OTC 2L ns: Difference between revisions
Wikispaces>spt3125 **Imported revision 591011642 - Original comment: ** |
Wikispaces>JosephRuhf **Imported revision 598358394 - Original comment: ** |
||
| Line 1: | Line 1: | ||
<h2>IMPORTED REVISION FROM WIKISPACES</h2> | <h2>IMPORTED REVISION FROM WIKISPACES</h2> | ||
This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br> | This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br> | ||
: This revision was by author [[User: | : This revision was by author [[User:JosephRuhf|JosephRuhf]] and made on <tt>2016-11-04 08:12:49 UTC</tt>.<br> | ||
: The original revision id was <tt> | : The original revision id was <tt>598358394</tt>.<br> | ||
: The revision comment was: <tt></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> | The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.<br> | ||
| Line 8: | Line 8: | ||
<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?** | <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?** | ||
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. | 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. | ||
In every case so far studied, the strings of 's' steps come in a small group and a large group. | 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 | * 9/8 = (y-x)s | ||
* 4/3 = L+xs | * 4/3 = L+xs | ||
| Line 32: | Line 32: | ||
These groups appear to share generators and temperaments. | These groups appear to share generators and temperaments. | ||
For some scale sizes (12, 17, 22, 29, 34, 41, 46, 53, and possibly others), more than one class of OTC scale is possible! | 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. | ||
|| **size** ||= ** | || **size** ||= **2L+_s** ||= **P** || **pattern** || | ||
|| 3 ||= 2L+s ||= 2.4424745962 || {{ L s L }} (MOS) | || 3 ||= 2L+s ||= 2.4424745962 || {{L s L}} (MOS) || | ||
|| 5 ||= [[OTC 2L 3s|2L+3s]] ||= 1.4424745962 || {{Ls s Ls}} (MOS) || | |||
|| 5 ||= [[OTC 2L 3s|2L+3s]] ||= 1.4424745962 || {{ Ls s Ls }} (MOS) || | || 6 ||= 2L+4s ||= 3.8849491924 || {{Ls ss Ls}} || | ||
|| 6 ||= 2L+4s ||= 3.8849491924 || {{ Ls ss Ls }} || | || 7 ||= [[OTC 2L 5s|2L+5s]] ||= 0.4424745962 || {{Lss s Lss}} (MOS) || | ||
|| 7 ||= [[OTC 2L 5s|2L+5s]] ||= 0.4424745962 || {{ Lss s Lss }} (MOS) || | || 8 ||= 2L+6s ||= 2.8849491924 || {{Lss ss Lss}} || | ||
|| 8 ||= 2L+6s ||= 2.8849491924 || {{ Lss ss Lss }} || | || 9 ||= 2L+7s ||= 5.3274237885 || {{Lss sss Lss}} || | ||
|| 9 ||= 2L+7s ||= 5.3274237885 || {{ Lss sss Lss }} || | || 10 ||= [[OTC 2L 8s|2L+8s]] ||= 1.8849491924 || {{Lsss ss Lsss}} || | ||
|| 10 ||= [[OTC 2L 8s|2L+8s]] ||= 1.8849491924 || {{ Lsss ss Lsss }} || | || 11 ||= 2L+9s ||= 4.3274237885 || {{Lsss sss Lsss}} || | ||
|| 11 ||= 2L+9s ||= 4.3274237885 || {{ Lsss sss Lsss }} || | || 12a ||= [[OTC 2L 10s|2L+10s]] ||= 0.8849491924 || {{Lssss ss Lssss}} || | ||
|| 12a ||= [[OTC 2L 10s|2L+10s]] ||= 0.8849491924 || {{ Lssss ss Lssss }} || | || 12b ||= [[OTC 2L 10s|2L+10s]] ||= 6.7698983847 || {{Lsss ssss Lsss}} || | ||
|| 12b ||= [[OTC 2L 10s|2L+10s]] ||= 6.7698983847 || {{ Lsss ssss Lsss }} || | || 13 ||= 2L+11s ||= 3.3274237885 || {{Lssss sss Lssss}} || | ||
|| 13 ||= 2L+11s ||= 3.3274237885 || {{ Lssss sss Lssss }} || | || 14 ||= 2L+12s ||= 5.7698983847 || {{Lssss ssss Lssss}} || | ||
|| 14 ||= 2L+12s ||= 5.7698983847 || {{ Lssss ssss Lssss }} || | || 15 ||= 2L+13s ||= 2.3274237885 || {{Lsssss sss Lsssss}} || | ||
|| 15 ||= 2L+13s ||= 2.3274237885 || {{ Lsssss sss Lsssss }} || | || 16 ||= 2L+14s ||= 4.7698983847 || {{Lsssss ssss Lsssss}} || | ||
|| 16 ||= 2L+14s ||= 4.7698983847 || {{ Lsssss ssss Lsssss }} || | || 17a ||= 2L+15s ||= 1.3274237885 || {{Lssssss sss Lssssss}} || | ||
|| 17a ||= 2L+15s ||= 1.3274237885 || {{ Lssssss sss Lssssss }} || | || 17b ||= 2L+15s ||= 7.2123729809 || {{Lsssss sssss Lsssss}} || | ||
|| 17b ||= 2L+15s ||= 7.2123729809 || {{ Lsssss sssss Lsssss }} || | || 18 ||= 2L+16s ||= 3.7698983847 || {{Lssssss ssss Lssssss}} || | ||
