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| <h2>IMPORTED REVISION FROM WIKISPACES</h2>
| | '''Omnitetrachordal scales of the form 2L+''n''s -- a special case?''' |
| 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:JosephRuhf|JosephRuhf]] and made on <tt>2016-11-04 08:12:49 UTC</tt>.<br>
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| : The original revision id was <tt>598358394</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 scales of the form 2L+//n//s -- a special case?**
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| An OTC scale of this form (example: LssssLsssssss) has been confirmed for every scale size from 3 to 53 (except 4), and probably exists for any larger scale size as well. With the exception of the 3-, 5-, and 7-note scales, these patterns are not MOS. | | An OTC scale of this form (example: LssssLsssssss) has been confirmed for every scale size from 3 to 53 (except 4), and probably exists for any larger scale size as well. With the exception of the 3-, 5-, and 7-note scales, these patterns are not MOS. |
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| In every case so far studied, the strings of 's' steps come in a small group and a large group. Let x be the number of 's' steps in the small group, and y the number of 's' steps in the large group. Then: | | In every case so far studied, the strings of 's' steps come in a small group and a large group. Let x be the number of 's' steps in the small group, and y the number of 's' steps in the large group. Then: |
| * 9/8 = (y-x)s
| | |
| * 4/3 = L+xs
| | <ul><li>9/8 = (y-x)s</li><li>4/3 = L+xs</li><li>3/2 = L+ys</li><li>If either x or y is odd, the scale has a symmetric mode (ex. sLsLs).</li><li>If both x and y are odd, there are two symmetric modes (ex. sLssssLs and ssLssLss).</li><li>If both x and y are even, no symmetric mode exists (ex. LsLsss).</li></ul> |
| * 3/2 = L+ys
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| * If either x or y is odd, the scale has a symmetric mode (ex. sLsLs).
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| * If both x and y are odd, there are two symmetric modes (ex. sLssssLs and ssLssLss).
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| * If both x and y are even, no symmetric mode exists (ex. LsLsss).
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| As scale size increases: | | As scale size increases: |
| * y/x appears to converge on a value around 0.6 .
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| * For odd size scales, the generator is large (at least 4/3 = 498 cents), and appears to approach sqrt(2) = 600 cents.
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| * For even size scales, the period is 1/2 octave, and the generator is small, and appears to approach 1/1 = 0 cents.
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|
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| Note the patterns in values of [[Gallery of omnitetrachordal scales#perfect|P]]:
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| * P(3) = P(5)+1 = P(7)+2
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| * P(6) = P(8)+1 = P(10)+2 = P(12a)+3
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| * P(9) = P(11)+1 = P(13)+2 = P(15)+3 = P(17)+4
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| * P(12b) = P(14)+1 = P(16)+2 = P(18)+3 = P(20)+4 = P(22)+5
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| * P(19) = P(21)+1 = P(23)+2 = P(25)+3 = P(27)+4 = P(29)+5
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| * etc.
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| These groups appear to share generators and temperaments.
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|
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|
| For some scale sizes (12, 17, 22, 29, 34, 41, 46, 53, and possibly others), more than one class of OTC scale is possible! In such cases, the two will have different tetrachordal divisions (i.e. representing 4/3 with different numbers of steps). One version will have P very near 1, and the other will have a much higher value of P. Note that these scale sizes tend to correspond to [[EDO]]s that represent 4/3 and 3/2 with relatively high accuracy. | | <ul><li>y/x appears to converge on a value around 0.6 .</li><li>For odd size scales, the generator is large (at least 4/3 = 498 cents), and appears to approach sqrt(2) = 600 cents.</li><li>For even size scales, the period is 1/2 octave, and the generator is small, and appears to approach 1/1 = 0 cents.</li></ul> |
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| || **size** ||= **2L+_s** ||= **P** || **pattern** ||
| | Note the patterns in values of [[Gallery_of_omnitetrachordal_scales#perfect|P]]: |
| || 3 ||= 2L+s ||= 2.4424745962 || {{L s L}} (MOS) ||
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| || 5 ||= [[OTC 2L 3s|2L+3s]] ||= 1.4424745962 || {{Ls s Ls}} (MOS) ||
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| || 6 ||= 2L+4s ||= 3.8849491924 || {{Ls ss Ls}} ||
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| || 7 ||= [[OTC 2L 5s|2L+5s]] ||= 0.4424745962 || {{Lss s Lss}} (MOS) ||
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| || 8 ||= 2L+6s ||= 2.8849491924 || {{Lss ss Lss}} ||
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| || 9 ||= 2L+7s ||= 5.3274237885 || {{Lss sss Lss}} ||
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| || 10 ||= [[OTC 2L 8s|2L+8s]] ||= 1.8849491924 || {{Lsss ss Lsss}} ||
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| || 11 ||= 2L+9s ||= 4.3274237885 || {{Lsss sss Lsss}} ||
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| || 12a ||= [[OTC 2L 10s|2L+10s]] ||= 0.8849491924 || {{Lssss ss Lssss}} ||
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| || 12b ||= [[OTC 2L 10s|2L+10s]] ||= 6.7698983847 || {{Lsss ssss Lsss}} ||
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| || 13 ||= 2L+11s ||= 3.3274237885 || {{Lssss sss Lssss}} ||
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| || 14 ||= 2L+12s ||= 5.7698983847 || {{Lssss ssss Lssss}} ||
