OTC 7L 12s: Difference between revisions

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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>2016-08-31 21:06:20 UTC</tt>.<br>
[[7L_12s|7L+12s]]
: The original revision id was <tt>590701416</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 12s|7L+12s]]
19 tones (8+3+8)
19 tones (8+3+8)


[[Meantone family#Flattone|Flattone]] MOS; [[Gallery of omnitetrachordal scales#perfect|P]]&lt;0 (oddly, neither this scale nor its [[{$page}#dual|dual]] can be tuned with a perfect 3/2!)
[[Meantone_family#Flattone|Flattone]] MOS; [[Gallery_of_omnitetrachordal_scales#perfect|P]]&lt;0 (oddly, neither this scale nor its [[OTC_7L_12s#dual|dual]] can be tuned with a perfect 3/2!)


P = -0.2063597584
P = -0.2063597584
[[Gallery of omnitetrachordal scales#Q|Q]] = 5.0713810872 (4/3 = 3L+4.5s)
 
[[Gallery_of_omnitetrachordal_scales#Q|Q]] = 5.0713810872 (4/3 = 3L+4.5s)


L = 63.16 to 171.43 cents (128.12 cents @ Q)
L = 63.16 to 171.43 cents (128.12 cents @ Q)
s = 0.00 to 63.16 cents (25.26 cents @ Q)
s = 0.00 to 63.16 cents (25.26 cents @ Q)


9/8 = L+2s (171.43 to 189.47 cents)
9/8 = L+2s (171.43 to 189.47 cents)
4/3 = 3L+5s (505.26 to 514.29 cents)
4/3 = 3L+5s (505.26 to 514.29 cents)
generator = 4/3
generator = 4/3


notable EDOs: 26, 33, 40, 45
notable EDOs: 26, 33, 40, 45


symmetric mode: {{ sLssLsLssLssLsLssLs }}
symmetric mode: <tt> sLssLsLssLssLsLssLs </tt>


all modes:
all modes:
|| {{ sLs sLsLssLs sLsLssLs }} || || {{ sLssLsLs sLssLsLs sLs }} ||
|| {{ Lss LsLssLss LsLssLss }} || || {{ LssLsLss LssLsLss Lss }} ||
|| {{ ssL sLssLssL sLssLssL }} || || {{ ssLsLssL ssLsLssL ssL }} ||
|| {{ sLs LssLssLs LssLssLs }} || || {{ sLsLssLs sLsLssLs sLs }} ||
|| || || {{ LsLssLss LsLssLss Lss }} ||
|| || {{ sLssLssL sLs sLssLssL }} || {{ sLssLssL sLssLssL ssL }} ||
|| || {{ LssLssLs Lss LssLssLs }} || {{ LssLssLs LssLssLs sLs }} ||
|| || {{ ssLssLsL ssL ssLssLsL }} || ||
|| || {{ sLssLsLs sLs sLssLsLs }} || ||
|| || {{ LssLsLss Lss LssLsLss }} || ||
|| || {{ ssLsLssL ssL ssLsLssL }} || ||
|| || {{ sLsLssLs sLs sLsLssLs }} || ||
|| || {{ LsLssLss Lss LsLssLss }} || ||
|| {{ sLs sLssLssL sLssLssL }} || {{ sLssLssL ssL sLssLssL }} || ||
|| {{ Lss LssLssLs LssLssLs }} || {{ LssLssLs sLs LssLssLs }} || ||
|| {{ ssL ssLssLsL ssLssLsL }} || || ||
|| {{ sLs sLssLsLs sLssLsLs }} || || {{ sLssLssL sLssLssL sLs }} ||
|| {{ Lss LssLsLss LssLsLss }} || || {{ LssLssLs LssLssLs Lss }} ||
|| {{ ssL ssLsLssL ssLsLssL }} || || {{ ssLssLsL ssLssLsL ssL }} ||