|| 18 ||= 2L+16s ||= 3.7698983847 || {{ Lssssss ssss Lssssss }} || | || 19 ||= 2L+17s ||= 6.2123729809 || {{Lssssss sssss Lssssss}} || | ||
|| 19 ||= 2L+17s ||= 6.2123729809 || {{ Lssssss sssss Lssssss }} || | || 20 ||= 2L+18s ||= 2.7698983847 || {{Lsssssss ssss Lsssssss}} || | ||
|| 20 ||= 2L+18s ||= 2.7698983847 || {{ Lsssssss ssss Lsssssss }} || | || 21 ||= 2L+19s ||= 5.2123729809 || {{Lsssssss sssss Lsssssss}} || | ||
|| 21 ||= 2L+19s ||= 5.2123729809 || {{ Lsssssss sssss Lsssssss }} || | || 22a ||= 2L+20s ||= 1.7698983847 || {{Lssssssss ssss Lssssssss}} || | ||
|| 22a ||= 2L+20s ||= 1.7698983847 || {{ Lssssssss ssss Lssssssss }} || | || 22b ||= 2L+20s ||= 7.6548475771 || {{Lsssssss ssssss Lsssssss}} || | ||
|| 22b ||= 2L+20s ||= 7.6548475771 || {{ Lsssssss ssssss Lsssssss }} || | || 23 ||= 2L+21s ||= 4.2123729809 || {{Lssssssss sssss Lssssssss}} || | ||
|| 23 ||= 2L+21s ||= 4.2123729809 || {{ Lssssssss sssss Lssssssss }} || | || 24 ||= 2L+22s ||= 6.6548475771 || {{Lssssssss ssssss Lssssssss}} || | ||
|| 24 ||= 2L+22s ||= 6.6548475771 || {{ Lssssssss ssssss Lssssssss }} || | || 25 ||= 2L+23s ||= 3.2123729809 || {{Lsssssssss sssss Lsssssssss}} || | ||
|| 25 ||= 2L+23s ||= 3.2123729809 || {{ Lsssssssss sssss Lsssssssss }} || | || 26 ||= 2L+24s ||= 5.6548475771 || {{Lsssssssss ssssss Lsssssssss}} || | ||
|| 26 ||= 2L+24s ||= 5.6548475771 || {{ Lsssssssss ssssss Lsssssssss }} || | || 27 ||= 2L+25s ||= 2.2123729809 || {{Lssssssssss sssss Lssssssssss}} || | ||
|| 27 ||= 2L+25s ||= 2.2123729809 || {{ Lssssssssss sssss Lssssssssss }} || | || 28 ||= 2L+26s ||= 4.6548475771 || {{Lssssssssss ssssss Lssssssssss}} || | ||
|| 28 ||= 2L+26s ||= 4.6548475771 || {{ Lssssssssss ssssss Lssssssssss }} || | || 29a ||= 2L+27s ||= 1.2123729809 || {{Lsssssssssss sssss Lsssssssssss}} || | ||
|| 29a ||= 2L+27s ||= 1.2123729809 || {{ Lsssssssssss sssss Lsssssssssss }} || | || 29b ||= 2L+27s ||= 7.0973221733 || {{Lssssssssss sssssss Lssssssssss}} || | ||
|| 29b ||= 2L+27s ||= 7.0973221733 || {{ Lssssssssss sssssss Lssssssssss }} || | || 30 ||= 2L+28s ||= 3.6548475771 || {{Lsssssssssss ssssss Lsssssssssss}} || | ||
|| 30 ||= 2L+28s ||= 3.6548475771 || {{ Lsssssssssss ssssss Lsssssssssss }} || | || 31 ||= 2L+29s ||= 6.0973221733 || {{Lsssssssssss sssssss Lsssssssssss}} || | ||
|| 31 ||= 2L+29s ||= 6.0973221733 || {{ Lsssssssssss sssssss Lsssssssssss }} || | || 32 ||= 2L+30s ||= 2.6548475771 || {{Lssssssssssss ssssss Lssssssssssss}} || | ||
|| 32 ||= 2L+30s ||= 2.6548475771 || {{ Lssssssssssss ssssss Lssssssssssss }} || | || 33 ||= 2L+31s ||= 5.0973221733 || {{Lssssssssssss sssssss Lssssssssssss}} || | ||
|| 33 ||= 2L+31s ||= 5.0973221733 || {{ Lssssssssssss sssssss Lssssssssssss }} || | || 34a ||= 2L+32s ||= 1.6548475771 || {{Lsssssssssssss ssssss Lsssssssssssss}} || | ||
|| 34a ||= 2L+32s ||= 1.6548475771 || {{ Lsssssssssssss ssssss Lsssssssssssss }} || | || 34b ||= 2L+32s ||= 6.5397967694 || {{Lssssssssssss ssssssss Lssssssssssss}} || | ||
|| 34b ||= 2L+32s ||= 6.5397967694 || {{ Lssssssssssss ssssssss Lssssssssssss }} || | || 35 ||= 2L+33s ||= 4.0973221733 || {{Lsssssssssssss sssssss Lsssssssssssss}} || | ||
|| 35 ||= 2L+33s ||= 4.0973221733 || {{ Lsssssssssssss sssssss Lsssssssssssss }} || | || 36 ||= 2L+34s ||= 6.5397967694 || {{Lsssssssssssss ssssssss Lsssssssssssss}} || | ||
|| 36 ||= 2L+34s ||= 6.5397967694 || {{ Lsssssssssssss ssssssss Lsssssssssssss }} || | || 37 ||= 2L+35s ||= 3.0973221733 || {{Lssssssssssssss sssssss Lssssssssssssss}} || | ||
|| 37 ||= 2L+35s ||= 3.0973221733 || {{ Lssssssssssssss sssssss Lssssssssssssss }} || | || 38 ||= 2L+36s ||= 5.5397967694 || {{Lssssssssssssss ssssssss Lssssssssssssss}} || | ||
|| 38 ||= 2L+36s ||= 5.5397967694 || {{ Lssssssssssssss ssssssss Lssssssssssssss }} || | || 39 ||= 2L+37s ||= 2.0973221733 || {{Lsssssssssssssss sssssss Lsssssssssssssss}} || | ||