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| || 15 ||= 2L+13s ||= 2.3274237885 || {{Lsssss sss Lsssss}} ||
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| || 16 ||= 2L+14s ||= 4.7698983847 || {{Lsssss ssss Lsssss}} ||
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| || 17a ||= 2L+15s ||= 1.3274237885 || {{Lssssss sss Lssssss}} ||
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| || 17b ||= 2L+15s ||= 7.2123729809 || {{Lsssss sssss Lsssss}} ||
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| || 18 ||= 2L+16s ||= 3.7698983847 || {{Lssssss ssss Lssssss}} ||
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| || 19 ||= 2L+17s ||= 6.2123729809 || {{Lssssss sssss Lssssss}} ||
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| || 20 ||= 2L+18s ||= 2.7698983847 || {{Lsssssss ssss Lsssssss}} ||
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| || 21 ||= 2L+19s ||= 5.2123729809 || {{Lsssssss sssss Lsssssss}} ||
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| || 22a ||= 2L+20s ||= 1.7698983847 || {{Lssssssss ssss Lssssssss}} ||
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| || 22b ||= 2L+20s ||= 7.6548475771 || {{Lsssssss ssssss Lsssssss}} ||
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| || 23 ||= 2L+21s ||= 4.2123729809 || {{Lssssssss sssss Lssssssss}} ||
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| || 24 ||= 2L+22s ||= 6.6548475771 || {{Lssssssss ssssss Lssssssss}} ||
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| || 25 ||= 2L+23s ||= 3.2123729809 || {{Lsssssssss sssss Lsssssssss}} ||
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| || 26 ||= 2L+24s ||= 5.6548475771 || {{Lsssssssss ssssss Lsssssssss}} ||
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| || 27 ||= 2L+25s ||= 2.2123729809 || {{Lssssssssss sssss Lssssssssss}} ||
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| || 28 ||= 2L+26s ||= 4.6548475771 || {{Lssssssssss ssssss Lssssssssss}} ||
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| || 29a ||= 2L+27s ||= 1.2123729809 || {{Lsssssssssss sssss Lsssssssssss}} ||
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| || 29b ||= 2L+27s ||= 7.0973221733 || {{Lssssssssss sssssss Lssssssssss}} ||
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| || 30 ||= 2L+28s ||= 3.6548475771 || {{Lsssssssssss ssssss Lsssssssssss}} ||
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| || 31 ||= 2L+29s ||= 6.0973221733 || {{Lsssssssssss sssssss Lsssssssssss}} ||
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| || 32 ||= 2L+30s ||= 2.6548475771 || {{Lssssssssssss ssssss Lssssssssssss}} ||
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| || 33 ||= 2L+31s ||= 5.0973221733 || {{Lssssssssssss sssssss Lssssssssssss}} ||
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| || 34a ||= 2L+32s ||= 1.6548475771 || {{Lsssssssssssss ssssss Lsssssssssssss}} ||
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| || 34b ||= 2L+32s ||= 6.5397967694 || {{Lssssssssssss ssssssss Lssssssssssss}} ||
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| || 35 ||= 2L+33s ||= 4.0973221733 || {{Lsssssssssssss sssssss Lsssssssssssss}} ||
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| || 36 ||= 2L+34s ||= 6.5397967694 || {{Lsssssssssssss ssssssss Lsssssssssssss}} ||
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| || 37 ||= 2L+35s ||= 3.0973221733 || {{Lssssssssssssss sssssss Lssssssssssssss}} ||
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| || 38 ||= 2L+36s ||= 5.5397967694 || {{Lssssssssssssss ssssssss Lssssssssssssss}} ||
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| || 39 ||= 2L+37s ||= 2.0973221733 || {{Lsssssssssssssss sssssss Lsssssssssssssss}} ||
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| || 40 ||= 2L+38s ||= 4.5397967694 || {{Lsssssssssssssss ssssssss Lsssssssssssssss}} ||
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| || 41a ||= 2L+39s ||= 1.0973221733 || {{Lssssssssssssssss sssssss Lssssssssssssssss}} ||
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| || 41b ||= 2L+39s ||= 6.9822713656 || {{Lsssssssssssssss sssssssss Lsssssssssssssss}} ||
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| || 42 ||= 2L+40s ||= 3.5397967694 || {{Lssssssssssssssss ssssssss Lssssssssssssssss}} ||
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| || 43 ||= 2L+41s ||= 5.9822713656 || {{Lssssssssssssssss sssssssss Lssssssssssssssss}} ||
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| || 44 ||= 2L+42s ||= 2.5397967694 || {{Lsssssssssssssssss ssssssss Lsssssssssssssssss}} ||
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| || 45 ||= 2L+43s ||= 4.9822713656 || {{Lsssssssssssssssss sssssssss Lsssssssssssssssss}} ||
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| || 46a ||= 2L+44s ||= 1.5397967694 || {{Lssssssssssssssssss ssssssss Lssssssssssssssssss}} ||
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| || 46b ||= 2L+44s ||= 7.4247459618 || {{Lsssssssssssssssss ssssssssss Lsssssssssssssssss}} ||
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| || 47 ||= 2L+45s ||= 3.9822713656 || {{Lssssssssssssssssss sssssssss Lssssssssssssssssss}} ||
| |
| || 48 ||= 2L+46s ||= 6.4247459618 || {{Lssssssssssssssssss ssssssssss Lssssssssssssssssss}} ||
| |
| || 49 ||= 2L+47s ||= 2.9822713656 || {{Lsssssssssssssssssss sssssssss Lsssssssssssssssssss}} ||
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| || 50 ||= 2L+48s ||= 5.4247459618 || {{Lsssssssssssssssssss ssssssssss Lsssssssssssssssssss}} ||
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| || 51 ||= 2L+49s ||= 1.9822713656 || {{Lssssssssssssssssssss sssssssss Lssssssssssssssssssss}} ||
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| || 52 ||= 2L+50s ||= 4.4247459618 || {{Lssssssssssssssssssss ssssssssss Lssssssssssssssssssss}} ||
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| || 53a ||= 2L+51s ||= 0.9822713656 || {{Lsssssssssssssssssssss sssssssss Lsssssssssssssssssssss}} ||
| |
| || 53b ||= 2L+51s ||= 6.8672205580 || {{Lssssssssssssssssssss sssssssssss Lssssssssssssssssssss}} ||
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| etc.
