OTC 12L 5s: 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 20:50:59 UTC</tt>.<br>
[[12L_5s|12L+5s]]
: The original revision id was <tt>590700730</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
[[12L 5s|12L+5s]]
17 tones (7+3+7)
17 tones (7+3+7)


Helmholtz / [[Schismatic family|schismatic]]
Helmholtz / [[Schismatic_family|schismatic]]


[[Gallery of omnitetrachordal scales#perfect|P]] = 3.8459060415 (L=[[256_243|256/243]], s=[[531441_524288|531441/524288]])
[[Gallery_of_omnitetrachordal_scales#perfect|P]] = 3.8459060415 (L=[[256/243|256/243]], s=[[531441/524288|531441/524288]])
[[Gallery of omnitetrachordal scales#Q|Q]] = 29.4213422908 (4/3 = 5L+1.5s)
 
[[Gallery_of_omnitetrachordal_scales#Q|Q]] = 29.4213422908 (4/3 = 5L+1.5s)


L = 70.59 to 100.00 cents (90.22 cents @ P, 98.60 cents @ Q)
L = 70.59 to 100.00 cents (90.22 cents @ P, 98.60 cents @ Q)
s = 0.00 to 70.59 cents (23.46 cents @ P, 3.35 cents @ Q)
s = 0.00 to 70.59 cents (23.46 cents @ P, 3.35 cents @ Q)


9/8 = 2L+s (200.00 to 211.76 cents)
9/8 = 2L+s (200.00 to 211.76 cents)
4/3 = 5L+2s (494.12 to 500.00 cents)
4/3 = 5L+2s (494.12 to 500.00 cents)
generator = 4/3
generator = 4/3


notable EDOs: 29, 41, 46, 53, 65
notable EDOs: 29, 41, 46, 53, 65


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


all modes:
all modes:
|| || {{ LsLLLsL LsL LsLLLsL }} || ||
|| || {{ sLLLsLL sLL sLLLsLL }} || ||
|| || {{ LLLsLLs LLs LLLsLLs }} || ||
|| {{ LLs LLsLLsL LLsLLsL }} || {{ LLsLLsL LsL LLsLLsL }} || ||
|| {{ LsL LsLLsLL LsLLsLL }} || {{ LsLLsLL sLL LsLLsLL }} || ||
|| {{ sLL sLLsLLL sLLsLLL }} || || ||
|| {{ LLs LLsLLLs LLsLLLs }} || || {{ LLsLLsL LLsLLsL LLs }} ||
|| {{ LsL LsLLLsL LsLLLsL }} || || {{ LsLLsLL LsLLsLL LsL }} ||
|| {{ sLL sLLLsLL sLLLsLL }} || || {{ sLLsLLL sLLsLLL sLL }} ||
|| {{ LLs LLLsLLs LLLsLLs }} || || {{ LLsLLLs LLsLLLs LLs }} ||
|| {{ LsL LLsLLsL LLsLLsL }} || || {{ LsLLLsL LsLLLsL LsL }} ||
|| {{ sLL LsLLsLL LsLLsLL }} || || {{ sLLLsLL sLLLsLL sLL }} ||
|| || || {{ LLLsLLs LLLsLLs LLs }} ||
|| || {{ LLsLLsL LLs LLsLLsL }} || {{ LLsLLsL LLsLLsL LsL }} ||
|| || {{ LsLLsLL LsL LsLLsLL }} || {{ LsLLsLL LsLLsLL sLL }} ||
|| || {{ sLLsLLL sLL sLLsLLL }} || ||
|| || {{ LLsLLLs LLs LLsLLLs }} || ||


