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<h2>IMPORTED REVISION FROM WIKISPACES</h2>
Omnitetrachordal MOS scale
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 20:20:58 UTC</tt>.<br>
[[5L_2s|5L+2s]]
: The original revision id was <tt>590306118</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
[[5L 2s|5L+2s]]
7 tones (3+1+3)
7 tones (3+1+3)


The classic diatonic scale ([[meantone]], Pythagorean, [[superpyth]]). [[{$page}#ref1|(1)]]
The classic diatonic scale ([[Meantone|meantone]], Pythagorean, [[Superpyth|superpyth]]). [[OTC_5L_2s#ref1|(1)]]


[[Gallery of omnitetrachordal scales#perfect|P]] = 2.2600167527 (L=9/8, s=[[256_243|256/243]])
[[Gallery_of_omnitetrachordal_scales#perfect|P]] = 2.2600167527 (L=9/8, s=[[256/243|256/243]])


L = 171.43 to 240.00 cents (203.91 cents @ P)
L = 171.43 to 240.00 cents (203.91 cents @ P)
s = 0.00 to 171.43 cents (90.22 cents @ P)
s = 0.00 to 171.43 cents (90.22 cents @ P)


9/8 = L (171.43 to 240.00 cents)
9/8 = L (171.43 to 240.00 cents)
4/3 = 2L+s (480.00 to 514.29 cents)
4/3 = 2L+s (480.00 to 514.29 cents)
generator = 3L+s (685.71 to 720.00 cents)
generator = 3L+s (685.71 to 720.00 cents)


Line 26: Line 24:


all modes:
all modes:
|| || {{ LLs L LLs }} || || Ionian ||=  5|1  ||
|| || {{ LsL L LsL }} || || Dorian ||= 3|3 ||
|| || {{ sLL L sLL }} || || Phrygian ||= 1|5 ||
|| {{ L LLs LLs }} || || || Lydian ||= 6|0 ||
|| {{ L LsL LsL }} || || {{ LLs LLs L }} || Mixolydian ||= 4|2 ||
|| {{ L sLL sLL }} || || {{ LsL LsL L }} || Aeolian ||= 2|4 ||
|| || || {{ sLL sLL L }} || Locrian ||= 0|6 ||


all modes in [[Modal UDP Notation|UDP]] order:
{| class="wikitable"
|| {{ L LLs LLs }} || || || Lydian ||=  6|0  ||
|-
|| || {{ LLs L LLs }} || || Ionian ||= 5|1 ||
| |  
|| {{ L LsL LsL }} || || {{ LLs LLs L }} || Mixolydian ||= 4|2 ||
| | <tt> LLs L LLs </tt>
|| || {{ LsL L LsL }} || || Dorian ||= 3|3 ||
| |  
|| {{ L sLL sLL }} || || {{ LsL LsL L }} || Aeolian ||= 2|4 ||
| | Ionian
|| || {{ sLL L sLL }} || || Phrygian ||= 1|5 ||
| style="text-align:center;" |  5|1 
|| || || {{ sLL sLL L }} || Locrian ||= 0|6 ||
|-
| |  
| | <tt> LsL L LsL </tt>
| |  
| | Dorian
| style="text-align:center;" | 3|3
|-
| |  
| | <tt> sLL L sLL </tt>
| |  
| | Phrygian
| style="text-align:center;" | 1|5
|-
| | <tt> L LLs LLs </tt>
| |  
| |  
| | Lydian
| style="text-align:center;" | 6|0
|-
| | <tt> L LsL LsL </tt>
| |  
| | <tt> LLs LLs L </tt>
| | Mixolydian
| style="text-align:center;" | 4|2
|-
| | <tt> L sLL sLL </tt>
| |  
| | <tt> LsL LsL L </tt>
| | Aeolian
| style="text-align:center;" | 2|4
|-
| |  
| |  
| | <tt> sLL sLL L </tt>
| | Locrian
| style="text-align:center;" | 0|6
|}


[[image:07_05_02_LsL_L_Ls.png]]
all modes in [[Modal_UDP_Notation|UDP]] order:
 
{| class="wikitable"
|-
| | <tt> L LLs LLs </tt>
| |
| |
| | Lydian
| style="text-align:center;" |  6|0 
|-
| |
| | <tt> LLs L LLs </tt>
| |
| | Ionian
| style="text-align:center;" | 5|1
|-
| | <tt> L LsL LsL </tt>
| |
| | <tt> LLs LLs L </tt>
| | Mixolydian
| style="text-align:center;" | 4|2
|-
| |
| | <tt> LsL L LsL </tt>
| |
| | Dorian
| style="text-align:center;" | 3|3
|-
| | <tt> L sLL sLL </tt>
| |
| | <tt> LsL LsL L </tt>
| | Aeolian
| style="text-align:center;" | 2|4
|-
| |
| | <tt> sLL L sLL </tt>
| |
| | Phrygian
| style="text-align:center;" | 1|5
|-
| |
| |
| | <tt> sLL sLL L </tt>
| | Locrian
| style="text-align:center;" | 0|6
|}
 