[[image:19_07_12_LssLsLss_Lss_LssLsLss.png]]
{| class="wikitable"
|-
| | <tt> sLs sLsLssLs sLsLssLs </tt>
| |
| | <tt> sLssLsLs sLssLsLs sLs </tt>
|-
| | <tt> Lss LsLssLss LsLssLss </tt>
| |
| | <tt> LssLsLss LssLsLss Lss </tt>
|-
| | <tt> ssL sLssLssL sLssLssL </tt>
| |
| | <tt> ssLsLssL ssLsLssL ssL </tt>
|-
| | <tt> sLs LssLssLs LssLssLs </tt>
| |
| | <tt> sLsLssLs sLsLssLs sLs </tt>
|-
| |
| |
| | <tt> LsLssLss LsLssLss Lss </tt>
|-
| |
| | <tt> sLssLssL sLs sLssLssL </tt>
| | <tt> sLssLssL sLssLssL ssL </tt>
|-
| |
| | <tt> LssLssLs Lss LssLssLs </tt>
| | <tt> LssLssLs LssLssLs sLs </tt>
|-
| |
| | <tt> ssLssLsL ssL ssLssLsL </tt>
| |
|-
| |
| | <tt> sLssLsLs sLs sLssLsLs </tt>
| |
|-
| |
| | <tt> LssLsLss Lss LssLsLss </tt>
| |
|-
| |
| | <tt> ssLsLssL ssL ssLsLssL </tt>
| |
|-
| |
| | <tt> sLsLssLs sLs sLsLssLs </tt>
| |
|-
| |
| | <tt> LsLssLss Lss LsLssLss </tt>
| |
|-
| | <tt> sLs sLssLssL sLssLssL </tt>
| | <tt> sLssLssL ssL sLssLssL </tt>
| |
|-
| | <tt> Lss LssLssLs LssLssLs </tt>
| | <tt> LssLssLs sLs LssLssLs </tt>
| |
|-
| | <tt> ssL ssLssLsL ssLssLsL </tt>
| |
| |
|-
| | <tt> sLs sLssLsLs sLssLsLs </tt>
| |
| | <tt> sLssLssL sLssLssL sLs </tt>
|-
| | <tt> Lss LssLsLss LssLsLss </tt>
| |
| | <tt> LssLssLs LssLssLs Lss </tt>
|-
| | <tt> ssL ssLsLssL ssLsLssL </tt>
| |
| | <tt> ssLssLsL ssLssLsL ssL </tt>
|}
 
[[File:19_07_12_LssLsLss_Lss_LssLsLss.png|alt=19_07_12_LssLsLss_Lss_LssLsLss.png|19_07_12_LssLsLss_Lss_LssLsLss.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:19-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 12s&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%2012s"&gt;7L+12s&lt;/a&gt;&lt;br /&gt;
[[Category:MODMOS]]
19 tones (8+3+8)&lt;br /&gt;
[[Category:Omnitetrachordal]]
&lt;br /&gt;
[[Category:Flattone]]
&lt;a class="wiki_link" href="/Meantone%20family#Flattone"&gt;Flattone&lt;/a&gt; MOS; &lt;a class="wiki_link" href="/Gallery%20of%20omnitetrachordal%20scales#perfect"&gt;P&lt;/a&gt;&amp;lt;0 (oddly, neither this scale nor its &lt;!-- ws:start:WikiTextVariableComponentRule:01:[[{$page}#dual|dual]] --&gt;&lt;a class="wiki_link" href="/OTC%207L%2012s#dual"&gt;dual&lt;/a&gt;&lt;!-- ws:end:WikiTextVariableComponentRule:01 --&gt; can be tuned with a perfect 3/2!)&lt;br /&gt;
&lt;br /&gt;
P = -0.2063597584&lt;br /&gt;
&lt;a class="wiki_link" href="/Gallery%20of%20omnitetrachordal%20scales#Q"&gt;Q&lt;/a&gt; = 5.0713810872 (4/3 = 3L+4.5s)&lt;br /&gt;
&lt;br /&gt;
L = 63.16 to 171.43 cents (128.12 cents @ Q)&lt;br /&gt;
s = 0.00 to 63.16 cents (25.26 cents @ Q)&lt;br /&gt;
&lt;br /&gt;
9/8 = L+2s (171.43 to 189.47 cents)&lt;br /&gt;
4/3 = 3L+5s (505.26 to 514.29 cents)&lt;br /&gt;
generator = 4/3&lt;br /&gt;
&lt;br /&gt;
notable EDOs: 26, 33, 40, 45&lt;br /&gt;
&lt;br /&gt;
symmetric mode: &lt;tt&gt; sLssLsLssLssLsLssLs &lt;/tt&gt;&lt;br /&gt;
&lt;br /&gt;
all modes:&lt;br /&gt;
 