[[image:17_12_05_LLLsLLs_LLs_LLLsLLs.png]]
{| class="wikitable"
|-
| |
| | <tt> LsLLLsL LsL LsLLLsL </tt>
| |
|-
| |
| | <tt> sLLLsLL sLL sLLLsLL </tt>
| |
|-
| |
| | <tt> LLLsLLs LLs LLLsLLs </tt>
| |
|-
| | <tt> LLs LLsLLsL LLsLLsL </tt>
| | <tt> LLsLLsL LsL LLsLLsL </tt>
| |
|-
| | <tt> LsL LsLLsLL LsLLsLL </tt>
| | <tt> LsLLsLL sLL LsLLsLL </tt>
| |
|-
| | <tt> sLL sLLsLLL sLLsLLL </tt>
| |
| |
|-
| | <tt> LLs LLsLLLs LLsLLLs </tt>
| |
| | <tt> LLsLLsL LLsLLsL LLs </tt>
|-
| | <tt> LsL LsLLLsL LsLLLsL </tt>
| |
| | <tt> LsLLsLL LsLLsLL LsL </tt>
|-
| | <tt> sLL sLLLsLL sLLLsLL </tt>
| |
| | <tt> sLLsLLL sLLsLLL sLL </tt>
|-
| | <tt> LLs LLLsLLs LLLsLLs </tt>
| |
| | <tt> LLsLLLs LLsLLLs LLs </tt>
|-
| | <tt> LsL LLsLLsL LLsLLsL </tt>
| |
| | <tt> LsLLLsL LsLLLsL LsL </tt>
|-
| | <tt> sLL LsLLsLL LsLLsLL </tt>
| |
| | <tt> sLLLsLL sLLLsLL sLL </tt>
|-
| |
| |
| | <tt> LLLsLLs LLLsLLs LLs </tt>
|-
| |
| | <tt> LLsLLsL LLs LLsLLsL </tt>
| | <tt> LLsLLsL LLsLLsL LsL </tt>
|-
| |
| | <tt> LsLLsLL LsL LsLLsLL </tt>
| | <tt> LsLLsLL LsLLsLL sLL </tt>
|-
| |
| | <tt> sLLsLLL sLL sLLsLLL </tt>
| |
|-
| |
| | <tt> LLsLLLs LLs LLsLLLs </tt>
| |
|}
 
[[File:17_12_05_LLLsLLs_LLs_LLLsLLs.png|alt=17_12_05_LLLsLLs_LLs_LLLsLLs.png|17_12_05_LLLsLLs_LLs_LLLsLLs.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>
<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">&lt;html&gt;&lt;head&gt;&lt;title&gt;OTC 12L 5s&lt;/title&gt;&lt;/head&gt;&lt;body&gt;Omnitetrachordal MOS scale&lt;br /&gt;
&lt;a class="wiki_link" href="/12L%205s"&gt;12L+5s&lt;/a&gt;&lt;br /&gt;
17 tones (7+3+7)&lt;br /&gt;
&lt;br /&gt;
Helmholtz / &lt;a class="wiki_link" href="/Schismatic%20family"&gt;schismatic&lt;/a&gt;&lt;br /&gt;
&lt;br /&gt;
&lt;a class="wiki_link" href="/Gallery%20of%20omnitetrachordal%20scales#perfect"&gt;P&lt;/a&gt; = 3.8459060415 (L=&lt;a class="wiki_link" href="/256_243"&gt;256/243&lt;/a&gt;, s=&lt;a class="wiki_link" href="/531441_524288"&gt;531441/524288&lt;/a&gt;)&lt;br /&gt;
&lt;a class="wiki_link" href="/Gallery%20of%20omnitetrachordal%20scales#Q"&gt;Q&lt;/a&gt; = 29.4213422908 (4/3 = 5L+1.5s)&lt;br /&gt;
&lt;br /&gt;
L = 70.59 to 100.00 cents (90.22 cents @ P, 98.60 cents @ Q)&lt;br /&gt;
s = 0.00 to 70.59 cents (23.46 cents @ P, 3.35 cents @ Q)&lt;br /&gt;
&lt;br /&gt;
9/8 = 2L+s (200.00 to 211.76 cents)&lt;br /&gt;
4/3 = 5L+2s (494.12 to 500.00 cents)&lt;br /&gt;
generator = 4/3&lt;br /&gt;
&lt;br /&gt;
notable EDOs: 29, 41, 46, 53, 65&lt;br /&gt;
&lt;br /&gt;
symmetric mode: &lt;tt&gt; LsLLLsLLsLLsLLLsL &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;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;tt&gt; LsLLLsL LsL LsLLLsL &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; sLLLsLL sLL sLLLsLL &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; LLLsLLs LLs LLLsLLs &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; LLs LLsLLsL LLsLLsL &lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;tt&gt; LLsLLsL LsL LLsLLsL &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; LsL LsLLsLL LsLLsLL &lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;tt&gt; LsLLsLL sLL LsLLsLL &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; sLL sLLsLLL sLLsLLL &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; LLs LLsLLLs LLsLLLs &lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;tt&gt; LLsLLsL LLsLLsL LLs &lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;tt&gt; LsL LsLLLsL LsLLLsL &lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;tt&gt; LsLLsLL LsLLsLL LsL &lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;tt&gt; sLL sLLLsLL sLLLsLL &lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;tt&gt; sLLsLLL sLLsLLL sLL &lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;tt&gt; LLs LLLsLLs LLLsLLs &lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;tt&gt; LLsLLLs LLsLLLs LLs &lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;tt&gt; LsL LLsLLsL LLsLLsL &lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;tt&gt; LsLLLsL LsLLLsL LsL &lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;tt&gt; sLL LsLLsLL LsLLsLL &lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;tt&gt; sLLLsLL sLLLsLL sLL &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; LLLsLLs LLLsLLs LLs &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; LLsLLsL LLs LLsLLsL &lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;tt&gt; LLsLLsL LLsLLsL LsL &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; LsLLsLL LsL LsLLsLL &lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;tt&gt; LsLLsLL LsLLsLL sLL &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; sLLsLLL sLL sLLsLLL &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; LLsLLLs LLs LLsLLLs &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:152:&amp;lt;img src=&amp;quot;/file/view/17_12_05_LLLsLLs_LLs_LLLsLLs.png/589273876/17_12_05_LLLsLLs_LLs_LLLsLLs.png&amp;quot; alt=&amp;quot;&amp;quot; title=&amp;quot;&amp;quot; /&amp;gt; --&gt;&lt;img src="/file/view/17_12_05_LLLsLLs_LLs_LLLsLLs.png/589273876/17_12_05_LLLsLLs_LLs_LLLsLLs.png" alt="17_12_05_LLLsLLs_LLs_LLLsLLs.png" title="17_12_05_LLLsLLs_LLs_LLLsLLs.png" /&gt;&lt;!-- ws:end:WikiTextLocalImageRule:152 --&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>