[[File:07_05_02_LsL_L_Ls.png|alt=07_05_02_LsL_L_Ls.png|07_05_02_LsL_L_Ls.png]]


===See also===
===See also===
* [[Omnitetrachordality]]
<ul><li>[[Omnitetrachordality|Omnitetrachordality]]</li><li>[[Gallery_of_omnitetrachordal_scales|Gallery of omnitetrachordal scales]]</li></ul>
* [[Gallery of omnitetrachordal scales]]


===References===
===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>
<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>
<h4>Original HTML content:</h4>
[[Category:7-tone scales]]
<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">&lt;html&gt;&lt;head&gt;&lt;title&gt;OTC 5L 2s&lt;/title&gt;&lt;/head&gt;&lt;body&gt;Omnitetrachordal MOS scale&lt;br /&gt;
[[Category:Tempered scales]]
&lt;a class="wiki_link" href="/5L%202s"&gt;5L+2s&lt;/a&gt;&lt;br /&gt;
[[Category:Pages with mostly numerical content]]
7 tones (3+1+3)&lt;br /&gt;
[[Category:MODMOS]]
&lt;br /&gt;
[[Category:Omnitetrachordal]]
The classic diatonic scale (&lt;a class="wiki_link" href="/meantone"&gt;meantone&lt;/a&gt;, Pythagorean, &lt;a class="wiki_link" href="/superpyth"&gt;superpyth&lt;/a&gt;). &lt;!-- ws:start:WikiTextVariableComponentRule:01:[[{$page}#ref1|(1)]] --&gt;&lt;a class="wiki_link" href="/OTC%205L%202s#ref1"&gt;(1)&lt;/a&gt;&lt;!-- ws:end:WikiTextVariableComponentRule:01 --&gt;&lt;br /&gt;
[[Category:Meantone]]
&lt;br /&gt;
[[Category:Pythagorean]]
&lt;a class="wiki_link" href="/Gallery%20of%20omnitetrachordal%20scales#perfect"&gt;P&lt;/a&gt; = 2.2600167527 (L=9/8, s=&lt;a class="wiki_link" href="/256_243"&gt;256/243&lt;/a&gt;)&lt;br /&gt;
[[Category:Superpyth]]
&lt;br /&gt;
L = 171.43 to 240.00 cents (203.91 cents @ P)&lt;br /&gt;
s = 0.00 to 171.43 cents (90.22 cents @ P)&lt;br /&gt;
&lt;br /&gt;
9/8 = L (171.43 to 240.00 cents)&lt;br /&gt;
4/3 = 2L+s (480.00 to 514.29 cents)&lt;br /&gt;
generator = 3L+s (685.71 to 720.00 cents)&lt;br /&gt;
&lt;br /&gt;
notable EDOs: 12, 17, 19, 22, 26, 29, 31, etc.&lt;br /&gt;
&lt;br /&gt;
symmetric mode: LsLLLsL&lt;br /&gt;
&lt;br /&gt;
all modes:&lt;br /&gt;
 
 
&lt;table class="wiki_table"&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;tt&gt; LLs L LLs &lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;Ionian&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt; 5|1 &lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;tt&gt; LsL L LsL &lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;Dorian&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;3|3&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;tt&gt; sLL L sLL &lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;Phrygian&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;1|5&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;tt&gt; L LLs LLs &lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;Lydian&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;6|0&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;tt&gt; L LsL LsL &lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;tt&gt; LLs LLs L &lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;Mixolydian&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;4|2&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;tt&gt; L sLL sLL &lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;tt&gt; LsL LsL L &lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;Aeolian&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;2|4&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;tt&gt; sLL sLL L &lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;Locrian&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;0|6&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
&lt;/table&gt;
 
&lt;br /&gt;
all modes in &lt;a class="wiki_link" href="/Modal%20UDP%20Notation"&gt;UDP&lt;/a&gt; order:&lt;br /&gt;
 
