OTC 2L 3s - Revision history

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

2025-06-24T03:07:41Z

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>(1) Noted as omnitetrachordal by Paul Erlich no later than 2002. See tuning-math list messages [http://robertinventor.com/tuning-math/s___4/msg_3675-3699.html#3685 3685] and [http://robertinventor.com/tuning-math/s__11/msg_10975-10999.html#10987 10987].</li></ul>		<ul><li>(1) Noted as omnitetrachordal by Paul Erlich no later than 2002. See tuning-math list messages [http://robertinventor.com/tuning-math/s___4/msg_3675-3699.html#3685 3685] and [http://robertinventor.com/tuning-math/s__11/msg_10975-10999.html#10987 10987].</li></ul>
	[[Category:5-tone scales]]		[[Category:5-tone scales]]
	[[Category:~~Tempered_scales~~]]		[[Category:Tempered scales]]
	[[Category:Pages with mostly numerical content]]		[[Category:Pages with mostly numerical content]]
	[[Category:MODMOS]]		[[Category:MODMOS]]

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

2025-06-24T02:39:49Z

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 02:39, 24 June 2025
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	<ul><li>(1) Noted as omnitetrachordal by Paul Erlich no later than 2002. See tuning-math list messages [http://robertinventor.com/tuning-math/s___4/msg_3675-3699.html#3685 3685] and [http://robertinventor.com/tuning-math/s__11/msg_10975-10999.html#10987 10987].</li></ul>		<ul><li>(1) Noted as omnitetrachordal by Paul Erlich no later than 2002. See tuning-math list messages [http://robertinventor.com/tuning-math/s___4/msg_3675-3699.html#3685 3685] and [http://robertinventor.com/tuning-math/s__11/msg_10975-10999.html#10987 10987].</li></ul>
	[[Category:5-tone scales]]		[[Category:5-tone scales]]
	[[Category:~~Tempered scales~~]]		[[Category:Tempered_scales]]
	[[Category:Pages with mostly numerical content]]		[[Category:Pages with mostly numerical content]]
	[[Category:MODMOS]]		[[Category:MODMOS]]

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

2025-06-24T02:36:09Z

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

← Older revision		Revision as of 02:36, 24 June 2025
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	[[Category:5-tone scales]]		[[Category:5-tone scales]]
	[[Category:Tempered scales]]		[[Category:Tempered scales]]
			[[Category:Pages with mostly numerical content]]
	[[Category:MODMOS]]		[[Category:MODMOS]]
	[[Category:Omnitetrachordal]]		[[Category:Omnitetrachordal]]

BudjarnLambeth: Categorised, added tags, removed blank lines

2023-05-02T04:26:11Z

Categorised, added tags, removed blank lines

← Older revision		Revision as of 04:26, 2 May 2023
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	===References===		===References===
	<ul><li>(1) Noted as omnitetrachordal by Paul Erlich no later than 2002. See tuning-math list messages [http://robertinventor.com/tuning-math/s___4/msg_3675-3699.html#3685 3685] and [http://robertinventor.com/tuning-math/s__11/msg_10975-10999.html#10987 10987].</li></ul>		<ul><li>(1) Noted as omnitetrachordal by Paul Erlich no later than 2002. See tuning-math list messages [http://robertinventor.com/tuning-math/s___4/msg_3675-3699.html#3685 3685] and [http://robertinventor.com/tuning-math/s__11/msg_10975-10999.html#10987 10987].</li></ul>
			[[Category:5-tone scales]]
			[[Category:Tempered scales]]
			[[Category:MODMOS]]
			[[Category:Omnitetrachordal]]
			[[Category:Superpyth]]
			[[Category:Pythagorean]]
			[[Category:Meantone]]
			[[Category:Mavila]]

Wikispaces>FREEZE at 00:00, 17 July 2018

2018-07-17T00:00:00Z

Show changes

Wikispaces>spt3125: Imported revision 590306360 - Original comment:

2016-08-28T20:28:09Z

**Imported revision 590306360 - 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:spt3125|spt3125]] and made on <tt>2016-08-28 20:28:09 UTC</tt>.<br>
: The original revision id was <tt>590306360</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">Omnitetrachordal MOS scale
[[2L 3s|2L+3s]]
5 tones (2+1+2)

The classic pentatonic scale. Can include [[superpyth]], [[https://en.wikipedia.org/wiki/Pythagorean_tuning|Pythagorean]], [[meantone]], and [[Mavila Temperament Modal Harmony|mavila]] tunings. [[{$page}#ref1|(1)]]

[[Gallery of omnitetrachordal scales#perfect|P]] = 1.4424745962 (L=[[32_27|32/27]], s=9/8)
[[Gallery of omnitetrachordal scales#Q|Q]] = 4.3849491924 (4/3 = L+0.5s)