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|
| ===See also===
| | <ul><li>P(3) = P(5)+1 = P(7)+2</li><li>P(6) = P(8)+1 = P(10)+2 = P(12a)+3</li><li>P(9) = P(11)+1 = P(13)+2 = P(15)+3 = P(17)+4</li><li>P(12b) = P(14)+1 = P(16)+2 = P(18)+3 = P(20)+4 = P(22)+5</li><li>P(19) = P(21)+1 = P(23)+2 = P(25)+3 = P(27)+4 = P(29)+5</li><li>etc.</li></ul>These groups appear to share generators and temperaments. |
| * [[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 ns</title></head><body><strong>Omnitetrachordal scales of the form 2L+<em>n</em>s -- a special case?</strong><br />
| |
| <br />
| |
| An OTC scale of this form (example: LssssLsssssss) has been confirmed for every scale size from 3 to 53 (except 4), and probably exists for any larger scale size as well. With the exception of the 3-, 5-, and 7-note scales, these patterns are not MOS.<br />
| |
| <br />
| |
| In every case so far studied, the strings of 's' steps come in a small group and a large group. Let x be the number of 's' steps in the small group, and y the number of 's' steps in the large group. Then:<br />
| |
| <ul><li>9/8 = (y-x)s</li><li>4/3 = L+xs</li><li>3/2 = L+ys</li><li>If either x or y is odd, the scale has a symmetric mode (ex. sLsLs).</li><li>If both x and y are odd, there are two symmetric modes (ex. sLssssLs and ssLssLss).</li><li>If both x and y are even, no symmetric mode exists (ex. LsLsss).</li></ul><br />
| |
| As scale size increases:<br />
| |
| <ul><li>y/x appears to converge on a value around 0.6 .</li><li>For odd size scales, the generator is large (at least 4/3 = 498 cents), and appears to approach sqrt(2) = 600 cents.</li><li>For even size scales, the period is 1/2 octave, and the generator is small, and appears to approach 1/1 = 0 cents.</li></ul><br />
| |
| Note the patterns in values of <a class="wiki_link" href="/Gallery%20of%20omnitetrachordal%20scales#perfect">P</a>:<br />
| |
| <ul><li>P(3) = P(5)+1 = P(7)+2</li><li>P(6) = P(8)+1 = P(10)+2 = P(12a)+3</li><li>P(9) = P(11)+1 = P(13)+2 = P(15)+3 = P(17)+4</li><li>P(12b) = P(14)+1 = P(16)+2 = P(18)+3 = P(20)+4 = P(22)+5</li><li>P(19) = P(21)+1 = P(23)+2 = P(25)+3 = P(27)+4 = P(29)+5</li><li>etc.</li></ul>These groups appear to share generators and temperaments.<br />
| |
| <br />
| |
| For some scale sizes (12, 17, 22, 29, 34, 41, 46, 53, and possibly others), more than one class of OTC scale is possible! In such cases, the two will have different tetrachordal divisions (i.e. representing 4/3 with different numbers of steps). One version will have P very near 1, and the other will have a much higher value of P. Note that these scale sizes tend to correspond to <a class="wiki_link" href="/EDO">EDO</a>s that represent 4/3 and 3/2 with relatively high accuracy.<br />
| |
| <br />
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|
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|
| | For some scale sizes (12, 17, 22, 29, 34, 41, 46, 53, and possibly others), more than one class of OTC scale is possible! In such cases, the two will have different tetrachordal divisions (i.e. representing 4/3 with different numbers of steps). One version will have P very near 1, and the other will have a much higher value of P. Note that these scale sizes tend to correspond to [[EDO|EDO]]s that represent 4/3 and 3/2 with relatively high accuracy. |
|
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|
| <table class="wiki_table">
| | {| class="wikitable" |
| <tr>
| | |- |
| <td><strong>size</strong><br />
| | | | '''size''' |
| </td>
| | | style="text-align:center;" | '''2L+_s''' |
| <td style="text-align: center;"><strong>2L+_s</strong><br />
| | | style="text-align:center;" | '''P''' |
| </td>
| | | | '''pattern''' |
| <td style="text-align: center;"><strong>P</strong><br />
| | |- |
| </td>
| | | | 3 |
| <td><strong>pattern</strong><br />
| | | style="text-align:center;" | 2L+s |
| </td>
| | | style="text-align:center;" | 2.4424745962 |
| </tr>
| | | | <tt>L s L</tt> (MOS) |
| <tr>
| | |- |
| <td>3<br />
| | | | 5 |
| </td>
| | | style="text-align:center;" | [[OTC_2L_3s|2L+3s]] |
| <td style="text-align: center;">2L+s<br />
| | | style="text-align:center;" | 1.4424745962 |
| </td>
| | | | <tt>Ls s Ls</tt> (MOS) |
| <td style="text-align: center;">2.4424745962<br />
| | |- |
| </td>
| | | | 6 |
| <td><tt>L s L</tt> (MOS)<br />
| | | style="text-align:center;" | 2L+4s |
| </td>
| | | style="text-align:center;" | 3.8849491924 |
| </tr>
| | | | <tt>Ls ss Ls</tt> |
| <tr>
| | |- |
| <td>5<br />
| | | | 7 |
| </td>
| | | style="text-align:center;" | [[OTC_2L_5s|2L+5s]] |
| <td style="text-align: center;"><a class="wiki_link" href="/OTC%202L%203s">2L+3s</a><br />