 
&lt;table class="wiki_table"&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;tt&gt; L LLs LLs &lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;Lydian&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt; 6|0 &lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;tt&gt; LLs L LLs &lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;Ionian&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;5|1&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;tt&gt; L LsL LsL &lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;tt&gt; LLs LLs L &lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;Mixolydian&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;4|2&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;tt&gt; LsL L LsL &lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;Dorian&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;3|3&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;tt&gt; L sLL sLL &lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;tt&gt; LsL LsL L &lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;Aeolian&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;2|4&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;tt&gt; sLL L sLL &lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;Phrygian&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;1|5&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;tt&gt; sLL sLL L &lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;Locrian&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;0|6&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
&lt;/table&gt;
 
&lt;br /&gt;
&lt;!-- ws:start:WikiTextLocalImageRule:189:&amp;lt;img src=&amp;quot;/file/view/07_05_02_LsL_L_Ls.png/589273784/07_05_02_LsL_L_Ls.png&amp;quot; alt=&amp;quot;&amp;quot; title=&amp;quot;&amp;quot; /&amp;gt; --&gt;&lt;img src="/file/view/07_05_02_LsL_L_Ls.png/589273784/07_05_02_LsL_L_Ls.png" alt="07_05_02_LsL_L_Ls.png" title="07_05_02_LsL_L_Ls.png" /&gt;&lt;!-- ws:end:WikiTextLocalImageRule:189 --&gt;&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:2:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc0"&gt;&lt;a name="x--See also"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:2 --&gt;See also&lt;/h3&gt;
&lt;ul&gt;&lt;li&gt;&lt;a class="wiki_link" href="/Omnitetrachordality"&gt;Omnitetrachordality&lt;/a&gt;&lt;/li&gt;&lt;li&gt;&lt;a class="wiki_link" href="/Gallery%20of%20omnitetrachordal%20scales"&gt;Gallery of omnitetrachordal scales&lt;/a&gt;&lt;/li&gt;&lt;/ul&gt;&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:4:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc1"&gt;&lt;a name="x--References"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:4 --&gt;References&lt;/h3&gt;
&lt;ul&gt;&lt;li&gt;&lt;!-- ws:start:WikiTextAnchorRule:6:&amp;lt;img src=&amp;quot;/i/anchor.gif&amp;quot; class=&amp;quot;WikiAnchor&amp;quot; alt=&amp;quot;Anchor&amp;quot; id=&amp;quot;wikitext@@anchor@@ref1&amp;quot; title=&amp;quot;Anchor: ref1&amp;quot;/&amp;gt; --&gt;&lt;a name="ref1"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextAnchorRule:6 --&gt;(1) Noted as omnitetrachordal by Paul Erlich no later than 2002. See tuning-math list messages &lt;a class="wiki_link_ext" href="http://robertinventor.com/tuning-math/s___4/msg_3675-3699.html#3685" rel="nofollow"&gt;3685&lt;/a&gt; and &lt;a class="wiki_link_ext" href="http://robertinventor.com/tuning-math/s__11/msg_10975-10999.html#10987" rel="nofollow"&gt;10987&lt;/a&gt;.&lt;/li&gt;&lt;/ul&gt;&lt;/body&gt;&lt;/html&gt;</pre></div>

Latest revision as of 03:13, 24 June 2025

Omnitetrachordal MOS scale

5L+2s

7 tones (3+1+3)

The classic diatonic scale (meantone, Pythagorean, superpyth). (1)

P = 2.2600167527 (L=9/8, s=256/243)

L = 171.43 to 240.00 cents (203.91 cents @ P)

s = 0.00 to 171.43 cents (90.22 cents @ P)

9/8 = L (171.43 to 240.00 cents)

4/3 = 2L+s (480.00 to 514.29 cents)

generator = 3L+s (685.71 to 720.00 cents)

notable EDOs: 12, 17, 19, 22, 26, 29, 31, etc.

symmetric mode: LsLLLsL

all modes:

LLs L LLs Ionian  5|1 
LsL L LsL Dorian 3|3
sLL L sLL Phrygian 1|5
L LLs LLs Lydian 6|0
L LsL LsL LLs LLs L Mixolydian 4|2
L sLL sLL LsL LsL L Aeolian 2|4
sLL sLL L Locrian 0|6

all modes in UDP order:

L LLs LLs Lydian  6|0 
LLs L LLs Ionian 5|1
L LsL LsL LLs LLs L Mixolydian 4|2
LsL L LsL Dorian 3|3
L sLL sLL LsL LsL L Aeolian 2|4
sLL L sLL Phrygian 1|5
sLL sLL L Locrian 0|6

07_05_02_LsL_L_Ls.png

See also

References

  • (1) Noted as omnitetrachordal by Paul Erlich no later than 2002. See tuning-math list messages 3685 and 10987.
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