|| 39 ||= 2L+37s ||= 2.0973221733 || {{ Lsssssssssssssss sssssss Lsssssssssssssss }} || | || 40 ||= 2L+38s ||= 4.5397967694 || {{Lsssssssssssssss ssssssss Lsssssssssssssss}} || | ||
|| 40 ||= 2L+38s ||= 4.5397967694 || {{ Lsssssssssssssss ssssssss Lsssssssssssssss }} || | || 41a ||= 2L+39s ||= 1.0973221733 || {{Lssssssssssssssss sssssss Lssssssssssssssss}} || | ||
|| 41a ||= 2L+39s ||= 1.0973221733 || {{ Lssssssssssssssss sssssss Lssssssssssssssss }} || | || 41b ||= 2L+39s ||= 6.9822713656 || {{Lsssssssssssssss sssssssss Lsssssssssssssss}} || | ||
|| 41b ||= 2L+39s ||= 6.9822713656 || {{ Lsssssssssssssss sssssssss Lsssssssssssssss }} || | || 42 ||= 2L+40s ||= 3.5397967694 || {{Lssssssssssssssss ssssssss Lssssssssssssssss}} || | ||
|| 42 ||= 2L+40s ||= 3.5397967694 || {{ Lssssssssssssssss ssssssss Lssssssssssssssss }} || | || 43 ||= 2L+41s ||= 5.9822713656 || {{Lssssssssssssssss sssssssss Lssssssssssssssss}} || | ||
|| 43 ||= 2L+41s ||= 5.9822713656 || {{ Lssssssssssssssss sssssssss Lssssssssssssssss }} || | || 44 ||= 2L+42s ||= 2.5397967694 || {{Lsssssssssssssssss ssssssss Lsssssssssssssssss}} || | ||
|| 44 ||= 2L+42s ||= 2.5397967694 || {{ Lsssssssssssssssss ssssssss Lsssssssssssssssss }} || | || 45 ||= 2L+43s ||= 4.9822713656 || {{Lsssssssssssssssss sssssssss Lsssssssssssssssss}} || | ||
|| 45 ||= 2L+43s ||= 4.9822713656 || {{ Lsssssssssssssssss sssssssss Lsssssssssssssssss }} || | || 46a ||= 2L+44s ||= 1.5397967694 || {{Lssssssssssssssssss ssssssss Lssssssssssssssssss}} || | ||
|| 46a ||= 2L+44s ||= 1.5397967694 || {{ Lssssssssssssssssss ssssssss Lssssssssssssssssss }} || | || 46b ||= 2L+44s ||= 7.4247459618 || {{Lsssssssssssssssss ssssssssss Lsssssssssssssssss}} || | ||
|| 46b ||= 2L+44s ||= 7.4247459618 || {{ Lsssssssssssssssss ssssssssss Lsssssssssssssssss }} || | || 47 ||= 2L+45s ||= 3.9822713656 || {{Lssssssssssssssssss sssssssss Lssssssssssssssssss}} || | ||
|| 47 ||= 2L+45s ||= 3.9822713656 || {{ Lssssssssssssssssss sssssssss Lssssssssssssssssss }} || | || 48 ||= 2L+46s ||= 6.4247459618 || {{Lssssssssssssssssss ssssssssss Lssssssssssssssssss}} || | ||
|| 48 ||= 2L+46s ||= 6.4247459618 || {{ Lssssssssssssssssss ssssssssss Lssssssssssssssssss }} || | || 49 ||= 2L+47s ||= 2.9822713656 || {{Lsssssssssssssssssss sssssssss Lsssssssssssssssssss}} || | ||
|| 49 ||= 2L+47s ||= 2.9822713656 || {{ Lsssssssssssssssssss sssssssss Lsssssssssssssssssss }} || | || 50 ||= 2L+48s ||= 5.4247459618 || {{Lsssssssssssssssssss ssssssssss Lsssssssssssssssssss}} || | ||
|| 50 ||= 2L+48s ||= 5.4247459618 || {{ Lsssssssssssssssssss ssssssssss Lsssssssssssssssssss }} || | || 51 ||= 2L+49s ||= 1.9822713656 || {{Lssssssssssssssssssss sssssssss Lssssssssssssssssssss}} || | ||
|| 51 ||= 2L+49s ||= 1.9822713656 || {{ Lssssssssssssssssssss sssssssss Lssssssssssssssssssss }} || | || 52 ||= 2L+50s ||= 4.4247459618 || {{Lssssssssssssssssssss ssssssssss Lssssssssssssssssssss}} || | ||
|| 52 ||= 2L+50s ||= 4.4247459618 || {{ Lssssssssssssssssssss ssssssssss Lssssssssssssssssssss }} || | || 53a ||= 2L+51s ||= 0.9822713656 || {{Lsssssssssssssssssssss sssssssss Lsssssssssssssssssssss}} || | ||
|| 53a ||= 2L+51s ||= 0.9822713656 || {{ Lsssssssssssssssssssss sssssssss Lsssssssssssssssssssss }} || | || 53b ||= 2L+51s ||= 6.8672205580 || {{Lssssssssssssssssssss sssssssssss Lssssssssssssssssssss}} || | ||
|| 53b ||= | etc. | ||
etc. | |||
===See also=== | ===See also=== | ||
* [[Omnitetrachordality]] | * [[Omnitetrachordality]] | ||
* [[Gallery of omnitetrachordal scales]]</pre></div> | * [[Gallery of omnitetrachordal scales]]</pre></div> | ||
| Line 102: | Line 101: | ||
<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 /> | <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 /> | <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. | 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 /> | <br /> | ||