| | | style="text-align:center;" | 0.4424745962 |
| </td>
| | | | <tt>Lss s Lss</tt> (MOS) |
| <td style="text-align: center;">1.4424745962<br />
| | |- |
| </td>
| | | | 8 |
| <td><tt>Ls s Ls</tt> (MOS)<br />
| | | style="text-align:center;" | 2L+6s |
| </td>
| | | style="text-align:center;" | 2.8849491924 |
| </tr>
| | | | <tt>Lss ss Lss</tt> |
| <tr>
| | |- |
| <td>6<br />
| | | | 9 |
| </td>
| | | style="text-align:center;" | 2L+7s |
| <td style="text-align: center;">2L+4s<br />
| | | style="text-align:center;" | 5.3274237885 |
| </td>
| | | | <tt>Lss sss Lss</tt> |
| <td style="text-align: center;">3.8849491924<br />
| | |- |
| </td>
| | | | 10 |
| <td><tt>Ls ss Ls</tt><br />
| | | style="text-align:center;" | [[OTC_2L_8s|2L+8s]] |
| </td>
| | | style="text-align:center;" | 1.8849491924 |
| </tr>
| | | | <tt>Lsss ss Lsss</tt> |
| <tr>
| | |- |
| <td>7<br />
| | | | 11 |
| </td>
| | | style="text-align:center;" | 2L+9s |
| <td style="text-align: center;"><a class="wiki_link" href="/OTC%202L%205s">2L+5s</a><br />
| | | style="text-align:center;" | 4.3274237885 |
| </td>
| | | | <tt>Lsss sss Lsss</tt> |
| <td style="text-align: center;">0.4424745962<br />
| | |- |
| </td>
| | | | 12a |
| <td><tt>Lss s Lss</tt> (MOS)<br />
| | | style="text-align:center;" | [[OTC_2L_10s|2L+10s]] |
| </td>
| | | style="text-align:center;" | 0.8849491924 |
| </tr>
| | | | <tt>Lssss ss Lssss</tt> |
| <tr>
| | |- |
| <td>8<br />
| | | | 12b |
| </td>
| | | style="text-align:center;" | [[OTC_2L_10s|2L+10s]] |
| <td style="text-align: center;">2L+6s<br />
| | | style="text-align:center;" | 6.7698983847 |
| </td>
| | | | <tt>Lsss ssss Lsss</tt> |
| <td style="text-align: center;">2.8849491924<br />
| | |- |
| </td>
| | | | 13 |
| <td><tt>Lss ss Lss</tt><br />
| | | style="text-align:center;" | 2L+11s |
| </td>
| | | style="text-align:center;" | 3.3274237885 |
| </tr>
| | | | <tt>Lssss sss Lssss</tt> |
| <tr>
| | |- |
| <td>9<br />
| | | | 14 |
| </td>
| | | style="text-align:center;" | 2L+12s |
| <td style="text-align: center;">2L+7s<br />
| | | style="text-align:center;" | 5.7698983847 |
| </td>
| | | | <tt>Lssss ssss Lssss</tt> |
| <td style="text-align: center;">5.3274237885<br />
| | |- |
| </td>
| | | | 15 |
| <td><tt>Lss sss Lss</tt><br />
| | | style="text-align:center;" | 2L+13s |
| </td>
| | | style="text-align:center;" | 2.3274237885 |
| </tr>
| | | | <tt>Lsssss sss Lsssss</tt> |
| <tr>
| | |- |
| <td>10<br />
| | | | 16 |
| </td>
| | | style="text-align:center;" | 2L+14s |
| <td style="text-align: center;"><a class="wiki_link" href="/OTC%202L%208s">2L+8s</a><br />
| | | style="text-align:center;" | 4.7698983847 |
| </td>
| | | | <tt>Lsssss ssss Lsssss</tt> |
| <td style="text-align: center;">1.8849491924<br />
| | |- |
| </td>
| | | | 17a |
| <td><tt>Lsss ss Lsss</tt><br />
| | | style="text-align:center;" | 2L+15s |
| </td>
| | | style="text-align:center;" | 1.3274237885 |
| </tr>
| | | | <tt>Lssssss sss Lssssss</tt> |
| <tr>
| | |- |
| <td>11<br />
| | | | 17b |
| </td>
| | | style="text-align:center;" | 2L+15s |
| <td style="text-align: center;">2L+9s<br />
| | | style="text-align:center;" | 7.2123729809 |
| </td>
| | | | <tt>Lsssss sssss Lsssss</tt> |
| <td style="text-align: center;">4.3274237885<br />
| | |- |
| </td>
| | | | 18 |
| <td><tt>Lsss sss Lsss</tt><br />
| | | style="text-align:center;" | 2L+16s |
| </td>
| | | style="text-align:center;" | 3.7698983847 |
| </tr>
| | | | <tt>Lssssss ssss Lssssss</tt> |
| <tr>
| | |- |
| <td>12a<br />
| | | | 19 |
| </td>
| | | style="text-align:center;" | 2L+17s |
| <td style="text-align: center;"><a class="wiki_link" href="/OTC%202L%2010s">2L+10s</a><br />
| | | style="text-align:center;" | 6.2123729809 |
| </td>
| | | | <tt>Lssssss sssss Lssssss</tt> |
| <td style="text-align: center;">0.8849491924<br />
| | |- |
| </td>
| | | | 20 |
| <td><tt>Lssss ss Lssss</tt><br />
| | | style="text-align:center;" | 2L+18s |
| </td>
| | | style="text-align:center;" | 2.7698983847 |
| </tr>
| | | | <tt>Lsssssss ssss Lsssssss</tt> |
| <tr>
| | |- |
| <td>12b<br />
| | | | 21 |
| </td>
| | | style="text-align:center;" | 2L+19s |
| <td style="text-align: center;"><a class="wiki_link" href="/OTC%202L%2010s">2L+10s</a><br />
| | | style="text-align:center;" | 5.2123729809 |
| </td>
| | | | <tt>Lsssssss sssss Lsssssss</tt> |
| <td style="text-align: center;">6.7698983847<br />
| | |- |
| </td>
| | | | 22a |
| <td><tt>Lsss ssss Lsss</tt><br />
| | | style="text-align:center;" | 2L+20s |
| </td>
| | | style="text-align:center;" | 1.7698983847 |
| </tr>
| | | | <tt>Lssssssss ssss Lssssssss</tt> |
| <tr>
| | |- |
| <td>13<br />
| | | | 22b |
| </td>
