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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 21:24:43 UTC</tt>.<br>
[[7L_5s|7L+5s]]
: The original revision id was <tt>590308978</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
[[7L 5s|7L+5s]]
12 tones (5+2+5)
12 tones (5+2+5)


MOS of the [[meantone]] and [[Meantone family#Flattone|flattone]] temperaments (slightly flat 3/2).  [[Gallery of omnitetrachordal scales#perfect|Imperfect]], but very usable at any L/s ratio.  Many modes may be pentachordally split in two ways.
MOS of the [[Meantone|meantone]] and [[Meantone_family#Flattone|flattone]] temperaments (slightly flat 3/2).  [[Gallery_of_omnitetrachordal_scales#perfect|Imperfect]], but very usable at any L/s ratio.  Many modes may be pentachordally split in two ways.


[[Gallery of omnitetrachordal scales#perfect|P]] = 0.7936402416
[[Gallery_of_omnitetrachordal_scales#perfect|P]] = 0.7936402416
[[Gallery of omnitetrachordal scales#Q|Q]] = 6.0713810872 (4/3 = 3L+1.5s)
 
[[Gallery_of_omnitetrachordal_scales#Q|Q]] = 6.0713810872 (4/3 = 3L+1.5s)


L = 100.00 to 171.43 cents (153.38 cents @ Q)
L = 100.00 to 171.43 cents (153.38 cents @ Q)
s = 0.00 to 100.00 cents (25.26 cents @ Q)
s = 0.00 to 100.00 cents (25.26 cents @ Q)


9/8 = L+s (171.43 to 200.00 cents)
9/8 = L+s (171.43 to 200.00 cents)
4/3 = 3L+2s (500.00 to 514.29 cents)
4/3 = 3L+2s (500.00 to 514.29 cents)
generator = 4/3
generator = 4/3


Line 25: Line 24:


all modes:
all modes:
|| || {{ sLLsL sL sLLsL }} || ||
|| || {{ LLsLs Ls LLsLs }} || ||
|| {{ Ls LsLsL LsLsL }} || {{ LsLsL sL LsLsL }} || ||
|| {{ sL sLsLL sLsLL }} || || ||
|| {{ Ls LsLLs LsLLs }} || || {{ LsLsL LsLsL Ls }} ||
|| {{ sL sLLsL sLLsL }} || || {{ sLsLL sLsLL sL }} ||
|| {{ Ls LLsLs LLsLs }} || || {{ LsLLs LsLLs Ls }} ||
|| {{ sL LsLsL LsLsL }} || || {{ sLLsL sLLsL sL }} ||
|| || || {{ LLsLs LLsLs Ls }} ||
|| || {{ LsLsL Ls LsLsL }} || {{ LsLsL LsLsL sL }} ||
|| || {{ sLsLL sL sLsLL }} || ||
|| || {{ LsLLs Ls LsLLs }} || ||


[[image:12_07_05_LsLLs_Ls_LsLLs.png]]
{| class="wikitable"
|-
| |
| | <tt> sLLsL sL sLLsL </tt>
| |
|-
| |
| | <tt> LLsLs Ls LLsLs </tt>
| |
|-
| | <tt> Ls LsLsL LsLsL </tt>
| | <tt> LsLsL sL LsLsL </tt>
| |
|-
| | <tt> sL sLsLL sLsLL </tt>
| |
| |
|-
| | <tt> Ls LsLLs LsLLs </tt>
| |
| | <tt> LsLsL LsLsL Ls </tt>
|-
| | <tt> sL sLLsL sLLsL </tt>
| |
| | <tt> sLsLL sLsLL sL </tt>
|-
| | <tt> Ls LLsLs LLsLs </tt>
| |
| | <tt> LsLLs LsLLs Ls </tt>
|-
| | <tt> sL LsLsL LsLsL </tt>
| |
| | <tt> sLLsL sLLsL sL </tt>
|-
| |
| |
| | <tt> LLsLs LLsLs Ls </tt>
|-
| |
| | <tt> LsLsL Ls LsLsL </tt>
| | <tt> LsLsL LsLsL sL </tt>
|-
| |
| | <tt> sLsLL sL sLsLL </tt>
| |
|-
| |
| | <tt> LsLLs Ls LsLLs </tt>
| |
|}
 