In every case so far studied, the strings of 's' steps come in a small group and a large group. | 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 /> | <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 /> | As scale size increases:<br /> | ||
| Line 111: | Line 110: | ||
<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 /> | <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 /> | <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! | 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 /> | <br /> | ||
| Line 119: | Line 118: | ||
<td><strong>size</strong><br /> | <td><strong>size</strong><br /> | ||
</td> | </td> | ||
<td style="text-align: center;"><strong> | <td style="text-align: center;"><strong>2L+_s</strong><br /> | ||
</td> | </td> | ||
<td style="text-align: center;"><strong>P</strong><br /> | <td style="text-align: center;"><strong>P</strong><br /> | ||
| Line 133: | Line 132: | ||
<td style="text-align: center;">2.4424745962<br /> | <td style="text-align: center;">2.4424745962<br /> | ||
</td> | </td> | ||
<td><tt> L s L </tt> (MOS) | <td><tt>L s L</tt> (MOS)<br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
| Line 153: | Line 142: | ||
<td style="text-align: center;">1.4424745962<br /> | <td style="text-align: center;">1.4424745962<br /> | ||
</td> | </td> | ||
<td><tt> Ls s Ls </tt> (MOS)<br /> | <td><tt>Ls s Ls</tt> (MOS)<br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
| Line 163: | Line 152: | ||
<td style="text-align: center;">3.8849491924<br /> | <td style="text-align: center;">3.8849491924<br /> | ||
</td> | </td> | ||
<td><tt> Ls ss Ls </tt><br /> | <td><tt>Ls ss Ls</tt><br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
| Line 173: | Line 162: | ||
<td style="text-align: center;">0.4424745962<br /> | <td style="text-align: center;">0.4424745962<br /> | ||
</td> | </td> | ||
<td><tt> Lss s Lss </tt> (MOS)<br /> | <td><tt>Lss s Lss</tt> (MOS)<br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
| Line 183: | Line 172: | ||
<td style="text-align: center;">2.8849491924<br /> | <td style="text-align: center;">2.8849491924<br /> | ||
</td> | </td> | ||
<td><tt> Lss ss Lss </tt><br /> | <td><tt>Lss ss Lss</tt><br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
| Line 193: | Line 182: | ||
<td style="text-align: center;">5.3274237885<br /> | <td style="text-align: center;">5.3274237885<br /> | ||
</td> | </td> | ||
<td><tt> Lss sss Lss </tt><br /> | <td><tt>Lss sss Lss</tt><br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
| Line 203: | Line 192: | ||
<td style="text-align: center;">1.8849491924<br /> | <td style="text-align: center;">1.8849491924<br /> | ||
</td> | </td> | ||
<td><tt> Lsss ss Lsss </tt><br /> | <td><tt>Lsss ss Lsss</tt><br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
| Line 213: | Line 202: | ||
<td style="text-align: center;">4.3274237885<br /> | <td style="text-align: center;">4.3274237885<br /> | ||
</td> | </td> | ||
<td><tt> Lsss sss Lsss </tt><br /> | <td><tt>Lsss sss Lsss</tt><br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
| Line 223: | Line 212: | ||
<td style="text-align: center;">0.8849491924<br /> | <td style="text-align: center;">0.8849491924<br /> | ||
</td> | </td> | ||
<td><tt> Lssss ss Lssss </tt><br /> | <td><tt>Lssss ss Lssss</tt><br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
| Line 233: | Line 222: | ||
<td style="text-align: center;">6.7698983847<br /> | <td style="text-align: center;">6.7698983847<br /> | ||
</td> | </td> | ||
<td><tt> Lsss ssss Lsss </tt><br /> | <td><tt>Lsss ssss Lsss</tt><br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
| Line 243: | Line 232: | ||
<td style="text-align: center;">3.3274237885<br /> | <td style="text-align: center;">3.3274237885<br /> | ||
</td> | </td> | ||
<td><tt> Lssss sss Lssss </tt><br /> | <td><tt>Lssss sss Lssss</tt><br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
| Line 253: | Line 242: | ||