 
&lt;table class="wiki_table"&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;tt&gt; sLs sLsLssLs sLsLssLs &lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;tt&gt; sLssLsLs sLssLsLs sLs &lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;tt&gt; Lss LsLssLss LsLssLss &lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;tt&gt; LssLsLss LssLsLss Lss &lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;tt&gt; ssL sLssLssL sLssLssL &lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;tt&gt; ssLsLssL ssLsLssL ssL &lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;tt&gt; sLs LssLssLs LssLssLs &lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;tt&gt; sLsLssLs sLsLssLs sLs &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; LsLssLss LsLssLss Lss &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; sLssLssL sLs sLssLssL &lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;tt&gt; sLssLssL sLssLssL ssL &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; LssLssLs Lss LssLssLs &lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;tt&gt; LssLssLs LssLssLs sLs &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; ssLssLsL ssL ssLssLsL &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; sLssLsLs sLs sLssLsLs &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; LssLsLss Lss LssLsLss &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; ssLsLssL ssL ssLsLssL &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; sLsLssLs sLs sLsLssLs &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; LsLssLss Lss LsLssLss &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; sLs sLssLssL sLssLssL &lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;tt&gt; sLssLssL ssL sLssLssL &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; Lss LssLssLs LssLssLs &lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;tt&gt; LssLssLs sLs LssLssLs &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; ssL ssLssLsL ssLssLsL &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; sLs sLssLsLs sLssLsLs &lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;tt&gt; sLssLssL sLssLssL sLs &lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;tt&gt; Lss LssLsLss LssLsLss &lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;tt&gt; LssLssLs LssLssLs Lss &lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;tt&gt; ssL ssLsLssL ssLsLssL &lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;tt&gt; ssLssLsL ssLssLsL ssL &lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
&lt;/table&gt;
 
&lt;br /&gt;
&lt;!-- ws:start:WikiTextLocalImageRule:170:&amp;lt;img src=&amp;quot;/file/view/19_07_12_LssLsLss_Lss_LssLsLss.png/589273882/19_07_12_LssLsLss_Lss_LssLsLss.png&amp;quot; alt=&amp;quot;&amp;quot; title=&amp;quot;&amp;quot; /&amp;gt; --&gt;&lt;img src="/file/view/19_07_12_LssLsLss_Lss_LssLsLss.png/589273882/19_07_12_LssLsLss_Lss_LssLsLss.png" alt="19_07_12_LssLsLss_Lss_LssLsLss.png" title="19_07_12_LssLsLss_Lss_LssLsLss.png" /&gt;&lt;!-- ws:end:WikiTextLocalImageRule:170 --&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;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 03:09, 24 June 2025

Omnitetrachordal MOS scale

7L+12s

19 tones (8+3+8)

Flattone MOS; P<0 (oddly, neither this scale nor its dual can be tuned with a perfect 3/2!)

P = -0.2063597584

Q = 5.0713810872 (4/3 = 3L+4.5s)

L = 63.16 to 171.43 cents (128.12 cents @ Q)

s = 0.00 to 63.16 cents (25.26 cents @ Q)

9/8 = L+2s (171.43 to 189.47 cents)

4/3 = 3L+5s (505.26 to 514.29 cents)

generator = 4/3

notable EDOs: 26, 33, 40, 45

symmetric mode: sLssLsLssLssLsLssLs

all modes:

sLs sLsLssLs sLsLssLs sLssLsLs sLssLsLs sLs
Lss LsLssLss LsLssLss LssLsLss LssLsLss Lss
ssL sLssLssL sLssLssL ssLsLssL ssLsLssL ssL
sLs LssLssLs LssLssLs sLsLssLs sLsLssLs sLs
LsLssLss LsLssLss Lss
sLssLssL sLs sLssLssL sLssLssL sLssLssL ssL
LssLssLs Lss LssLssLs LssLssLs LssLssLs sLs
ssLssLsL ssL ssLssLsL
sLssLsLs sLs sLssLsLs
LssLsLss Lss LssLsLss
ssLsLssL ssL ssLsLssL
sLsLssLs sLs sLsLssLs
LsLssLss Lss LsLssLss
sLs sLssLssL sLssLssL sLssLssL ssL sLssLssL
Lss LssLssLs LssLssLs LssLssLs sLs LssLssLs
ssL ssLssLsL ssLssLsL
sLs sLssLsLs sLssLsLs sLssLssL sLssLssL sLs
Lss LssLsLss LssLsLss LssLssLs LssLssLs Lss
ssL ssLsLssL ssLsLssL ssLssLsL ssLssLsL ssL

19_07_12_LssLsLss_Lss_LssLsLss.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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