5L 2s: Difference between revisions

Wikispaces>JosephRuhf
**Imported revision 508685194 - Original comment: **
Wikispaces>JosephRuhf
**Imported revision 512838698 - Original comment: **
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<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:JosephRuhf|JosephRuhf]] and made on <tt>2014-05-13 16:43:45 UTC</tt>.<br>
: This revision was by author [[User:JosephRuhf|JosephRuhf]] and made on <tt>2014-06-04 14:39:51 UTC</tt>.<br>
: The original revision id was <tt>508685194</tt>.<br>
: The original revision id was <tt>512838698</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>
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If we carry this freshman-summing out a little further, new, larger [[edo]]s pop up in our continuum.
If we carry this freshman-summing out a little further, new, larger [[edo]]s pop up in our continuum.


||||||||||||~ generator ||~ in cents ||~ scale in steps of an [[edo]] ||~  ||~  ||~ comments ||
||||||||||||~ generator ||~ in cents ||~ scale in steps of an [[edo]] ||~  ||~  ||~  ||~  ||~ comments ||
||= 3\7 ||=  ||=  ||=  ||=  ||=  ||= 514.286 ||= 1 1 1 1 1 1 1 || 307.521 || 378.193 ||=  ||
||= 3\7 ||=  ||=  ||=  ||=  ||=  ||= 514.286 ||= 1 1 1 1 1 1 1 || 239.2945 || 274.991 || 307.521 || 378.193 ||=  ||
||=  ||=  ||=  ||=  ||=  ||= 17\40 ||= 510.000 ||= 6 6 5 6 6 6 5 || 309.664 || 380.336 ||=  ||
||=  ||=  ||=  ||=  ||=  ||= 17\40 ||= 510.000 ||= 6 6 5 6 6 6 5 || 237.152 || 272.848 || 309.664 || 380.336 ||=  ||
||=  ||=  ||=  ||=  ||= 14\33 ||=  ||= 509.091 ||= 5 5 4 5 5 5 4 || 310.118 || 380.791 ||=  ||
||=  ||=  ||=  ||=  ||= 14\33 ||=  ||= 509.091 ||= 5 5 4 5 5 5 4 || 236.697 || 272.394 || 310.118 || 380.791 ||=  ||
||=  ||=  ||=  ||=  ||=  ||= 25\59 ||= 508.475 ||= 9 9 7 9 9 9 7 || 310.4265 || 381.0485 ||=  ||
||=  ||=  ||=  ||=  ||=  ||= 25\59 ||= 508.475 ||= 9 9 7 9 9 9 7 || 236.389 || 272.086 || 310.4265 || 381.0985 ||=  ||
||=  ||=  ||=  ||= 11\26 ||=  ||=  ||= 507.692 ||= 4 4 3 4 4 4 3 || 310.817 || 381.491 ||=  ||
||=  ||=  ||=  ||= 11\26 ||=  ||=  ||= 507.692 ||= 4 4 3 4 4 4 3 || 235.998 || 271.695 || 310.817 || 381.491 ||=  ||
||=  ||=  ||=  ||=  ||=  ||= 30\71 ||= 507.042 ||= 11 11 8 11 11 11 8 || 311.142 || 381.846 ||=  ||
||=  ||=  ||=  ||=  ||=  ||= 30\71 ||= 507.042 ||= 11 11 8 11 11 11 8 || 235.672 || 271.3695 || 311.142 || 381.846 ||=  ||
||=  ||=  ||=  ||=  ||= 19\45 ||=  ||= 506.667 ||= 7 7 5 7 7 7 5 || 311.33 || 382.003 ||=  ||
||=  ||=  ||=  ||=  ||= 19\45 ||=  ||= 506.667 ||= 7 7 5 7 7 7 5 || 235.485 || 271.182 || 311.33 || 382.003 ||=  ||
||=  ||=  ||=  ||=  ||=  ||= 27\64 ||= 506.250 ||= 10 10 7 10 10 10 7 || 311.539 || 382.211 ||=  ||
||=  ||=  ||=  ||=  ||=  ||= 27\64 ||= 506.250 ||= 10 10 7 10 10 10 7 || 235.277 || 270.973 || 311.539 || 382.211 ||=  ||
