OTC 5L 7s: 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>2016-08-28 21:22:18 UTC</tt>.<br>
[[5L_7s|5L+7s]]
: The original revision id was <tt>590308854</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 7s|5L+7s]]
12 tones (5+2+5)
12 tones (5+2+5)


MOS of the helmholtz / garibaldi / [[Schismatic family|schismatic]] and [[superpyth]] temperaments, as well as Pythagorean.  Very good 3/2 at almost any L/s ratio.  Many modes may be pentachordally split in two ways.  See also [[OTC 7L 5s|OTC 7L+5s]].
MOS of the helmholtz / garibaldi / [[Schismatic_family|schismatic]] and [[Superpyth|superpyth]] temperaments, as well as Pythagorean.  Very good 3/2 at almost any L/s ratio.  Many modes may be pentachordally split in two ways.  See also [[OTC_7L_5s|OTC 7L+5s]].


[[Gallery of omnitetrachordal scales#perfect|P]] = 1.2600167527 (L=[[2187_2048|2187/2048]], s=[[256_243|256/243]])
[[Gallery_of_omnitetrachordal_scales#perfect|P]] = 1.2600167527 (L=[[2187/2048|2187/2048]], s=[[256/243|256/243]])
[[Gallery of omnitetrachordal scales#Q|Q]] = 7.9100586343 (2L+3.5s)
 
[[Gallery_of_omnitetrachordal_scales#Q|Q]] = 7.9100586343 (2L+3.5s)


L = 100.00 to 240.00 cents (113.68 cents @ P, 203.91 cents @ Q)
L = 100.00 to 240.00 cents (113.68 cents @ P, 203.91 cents @ Q)
s = 0.00 to 100.00 cents (90.23 cents @ P, 25.78 cents @ Q)
s = 0.00 to 100.00 cents (90.23 cents @ P, 25.78 cents @ Q)


9/8 = L+s (200.00 to 240.00 cents)
9/8 = L+s (200.00 to 240.00 cents)
4/3 = 2L+3s (480.00 to 500.00 cents)
4/3 = 2L+3s (480.00 to 500.00 cents)
generator = 4/3
generator = 4/3


Line 25: Line 24:


all modes:
all modes:
|| {{ Ls LsLss LsLss }} || || ||
|| {{ sL sLssL sLssL }} || || {{ sLsLs sLsLs sL }} ||
|| {{ Ls LssLs LssLs }} || || {{ LsLss LsLss Ls }} ||
|| {{ sL ssLsL ssLsL }} || || {{ sLssL sLssL sL }} ||
|| {{ Ls sLsLs sLsLs }} || || {{ LssLs LssLs Ls }} ||
|| || || {{ ssLsL ssLsL sL }} ||
|| || {{ sLsLs sL sLsLs }} || {{ sLsLs sLsLs Ls }} ||
|| || {{ LsLss Ls LsLss }} || ||
|| || {{ sLssL sL sLssL }} || ||
|| || {{ LssLs Ls LssLs }} || ||
|| || {{ ssLsL sL ssLsL }} || ||
|| {{ sL sLsLs sLsLs }} || {{ sLsLs Ls sLsLs }} || ||


[[image:12_05_07_sLssL_sL_sLssL.png]]
{| class="wikitable"
|-
| | <tt> Ls LsLss LsLss </tt>
| |
| |
|-
| | <tt> sL sLssL sLssL </tt>
| |
| | <tt> sLsLs sLsLs sL </tt>
|-
| | <tt> Ls LssLs LssLs </tt>
| |
| | <tt> LsLss LsLss Ls </tt>
|-
| | <tt> sL ssLsL ssLsL </tt>
| |
| | <tt> sLssL sLssL sL </tt>
|-
| | <tt> Ls sLsLs sLsLs </tt>
| |
| | <tt> LssLs LssLs Ls </tt>
|-
| |
| |
| | <tt> ssLsL ssLsL sL </tt>
|-
| |
| | <tt> sLsLs sL sLsLs </tt>
| | <tt> sLsLs sLsLs Ls </tt>
|-
| |
| | <tt> LsLss Ls LsLss </tt>
| |
|-
| |
| | <tt> sLssL sL sLssL </tt>
| |
|-
| |
| | <tt> LssLs Ls LssLs </tt>
| |
|-
| |
| | <tt> ssLsL sL ssLsL </tt>
| |
|-
| | <tt> sL sLsLs sLsLs </tt>
| | <tt> sLsLs Ls sLsLs </tt>
| |
|}
 