L = 240.00 to 600.00 cents (294.13 cents @ P, 447.07 cents @ Q)
s = 0.00 to 240.00 cents (203.91 cents @ P, 101.96 cents @ Q)

9/8 = s (0.00 to 240.00 cents)
4/3 = L+s (480.00 to 600.00 cents)
generator = 4/3

notable [[EDO]]s: 7, 9, 12, 16, 17, 19, 22, 26, 29, 31

symmetric mode: {{ sLsLs }}

all modes:
|| || {{ sL s sL }} || ||= [[Modal UDP Notation|1|3]] ||
|| || {{ Ls s Ls }} || ||= 3|1 ||
|| {{ s sL sL }} || || ||= 0|4 ||
|| {{ s Ls Ls }} || || {{ sL sL s }} ||= 2|2 ||
|| || || {{ Ls Ls s }} ||= 4|0 ||

[[image:05_02_03_sL_s_sL.png]]

===See also===
* [[Omnitetrachordality]]
* [[Gallery of omnitetrachordal scales]]

===References===
* [[#ref1]](1) Noted as omnitetrachordal by Paul Erlich no later than 2002. See tuning-math list messages [[http://robertinventor.com/tuning-math/s___4/msg_3675-3699.html#3685|3685]] and [[http://robertinventor.com/tuning-math/s__11/msg_10975-10999.html#10987|10987]].</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 3s</title></head><body>Omnitetrachordal MOS scale<br />
<a class="wiki_link" href="/2L%203s">2L+3s</a><br />
5 tones (2+1+2)<br />
<br />
The classic pentatonic scale. Can include <a class="wiki_link" href="/superpyth">superpyth</a>, <a class="wiki_link_ext" href="https://en.wikipedia.org/wiki/Pythagorean_tuning" rel="nofollow">Pythagorean</a>, <a class="wiki_link" href="/meantone">meantone</a>, and <a class="wiki_link" href="/Mavila%20Temperament%20Modal%20Harmony">mavila</a> tunings. <a class="wiki_link" href="/OTC%202L%203s#ref1">(1)</a><br />
<br />
<a class="wiki_link" href="/Gallery%20of%20omnitetrachordal%20scales#perfect">P</a> = 1.4424745962 (L=<a class="wiki_link" href="/32_27">32/27</a>, s=9/8)<br />
<a class="wiki_link" href="/Gallery%20of%20omnitetrachordal%20scales#Q">Q</a> = 4.3849491924 (4/3 = L+0.5s)<br />
<br />
L = 240.00 to 600.00 cents (294.13 cents @ P, 447.07 cents @ Q)<br />
s = 0.00 to 240.00 cents (203.91 cents @ P, 101.96 cents @ Q)<br />
<br />
9/8 = s (0.00 to 240.00 cents)<br />
4/3 = L+s (480.00 to 600.00 cents)<br />
generator = 4/3<br />
<br />
notable <a class="wiki_link" href="/EDO">EDO</a>s: 7, 9, 12, 16, 17, 19, 22, 26, 29, 31<br />
<br />
symmetric mode: <tt> sLsLs </tt><br />
<br />
all modes:<br />

<table class="wiki_table">
<tr>
<td><br />
</td>
<td><tt> sL s sL </tt><br />
</td>
<td><br />
</td>
<td style="text-align: center;"> <a class="wiki_link" href="/Modal%20UDP%20Notation">1|3</a> <br />
</td>
</tr>
<tr>
<td><br />
</td>
<td><tt> Ls s Ls </tt><br />
</td>
<td><br />
</td>
<td style="text-align: center;">3|1<br />
</td>
</tr>
<tr>
<td><tt> s sL sL </tt><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td style="text-align: center;">0|4<br />
</td>
</tr>
<tr>
<td><tt> s Ls Ls </tt><br />
</td>
<td><br />
</td>
<td><tt> sL sL s </tt><br />
</td>
<td style="text-align: center;">2|2<br />
</td>
</tr>
<tr>
<td><br />
</td>
<td><br />
</td>
<td><tt> Ls Ls s </tt><br />
</td>
<td style="text-align: center;">4|0<br />
</td>
</tr>
</table>

<br />
<img src="/file/view/05_02_03_sL_s_sL.png/589273764/05_02_03_sL_s_sL.png" alt="05_02_03_sL_s_sL.png" title="05_02_03_sL_s_sL.png" /><br />
<br />
<h3 id="toc0"><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><br />
<h3 id="toc1"><a name="x--References"></a>References</h3>
<ul><li><a name="ref1"></a>(1) Noted as omnitetrachordal by Paul Erlich no later than 2002. See tuning-math list messages <a class="wiki_link_ext" href="http://robertinventor.com/tuning-math/s___4/msg_3675-3699.html#3685" rel="nofollow">3685</a> and <a class="wiki_link_ext" href="http://robertinventor.com/tuning-math/s__11/msg_10975-10999.html#10987" rel="nofollow">10987</a>.</li></ul></body></html></pre></div>