||=  ||=  ||= 8\19 ||=  ||=  ||=  ||= 505.263 ||= 3 3 2 3 3 3 2 || 312.032 || 382.705 ||= Optimum rank range (L/s=3/2) diatonic ||
||=  ||=  ||= 8\19 ||=  ||=  ||=  ||= 505.263 ||= 3 3 2 3 3 3 2 ||  ||  || 312.032 || 382.705 ||= Optimum rank range (L/s=3/2) diatonic ||
||=  ||=  ||=  ||=  ||=  ||= 29\69 ||= 504.348 ||= 11 11 7 11 11 11 7 || 312.490 || 383.172 ||=  ||
||=  ||=  ||=  ||=  ||=  ||= 29\69 ||= 504.348 ||= 11 11 7 11 11 11 7 ||  ||  || 312.490 || 383.172 ||=  ||
||=  ||=  ||=  ||=  ||= 21\50 ||=  ||= 504.000 ||= 8 8 5 8 8 8 5 || 312.664 || 383.336 ||=  ||
||=  ||=  ||=  ||=  ||= 21\50 ||=  ||= 504.000 ||= 8 8 5 8 8 8 5 ||  ||  || 312.664 || 383.336 ||=  ||
||=  ||=  ||=  ||=  ||=  ||= 34\81 ||= 503.704 ||= 13 13 8 13 13 13 8 || 312.811 || 383.485 ||= Golden meantone ||
||=  ||=  ||=  ||=  ||=  ||= 34\81 ||= 503.704 ||= 13 13 8 13 13 13 8 ||  ||  || 312.811 || 383.485 ||= Golden meantone ||
||=  ||=  ||=  ||= 13\31 ||=  ||=  ||= 503.226 ||= 5 5 3 5 5 5 3 || 313.051 || 383.723 ||= Meantone is in this region ||
||=  ||=  ||=  ||= 13\31 ||=  ||=  ||= 503.226 ||= 5 5 3 5 5 5 3 ||  ||  || 313.051 || 383.723 ||= Meantone is in this region ||
||=  ||=  ||=  ||=  ||=  ||= 31\74 ||= 502.703 ||= 12 12 7 12 12 12 7 || 313.312 || 383.985 ||=  ||
||=  ||=  ||=  ||=  ||=  ||= 31\74 ||= 502.703 ||= 12 12 7 12 12 12 7 ||  ||  || 313.312 || 383.985 ||=  ||
||=  ||=  ||=  ||=  ||= 18\43 ||=  ||= 502.326 ||= 7 7 4 7 7 7 4 || 313.501 || 384.183 ||=  ||
||=  ||=  ||=  ||=  ||= 18\43 ||=  ||= 502.326 ||= 7 7 4 7 7 7 4 ||  ||  || 313.501 || 384.183 ||=  ||
||=  ||=  ||=  ||=  ||=  ||= 23\55 ||= 501.818 ||= 9 9 5 9 9 9 5 || 313.754 || 384.428 ||=  ||
||=  ||=  ||=  ||=  ||=  ||= 23\55 ||= 501.818 ||= 9 9 5 9 9 9 5 ||  ||  || 313.754 || 384.428 ||=  ||
||=  ||= 5\12 ||=  ||=  ||=  ||=  ||= 500.000 ||= 2 2 1 2 2 2 1 || 314.664 || 385.336 ||= Boundary of propriety (generators
||=  ||= 5\12 ||=  ||=  ||=  ||=  ||= 500.000 ||= 2 2 1 2 2 2 1 ||  ||  || 314.664 || 385.336 ||= Boundary of propriety (generators
larger than this are proper) ||
larger than this are proper) ||
||=  ||=  ||=  ||=  ||=  ||= 22\53 ||= 498.113 ||= 9 9 4 9 9 9 4 || 315.609 || 386.278 ||= Pythagorean is around here ||
||=  ||=  ||=  ||=  ||=  ||= 22\53 ||= 498.113 ||= 9 9 4 9 9 9 4 ||  ||  || 315.609 || 386.278 ||= Pythagorean is around here ||
||=  ||=  ||=  ||=  ||= 17\41 ||=  ||= 497.591 ||= 7 7 3 7 7 7 3 || 315.883 || 386.556 ||=  ||
||=  ||=  ||=  ||=  ||= 17\41 ||=  ||= 497.591 ||= 7 7 3 7 7 7 3 ||  ||  || 315.883 || 386.556 ||=  ||
||=  ||=  ||=  ||=  ||=  ||= 29\70 ||= 497.143 ||= 12 12 5 12 12 12 5 || 316.092 || 386.765 ||=  ||
||=  ||=  ||=  ||=  ||=  ||= 29\70 ||= 497.143 ||= 12 12 5 12 12 12 5 ||  ||  || 316.092 || 386.765 ||=  ||
||=  ||=  ||=  ||= 12\29 ||=  ||=  ||= 496.552 ||= 5 5 2 5 5 5 2 || 316.388 || 387.061 ||=  ||
||=  ||=  ||=  ||= 12\29 ||=  ||=  ||= 496.552 ||= 5 5 2 5 5 5 2 ||  ||  || 316.388 || 387.061 ||=  ||
