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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"><html><head><title>OTC 2L 10s</title></head><body>Omnitetrachordal MODMOS scales<br />
| |
| <a class="wiki_link" href="/2L%2010s">2L+10s</a><br />
| |
| <br />
| |
| This OTC scale pattern has two classes (with different tetrachordal divisions). Only a few other scales of the form <a class="wiki_link" href="/OTC%202L%20ns">2L+ns</a> are known to have this property.<br />
| |
| <br />
| |
| temperaments: <a class="wiki_link" href="/injera">injera</a> ?<br />
| |
| <br />
| |
| <hr />
| |
| <br />
| |
| <!-- ws:start:WikiTextHeadingRule:0:&lt;h3&gt; --><h3 id="toc0"><a name="x--Class 1"></a><!-- ws:end:WikiTextHeadingRule:0 -->Class 1</h3>
| |
| 12 tones (5+2+5)<br />
| |
| <br />
| |
| <a class="wiki_link" href="/Gallery%20of%20omnitetrachordal%20scales#dual">Dual</a> of <a class="wiki_link" href="/OTC%2010L%202s">OTC 10L+2s</a>. Probably only useful for small values of L/s.<br />
| |
| <br />
| |
| <a class="wiki_link" href="/Gallery%20of%20omnitetrachordal%20scales#perfect">P</a> = 0.8849491924<br />
| |
| <a class="wiki_link" href="/Gallery%20of%20omnitetrachordal%20scales#Q">Q</a> = 3.8274237885 (4/3 = L+3.5s)<br />
| |
| <br />
| |
| L = 100.00 to 600.00 cents (260.15 cents @ Q)<br />
| |
| s = 0.00 to 100.00 cents (67.97 cents @ Q)<br />
| |
| <br />
| |
| 9/8 = 2s (0.00 to 200.00 cents)<br />
| |
| 4/3 = L+4s (500.00 to 600.00 cents)<br />
| |
| MOS generator = s (0.00 to 100.00 cents)<br />
| |
| MOS period = 1/2 octave (600.00 cents)<br />
| |
| <br />
| |
| notable EDOs: 14, 16, 26, 38<br />
| |
| <br />
| |
| <tt> LsssssLsssss </tt> (MOS, not OTC)<br />
| |
| <tt> || </tt><br />
| |
| <tt> LssssLssssss </tt> (OTC MODMOS) - gen chains 7,5<br />
| |
| <br />
| |
| symmetric modes:<br />
| |
| <tt> sssLssssLsss </tt><br />
| |
| <tt> ssLssssssLss </tt><br />
| |
| <br />
| |
| all modes:<br />
| |
|
| |
|
| | all modes: |
|
| |
|
| <table class="wiki_table">
| | {| class="wikitable" |
| <tr>
| | |- |
| <td><br />
| | | | |
| </td>
| | | | |
| <td><tt> ssLss ss ssLss </tt><br />
| | | | <tt> Lsss Lsss ssss </tt> |
| </td>
| | |- |
| <td><br />
| | | | |
| </td>
| | | | <tt> sssL ssss sssL </tt> |
| </tr>
| | | | |
| <tr>
| | |- |
| <td><br />
| | | | |
| </td>
| | | | <tt> ssLs ssss ssLs </tt> |
| <td><tt> sLsss ss sLsss </tt><br />
| | | | |
| </td>
| | |- |
| <td><br />
| | | | |
| </td>
| | | | <tt> sLss ssss sLss </tt> |
| </tr>
| | | | |
| <tr>
| | |- |
| <td><br />
| | | | |
| </td>
| | | | <tt> Lsss ssss Lsss </tt> |
| <td><tt> Lssss ss Lssss </tt><br />
| | | | |
| </td>
| | |- |
| <td><br />
| | | | <tt> ssss sssL sssL </tt> |
| </td>
| | | | |
| </tr>
| | | | |
| <tr>
| | |- |
| <td><tt> ss ssssL ssssL </tt><br />
| | | | <tt> ssss ssLs ssLs </tt> |
| </td>
| | | | |
| <td><br />
| | | | |
| </td>
| | |- |
| <td><br />
| | | | <tt> ssss sLss sLss </tt> |
| </td>
| | | | |
| </tr>
| | | | |
| <tr>
| | |- |
| <td><tt> ss sssLs sssLs </tt><br />
| | | | <tt> ssss Lsss Lsss </tt> |
| </td>
| | | | |
| <td><br />
| | | | |
| </td>
| | |- |
| <td><br />
| | | | |
| </td>
| | | | |
| </tr>
| | | | <tt> sssL sssL ssss </tt> |
| <tr>
| | |- |
| <td><tt> ss ssLss ssLss </tt><br />
| | | | |
| </td>
| | | | |
| <td><br />
| | | | <tt> ssLs ssLs ssss </tt> |
| </td>
| | |- |
| <td><tt> ssssL ssssL ss </tt><br />
| | | | |
| </td>
| | | | |
| </tr>
| | | | <tt> sLss sLss ssss </tt> |
| <tr>
| | |} |
| <td><tt> ss sLsss sLsss </tt><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><tt> sssLs sssLs ss </tt><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><tt> ss Lssss Lssss </tt><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><tt> ssLss ssLss ss </tt><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><tt> sLsss sLsss ss </tt><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><tt> Lssss Lssss ss </tt><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><br />
| |
| </td>
| |
| <td><tt> ssssL ss ssssL </tt><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><br />
| |
| </td>
| |