<td style="text-align: center;">5.7698983847<br /> | <td style="text-align: center;">5.7698983847<br /> | ||
</td> | </td> | ||
<td><tt> Lssss ssss Lssss </tt><br /> | <td><tt>Lssss ssss Lssss</tt><br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
| Line 263: | Line 252: | ||
<td style="text-align: center;">2.3274237885<br /> | <td style="text-align: center;">2.3274237885<br /> | ||
</td> | </td> | ||
<td><tt> Lsssss sss Lsssss </tt><br /> | <td><tt>Lsssss sss Lsssss</tt><br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
| Line 273: | Line 262: | ||
<td style="text-align: center;">4.7698983847<br /> | <td style="text-align: center;">4.7698983847<br /> | ||
</td> | </td> | ||
<td><tt> Lsssss ssss Lsssss </tt><br /> | <td><tt>Lsssss ssss Lsssss</tt><br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
| Line 283: | Line 272: | ||
<td style="text-align: center;">1.3274237885<br /> | <td style="text-align: center;">1.3274237885<br /> | ||
</td> | </td> | ||
<td><tt> Lssssss sss Lssssss </tt><br /> | <td><tt>Lssssss sss Lssssss</tt><br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
| Line 293: | Line 282: | ||
<td style="text-align: center;">7.2123729809<br /> | <td style="text-align: center;">7.2123729809<br /> | ||
</td> | </td> | ||
<td><tt> Lsssss sssss Lsssss </tt><br /> | <td><tt>Lsssss sssss Lsssss</tt><br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
| Line 303: | Line 292: | ||
<td style="text-align: center;">3.7698983847<br /> | <td style="text-align: center;">3.7698983847<br /> | ||
</td> | </td> | ||
<td><tt> Lssssss ssss Lssssss </tt><br /> | <td><tt>Lssssss ssss Lssssss</tt><br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
| Line 313: | Line 302: | ||
<td style="text-align: center;">6.2123729809<br /> | <td style="text-align: center;">6.2123729809<br /> | ||
</td> | </td> | ||
<td><tt> Lssssss sssss Lssssss </tt><br /> | <td><tt>Lssssss sssss Lssssss</tt><br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
| Line 323: | Line 312: | ||
<td style="text-align: center;">2.7698983847<br /> | <td style="text-align: center;">2.7698983847<br /> | ||
</td> | </td> | ||
<td><tt> Lsssssss ssss Lsssssss </tt><br /> | <td><tt>Lsssssss ssss Lsssssss</tt><br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
| Line 333: | Line 322: | ||
<td style="text-align: center;">5.2123729809<br /> | <td style="text-align: center;">5.2123729809<br /> | ||
</td> | </td> | ||
<td><tt> Lsssssss sssss Lsssssss </tt><br /> | <td><tt>Lsssssss sssss Lsssssss</tt><br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
| Line 343: | Line 332: | ||
<td style="text-align: center;">1.7698983847<br /> | <td style="text-align: center;">1.7698983847<br /> | ||
</td> | </td> | ||
<td><tt> Lssssssss ssss Lssssssss </tt><br /> | <td><tt>Lssssssss ssss Lssssssss</tt><br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
| Line 353: | Line 342: | ||
<td style="text-align: center;">7.6548475771<br /> | <td style="text-align: center;">7.6548475771<br /> | ||
</td> | </td> | ||
<td><tt> Lsssssss ssssss Lsssssss </tt><br /> | <td><tt>Lsssssss ssssss Lsssssss</tt><br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
| Line 363: | Line 352: | ||
<td style="text-align: center;">4.2123729809<br /> | <td style="text-align: center;">4.2123729809<br /> | ||
</td> | </td> | ||
<td><tt> Lssssssss sssss Lssssssss </tt><br /> | <td><tt>Lssssssss sssss Lssssssss</tt><br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
| Line 373: | Line 362: | ||
<td style="text-align: center;">6.6548475771<br /> | <td style="text-align: center;">6.6548475771<br /> | ||
</td> | </td> | ||
<td><tt> Lssssssss ssssss Lssssssss </tt><br /> | <td><tt>Lssssssss ssssss Lssssssss</tt><br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
| Line 383: | Line 372: | ||
<td style="text-align: center;">3.2123729809<br /> | <td style="text-align: center;">3.2123729809<br /> | ||