||=  ||=  ||=  ||=  ||=  ||= 31\75 ||= 496.000 ||= 13 13 5 13 13 13 5 || 316.664 || 387.336 ||=  ||
||=  ||=  ||=  ||=  ||=  ||= 31\75 ||= 496.000 ||= 13 13 5 13 13 13 5 ||  ||  || 316.664 || 387.336 ||=  ||
||=  ||=  ||=  ||=  ||= 19\46 ||=  ||= 495.652 ||= 8 8 3 8 8 8 3 || 316.837 || 387.511 ||=  ||
||=  ||=  ||=  ||=  ||= 19\46 ||=  ||= 495.652 ||= 8 8 3 8 8 8 3 ||  ||  || 316.837 || 387.511 ||=  ||
||=  ||=  ||=  ||=  ||=  ||= 26\63 ||= 495.238 ||= 11 11 4 11 11 11 4 || 317.045 || 387.717 ||=  ||
||=  ||=  ||=  ||=  ||=  ||= 26\63 ||= 495.238 ||= 11 11 4 11 11 11 4 ||  ||  || 317.045 || 387.717 ||=  ||
||=  ||=  ||= 7\17 ||=  ||=  ||=  ||= 494.118 ||= 3 3 1 3 3 3 1 || 317.596 || 388.286 ||= L/s = 3 ||
||=  ||=  ||= 7\17 ||=  ||=  ||=  ||= 494.118 ||= 3 3 1 3 3 3 1 ||  ||  || 317.596 || 388.286 ||= L/s = 3 ||
||=  ||=  ||=  ||=  ||=  ||= 23\56 ||= 492.857 ||= 10 10 3 10 10 10 3 || 318.235 || 388.908 ||=  ||
||=  ||=  ||=  ||=  ||=  ||= 23\56 ||= 492.857 ||= 10 10 3 10 10 10 3 ||  ||  || 318.235 || 388.908 ||=  ||
||=  ||=  ||=  ||=  ||= 16\39 ||=  ||= 492.308 ||= 7 7 2 7 7 7 2 || 318.51 || 389.182 ||=  ||
||=  ||=  ||=  ||=  ||= 16\39 ||=  ||= 492.308 ||= 7 7 2 7 7 7 2 ||  ||  || 318.51 || 389.182 ||=  ||
||=  ||=  ||=  ||=  ||=  ||= 25\61 ||= 491.803 ||= 11 11 3 11 11 11 3 || 318.761 || 389.436 ||=  ||
||=  ||=  ||=  ||=  ||=  ||= 25\61 ||= 491.803 ||= 11 11 3 11 11 11 3 ||  ||  || 318.761 || 389.436 ||=  ||
||=  ||=  ||=  ||= 9\22 ||=  ||=  ||= 490.909 ||= 4 4 1 4 4 4 1 || 319.209 || 389.882 ||= (No-5's) superpyth is in this region
||=  ||=  ||=  ||= 9\22 ||=  ||=  ||= 490.909 ||= 4 4 1 4 4 4 1 ||  ||  || 319.209 || 389.882 ||= (No-5's) superpyth is in this region
L/s = 4 ||
L/s = 4 ||
||=  ||=  ||=  ||=  ||=  ||= 20\49 ||= 489.796 ||= 9 9 2 9 9 9 2 || 319.766 || 390.438 ||=  ||
||=  ||=  ||=  ||=  ||=  ||= 20\49 ||= 489.796 ||= 9 9 2 9 9 9 2 ||  ||  || 319.766 || 390.438 ||=  ||
||=  ||=  ||=  ||=  ||= 11\27 ||=  ||= 488.889 ||= 5 5 1 5 5 5 1 || 320.219 || 390.892 ||=  ||
||=  ||=  ||=  ||=  ||= 11\27 ||=  ||= 488.889 ||= 5 5 1 5 5 5 1 ||  ||  || 320.219 || 390.892 ||=  ||
||=  ||=  ||=  ||=  ||=  ||= 13\32 ||= 487.500 ||= 6 6 1 6 6 6 1 || 320.914 || 391.596 ||=  ||
||=  ||=  ||=  ||=  ||=  ||= 13\32 ||= 487.500 ||= 6 6 1 6 6 6 1 ||  ||  || 320.914 || 391.596 ||=  ||
||= 2\5 ||=  ||=  ||=  ||=  ||=  ||= 480.000 ||= 1 1 0 1 1 1 0 || 324.664 || 395.336 ||=  ||
||= 2\5 ||=  ||=  ||=  ||=  ||=  ||= 480.000 ||= 1 1 0 1 1 1 0 ||  ||  || 324.664 || 395.336 ||=  ||


Temperaments above 5\12 on this chart are called "negative temperaments" (as they lessen the size of the fifth) and include meantone systems such as 1/3-comma (close to 8\19) and 1/4-comma (close to 13\31). As these tunings approach 3\7, the majors become flatter and the minors become sharper.