| <td><tt> sssLs ss sssLs </tt><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| </tr>
| |
| </table>
| |
|
| |
|
| <br />
| | ----- |
| <!-- ws:start:WikiTextLocalImageRule:211:&lt;img src=&quot;/file/view/12_02_10_ssLss_ss_ssLss.png/589273820/12_02_10_ssLss_ss_ssLss.png&quot; alt=&quot;&quot; title=&quot;&quot; /&gt; --><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" /><!-- ws:end:WikiTextLocalImageRule:211 --><br />
| |
| <br />
| |
| <hr />
| |
| <br />
| |
| <!-- ws:start:WikiTextHeadingRule:2:&lt;h3&gt; --><h3 id="toc1"><a name="x--Class 2"></a><!-- ws:end:WikiTextHeadingRule:2 -->Class 2</h3>
| |
| 12 tones (4+4+4)<br />
| |
| <br />
| |
| Only works at high values of L/s.<br />
| |
| <br />
| |
| P = 6.7698983847<br />
| |
| Q = 9.7123729809 (4/3 = L+2.5s)<br />
| |
| <br />
| |
| L = 100.00 to 600.00 cents (345.11 cents @ P, 396.09 cents @ Q)<br />
| |
| s = 0.00 to 100.00 cents (50.98 cents @ P, 40.78 cents @ Q)<br />
| |
| <br />
| |
| 9/8 = 4s (0.00 to 400.00 cents)<br />
| |
| 4/3 = L+3s (400.00 to 600.00 cents)<br />
| |
| MOS generator = s (0.00 to 100.00 cents)<br />
| |
| MOS period = 1/2 octave (600.00 cents)<br />
| |
| <br />
| |
| notable EDOs: 20, 22, 24<br />
| |
| <br />
| |
| <tt> LsssssLsssss </tt> (MOS, not OTC)<br />
| |
| <tt> | | </tt><br />
| |
| <tt> LsssLsssssss </tt> (OTC MODMOS) - gen chains 8,4<br />
| |
| <br />
| |
| all modes:<br />
| |
|
| |
|
| | | ===See also=== |
| <table class="wiki_table">
| | <ul><li>[[Omnitetrachordality|Omnitetrachordality]]</li><li>[[Gallery_of_omnitetrachordal_scales|Gallery of omnitetrachordal scales]]</li></ul> |
| <tr>
| | [[Category:12-tone scales]] |
| <td><br />
| | [[Category:Tempered scales]] |
| </td>
| | [[Category:Pages with mostly numerical content]] |
| <td><br />
| | [[Category:MODMOS]] |
| </td>
| | [[Category:Omnitetrachordal]] |
| <td><tt> Lsss Lsss ssss </tt><br />
| | [[Category:Injera]] |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><br />
| |
| </td>
| |
| <td><tt> sssL ssss sssL </tt><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><br />
| |
| </td>
| |
| <td><tt> ssLs ssss ssLs </tt><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><br />
| |
| </td>
| |
| <td><tt> sLss ssss sLss </tt><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><br />
| |
| </td>
| |
| <td><tt> Lsss ssss Lsss </tt><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><tt> ssss sssL sssL </tt><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><tt> ssss ssLs ssLs </tt><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><tt> ssss sLss sLss </tt><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><tt> ssss Lsss Lsss </tt><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><tt> sssL sssL ssss </tt><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><tt> ssLs ssLs ssss </tt><br />
| |
| </td>
| |
| </tr>
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| <tr>
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| <td><br />
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| </td>
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| <td><br />
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| </td>
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| <td><tt> sLss sLss ssss </tt><br />
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| </td>
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| </tr>
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| </table>
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| <br />
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| <hr />
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| <br />
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| <!-- ws:start:WikiTextHeadingRule:4:&lt;h3&gt; --><h3 id="toc2"><a name="x--See also"></a><!-- ws:end:WikiTextHeadingRule:4 -->See also</h3>
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| <ul><li><a class="wiki_link" href="/Omnitetrachordality">Omnitetrachordality</a></li><li><a class="wiki_link" href="/Gallery%20of%20omnitetrachordal%20scales">Gallery of omnitetrachordal scales</a></li></ul></body></html></pre></div>
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