Revision as of 00:00, 17 July 2018

Omnitetrachordal MOS scale

12L+5s

17 tones (7+3+7)

Helmholtz / schismatic

P = 3.8459060415 (L=256/243, s=531441/524288)

Q = 29.4213422908 (4/3 = 5L+1.5s)

L = 70.59 to 100.00 cents (90.22 cents @ P, 98.60 cents @ Q)

s = 0.00 to 70.59 cents (23.46 cents @ P, 3.35 cents @ Q)

9/8 = 2L+s (200.00 to 211.76 cents)

4/3 = 5L+2s (494.12 to 500.00 cents)

generator = 4/3

notable EDOs: 29, 41, 46, 53, 65

symmetric mode: LsLLLsLLsLLsLLLsL

all modes:

LsLLLsL LsL LsLLLsL
sLLLsLL sLL sLLLsLL
LLLsLLs LLs LLLsLLs
LLs LLsLLsL LLsLLsL LLsLLsL LsL LLsLLsL
LsL LsLLsLL LsLLsLL LsLLsLL sLL LsLLsLL
sLL sLLsLLL sLLsLLL
LLs LLsLLLs LLsLLLs LLsLLsL LLsLLsL LLs
LsL LsLLLsL LsLLLsL LsLLsLL LsLLsLL LsL
sLL sLLLsLL sLLLsLL sLLsLLL sLLsLLL sLL
LLs LLLsLLs LLLsLLs LLsLLLs LLsLLLs LLs
LsL LLsLLsL LLsLLsL LsLLLsL LsLLLsL LsL
sLL LsLLsLL LsLLsLL sLLLsLL sLLLsLL sLL
LLLsLLs LLLsLLs LLs
LLsLLsL LLs LLsLLsL LLsLLsL LLsLLsL LsL
LsLLsLL LsL LsLLsLL LsLLsLL LsLLsLL sLL
sLLsLLL sLL sLLsLLL
LLsLLLs LLs LLsLLLs

17_12_05_LLLsLLs_LLs_LLLsLLs.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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