[[File:12_07_05_LsLLs_Ls_LsLLs.png|alt=12_07_05_LsLLs_Ls_LsLLs.png|12_07_05_LsLLs_Ls_LsLLs.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===
* 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]].
<ul><li>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>
</pre></div>
[[Category:12-tone scales]]
<h4>Original HTML content:</h4>
[[Category:Tempered 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 7L 5s&lt;/title&gt;&lt;/head&gt;&lt;body&gt;Omnitetrachordal MOS scale&lt;br /&gt;
[[Category:Pages with mostly numerical content]]
&lt;a class="wiki_link" href="/7L%205s"&gt;7L+5s&lt;/a&gt;&lt;br /&gt;
[[Category:MODMOS]]
12 tones (5+2+5)&lt;br /&gt;
[[Category:Omnitetrachordal]]
&lt;br /&gt;
[[Category:Flattone]]
MOS of the &lt;a class="wiki_link" href="/meantone"&gt;meantone&lt;/a&gt; and &lt;a class="wiki_link" href="/Meantone%20family#Flattone"&gt;flattone&lt;/a&gt; temperaments (slightly flat 3/2).  &lt;a class="wiki_link" href="/Gallery%20of%20omnitetrachordal%20scales#perfect"&gt;Imperfect&lt;/a&gt;, but very usable at any L/s ratio.  Many modes may be pentachordally split in two ways.&lt;br /&gt;
[[Category:Meantone]]
&lt;br /&gt;
&lt;a class="wiki_link" href="/Gallery%20of%20omnitetrachordal%20scales#perfect"&gt;P&lt;/a&gt; = 0.7936402416&lt;br /&gt;
&lt;a class="wiki_link" href="/Gallery%20of%20omnitetrachordal%20scales#Q"&gt;Q&lt;/a&gt; = 6.0713810872 (4/3 = 3L+1.5s)&lt;br /&gt;
&lt;br /&gt;
L = 100.00 to 171.43 cents (153.38 cents @ Q)&lt;br /&gt;
s = 0.00 to 100.00 cents (25.26 cents @ Q)&lt;br /&gt;
&lt;br /&gt;
9/8 = L+s (171.43 to 200.00 cents)&lt;br /&gt;
4/3 = 3L+2s (500.00 to 514.29 cents)&lt;br /&gt;
generator = 4/3&lt;br /&gt;
&lt;br /&gt;
notable EDOs: 19, 26, 31, 33, 43, 45, 50, etc.&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; sLLsL sL sLLsL &lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&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; LLsLs Ls LLsLs &lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;tt&gt; Ls LsLsL LsLsL &lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;tt&gt; LsLsL sL LsLsL &lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;tt&gt; sL sLsLL sLsLL &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;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;tt&gt; Ls LsLLs LsLLs &lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;tt&gt; LsLsL LsLsL Ls &lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;tt&gt; sL sLLsL sLLsL &lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;tt&gt; sLsLL sLsLL sL &lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;tt&gt; Ls LLsLs LLsLs &lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;tt&gt; LsLLs LsLLs Ls &lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;tt&gt; sL LsLsL LsLsL &lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;tt&gt; sLLsL sLLsL sL &lt;/tt&gt;&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; LLsLs LLsLs Ls &lt;/tt&gt;&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; LsLsL Ls LsLsL &lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;tt&gt; LsLsL LsLsL sL &lt;/tt&gt;&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; sLsLL sL sLsLL &lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&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; LsLLs Ls LsLLs &lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
&lt;/table&gt;
 
&lt;br /&gt;
&lt;!-- ws:start:WikiTextLocalImageRule:112:&amp;lt;img src=&amp;quot;/file/view/12_07_05_LsLLs_Ls_LsLLs.png/589273828/12_07_05_LsLLs_Ls_LsLLs.png&amp;quot; alt=&amp;quot;&amp;quot; title=&amp;quot;&amp;quot; /&amp;gt; --&gt;&lt;img src="/file/view/12_07_05_LsLLs_Ls_LsLLs.png/589273828/12_07_05_LsLLs_Ls_LsLLs.png" alt="12_07_05_LsLLs_Ls_LsLLs.png" title="12_07_05_LsLLs_Ls_LsLLs.png" /&gt;&lt;!-- ws:end:WikiTextLocalImageRule:112 --&gt;&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:0:&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:0 --&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:2:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc1"&gt;&lt;a name="x--References"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:2 --&gt;References&lt;/h3&gt;
&lt;ul&gt;&lt;li&gt;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 03:11, 24 June 2025

Omnitetrachordal MOS scale

7L+5s

12 tones (5+2+5)

MOS of the meantone and flattone temperaments (slightly flat 3/2). Imperfect, but very usable at any L/s ratio. Many modes may be pentachordally split in two ways.

P = 0.7936402416

Q = 6.0713810872 (4/3 = 3L+1.5s)

L = 100.00 to 171.43 cents (153.38 cents @ Q)

s = 0.00 to 100.00 cents (25.26 cents @ Q)

9/8 = L+s (171.43 to 200.00 cents)

4/3 = 3L+2s (500.00 to 514.29 cents)

generator = 4/3

notable EDOs: 19, 26, 31, 33, 43, 45, 50, etc.

all modes:

sLLsL sL sLLsL
LLsLs Ls LLsLs
Ls LsLsL LsLsL LsLsL sL LsLsL
sL sLsLL sLsLL
Ls LsLLs LsLLs LsLsL LsLsL Ls
sL sLLsL sLLsL sLsLL sLsLL sL
Ls LLsLs LLsLs LsLLs LsLLs Ls
sL LsLsL LsLsL sLLsL sLLsL sL
LLsLs LLsLs Ls
LsLsL Ls LsLsL LsLsL LsLsL sL
sLsLL sL sLsLL
LsLLs Ls LsLLs

12_07_05_LsLLs_Ls_LsLLs.png

See also

References

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