OTC 2L 10s: Difference between revisions

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<h2>IMPORTED REVISION FROM WIKISPACES</h2>
Omnitetrachordal MODMOS scales
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 21:12:26 UTC</tt>.<br>
: The original revision id was <tt>590308376</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 MODMOS scales
[[2L 10s|2L+10s]]


This OTC scale pattern has two classes (with different tetrachordal divisions).  Only a few other scales of the form [[OTC 2L ns|2L+ns]] are known to have this property.
[[2L_10s|2L+10s]]


temperaments: [[injera]] ?
This OTC scale pattern has two classes (with different tetrachordal divisions).  Only a few other scales of the form [[OTC_2L_ns|2L+ns]] are known to have this property.


----
temperaments: [[Injera|injera]] ?
 
-----


===Class 1===
===Class 1===
12 tones (5+2+5)
12 tones (5+2+5)


[[Gallery of omnitetrachordal scales#dual|Dual]] of [[OTC 10L 2s|OTC 10L+2s]].  Probably only useful for small values of L/s.
[[Gallery_of_omnitetrachordal_scales#dual|Dual]] of [[OTC_10L_2s|OTC 10L+2s]].  Probably only useful for small values of L/s.


[[Gallery of omnitetrachordal scales#perfect|P]] = 0.8849491924
[[Gallery_of_omnitetrachordal_scales#perfect|P]] = 0.8849491924
[[Gallery of omnitetrachordal scales#Q|Q]] = 3.8274237885 (4/3 = L+3.5s)
 
[[Gallery_of_omnitetrachordal_scales#Q|Q]] = 3.8274237885 (4/3 = L+3.5s)


L = 100.00 to 600.00 cents (260.15 cents @ Q)
L = 100.00 to 600.00 cents (260.15 cents @ Q)
s = 0.00 to 100.00 cents (67.97 cents @ Q)
s = 0.00 to 100.00 cents (67.97 cents @ Q)


9/8 = 2s (0.00 to 200.00 cents)
9/8 = 2s (0.00 to 200.00 cents)
4/3 = L+4s (500.00 to 600.00 cents)
4/3 = L+4s (500.00 to 600.00 cents)
MOS generator = s (0.00 to 100.00 cents)
MOS generator = s (0.00 to 100.00 cents)
MOS period = 1/2 octave (600.00 cents)
MOS period = 1/2 octave (600.00 cents)


notable EDOs: 14, 16, 26, 38
notable EDOs: 14, 16, 26, 38


{{ LsssssLsssss }} (MOS, not OTC)
<tt> LsssssLsssss </tt> (MOS, not OTC)
{{      ||      }}
 
{{ LssssLssssss }} (OTC MODMOS) - gen chains 7,5
<tt>      ||      </tt>
 
<tt> LssssLssssss </tt> (OTC MODMOS) - gen chains 7,5


symmetric modes:
symmetric modes:
{{ sssLssssLsss }}
 
{{ ssLssssssLss }}
<tt> sssLssssLsss </tt>
 
<tt> ssLssssssLss </tt>


all modes:
all modes:
|| || {{ ssLss ss ssLss }} || ||
|| || {{ sLsss ss sLsss }} || ||
|| || {{ Lssss ss Lssss }} || ||
|| {{ ss ssssL ssssL }} || || ||
|| {{ ss sssLs sssLs }} || || ||
|| {{ ss ssLss ssLss }} || || {{ ssssL ssssL ss }} ||
|| {{ ss sLsss sLsss }} || || {{ sssLs sssLs ss }} ||
|| {{ ss Lssss Lssss }} || || {{ ssLss ssLss ss }} ||
|| || || {{ sLsss sLsss ss }} ||
|| || || {{ Lssss Lssss ss }} ||
|| || {{ ssssL ss ssssL }} || ||
|| || {{ sssLs ss sssLs }} || ||