| | | style="text-align:center;" | 2L+20s |
| <td style="text-align: center;">2L+11s<br />
| | | style="text-align:center;" | 7.6548475771 |
| </td>
| | | | <tt>Lsssssss ssssss Lsssssss</tt> |
| <td style="text-align: center;">3.3274237885<br />
| | |- |
| </td>
| | | | 23 |
| <td><tt>Lssss sss Lssss</tt><br />
| | | style="text-align:center;" | 2L+21s |
| </td>
| | | style="text-align:center;" | 4.2123729809 |
| </tr>
| | | | <tt>Lssssssss sssss Lssssssss</tt> |
| <tr>
| | |- |
| <td>14<br />
| | | | 24 |
| </td>
| | | style="text-align:center;" | 2L+22s |
| <td style="text-align: center;">2L+12s<br />
| | | style="text-align:center;" | 6.6548475771 |
| </td>
| | | | <tt>Lssssssss ssssss Lssssssss</tt> |
| <td style="text-align: center;">5.7698983847<br />
| | |- |
| </td>
| | | | 25 |
| <td><tt>Lssss ssss Lssss</tt><br />
| | | style="text-align:center;" | 2L+23s |
| </td>
| | | style="text-align:center;" | 3.2123729809 |
| </tr>
| | | | <tt>Lsssssssss sssss Lsssssssss</tt> |
| <tr>
| | |- |
| <td>15<br />
| | | | 26 |
| </td>
| | | style="text-align:center;" | 2L+24s |
| <td style="text-align: center;">2L+13s<br />
| | | style="text-align:center;" | 5.6548475771 |
| </td>
| | | | <tt>Lsssssssss ssssss Lsssssssss</tt> |
| <td style="text-align: center;">2.3274237885<br />
| | |- |
| </td>
| | | | 27 |
| <td><tt>Lsssss sss Lsssss</tt><br />
| | | style="text-align:center;" | 2L+25s |
| </td>
| | | style="text-align:center;" | 2.2123729809 |
| </tr>
| | | | <tt>Lssssssssss sssss Lssssssssss</tt> |
| <tr>
| | |- |
| <td>16<br />
| | | | 28 |
| </td>
| | | style="text-align:center;" | 2L+26s |
| <td style="text-align: center;">2L+14s<br />
| | | style="text-align:center;" | 4.6548475771 |
| </td>
| | | | <tt>Lssssssssss ssssss Lssssssssss</tt> |
| <td style="text-align: center;">4.7698983847<br />
| | |- |
| </td>
| | | | 29a |
| <td><tt>Lsssss ssss Lsssss</tt><br />
| | | style="text-align:center;" | 2L+27s |
| </td>
| | | style="text-align:center;" | 1.2123729809 |
| </tr>
| | | | <tt>Lsssssssssss sssss Lsssssssssss</tt> |
| <tr>
| | |- |
| <td>17a<br />
| | | | 29b |
| </td>
| | | style="text-align:center;" | 2L+27s |
| <td style="text-align: center;">2L+15s<br />
| | | style="text-align:center;" | 7.0973221733 |
| </td>
| | | | <tt>Lssssssssss sssssss Lssssssssss</tt> |
| <td style="text-align: center;">1.3274237885<br />
| | |- |
| </td>
| | | | 30 |
| <td><tt>Lssssss sss Lssssss</tt><br />
| | | style="text-align:center;" | 2L+28s |
| </td>
| | | style="text-align:center;" | 3.6548475771 |
| </tr>
| | | | <tt>Lsssssssssss ssssss Lsssssssssss</tt> |
| <tr>
| | |- |
| <td>17b<br />
| | | | 31 |
| </td>
| | | style="text-align:center;" | 2L+29s |
| <td style="text-align: center;">2L+15s<br />
| | | style="text-align:center;" | 6.0973221733 |
| </td>
| | | | <tt>Lsssssssssss sssssss Lsssssssssss</tt> |
| <td style="text-align: center;">7.2123729809<br />
| | |- |
| </td>
| | | | 32 |
| <td><tt>Lsssss sssss Lsssss</tt><br />
| | | style="text-align:center;" | 2L+30s |
| </td>
| | | style="text-align:center;" | 2.6548475771 |
| </tr>
| | | | <tt>Lssssssssssss ssssss Lssssssssssss</tt> |
| <tr>
| | |- |
| <td>18<br />
| | | | 33 |
| </td>
| | | style="text-align:center;" | 2L+31s |
| <td style="text-align: center;">2L+16s<br />
| | | style="text-align:center;" | 5.0973221733 |
| </td>
| | | | <tt>Lssssssssssss sssssss Lssssssssssss</tt> |
| <td style="text-align: center;">3.7698983847<br />
| | |- |
| </td>
| | | | 34a |
| <td><tt>Lssssss ssss Lssssss</tt><br />
| | | style="text-align:center;" | 2L+32s |
| </td>
| | | style="text-align:center;" | 1.6548475771 |
| </tr>
| | | | <tt>Lsssssssssssss ssssss Lsssssssssssss</tt> |
| <tr>
| | |- |
| <td>19<br />
| | | | 34b |
| </td>
| | | style="text-align:center;" | 2L+32s |
| <td style="text-align: center;">2L+17s<br />
| | | style="text-align:center;" | 6.5397967694 |
| </td>
| | | | <tt>Lssssssssssss ssssssss Lssssssssssss</tt> |
| <td style="text-align: center;">6.2123729809<br />
| | |- |
| </td>
| | | | 35 |
| <td><tt>Lssssss sssss Lssssss</tt><br />
| | | style="text-align:center;" | 2L+33s |
| </td>
| | | style="text-align:center;" | 4.0973221733 |
| </tr>
| | | | <tt>Lsssssssssssss sssssss Lsssssssssssss</tt> |
| <tr>
| | |- |
| <td>20<br />
| | | | 36 |
| </td>
| | | style="text-align:center;" | 2L+34s |
| <td style="text-align: center;">2L+18s<br />
| | | style="text-align:center;" | 6.5397967694 |
| </td>
| | | | <tt>Lsssssssssssss ssssssss Lsssssssssssss</tt> |
| <td style="text-align: center;">2.7698983847<br />
| | |- |
| </td>
| | | | 37 |
| <td><tt>Lsssssss ssss Lsssssss</tt><br />
| | | style="text-align:center;" | 2L+35s |
| </td>