Temperaments above 5\12 on this chart are called "negative temperaments" (as they lessen the size of the fifth) and include meantone systems such as 1/3-comma (close to 8\19) and 1/4-comma (close to 13\31). As these tunings approach 3\7, the majors become flatter and the minors become sharper.
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&lt;/th&gt;
&lt;/th&gt;
         &lt;th&gt;scale in steps of an &lt;a class="wiki_link" href="/edo"&gt;edo&lt;/a&gt;&lt;br /&gt;
         &lt;th&gt;scale in steps of an &lt;a class="wiki_link" href="/edo"&gt;edo&lt;/a&gt;&lt;br /&gt;
&lt;/th&gt;
        &lt;th&gt;&lt;br /&gt;
&lt;/th&gt;
        &lt;th&gt;&lt;br /&gt;
&lt;/th&gt;
&lt;/th&gt;
         &lt;th&gt;&lt;br /&gt;
         &lt;th&gt;&lt;br /&gt;
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&lt;/td&gt;
&lt;/td&gt;
         &lt;td style="text-align: center;"&gt;1 1 1 1 1 1 1&lt;br /&gt;
         &lt;td style="text-align: center;"&gt;1 1 1 1 1 1 1&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;239.2945&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;274.991&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;307.521&lt;br /&gt;
         &lt;td&gt;307.521&lt;br /&gt;
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&lt;/td&gt;
&lt;/td&gt;
         &lt;td style="text-align: center;"&gt;6 6 5 6 6 6 5&lt;br /&gt;
         &lt;td style="text-align: center;"&gt;6 6 5 6 6 6 5&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;237.152&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;272.848&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;309.664&lt;br /&gt;
         &lt;td&gt;309.664&lt;br /&gt;
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&lt;/td&gt;
&lt;/td&gt;
         &lt;td style="text-align: center;"&gt;5 5 4 5 5 5 4&lt;br /&gt;
         &lt;td style="text-align: center;"&gt;5 5 4 5 5 5 4&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;236.697&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;272.394&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;310.118&lt;br /&gt;
         &lt;td&gt;310.118&lt;br /&gt;
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&lt;/td&gt;
&lt;/td&gt;
         &lt;td style="text-align: center;"&gt;9 9 7 9 9 9 7&lt;br /&gt;
         &lt;td style="text-align: center;"&gt;9 9 7 9 9 9 7&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;236.389&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;272.086&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;310.4265&lt;br /&gt;
         &lt;td&gt;310.4265&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;381.0485&lt;br /&gt;
         &lt;td&gt;381.0985&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td style="text-align: center;"&gt;&lt;br /&gt;
         &lt;td style="text-align: center;"&gt;&lt;br /&gt;
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&lt;/td&gt;
&lt;/td&gt;
         &lt;td style="text-align: center;"&gt;4 4 3 4 4 4 3&lt;br /&gt;
         &lt;td style="text-align: center;"&gt;4 4 3 4 4 4 3&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;235.998&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;271.695&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;310.817&lt;br /&gt;
         &lt;td&gt;310.817&lt;br /&gt;
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&lt;/td&gt;
&lt;/td&gt;
         &lt;td style="text-align: center;"&gt;11 11 8 11 11 11 8&lt;br /&gt;
         &lt;td style="text-align: center;"&gt;11 11 8 11 11 11 8&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;235.672&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;271.3695&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;311.142&lt;br /&gt;
