a class="wiki_link" href="/OTC%2010L%202s">OTC 10L+2s</a>. Probably only useful for small values of L/s. 
 
<a class="wiki_link" href="/Gallery%20of%20omnitetrachordal%20scales#perfect">P</a> = 0.8849491924 
<a class="wiki_link" href="/Gallery%20of%20omnitetrachordal%20scales#Q">Q</a> = 3.8274237885 (4/3 = L+3.5s) 
 
L = 100.00 to 600.00 cents (260.15 cents @ Q) 
s = 0.00 to 100.00 cents (67.97 cents @ Q) 
 
9/8 = 2s (0.00 to 200.00 cents) 
4/3 = L+4s (500.00 to 600.00 cents) 
MOS generator = s (0.00 to 100.00 cents) 
MOS period = 1/2 octave (600.00 cents) 
 
notable EDOs: 14, 16, 26, 38 
 
<tt> LsssssLsssss </tt> (MOS, not OTC) 
<tt> || </tt> 
<tt> LssssLssssss </tt> (OTC MODMOS) - gen chains 7,5 
 
symmetric modes: 
<tt> sssLssssLsss </tt> 
<tt> ssLssssssLss </tt> 
 
all modes: 

<table class="wiki_table">
<tr>
<td> 
</td>
<td><tt> ssLss ss ssLss </tt> 
</td>
<td> 
</td>
</tr>
<tr>
<td> 
</td>
<td><tt> sLsss ss sLsss </tt> 
</td>
<td> 
</td>
</tr>
<tr>
<td> 
</td>
<td><tt> Lssss ss Lssss </tt> 
</td>
<td> 
</td>
</tr>
<tr>
<td><tt> ss ssssL ssssL </tt> 
</td>
<td> 
</td>
<td> 
</td>
</tr>
<tr>
<td><tt> ss sssLs sssLs </tt> 
</td>
<td> 
</td>
<td> 
</td>
</tr>
<tr>
<td><tt> ss ssLss ssLss </tt> 
</td>
<td> 
</td>
<td><tt> ssssL ssssL ss </tt> 
</td>
</tr>
<tr>
<td><tt> ss sLsss sLsss </tt> 
</td>
<td> 
</td>
<td><tt> sssLs sssLs ss </tt> 
</td>
</tr>
<tr>
<td><tt> ss Lssss Lssss </tt> 
</td>
<td> 
</td>
<td><tt> ssLss ssLss ss </tt> 
</td>
</tr>
<tr>
<td> 
</td>
<td> 
</td>
<td><tt> sLsss sLsss ss </tt> 
</td>
</tr>
<tr>
<td> 
</td>
<td> 
</td>
<td><tt> Lssss Lssss ss </tt> 
</td>
</tr>
<tr>
<td> 
</td>
<td><tt> ssssL ss ssssL </tt> 
</td>
<td> 
</td>
</tr>
<tr>
<td> 
</td>
<td><tt> sssLs ss sssLs </tt> 
</td>
<td> 
</td>
</tr>
</table>

 
<img src="/file/view/12_02_10_ssLss_ss_ssLss.png/589273820/12_02_10_ssLss_ss_ssLss.png" alt="12_02_10_ssLss_ss_ssLss.png" title="12_02_10_ssLss_ss_ssLss.png" /> 
 
<hr />
 
<h3 id="toc1"><a name="x--Class 2"></a>Class 2</h3>
12 tones (4+4+4) 
 
Only works at high values of L/s. 
 
P = 6.7698983847 
Q = 9.7123729809 (4/3 = L+2.5s) 
 
L = 100.00 to 600.00 cents (345.11 cents @ P, 396.09 cents @ Q) 
s = 0.00 to 100.00 cents (50.98 cents @ P, 40.78 cents @ Q) 
 
9/8 = 4s (0.00 to 400.00 cents) 
4/3 = L+3s (400.00 to 600.00 cents) 
MOS generator = s (0.00 to 100.00 cents) 
MOS period = 1/2 octave (600.00 cents) 
 
notable EDOs: 20, 22, 24 
 
<tt> LsssssLsssss </tt> (MOS, not OTC) 
<tt> | | </tt> 
<tt> LsssLsssssss </tt> (OTC MODMOS) - gen chains 8,4 
 
all modes: 

<table class="wiki_table">
<tr>
<td> 
</td>
<td> 
</td>
<td><tt> Lsss Lsss ssss </tt> 
</td>
</tr>
<tr>
<td> 
</td>
<td><tt> sssL ssss sssL </tt> 
</td>
<td> 
</td>
</tr>
<tr>
<td> 
</td>
<td><tt> ssLs ssss ssLs </tt> 
</td>
<td> 
</td>
</tr>
<tr>
<td> 
</td>
<td><tt> sLss ssss sLss </tt> 
</td>
<td> 
</td>
</tr>
<tr>
<td> 
</td>
<td><tt> Lsss ssss Lsss </tt> 
</td>
<td> 
</td>
</tr>
<tr>
<td><tt> ssss sssL sssL </tt> 
</td>
<td> 
</td>
<td> 
</td>
</tr>
<tr>
<td><tt> ssss ssLs ssLs </tt> 
</td>
<td> 
</td>
<td> 
</td>
</tr>
<tr>
<td><tt> ssss sLss sLss </tt> 
</td>
<td> 
</td>
<td> 
</td>
</tr>
<tr>
<td><tt> ssss Lsss Lsss </tt> 
</td>
<td> 
</td>
<td> 
</td>
</tr>
<tr>
<td> 
</td>
<td> 
</td>
<td><tt> sssL sssL ssss </tt> 
</td>
</tr>
<tr>
<td> 
</td>
<td> 
</td>
<td><tt> ssLs ssLs ssss </tt> 
</td>
</tr>
<tr>
<td> 
</td>
<td> 
</td>
<td><tt> sLss sLss ssss </tt> 
</td>
</tr>
</table>

 
<hr />
 
<h3 id="toc2"><a name="x--See also"></a>See also</h3>
<ul><li><a class="wiki_link" href="/Omnitetrachordality">Omnitetrachordality</a></li><li><a class="wiki_link" href="/Gallery%20of%20omnitetrachordal%20scales">Gallery of omnitetrachordal scales</a></li></ul></body></html></pre></div>