</td> | </td> | ||
<td><tt> Lsssssssss sssss Lsssssssss </tt><br /> | <td><tt>Lsssssssss sssss Lsssssssss</tt><br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
| Line 393: | Line 382: | ||
<td style="text-align: center;">5.6548475771<br /> | <td style="text-align: center;">5.6548475771<br /> | ||
</td> | </td> | ||
<td><tt> Lsssssssss ssssss Lsssssssss </tt><br /> | <td><tt>Lsssssssss ssssss Lsssssssss</tt><br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
| Line 403: | Line 392: | ||
<td style="text-align: center;">2.2123729809<br /> | <td style="text-align: center;">2.2123729809<br /> | ||
</td> | </td> | ||
<td><tt> Lssssssssss sssss Lssssssssss </tt><br /> | <td><tt>Lssssssssss sssss Lssssssssss</tt><br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
| Line 413: | Line 402: | ||
<td style="text-align: center;">4.6548475771<br /> | <td style="text-align: center;">4.6548475771<br /> | ||
</td> | </td> | ||
<td><tt> Lssssssssss ssssss Lssssssssss </tt><br /> | <td><tt>Lssssssssss ssssss Lssssssssss</tt><br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
| Line 423: | Line 412: | ||
<td style="text-align: center;">1.2123729809<br /> | <td style="text-align: center;">1.2123729809<br /> | ||
</td> | </td> | ||
<td><tt> Lsssssssssss sssss Lsssssssssss </tt><br /> | <td><tt>Lsssssssssss sssss Lsssssssssss</tt><br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
| Line 433: | Line 422: | ||
<td style="text-align: center;">7.0973221733<br /> | <td style="text-align: center;">7.0973221733<br /> | ||
</td> | </td> | ||
<td><tt> Lssssssssss sssssss Lssssssssss </tt><br /> | <td><tt>Lssssssssss sssssss Lssssssssss</tt><br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
| Line 443: | Line 432: | ||
<td style="text-align: center;">3.6548475771<br /> | <td style="text-align: center;">3.6548475771<br /> | ||
</td> | </td> | ||
<td><tt> Lsssssssssss ssssss Lsssssssssss </tt><br /> | <td><tt>Lsssssssssss ssssss Lsssssssssss</tt><br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
| Line 453: | Line 442: | ||
<td style="text-align: center;">6.0973221733<br /> | <td style="text-align: center;">6.0973221733<br /> | ||
</td> | </td> | ||
<td><tt> Lsssssssssss sssssss Lsssssssssss </tt><br /> | <td><tt>Lsssssssssss sssssss Lsssssssssss</tt><br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
| Line 463: | Line 452: | ||
<td style="text-align: center;">2.6548475771<br /> | <td style="text-align: center;">2.6548475771<br /> | ||
</td> | </td> | ||
<td><tt> Lssssssssssss ssssss Lssssssssssss </tt><br /> | <td><tt>Lssssssssssss ssssss Lssssssssssss</tt><br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
| Line 473: | Line 462: | ||
<td style="text-align: center;">5.0973221733<br /> | <td style="text-align: center;">5.0973221733<br /> | ||
</td> | </td> | ||
<td><tt> Lssssssssssss sssssss Lssssssssssss </tt><br /> | <td><tt>Lssssssssssss sssssss Lssssssssssss</tt><br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
| Line 483: | Line 472: | ||
<td style="text-align: center;">1.6548475771<br /> | <td style="text-align: center;">1.6548475771<br /> | ||
</td> | </td> | ||
<td><tt> Lsssssssssssss ssssss Lsssssssssssss </tt><br /> | <td><tt>Lsssssssssssss ssssss Lsssssssssssss</tt><br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
| Line 493: | Line 482: | ||
<td style="text-align: center;">6.5397967694<br /> | <td style="text-align: center;">6.5397967694<br /> | ||
</td> | </td> | ||
<td><tt> Lssssssssssss ssssssss Lssssssssssss </tt><br /> | <td><tt>Lssssssssssss ssssssss Lssssssssssss</tt><br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
| Line 503: | Line 492: | ||
<td style="text-align: center;">4.0973221733<br /> | <td style="text-align: center;">4.0973221733<br /> | ||
</td> | </td> | ||