[[image:12_02_10_ssLss_ss_ssLss.png]]
{| class="wikitable"
|-
| |
| | <tt> ssLss ss ssLss </tt>
| |
|-
| |
| | <tt> sLsss ss sLsss </tt>
| |
|-
| |
| | <tt> Lssss ss Lssss </tt>
| |
|-
| | <tt> ss ssssL ssssL </tt>
| |
| |
|-
| | <tt> ss sssLs sssLs </tt>
| |
| |
|-
| | <tt> ss ssLss ssLss </tt>
| |
| | <tt> ssssL ssssL ss </tt>
|-
| | <tt> ss sLsss sLsss </tt>
| |
| | <tt> sssLs sssLs ss </tt>
|-
| | <tt> ss Lssss Lssss </tt>
| |
| | <tt> ssLss ssLss ss </tt>
|-
| |
| |
| | <tt> sLsss sLsss ss </tt>
|-
| |
| |
| | <tt> Lssss Lssss ss </tt>
|-
| |
| | <tt> ssssL ss ssssL </tt>
| |
|-
| |
| | <tt> sssLs ss sssLs </tt>
| |
|}


----
[[File:12_02_10_ssLss_ss_ssLss.png|alt=12_02_10_ssLss_ss_ssLss.png|12_02_10_ssLss_ss_ssLss.png]]
 
-----


===Class 2===
===Class 2===
Line 63: Line 105:


Only works at high values of L/s.
Only works at high values of L/s.
Q<span style="vertical-align: sub;">2</span> = 3.8274237885 (4/3 = L+3.5s)


P = 6.7698983847
P = 6.7698983847
Q = 9.7123729809 (4/3 = L+2.5s)


L = 100.00 to 600.00 cents (345.11 cents @ P, 396.09 cents @ Q)
Q<span style="vertical-align: sub;">1</span> = 9.7123729809 (4/3 = L+2.5s)
s = 0.00 to 100.00 cents (50.98 cents @ P, 40.78 cents @ Q)
 
L = 100.00 to 600.00 cents (260.15 cents @ Q<span style="vertical-align: sub;">2</span>, 345.11 cents @ P, 396.09 cents @ Q<span style="vertical-align: sub;">1</span>)
 
s = 0.00 to 100.00 cents (67.97 cents @ Q<span style="vertical-align: sub;">2</span>, 50.98 cents @ P, 40.78 cents @ Q<span style="vertical-align: sub;">1</span>)


9/8 = 4s (0.00 to 400.00 cents)
9/8 = 4s (0.00 to 400.00 cents)
4/3 = L+3s (400.00 to 600.00 cents)
4/3 = L+3s (400.00 to 600.00 cents)
MOS generator = s (0.00 to 100.00 cents)
MOS generator = s (0.00 to 100.00 cents)
MOS period = 1/2 octave (600.00 cents)
MOS period = 1/2 octave (600.00 cents)


notable EDOs: 20, 22, 24
notable EDOs: 20, 22, 24


{{ LsssssLsssss }} (MOS, not OTC)
<tt> LsssssLsssss </tt> (MOS, not OTC)
{{     | |      }}
{{ LsssLsssssss }} (OTC MODMOS) - gen chains 8,4
 
all modes:
|| || || {{ Lsss Lsss ssss }} ||
|| || {{ sssL ssss sssL }} || ||
|| || {{ ssLs ssss ssLs }} || ||
|| || {{ sLss ssss sLss }} || ||
|| || {{ Lsss ssss Lsss }} || ||
|| {{ ssss sssL sssL }} || || ||
|| {{ ssss ssLs ssLs }} || || ||
|| {{ ssss sLss sLss }} || || ||
|| {{ ssss Lsss Lsss }} || || ||
|| || || {{ sssL sssL ssss }} ||
|| || || {{ ssLs ssLs ssss }} ||
|| || || {{ sLss sLss ssss }} ||