[[File:12_05_07_sLssL_sL_sLssL.png|alt=12_05_07_sLssL_sL_sLssL.png|12_05_07_sLssL_sL_sLssL.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 5L 7s&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="/5L%207s"&gt;5L+7s&lt;/a&gt;&lt;br /&gt;
[[Category:MODMOS]]
12 tones (5+2+5)&lt;br /&gt;
[[Category:Omnitetrachordal]]
&lt;br /&gt;
[[Category:Helmholtz]]
MOS of the helmholtz / garibaldi / &lt;a class="wiki_link" href="/Schismatic%20family"&gt;schismatic&lt;/a&gt; and &lt;a class="wiki_link" href="/superpyth"&gt;superpyth&lt;/a&gt; temperaments, as well as Pythagorean.  Very good 3/2 at almost any L/s ratio.  Many modes may be pentachordally split in two ways.  See also &lt;a class="wiki_link" href="/OTC%207L%205s"&gt;OTC 7L+5s&lt;/a&gt;.&lt;br /&gt;
[[Category:Garibaldi]]
&lt;br /&gt;
[[Category:Schismatic]]
&lt;a class="wiki_link" href="/Gallery%20of%20omnitetrachordal%20scales#perfect"&gt;P&lt;/a&gt; = 1.2600167527 (L=&lt;a class="wiki_link" href="/2187_2048"&gt;2187/2048&lt;/a&gt;, s=&lt;a class="wiki_link" href="/256_243"&gt;256/243&lt;/a&gt;)&lt;br /&gt;
[[Category:Superpyth]]
&lt;a class="wiki_link" href="/Gallery%20of%20omnitetrachordal%20scales#Q"&gt;Q&lt;/a&gt; = 7.9100586343 (2L+3.5s)&lt;br /&gt;
[[Category:Pythagorean]]
&lt;br /&gt;
L = 100.00 to 240.00 cents (113.68 cents @ P, 203.91 cents @ Q)&lt;br /&gt;
s = 0.00 to 100.00 cents (90.23 cents @ P, 25.78 cents @ Q)&lt;br /&gt;
&lt;br /&gt;
9/8 = L+s (200.00 to 240.00 cents)&lt;br /&gt;
4/3 = 2L+3s (480.00 to 500.00 cents)&lt;br /&gt;
generator = 4/3&lt;br /&gt;
&lt;br /&gt;
notable EDOs: 17, 22, 27, 29, 41, 53, 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;tt&gt; Ls LsLss LsLss &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; sL sLssL sLssL &lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;tt&gt; sLsLs sLsLs sL &lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;tt&gt; Ls LssLs LssLs &lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;tt&gt; LsLss LsLss Ls &lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;tt&gt; sL ssLsL ssLsL &lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;tt&gt; sLssL sLssL sL &lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;tt&gt; Ls sLsLs sLsLs &lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;tt&gt; LssLs LssLs 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;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;tt&gt; ssLsL ssLsL 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; sLsLs sL sLsLs &lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;tt&gt; sLsLs sLsLs 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; LsLss Ls LsLss &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; sLssL sL sLssL &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; LssLs Ls LssLs &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; ssLsL sL ssLsL &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 sLsLs sLsLs &lt;/tt&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;tt&gt; sLsLs Ls sLsLs &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_05_07_sLssL_sL_sLssL.png/589273824/12_05_07_sLssL_sL_sLssL.png&amp;quot; alt=&amp;quot;&amp;quot; title=&amp;quot;&amp;quot; /&amp;gt; --&gt;&lt;img src="/file/view/12_05_07_sLssL_sL_sLssL.png/589273824/12_05_07_sLssL_sL_sLssL.png" alt="12_05_07_sLssL_sL_sLssL.png" title="12_05_07_sLssL_sL_sLssL.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 03:13, 24 June 2025

Omnitetrachordal MOS scale

5L+7s

12 tones (5+2+5)

MOS of the helmholtz / garibaldi / schismatic and superpyth temperaments, as well as Pythagorean. Very good 3/2 at almost any L/s ratio. Many modes may be pentachordally split in two ways. See also OTC 7L+5s.

P = 1.2600167527 (L=2187/2048, s=256/243)

Q = 7.9100586343 (2L+3.5s)

L = 100.00 to 240.00 cents (113.68 cents @ P, 203.91 cents @ Q)

s = 0.00 to 100.00 cents (90.23 cents @ P, 25.78 cents @ Q)

9/8 = L+s (200.00 to 240.00 cents)

4/3 = 2L+3s (480.00 to 500.00 cents)

generator = 4/3

notable EDOs: 17, 22, 27, 29, 41, 53, etc.

all modes:

Ls LsLss LsLss
sL sLssL sLssL sLsLs sLsLs sL
Ls LssLs LssLs LsLss LsLss Ls
sL ssLsL ssLsL sLssL sLssL sL
Ls sLsLs sLsLs LssLs LssLs Ls
ssLsL ssLsL sL
sLsLs sL sLsLs sLsLs sLsLs Ls
LsLss Ls LsLss
sLssL sL sLssL
LssLs Ls LssLs
ssLsL sL ssLsL
sL sLsLs sLsLs sLsLs Ls sLsLs

12_05_07_sLssL_sL_sLssL.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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