| | | style="text-align:center;" | 3.0973221733 |
| </tr>
| | | | <tt>Lssssssssssssss sssssss Lssssssssssssss</tt> |
| <tr>
| | |- |
| <td>21<br />
| | | | 38 |
| </td>
| | | style="text-align:center;" | 2L+36s |
| <td style="text-align: center;">2L+19s<br />
| | | style="text-align:center;" | 5.5397967694 |
| </td>
| | | | <tt>Lssssssssssssss ssssssss Lssssssssssssss</tt> |
| <td style="text-align: center;">5.2123729809<br />
| | |- |
| </td>
| | | | 39 |
| <td><tt>Lsssssss sssss Lsssssss</tt><br />
| | | style="text-align:center;" | 2L+37s |
| </td>
| | | style="text-align:center;" | 2.0973221733 |
| </tr>
| | | | <tt>Lsssssssssssssss sssssss Lsssssssssssssss</tt> |
| <tr>
| | |- |
| <td>22a<br />
| | | | 40 |
| </td>
| | | style="text-align:center;" | 2L+38s |
| <td style="text-align: center;">2L+20s<br />
| | | style="text-align:center;" | 4.5397967694 |
| </td>
| | | | <tt>Lsssssssssssssss ssssssss Lsssssssssssssss</tt> |
| <td style="text-align: center;">1.7698983847<br />
| | |- |
| </td>
| | | | 41a |
| <td><tt>Lssssssss ssss Lssssssss</tt><br />
| | | style="text-align:center;" | 2L+39s |
| </td>
| | | style="text-align:center;" | 1.0973221733 |
| </tr>
| | | | <tt>Lssssssssssssssss sssssss Lssssssssssssssss</tt> |
| <tr>
| | |- |
| <td>22b<br />
| | | | 41b |
| </td>
| | | style="text-align:center;" | 2L+39s |
| <td style="text-align: center;">2L+20s<br />
| | | style="text-align:center;" | 6.9822713656 |
| </td>
| | | | <tt>Lsssssssssssssss sssssssss Lsssssssssssssss</tt> |
| <td style="text-align: center;">7.6548475771<br />
| | |- |
| </td>
| | | | 42 |
| <td><tt>Lsssssss ssssss Lsssssss</tt><br />
| | | style="text-align:center;" | 2L+40s |
| </td>
| | | style="text-align:center;" | 3.5397967694 |
| </tr>
| | | | <tt>Lssssssssssssssss ssssssss Lssssssssssssssss</tt> |
| <tr>
| | |- |
| <td>23<br />
| | | | 43 |
| </td>
| | | style="text-align:center;" | 2L+41s |
| <td style="text-align: center;">2L+21s<br />
| | | style="text-align:center;" | 5.9822713656 |
| </td>
| | | | <tt>Lssssssssssssssss sssssssss Lssssssssssssssss</tt> |
| <td style="text-align: center;">4.2123729809<br />
| | |- |
| </td>
| | | | 44 |
| <td><tt>Lssssssss sssss Lssssssss</tt><br />
| | | style="text-align:center;" | 2L+42s |
| </td>
| | | style="text-align:center;" | 2.5397967694 |
| </tr>
| | | | <tt>Lsssssssssssssssss ssssssss Lsssssssssssssssss</tt> |
| <tr>
| | |- |
| <td>24<br />
| | | | 45 |
| </td>
| | | style="text-align:center;" | 2L+43s |
| <td style="text-align: center;">2L+22s<br />
| | | style="text-align:center;" | 4.9822713656 |
| </td>
| | | | <tt>Lsssssssssssssssss sssssssss Lsssssssssssssssss</tt> |
| <td style="text-align: center;">6.6548475771<br />
| | |- |
| </td>
| | | | 46a |
| <td><tt>Lssssssss ssssss Lssssssss</tt><br />
| | | style="text-align:center;" | 2L+44s |
| </td>
| | | style="text-align:center;" | 1.5397967694 |
| </tr>
| | | | <tt>Lssssssssssssssssss ssssssss Lssssssssssssssssss</tt> |
| <tr>
| | |- |
| <td>25<br />
| | | | 46b |
| </td>
| | | style="text-align:center;" | 2L+44s |
| <td style="text-align: center;">2L+23s<br />
| | | style="text-align:center;" | 7.4247459618 |
| </td>
| | | | <tt>Lsssssssssssssssss ssssssssss Lsssssssssssssssss</tt> |
| <td style="text-align: center;">3.2123729809<br />
| | |- |
| </td>
| | | | 47 |
| <td><tt>Lsssssssss sssss Lsssssssss</tt><br />
| | | style="text-align:center;" | 2L+45s |
| </td>
| | | style="text-align:center;" | 3.9822713656 |
| </tr>
| | | | <tt>Lssssssssssssssssss sssssssss Lssssssssssssssssss</tt> |
| <tr>
| | |- |
| <td>26<br />
| | | | 48 |
| </td>
| | | style="text-align:center;" | 2L+46s |
| <td style="text-align: center;">2L+24s<br />
| | | style="text-align:center;" | 6.4247459618 |
| </td>
| | | | <tt>Lssssssssssssssssss ssssssssss Lssssssssssssssssss</tt> |
| <td style="text-align: center;">5.6548475771<br />
| | |- |
| </td>
| | | | 49 |
| <td><tt>Lsssssssss ssssss Lsssssssss</tt><br />
| | | style="text-align:center;" | 2L+47s |
| </td>
| | | style="text-align:center;" | 2.9822713656 |
| </tr>
| | | | <tt>Lsssssssssssssssssss sssssssss Lsssssssssssssssssss</tt> |
| <tr>
| | |- |
| <td>27<br />
| | | | 50 |
| </td>
| | | style="text-align:center;" | 2L+48s |
| <td style="text-align: center;">2L+25s<br />
| | | style="text-align:center;" | 5.4247459618 |
| </td>
| | | | <tt>Lsssssssssssssssssss ssssssssss Lsssssssssssssssssss</tt> |
| <td style="text-align: center;">2.2123729809<br />
| | |- |
| </td>
| | | | 51 |
| <td><tt>Lssssssssss sssss Lssssssssss</tt><br />
| | | style="text-align:center;" | 2L+49s |
| </td>
| | | style="text-align:center;" | 1.9822713656 |
| </tr>