<td><tt> Lsssssssssssss sssssss Lsssssssssssss </tt><br /> | <td><tt>Lsssssssssssss sssssss Lsssssssssssss</tt><br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
| Line 513: | Line 502: | ||
<td style="text-align: center;">6.5397967694<br /> | <td style="text-align: center;">6.5397967694<br /> | ||
</td> | </td> | ||
<td><tt> Lsssssssssssss ssssssss Lsssssssssssss </tt><br /> | <td><tt>Lsssssssssssss ssssssss Lsssssssssssss</tt><br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
| Line 523: | Line 512: | ||
<td style="text-align: center;">3.0973221733<br /> | <td style="text-align: center;">3.0973221733<br /> | ||
</td> | </td> | ||
<td><tt> Lssssssssssssss sssssss Lssssssssssssss </tt><br /> | <td><tt>Lssssssssssssss sssssss Lssssssssssssss</tt><br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
| Line 533: | Line 522: | ||
<td style="text-align: center;">5.5397967694<br /> | <td style="text-align: center;">5.5397967694<br /> | ||
</td> | </td> | ||
<td><tt> Lssssssssssssss ssssssss Lssssssssssssss </tt><br /> | <td><tt>Lssssssssssssss ssssssss Lssssssssssssss</tt><br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
| Line 543: | Line 532: | ||
<td style="text-align: center;">2.0973221733<br /> | <td style="text-align: center;">2.0973221733<br /> | ||
</td> | </td> | ||
<td><tt> Lsssssssssssssss sssssss Lsssssssssssssss </tt><br /> | <td><tt>Lsssssssssssssss sssssss Lsssssssssssssss</tt><br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
| Line 553: | Line 542: | ||
<td style="text-align: center;">4.5397967694<br /> | <td style="text-align: center;">4.5397967694<br /> | ||
</td> | </td> | ||
<td><tt> Lsssssssssssssss ssssssss Lsssssssssssssss </tt><br /> | <td><tt>Lsssssssssssssss ssssssss Lsssssssssssssss</tt><br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
| Line 563: | Line 552: | ||
<td style="text-align: center;">1.0973221733<br /> | <td style="text-align: center;">1.0973221733<br /> | ||
</td> | </td> | ||
<td><tt> Lssssssssssssssss sssssss Lssssssssssssssss </tt><br /> | <td><tt>Lssssssssssssssss sssssss Lssssssssssssssss</tt><br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
| Line 573: | Line 562: | ||
<td style="text-align: center;">6.9822713656<br /> | <td style="text-align: center;">6.9822713656<br /> | ||
</td> | </td> | ||
<td><tt> Lsssssssssssssss sssssssss Lsssssssssssssss </tt><br /> | <td><tt>Lsssssssssssssss sssssssss Lsssssssssssssss</tt><br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
| Line 583: | Line 572: | ||
<td style="text-align: center;">3.5397967694<br /> | <td style="text-align: center;">3.5397967694<br /> | ||
</td> | </td> | ||
<td><tt> Lssssssssssssssss ssssssss Lssssssssssssssss </tt><br /> | <td><tt>Lssssssssssssssss ssssssss Lssssssssssssssss</tt><br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
| Line 593: | Line 582: | ||
<td style="text-align: center;">5.9822713656<br /> | <td style="text-align: center;">5.9822713656<br /> | ||
</td> | </td> | ||
<td><tt> Lssssssssssssssss sssssssss Lssssssssssssssss </tt><br /> | <td><tt>Lssssssssssssssss sssssssss Lssssssssssssssss</tt><br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
| Line 603: | Line 592: | ||
<td style="text-align: center;">2.5397967694<br /> | <td style="text-align: center;">2.5397967694<br /> | ||
</td> | </td> | ||
<td><tt> Lsssssssssssssssss ssssssss Lsssssssssssssssss </tt><br /> | <td><tt>Lsssssssssssssssss ssssssss Lsssssssssssssssss</tt><br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
| Line 613: | Line 602: | ||
<td style="text-align: center;">4.9822713656<br /> | <td style="text-align: center;">4.9822713656<br /> | ||
</td> | </td> | ||
<td><tt> Lsssssssssssssssss sssssssss Lsssssssssssssssss </tt><br /> | <td><tt>Lsssssssssssssssss sssssssss Lsssssssssssssssss</tt><br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
| Line 623: | Line 612: | ||
<td style="text-align: center;">1.5397967694<br /> | <td style="text-align: center;">1.5397967694<br /> | ||