         &lt;td&gt;311.142&lt;br /&gt;
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&lt;/td&gt;
&lt;/td&gt;
         &lt;td style="text-align: center;"&gt;7 7 5 7 7 7 5&lt;br /&gt;
         &lt;td style="text-align: center;"&gt;7 7 5 7 7 7 5&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;235.485&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;271.182&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;311.33&lt;br /&gt;
         &lt;td&gt;311.33&lt;br /&gt;
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&lt;/td&gt;
&lt;/td&gt;
         &lt;td style="text-align: center;"&gt;10 10 7 10 10 10 7&lt;br /&gt;
         &lt;td style="text-align: center;"&gt;10 10 7 10 10 10 7&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;235.277&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;270.973&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;311.539&lt;br /&gt;
         &lt;td&gt;311.539&lt;br /&gt;
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&lt;/td&gt;
&lt;/td&gt;
         &lt;td style="text-align: center;"&gt;3 3 2 3 3 3 2&lt;br /&gt;
         &lt;td style="text-align: center;"&gt;3 3 2 3 3 3 2&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;312.032&lt;br /&gt;
         &lt;td&gt;312.032&lt;br /&gt;
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&lt;/td&gt;
&lt;/td&gt;
         &lt;td style="text-align: center;"&gt;11 11 7 11 11 11 7&lt;br /&gt;
         &lt;td style="text-align: center;"&gt;11 11 7 11 11 11 7&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;312.490&lt;br /&gt;
         &lt;td&gt;312.490&lt;br /&gt;
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&lt;/td&gt;
&lt;/td&gt;
         &lt;td style="text-align: center;"&gt;8 8 5 8 8 8 5&lt;br /&gt;
         &lt;td style="text-align: center;"&gt;8 8 5 8 8 8 5&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;312.664&lt;br /&gt;
         &lt;td&gt;312.664&lt;br /&gt;
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&lt;/td&gt;
&lt;/td&gt;
         &lt;td style="text-align: center;"&gt;13 13 8 13 13 13 8&lt;br /&gt;
         &lt;td style="text-align: center;"&gt;13 13 8 13 13 13 8&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;312.811&lt;br /&gt;
         &lt;td&gt;312.811&lt;br /&gt;
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&lt;/td&gt;
&lt;/td&gt;
         &lt;td style="text-align: center;"&gt;5 5 3 5 5 5 3&lt;br /&gt;
         &lt;td style="text-align: center;"&gt;5 5 3 5 5 5 3&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;313.051&lt;br /&gt;
         &lt;td&gt;313.051&lt;br /&gt;
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&lt;/td&gt;
&lt;/td&gt;
         &lt;td style="text-align: center;"&gt;12 12 7 12 12 12 7&lt;br /&gt;
         &lt;td style="text-align: center;"&gt;12 12 7 12 12 12 7&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;313.312&lt;br /&gt;
         &lt;td&gt;313.312&lt;br /&gt;
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&lt;/td&gt;
&lt;/td&gt;
         &lt;td style="text-align: center;"&gt;7 7 4 7 7 7 4&lt;br /&gt;
         &lt;td style="text-align: center;"&gt;7 7 4 7 7 7 4&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;313.501&lt;br /&gt;
         &lt;td&gt;313.501&lt;br /&gt;
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&lt;/td&gt;
&lt;/td&gt;
         &lt;td style="text-align: center;"&gt;9 9 5 9 9 9 5&lt;br /&gt;
         &lt;td style="text-align: center;"&gt;9 9 5 9 9 9 5&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;313.754&lt;br /&gt;
         &lt;td&gt;313.754&lt;br /&gt;
Line 596: Line 664:
&lt;/td&gt;
&lt;/td&gt;
         &lt;td style="text-align: center;"&gt;2 2 1 2 2 2 1&lt;br /&gt;
         &lt;td style="text-align: center;"&gt;2 2 1 2 2 2 1&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;314.664&lt;br /&gt;
         &lt;td&gt;314.664&lt;br /&gt;
Line 621: Line 693:
&lt;/td&gt;
&lt;/td&gt;
         &lt;td style="text-align: center;"&gt;9 9 4 9 9 9 4&lt;br /&gt;
         &lt;td style="text-align: center;"&gt;9 9 4 9 9 9 4&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;315.609&lt;br /&gt;
         &lt;td&gt;315.609&lt;br /&gt;
Line 645: Line 721:
&lt;/td&gt;
&lt;/td&gt;
         &lt;td style="text-align: center;"&gt;7 7 3 7 7 7 3&lt;br /&gt;
         &lt;td style="text-align: center;"&gt;7 7 3 7 7 7 3&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;315.883&lt;br /&gt;
         &lt;td&gt;315.883&lt;br /&gt;
Line 669: Line 749:
&lt;/td&gt;
&lt;/td&gt;
         &lt;td style="text-align: center;"&gt;12 12 5 12 12 12 5&lt;br /&gt;
         &lt;td style="text-align: center;"&gt;12 12 5 12 12 12 5&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;316.092&lt;br /&gt;
         &lt;td&gt;316.092&lt;br /&gt;
Line 693: Line 777:
&lt;/td&gt;
&lt;/td&gt;
         &lt;td style="text-align: center;"&gt;5 5 2 5 5 5 2&lt;br /&gt;
         &lt;td style="text-align: center;"&gt;5 5 2 5 5 5 2&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;316.388&lt;br /&gt;
         &lt;td&gt;316.388&lt;br /&gt;
Line 717: Line 805:
&lt;/td&gt;
&lt;/td&gt;
         &lt;td style="text-align: center;"&gt;13 13 5 13 13 13 5&lt;br /&gt;
         &lt;td style="text-align: center;"&gt;13 13 5 13 13 13 5&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;316.664&lt;br /&gt;
         &lt;td&gt;316.664&lt;br /&gt;
Line 741: Line 833:
&lt;/td&gt;
&lt;/td&gt;
         &lt;td style="text-align: center;"&gt;8 8 3 8 8 8 3&lt;br /&gt;
         &lt;td style="text-align: center;"&gt;8 8 3 8 8 8 3&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;316.837&lt;br /&gt;
         &lt;td&gt;316.837&lt;br /&gt;
Line 765: Line 861:
&lt;/td&gt;
&lt;/td&gt;
         &lt;td style="text-align: center;"&gt;11 11 4 11 11 11 4&lt;br /&gt;
         &lt;td style="text-align: center;"&gt;11 11 4 11 11 11 4&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;317.045&lt;br /&gt;
         &lt;td&gt;317.045&lt;br /&gt;
Line 789: Line 889:
&lt;/td&gt;
&lt;/td&gt;
         &lt;td style="text-align: center;"&gt;3 3 1 3 3 3 1&lt;br /&gt;
         &lt;td style="text-align: center;"&gt;3 3 1 3 3 3 1&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;317.596&lt;br /&gt;
         &lt;td&gt;317.596&lt;br /&gt;
Line 813: Line 917:
&lt;/td&gt;
&lt;/td&gt;
         &lt;td style="text-align: center;"&gt;10 10 3 10 10 10 3&lt;br /&gt;
         &lt;td style="text-align: center;"&gt;10 10 3 10 10 10 3&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;318.235&lt;br /&gt;
         &lt;td&gt;318.235&lt;br /&gt;
Line 837: Line 945:
&lt;/td&gt;
&lt;/td&gt;
         &lt;td style="text-align: center;"&gt;7 7 2 7 7 7 2&lt;br /&gt;
         &lt;td style="text-align: center;"&gt;7 7 2 7 7 7 2&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;318.51&lt;br /&gt;
         &lt;td&gt;318.51&lt;br /&gt;
Line 861: Line 973:
&lt;/td&gt;
&lt;/td&gt;
         &lt;td style="text-align: center;"&gt;11 11 3 11 11 11 3&lt;br /&gt;
         &lt;td style="text-align: center;"&gt;11 11 3 11 11 11 3&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;318.761&lt;br /&gt;
         &lt;td&gt;318.761&lt;br /&gt;
Line 885: Line 1,001:
&lt;/td&gt;
&lt;/td&gt;
         &lt;td style="text-align: center;"&gt;4 4 1 4 4 4 1&lt;br /&gt;