| | | | <tt>Lssssssssssssssssssss sssssssss Lssssssssssssssssssss</tt> |
| <tr>
| | |- |
| <td>28<br />
| | | | 52 |
| </td>
| | | style="text-align:center;" | 2L+50s |
| <td style="text-align: center;">2L+26s<br />
| | | style="text-align:center;" | 4.4247459618 |
| </td>
| | | | <tt>Lssssssssssssssssssss ssssssssss Lssssssssssssssssssss</tt> |
| <td style="text-align: center;">4.6548475771<br />
| | |- |
| </td>
| | | | 53a |
| <td><tt>Lssssssssss ssssss Lssssssssss</tt><br />
| | | style="text-align:center;" | 2L+51s |
| </td>
| | | style="text-align:center;" | 0.9822713656 |
| </tr>
| | | | <tt>Lsssssssssssssssssssss sssssssss Lsssssssssssssssssssss</tt> |
| <tr>
| | |- |
| <td>29a<br />
| | | | 53b |
| </td>
| | | style="text-align:center;" | 2L+51s |
| <td style="text-align: center;">2L+27s<br />
| | | style="text-align:center;" | 6.8672205580 |
| </td>
| | | | <tt>Lssssssssssssssssssss sssssssssss Lssssssssssssssssssss</tt> |
| <td style="text-align: center;">1.2123729809<br />
| | |} |
| </td>
| | etc. |
| <td><tt>Lsssssssssss sssss Lsssssssssss</tt><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>29b<br />
| |
| </td>
| |
| <td style="text-align: center;">2L+27s<br />
| |
| </td>
| |
| <td style="text-align: center;">7.0973221733<br />
| |
| </td>
| |
| <td><tt>Lssssssssss sssssss Lssssssssss</tt><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>30<br />
| |
| </td>
| |
| <td style="text-align: center;">2L+28s<br />
| |
| </td>
| |
| <td style="text-align: center;">3.6548475771<br />
| |
| </td>
| |
| <td><tt>Lsssssssssss ssssss Lsssssssssss</tt><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>31<br />
| |
| </td>
| |
| <td style="text-align: center;">2L+29s<br />
| |
| </td>
| |
| <td style="text-align: center;">6.0973221733<br />
| |
| </td>
| |
| <td><tt>Lsssssssssss sssssss Lsssssssssss</tt><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>32<br />
| |
| </td>
| |
| <td style="text-align: center;">2L+30s<br />
| |
| </td>
| |
| <td style="text-align: center;">2.6548475771<br />
| |
| </td>
| |
| <td><tt>Lssssssssssss ssssss Lssssssssssss</tt><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>33<br />
| |
| </td>
| |
| <td style="text-align: center;">2L+31s<br />
| |
| </td>
| |
| <td style="text-align: center;">5.0973221733<br />
| |
| </td>
| |
| <td><tt>Lssssssssssss sssssss Lssssssssssss</tt><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>34a<br />
| |
| </td>
| |
| <td style="text-align: center;">2L+32s<br />
| |
| </td>
| |
| <td style="text-align: center;">1.6548475771<br />
| |
| </td>
| |
| <td><tt>Lsssssssssssss ssssss Lsssssssssssss</tt><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>34b<br />
| |
| </td>
| |
| <td style="text-align: center;">2L+32s<br />
| |
| </td>
| |
| <td style="text-align: center;">6.5397967694<br />
| |
| </td>
| |
| <td><tt>Lssssssssssss ssssssss Lssssssssssss</tt><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>35<br />
| |
| </td>
| |
| <td style="text-align: center;">2L+33s<br />
| |
| </td>
| |
| <td style="text-align: center;">4.0973221733<br />
| |
| </td>
| |
| <td><tt>Lsssssssssssss sssssss Lsssssssssssss</tt><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>36<br />
| |
| </td>
| |
| <td style="text-align: center;">2L+34s<br />
| |
| </td>
| |
| <td style="text-align: center;">6.5397967694<br />
| |
| </td>
| |
| <td><tt>Lsssssssssssss ssssssss Lsssssssssssss</tt><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>37<br />
| |
| </td>
| |
| <td style="text-align: center;">2L+35s<br />
| |
| </td>
| |
| <td style="text-align: center;">3.0973221733<br />
| |
| </td>
| |
| <td><tt>Lssssssssssssss sssssss Lssssssssssssss</tt><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>38<br />
| |
| </td>
| |
| <td style="text-align: center;">2L+36s<br />
| |
| </td>
| |
| <td style="text-align: center;">5.5397967694<br />
| |
| </td>
| |
| <td><tt>Lssssssssssssss ssssssss Lssssssssssssss</tt><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>39<br />
| |
| </td>
| |
| <td style="text-align: center;">2L+37s<br />
| |
| </td>
| |
| <td style="text-align: center;">2.0973221733<br />
| |
| </td>
| |
| <td><tt>Lsssssssssssssss sssssss Lsssssssssssssss</tt><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>40<br />
| |
| </td>
| |
| <td style="text-align: center;">2L+38s<br />
| |
| </td>
| |
| <td style="text-align: center;">4.5397967694<br />
| |
| </td>
| |
| <td><tt>Lsssssssssssssss ssssssss Lsssssssssssssss</tt><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>41a<br />
| |
| </td>
| |
| <td style="text-align: center;">2L+39s<br />
| |
| </td>
| |
| <td style="text-align: center;">1.0973221733<br />
| |
| </td>