</td> | </td> | ||
<td><tt> Lssssssssssssssssss ssssssss Lssssssssssssssssss </tt><br /> | <td><tt>Lssssssssssssssssss ssssssss Lssssssssssssssssss</tt><br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
| Line 633: | Line 622: | ||
<td style="text-align: center;">7.4247459618<br /> | <td style="text-align: center;">7.4247459618<br /> | ||
</td> | </td> | ||
<td><tt> Lsssssssssssssssss ssssssssss Lsssssssssssssssss </tt><br /> | <td><tt>Lsssssssssssssssss ssssssssss Lsssssssssssssssss</tt><br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
| Line 643: | Line 632: | ||
<td style="text-align: center;">3.9822713656<br /> | <td style="text-align: center;">3.9822713656<br /> | ||
</td> | </td> | ||
<td><tt> Lssssssssssssssssss sssssssss Lssssssssssssssssss </tt><br /> | <td><tt>Lssssssssssssssssss sssssssss Lssssssssssssssssss</tt><br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
| Line 653: | Line 642: | ||
<td style="text-align: center;">6.4247459618<br /> | <td style="text-align: center;">6.4247459618<br /> | ||
</td> | </td> | ||
<td><tt> Lssssssssssssssssss ssssssssss Lssssssssssssssssss </tt><br /> | <td><tt>Lssssssssssssssssss ssssssssss Lssssssssssssssssss</tt><br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
| Line 663: | Line 652: | ||
<td style="text-align: center;">2.9822713656<br /> | <td style="text-align: center;">2.9822713656<br /> | ||
</td> | </td> | ||
<td><tt> Lsssssssssssssssssss sssssssss Lsssssssssssssssssss </tt><br /> | <td><tt>Lsssssssssssssssssss sssssssss Lsssssssssssssssssss</tt><br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
| Line 673: | Line 662: | ||
<td style="text-align: center;">5.4247459618<br /> | <td style="text-align: center;">5.4247459618<br /> | ||
</td> | </td> | ||
<td><tt> Lsssssssssssssssssss ssssssssss Lsssssssssssssssssss </tt><br /> | <td><tt>Lsssssssssssssssssss ssssssssss Lsssssssssssssssssss</tt><br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
| Line 683: | Line 672: | ||
<td style="text-align: center;">1.9822713656<br /> | <td style="text-align: center;">1.9822713656<br /> | ||
</td> | </td> | ||
<td><tt> Lssssssssssssssssssss sssssssss Lssssssssssssssssssss </tt><br /> | <td><tt>Lssssssssssssssssssss sssssssss Lssssssssssssssssssss</tt><br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
| Line 693: | Line 682: | ||
<td style="text-align: center;">4.4247459618<br /> | <td style="text-align: center;">4.4247459618<br /> | ||
</td> | </td> | ||
<td><tt> Lssssssssssssssssssss ssssssssss Lssssssssssssssssssss </tt><br /> | <td><tt>Lssssssssssssssssssss ssssssssss Lssssssssssssssssssss</tt><br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
| Line 703: | Line 692: | ||
<td style="text-align: center;">0.9822713656<br /> | <td style="text-align: center;">0.9822713656<br /> | ||
</td> | </td> | ||
<td><tt> Lsssssssssssssssssssss sssssssss Lsssssssssssssssssssss </tt><br /> | <td><tt>Lsssssssssssssssssssss sssssssss Lsssssssssssssssssssss</tt><br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
| Line 709: | Line 698: | ||
<td>53b<br /> | <td>53b<br /> | ||
</td> | </td> | ||
<td style="text-align: center;"> | <td style="text-align: center;">2L+51s<br /> | ||
</td> | </td> | ||
<td style="text-align: center;"> | <td style="text-align: center;">6.8672205580<br /> | ||
</td> | </td> | ||
<td><tt> Lssssssssssssssssssss sssssssssss Lssssssssssssssssssss </tt><br /> | <td><tt>Lssssssssssssssssssss sssssssssss Lssssssssssssssssssss</tt><br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
</table> | </table> | ||
etc. <br /> | etc.<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule:0:&lt;h3&gt; --><h3 id="toc0"><a name="x--See also"></a><!-- ws:end:WikiTextHeadingRule:0 -->See also</h3> | <!-- 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> | <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> | ||