----
<tt>     | |      </tt>


===See also===
<tt> LsssLsssssss </tt> (OTC MODMOS) - gen chains 8,4
* [[Omnitetrachordality]]
* [[Gallery of omnitetrachordal scales]]
</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 2L 10s&lt;/title&gt;&lt;/head&gt;&lt;body&gt;Omnitetrachordal MODMOS scales&lt;br /&gt;
&lt;a class="wiki_link" href="/2L%2010s"&gt;2L+10s&lt;/a&gt;&lt;br /&gt;
&lt;br /&gt;
This OTC scale pattern has two classes (with different tetrachordal divisions).  Only a few other scales of the form &lt;a class="wiki_link" href="/OTC%202L%20ns"&gt;2L+ns&lt;/a&gt; are known to have this property.&lt;br /&gt;
&lt;br /&gt;
temperaments: &lt;a class="wiki_link" href="/injera"&gt;injera&lt;/a&gt; ?&lt;br /&gt;
&lt;br /&gt;
&lt;hr /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:0:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc0"&gt;&lt;a name="x--Class 1"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:0 --&gt;Class 1&lt;/h3&gt;
12 tones (5+2+5)&lt;br /&gt;
&lt;br /&gt;
&lt;a class="wiki_link" href="/Gallery%20of%20omnitetrachordal%20scales#dual"&gt;Dual&lt;/a&gt; of &lt;a class="wiki_link" href="/OTC%2010L%202s"&gt;OTC 10L+2s&lt;/a&gt;.  Probably only useful for small values of L/s.&lt;br /&gt;
&lt;br /&gt;
&lt;a class="wiki_link" href="/Gallery%20of%20omnitetrachordal%20scales#perfect"&gt;P&lt;/a&gt; = 0.8849491924&lt;br /&gt;
&lt;a class="wiki_link" href="/Gallery%20of%20omnitetrachordal%20scales#Q"&gt;Q&lt;/a&gt; = 3.8274237885 (4/3 = L+3.5s)&lt;br /&gt;
&lt;br /&gt;
L = 100.00 to 600.00 cents (260.15 cents @ Q)&lt;br /&gt;
s = 0.00 to 100.00 cents (67.97 cents @ Q)&lt;br /&gt;
&lt;br /&gt;
9/8 = 2s (0.00 to 200.00 cents)&lt;br /&gt;
4/3 = L+4s (500.00 to 600.00 cents)&lt;br /&gt;
MOS generator = s (0.00 to 100.00 cents)&lt;br /&gt;
MOS period = 1/2 octave (600.00 cents)&lt;br /&gt;
&lt;br /&gt;
notable EDOs: 14, 16, 26, 38&lt;br /&gt;
&lt;br /&gt;
&lt;tt&gt; LsssssLsssss &lt;/tt&gt; (MOS, not OTC)&lt;br /&gt;
&lt;tt&gt;      ||      &lt;/tt&gt;&lt;br /&gt;
&lt;tt&gt; LssssLssssss &lt;/tt&gt; (OTC MODMOS) - gen chains 7,5&lt;br /&gt;
&lt;br /&gt;
symmetric modes:&lt;br /&gt;
&lt;tt&gt; sssLssssLsss &lt;/tt&gt;&lt;br /&gt;
&lt;tt&gt; ssLssssssLss &lt;/tt&gt;&lt;br /&gt;
&lt;br /&gt;
all modes:&lt;br /&gt;


all modes:


