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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>
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| : This revision was by author [[User:spt3125|spt3125]] and made on <tt>2016-08-28 20:54:05 UTC</tt>.<br>
| | [[5L_5s|5L+5s]] |
| : The original revision id was <tt>590307632</tt>.<br>
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| : The revision comment was: <tt></tt><br>
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| The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.<br>
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| <h4>Original Wikitext content:</h4>
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| <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
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| [[5L 5s|5L+5s]] | |
| 10 tones (4+2+4) | | 10 tones (4+2+4) |
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| temperament: [[blackwood]] | | temperament: [[Blackwood|blackwood]] |
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| This scale has some unusual properties: | | This scale has some unusual properties: |
| * it has only two modes
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| * either mode may be split in any of the three possible omnitetrachordal ways (9/8-4/3-4/3, 4/3-9/8-4/3, 4/3-4/3-9/8)
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| * it is its own [[Gallery of omnitetrachordal scales#dual|dual]] (changing all L to s, and vice versa, gives the same scale)
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| * the (imperfect) tunings of 9/8 and 4/3 are independent of L/s ratio
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| See also [[OTC 7L 7s|OTC 7L+7s]] (whitewood) and [[OTC 12L 12s|OTC 12L+12s]] (catler/compton), which have similar properties. | | <ul><li>it has only two modes</li><li>either mode may be split in any of the three possible omnitetrachordal ways (9/8-4/3-4/3, 4/3-9/8-4/3, 4/3-4/3-9/8)</li><li>it is its own [[Gallery_of_omnitetrachordal_scales#dual|dual]] (changing all L to s, and vice versa, gives the same scale)</li><li>the (imperfect) tunings of 9/8 and 4/3 are independent of L/s ratio</li></ul> |
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| | See also [[OTC_7L_7s|OTC 7L+7s]] (whitewood) and [[OTC_12L_12s|OTC 12L+12s]] (catler/compton), which have similar properties. |
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| | [[Gallery_of_omnitetrachordal_scales#perfect|P]] = undefined (or -1?) |
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| [[Gallery of omnitetrachordal scales#perfect|P]] = undefined (or -1?) | | [[Gallery_of_omnitetrachordal_scales#Q|Q]] = 5.6500418817 (4/3 = 2L+2.5s) |
| [[Gallery of omnitetrachordal scales#Q|Q]] = 5.6500418817 (4/3 = 2L+2.5s)
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| L = 120.00 to 240.00 cents (203.91 cents @ Q) | | L = 120.00 to 240.00 cents (203.91 cents @ Q) |
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| s = 0.00 to 120.00 cents (36.09 cents @ Q) | | s = 0.00 to 120.00 cents (36.09 cents @ Q) |
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| 9/8 = L+s (240.00 cents for any L/s) | | 9/8 = L+s (240.00 cents for any L/s) |
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| 4/3 = 2L+2s (480.00 cents for any L/s) | | 4/3 = 2L+2s (480.00 cents for any L/s) |
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| generator = s (0.00 to 120.00 cents) | | generator = s (0.00 to 120.00 cents) |
| [[periods and generators|period]] = 1/5 octave (240.00 cents) | | |
| | [[periods_and_generators|period]] = 1/5 octave (240.00 cents) |
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| notable EDOs: 15, 20, 25 | | notable EDOs: 15, 20, 25 |
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| all modes: | | all modes: |
| || {{ Ls LsLs LsLs }} || {{ LsLs Ls LsLs }} || {{ LsLs LsLs Ls }} ||
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| || {{ sL sLsL sLsL }} || {{ sLsL sL sLsL }} || {{ sLsL sLsL sL }} ||
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| [[image:10_05_05_LsLs_Ls_LsLs.png]] | | {| class="wikitable" |
| | |- |
| | | | <tt> Ls LsLs LsLs </tt> |
| | | | <tt> LsLs Ls LsLs </tt> |
| | | | <tt> LsLs LsLs Ls </tt> |
| | |- |
| | | | <tt> sL sLsL sLsL </tt> |
| | | | <tt> sLsL sL sLsL </tt> |
| | | | <tt> sLsL sLsL sL </tt> |
| | |} |
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| | [[File:10_05_05_LsLs_Ls_LsLs.png|alt=10_05_05_LsLs_Ls_LsLs.png|10_05_05_LsLs_Ls_LsLs.png]] |
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| ===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]]
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| </pre></div> | |
| <h4>Original HTML content:</h4>
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| <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 5L 5s</title></head><body>Omnitetrachordal MOS scale<br />
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| <a class="wiki_link" href="/5L%205s">5L+5s</a><br />
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| 10 tones (4+2+4)<br />
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| <br />
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| temperament: <a class="wiki_link" href="/blackwood">blackwood</a><br />
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| <br />