| |
| <td><tt>Lssssssssssssssss sssssss Lssssssssssssssss</tt><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>41b<br />
| |
| </td>
| |
| <td style="text-align: center;">2L+39s<br />
| |
| </td>
| |
| <td style="text-align: center;">6.9822713656<br />
| |
| </td>
| |
| <td><tt>Lsssssssssssssss sssssssss Lsssssssssssssss</tt><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>42<br />
| |
| </td>
| |
| <td style="text-align: center;">2L+40s<br />
| |
| </td>
| |
| <td style="text-align: center;">3.5397967694<br />
| |
| </td>
| |
| <td><tt>Lssssssssssssssss ssssssss Lssssssssssssssss</tt><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>43<br />
| |
| </td>
| |
| <td style="text-align: center;">2L+41s<br />
| |
| </td>
| |
| <td style="text-align: center;">5.9822713656<br />
| |
| </td>
| |
| <td><tt>Lssssssssssssssss sssssssss Lssssssssssssssss</tt><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>44<br />
| |
| </td>
| |
| <td style="text-align: center;">2L+42s<br />
| |
| </td>
| |
| <td style="text-align: center;">2.5397967694<br />
| |
| </td>
| |
| <td><tt>Lsssssssssssssssss ssssssss Lsssssssssssssssss</tt><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>45<br />
| |
| </td>
| |
| <td style="text-align: center;">2L+43s<br />
| |
| </td>
| |
| <td style="text-align: center;">4.9822713656<br />
| |
| </td>
| |
| <td><tt>Lsssssssssssssssss sssssssss Lsssssssssssssssss</tt><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>46a<br />
| |
| </td>
| |
| <td style="text-align: center;">2L+44s<br />
| |
| </td>
| |
| <td style="text-align: center;">1.5397967694<br />
| |
| </td>
| |
| <td><tt>Lssssssssssssssssss ssssssss Lssssssssssssssssss</tt><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>46b<br />
| |
| </td>
| |
| <td style="text-align: center;">2L+44s<br />
| |
| </td>
| |
| <td style="text-align: center;">7.4247459618<br />
| |
| </td>
| |
| <td><tt>Lsssssssssssssssss ssssssssss Lsssssssssssssssss</tt><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>47<br />
| |
| </td>
| |
| <td style="text-align: center;">2L+45s<br />
| |
| </td>
| |
| <td style="text-align: center;">3.9822713656<br />
| |
| </td>
| |
| <td><tt>Lssssssssssssssssss sssssssss Lssssssssssssssssss</tt><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>48<br />
| |
| </td>
| |
| <td style="text-align: center;">2L+46s<br />
| |
| </td>
| |
| <td style="text-align: center;">6.4247459618<br />
| |
| </td>
| |
| <td><tt>Lssssssssssssssssss ssssssssss Lssssssssssssssssss</tt><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>49<br />
| |
| </td>
| |
| <td style="text-align: center;">2L+47s<br />
| |
| </td>
| |
| <td style="text-align: center;">2.9822713656<br />
| |
| </td>
| |
| <td><tt>Lsssssssssssssssssss sssssssss Lsssssssssssssssssss</tt><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>50<br />
| |
| </td>
| |
| <td style="text-align: center;">2L+48s<br />
| |
| </td>
| |
| <td style="text-align: center;">5.4247459618<br />
| |
| </td>
| |
| <td><tt>Lsssssssssssssssssss ssssssssss Lsssssssssssssssssss</tt><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>51<br />
| |
| </td>
| |
| <td style="text-align: center;">2L+49s<br />
| |
| </td>
| |
| <td style="text-align: center;">1.9822713656<br />
| |
| </td>
| |
| <td><tt>Lssssssssssssssssssss sssssssss Lssssssssssssssssssss</tt><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>52<br />
| |
| </td>
| |
| <td style="text-align: center;">2L+50s<br />
| |
| </td>
| |
| <td style="text-align: center;">4.4247459618<br />
| |
| </td>
| |
| <td><tt>Lssssssssssssssssssss ssssssssss Lssssssssssssssssssss</tt><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>53a<br />
| |
| </td>
| |
| <td style="text-align: center;">2L+51s<br />
| |
| </td>
| |
| <td style="text-align: center;">0.9822713656<br />
| |
| </td>
| |
| <td><tt>Lsssssssssssssssssssss sssssssss Lsssssssssssssssssssss</tt><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>53b<br />
| |
| </td>
| |
| <td style="text-align: center;">2L+51s<br />
| |
| </td>
| |
| <td style="text-align: center;">6.8672205580<br />
| |
| </td>
| |
| <td><tt>Lssssssssssssssssssss sssssssssss Lssssssssssssssssssss</tt><br />
| |
| </td>
| |
| </tr>
| |
| </table>
| |
|
| |
|
| etc.<br />
| | ===See also=== |
| <br />
| | <ul><li>[[Omnitetrachordality|Omnitetrachordality]]</li><li>[[Gallery_of_omnitetrachordal_scales|Gallery of omnitetrachordal scales]]</li></ul> |
| <!-- ws:start:WikiTextHeadingRule:0:&lt;h3&gt; --><h3 id="toc0"><a name="x--See also"></a><!-- ws:end:WikiTextHeadingRule:0 -->See also</h3>
| |
| <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>
| |