&lt;table class="wiki_table"&gt;
{| class="wikitable"
    &lt;tr&gt;
|-
        &lt;td&gt;&lt;br /&gt;
| |
&lt;/td&gt;
| |
        &lt;td&gt;&lt;tt&gt; ssLss ss ssLss &lt;/tt&gt;&lt;br /&gt;
| | <tt> Lsss Lsss ssss </tt>
&lt;/td&gt;
|-
        &lt;td&gt;&lt;br /&gt;
| |
&lt;/td&gt;
| | <tt> sssL ssss sssL </tt>
    &lt;/tr&gt;
| |
    &lt;tr&gt;
|-
        &lt;td&gt;&lt;br /&gt;
| |
&lt;/td&gt;
| | <tt> ssLs ssss ssLs </tt>
        &lt;td&gt;&lt;tt&gt; sLsss ss sLsss &lt;/tt&gt;&lt;br /&gt;
| |
&lt;/td&gt;
|-
        &lt;td&gt;&lt;br /&gt;
| |
&lt;/td&gt;
| | <tt> sLss ssss sLss </tt>
    &lt;/tr&gt;
| |
    &lt;tr&gt;
|-
        &lt;td&gt;&lt;br /&gt;
| |
&lt;/td&gt;
| | <tt> Lsss ssss Lsss </tt>
        &lt;td&gt;&lt;tt&gt; Lssss ss Lssss &lt;/tt&gt;&lt;br /&gt;
| |
&lt;/td&gt;
|-
        &lt;td&gt;&lt;br /&gt;
| | <tt> ssss sssL sssL </tt>
&lt;/td&gt;
| |
    &lt;/tr&gt;
| |
    &lt;tr&gt;
|-
        &lt;td&gt;&lt;tt&gt; ss ssssL ssssL &lt;/tt&gt;&lt;br /&gt;
| | <tt> ssss ssLs ssLs </tt>
&lt;/td&gt;
| |
        &lt;td&gt;&lt;br /&gt;
| |
&lt;/td&gt;
|-
        &lt;td&gt;&lt;br /&gt;
| | <tt> ssss sLss sLss </tt>
&lt;/td&gt;
| |
    &lt;/tr&gt;
| |
    &lt;tr&gt;
|-
        &lt;td&gt;&lt;tt&gt; ss sssLs sssLs &lt;/tt&gt;&lt;br /&gt;
| | <tt> ssss Lsss Lsss </tt>
&lt;/td&gt;
| |
        &lt;td&gt;&lt;br /&gt;
| |
&lt;/td&gt;
|-
        &lt;td&gt;&lt;br /&gt;
| |
&lt;/td&gt;
| |
    &lt;/tr&gt;
| | <tt> sssL sssL ssss </tt>
    &lt;tr&gt;
|-
        &lt;td&gt;&lt;tt&gt; ss ssLss ssLss &lt;/tt&gt;&lt;br /&gt;
| |
&lt;/td&gt;
| |
        &lt;td&gt;&lt;br /&gt;
| | <tt> ssLs ssLs ssss </tt>
&lt;/td&gt;
|-
        &lt;td&gt;&lt;tt&gt; ssssL ssssL ss &lt;/tt&gt;&lt;br /&gt;
| |
&lt;/td&gt;
| |
    &lt;/tr&gt;
| | <tt> sLss sLss ssss </tt>
    &lt;tr&gt;
|}
        &lt;td&gt;&lt;tt&gt; ss sLsss sLsss &lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;tt&gt; sssLs sssLs ss &lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;tt&gt; ss Lssss Lssss &lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;tt&gt; ssLss ssLss ss &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; sLsss sLsss ss &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; Lssss Lssss ss &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; ssssL ss ssssL &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; sssLs ss sssLs &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:211:&amp;lt;img src=&amp;quot;/file/view/12_02_10_ssLss_ss_ssLss.png/589273820/12_02_10_ssLss_ss_ssLss.png&amp;quot; alt=&amp;quot;&amp;quot; title=&amp;quot;&amp;quot; /&amp;gt; --&gt;&lt;img src="/file/view/12_02_10_ssLss_ss_ssLss.png/589273820/12_02_10_ssLss_ss_ssLss.png" alt="12_02_10_ssLss_ss_ssLss.png" title="12_02_10_ssLss_ss_ssLss.png" /&gt;&lt;!-- ws:end:WikiTextLocalImageRule:211 --&gt;&lt;br /&gt;
&lt;br /&gt;
&lt;hr /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:2:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc1"&gt;&lt;a name="x--Class 2"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:2 --&gt;Class 2&lt;/h3&gt;
12 tones (4+4+4)&lt;br /&gt;
&lt;br /&gt;
Only works at high values of L/s.&lt;br /&gt;
&lt;br /&gt;
P = 6.7698983847&lt;br /&gt;
Q = 9.7123729809 (4/3 = L+2.5s)&lt;br /&gt;
&lt;br /&gt;
L = 100.00 to 600.00 cents (345.11 cents @ P, 396.09 cents @ Q)&lt;br /&gt;
s = 0.00 to 100.00 cents (50.98 cents @ P, 40.78 cents @ Q)&lt;br /&gt;
&lt;br /&gt;
9/8 = 4s (0.00 to 400.00 cents)&lt;br /&gt;
4/3 = L+3s (400.00 to 600.00 cents)&lt;br /&gt;
MOS generator = s (0.00 to 100.00 cents)&lt;br /&gt;
MOS period = 1/2 octave (600.00 cents)&lt;br /&gt;
&lt;br /&gt;
notable EDOs: 20, 22, 24&lt;br /&gt;
&lt;br /&gt;
&lt;tt&gt; LsssssLsssss &lt;/tt&gt; (MOS, not OTC)&lt;br /&gt;
&lt;tt&gt;     | |      &lt;/tt&gt;&lt;br /&gt;
&lt;tt&gt; LsssLsssssss &lt;/tt&gt; (OTC MODMOS) - gen chains 8,4&lt;br /&gt;
&lt;br /&gt;
all modes:&lt;br /&gt;