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| This scale has some unusual properties:<br />
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| <ul><li>it has only two modes</li><li>either mode may be split in any of the three possible omnitetrachordal ways (9/8-4/3-4/3, 4/3-9/8-4/3, 4/3-4/3-9/8)</li><li>it is its own <a class="wiki_link" href="/Gallery%20of%20omnitetrachordal%20scales#dual">dual</a> (changing all L to s, and vice versa, gives the same scale)</li><li>the (imperfect) tunings of 9/8 and 4/3 are independent of L/s ratio</li></ul><br />
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| See also <a class="wiki_link" href="/OTC%207L%207s">OTC 7L+7s</a> (whitewood) and <a class="wiki_link" href="/OTC%2012L%2012s">OTC 12L+12s</a> (catler/compton), which have similar properties.<br />
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| <br />
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| <a class="wiki_link" href="/Gallery%20of%20omnitetrachordal%20scales#perfect">P</a> = undefined (or -1?)<br />
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| <a class="wiki_link" href="/Gallery%20of%20omnitetrachordal%20scales#Q">Q</a> = 5.6500418817 (4/3 = 2L+2.5s)<br />
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| <br />
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| L = 120.00 to 240.00 cents (203.91 cents @ Q)<br />
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| s = 0.00 to 120.00 cents (36.09 cents @ Q)<br />
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| <br />
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| 9/8 = L+s (240.00 cents for any L/s)<br />
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| 4/3 = 2L+2s (480.00 cents for any L/s)<br />
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| generator = s (0.00 to 120.00 cents)<br />
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| <a class="wiki_link" href="/periods%20and%20generators">period</a> = 1/5 octave (240.00 cents)<br />
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| <br />
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| notable EDOs: 15, 20, 25<br />
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| <br />
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| all modes:<br />
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| <table class="wiki_table">
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| <tr>
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| <td><tt> Ls LsLs LsLs </tt><br />
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| </td>
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| <td><tt> LsLs Ls LsLs </tt><br />
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| </td>
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| <td><tt> LsLs LsLs Ls </tt><br />
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| </td>
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| </tr>
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| <tr>
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| <td><tt> sL sLsL sLsL </tt><br />
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| </td>
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| <td><tt> sLsL sL sLsL </tt><br />
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| </td>
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| <td><tt> sLsL sLsL sL </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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| <!-- ws:start:WikiTextLocalImageRule:36:&lt;img src=&quot;/file/view/10_05_05_LsLs_Ls_LsLs.png/589273800/10_05_05_LsLs_Ls_LsLs.png&quot; alt=&quot;&quot; title=&quot;&quot; /&gt; --><img src="/file/view/10_05_05_LsLs_Ls_LsLs.png/589273800/10_05_05_LsLs_Ls_LsLs.png" alt="10_05_05_LsLs_Ls_LsLs.png" title="10_05_05_LsLs_Ls_LsLs.png" /><!-- ws:end:WikiTextLocalImageRule:36 --><br />
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| <br />
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| <!-- ws:start:WikiTextHeadingRule:0:&lt;h3&gt; --><h3 id="toc0"><a name="x--See also"></a><!-- ws:end:WikiTextHeadingRule:0 -->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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Omnitetrachordal MOS scale
5L+5s
10 tones (4+2+4)
temperament: blackwood
This scale has some unusual properties:
- it has only two modes
- either mode may be split in any of the three possible omnitetrachordal ways (9/8-4/3-4/3, 4/3-9/8-4/3, 4/3-4/3-9/8)
- it is its own dual (changing all L to s, and vice versa, gives the same scale)
- the (imperfect) tunings of 9/8 and 4/3 are independent of L/s ratio
See also OTC 7L+7s (whitewood) and OTC 12L+12s (catler/compton), which have similar properties.
P = undefined (or -1?)
Q = 5.6500418817 (4/3 = 2L+2.5s)
L = 120.00 to 240.00 cents (203.91 cents @ Q)
s = 0.00 to 120.00 cents (36.09 cents @ Q)
9/8 = L+s (240.00 cents for any L/s)
4/3 = 2L+2s (480.00 cents for any L/s)
generator = s (0.00 to 120.00 cents)
period = 1/5 octave (240.00 cents)
notable EDOs: 15, 20, 25
all modes:
| Ls LsLs LsLs
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LsLs Ls LsLs
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LsLs LsLs Ls
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| sL sLsL sLsL
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sLsL sL sLsL
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sLsL sLsL sL
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See also