 
===See also===
&lt;table class="wiki_table"&gt;
<ul><li>[[Omnitetrachordality|Omnitetrachordality]]</li><li>[[Gallery_of_omnitetrachordal_scales|Gallery of omnitetrachordal scales]]</li></ul>
    &lt;tr&gt;
[[Category:12-tone scales]]
        &lt;td&gt;&lt;br /&gt;
[[Category:Tempered scales]]
&lt;/td&gt;
[[Category:Pages with mostly numerical content]]
        &lt;td&gt;&lt;br /&gt;
[[Category:MODMOS]]
&lt;/td&gt;
[[Category:Omnitetrachordal]]
        &lt;td&gt;&lt;tt&gt; Lsss Lsss ssss &lt;/tt&gt;&lt;br /&gt;
[[Category:Injera]]
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;tt&gt; sssL ssss sssL &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; ssLs ssss ssLs &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; sLss ssss sLss &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; Lsss ssss Lsss &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; ssss sssL sssL &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; ssss ssLs ssLs &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; ssss sLss sLss &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; ssss Lsss Lsss &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;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;tt&gt; sssL sssL ssss &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; ssLs ssLs ssss &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; sLss sLss ssss &lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
&lt;/table&gt;
 
&lt;br /&gt;
&lt;hr /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:4:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc2"&gt;&lt;a name="x--See also"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:4 --&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;/body&gt;&lt;/html&gt;</pre></div>

Latest revision as of 03:07, 24 June 2025

Omnitetrachordal MODMOS scales

2L+10s

This OTC scale pattern has two classes (with different tetrachordal divisions). Only a few other scales of the form 2L+ns are known to have this property.

temperaments: injera ?

Class 1

12 tones (5+2+5)

Dual of OTC 10L+2s. Probably only useful for small values of L/s.

P = 0.8849491924

Q = 3.8274237885 (4/3 = L+3.5s)

L = 100.00 to 600.00 cents (260.15 cents @ Q)

s = 0.00 to 100.00 cents (67.97 cents @ Q)

9/8 = 2s (0.00 to 200.00 cents)

4/3 = L+4s (500.00 to 600.00 cents)

MOS generator = s (0.00 to 100.00 cents)

MOS period = 1/2 octave (600.00 cents)

notable EDOs: 14, 16, 26, 38

LsssssLsssss (MOS, not OTC)

     ||     

LssssLssssss (OTC MODMOS) - gen chains 7,5

symmetric modes:

sssLssssLsss

ssLssssssLss

all modes:

ssLss ss ssLss
sLsss ss sLsss
Lssss ss Lssss
ss ssssL ssssL
ss sssLs sssLs
ss ssLss ssLss ssssL ssssL ss
ss sLsss sLsss sssLs sssLs ss
ss Lssss Lssss ssLss ssLss ss
sLsss sLsss ss
Lssss Lssss ss
ssssL ss ssssL
sssLs ss sssLs

12_02_10_ssLss_ss_ssLss.png

Class 2

12 tones (4+4+4)

Only works at high values of L/s.

Q2 = 3.8274237885 (4/3 = L+3.5s)

P = 6.7698983847

Q1 = 9.7123729809 (4/3 = L+2.5s)

L = 100.00 to 600.00 cents (260.15 cents @ Q2, 345.11 cents @ P, 396.09 cents @ Q1)

s = 0.00 to 100.00 cents (67.97 cents @ Q2, 50.98 cents @ P, 40.78 cents @ Q1)

9/8 = 4s (0.00 to 400.00 cents)

4/3 = L+3s (400.00 to 600.00 cents)

MOS generator = s (0.00 to 100.00 cents)

MOS period = 1/2 octave (600.00 cents)

notable EDOs: 20, 22, 24

LsssssLsssss (MOS, not OTC)

    | |     

LsssLsssssss (OTC MODMOS) - gen chains 8,4

all modes:

Lsss Lsss ssss
sssL ssss sssL
ssLs ssss ssLs
sLss ssss sLss
Lsss ssss Lsss
ssss sssL sssL
ssss ssLs ssLs
ssss sLss sLss
ssss Lsss Lsss
sssL sssL ssss
ssLs ssLs ssss
sLss sLss ssss

See also

Retrieved from "https://en.xen.wiki/index.php?title=OTC_2L_10s&oldid=203239"