         &lt;td style="text-align: center;"&gt;4 4 1 4 4 4 1&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;319.209&lt;br /&gt;
         &lt;td&gt;319.209&lt;br /&gt;
Line 910: Line 1,030:
&lt;/td&gt;
&lt;/td&gt;
         &lt;td style="text-align: center;"&gt;9 9 2 9 9 9 2&lt;br /&gt;
         &lt;td style="text-align: center;"&gt;9 9 2 9 9 9 2&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;319.766&lt;br /&gt;
         &lt;td&gt;319.766&lt;br /&gt;
Line 934: Line 1,058:
&lt;/td&gt;
&lt;/td&gt;
         &lt;td style="text-align: center;"&gt;5 5 1 5 5 5 1&lt;br /&gt;
         &lt;td style="text-align: center;"&gt;5 5 1 5 5 5 1&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;320.219&lt;br /&gt;
         &lt;td&gt;320.219&lt;br /&gt;
Line 958: Line 1,086:
&lt;/td&gt;
&lt;/td&gt;
         &lt;td style="text-align: center;"&gt;6 6 1 6 6 6 1&lt;br /&gt;
         &lt;td style="text-align: center;"&gt;6 6 1 6 6 6 1&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;320.914&lt;br /&gt;
         &lt;td&gt;320.914&lt;br /&gt;
Line 982: Line 1,114:
&lt;/td&gt;
&lt;/td&gt;
         &lt;td style="text-align: center;"&gt;1 1 0 1 1 1 0&lt;br /&gt;
         &lt;td style="text-align: center;"&gt;1 1 0 1 1 1 0&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;324.664&lt;br /&gt;
         &lt;td&gt;324.664&lt;br /&gt;
Line 997: Line 1,133:
Temperaments below 5\12 on this chart are called &amp;quot;positive temperaments&amp;quot; and they include Pythagorean tuning itself (well approximated by 22\53) as well as superpyth temperaments such as 7\17 and 9\22. As these tunings approach 2\5, the majors become sharper and the minors become flatter. Around 9\22, the thirds fall closer to 7-limit than 5-limit intervals: 7:6 and 9:7 as opposed to 6:5 and 5:4.&lt;br /&gt;
Temperaments below 5\12 on this chart are called &amp;quot;positive temperaments&amp;quot; and they include Pythagorean tuning itself (well approximated by 22\53) as well as superpyth temperaments such as 7\17 and 9\22. As these tunings approach 2\5, the majors become sharper and the minors become flatter. Around 9\22, the thirds fall closer to 7-limit than 5-limit intervals: 7:6 and 9:7 as opposed to 6:5 and 5:4.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextLocalImageRule:834:&amp;lt;img src=&amp;quot;/file/view/5L2s.jpg/103741463/5L2s.jpg&amp;quot; alt=&amp;quot;&amp;quot; title=&amp;quot;&amp;quot; /&amp;gt; --&gt;&lt;img src="/file/view/5L2s.jpg/103741463/5L2s.jpg" alt="5L2s.jpg" title="5L2s.jpg" /&gt;&lt;!-- ws:end:WikiTextLocalImageRule:834 --&gt;&lt;br /&gt;
&lt;!-- ws:start:WikiTextLocalImageRule:970:&amp;lt;img src=&amp;quot;/file/view/5L2s.jpg/103741463/5L2s.jpg&amp;quot; alt=&amp;quot;&amp;quot; title=&amp;quot;&amp;quot; /&amp;gt; --&gt;&lt;img src="/file/view/5L2s.jpg/103741463/5L2s.jpg" alt="5L2s.jpg" title="5L2s.jpg" /&gt;&lt;!-- ws:end:WikiTextLocalImageRule:970 --&gt;&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
5L 2s contains the pentatonic MOS &lt;a class="wiki_link" href="/2L%203s"&gt;2L 3s&lt;/a&gt; and (with the sole exception of the 5L 2s of 12edo) is itself contained in a dodecaphonic MOS: either &lt;a class="wiki_link" href="/7L%205s"&gt;7L 5s&lt;/a&gt; or &lt;a class="wiki_link" href="/5L%207s"&gt;5L 7s&lt;/a&gt;.&lt;/body&gt;&lt;/html&gt;</pre></div>
5L 2s contains the pentatonic MOS &lt;a class="wiki_link" href="/2L%203s"&gt;2L 3s&lt;/a&gt; and (with the sole exception of the 5L 2s of 12edo) is itself contained in a dodecaphonic MOS: either &lt;a class="wiki_link" href="/7L%205s"&gt;7L 5s&lt;/a&gt; or &lt;a class="wiki_link" href="/5L%207s"&gt;5L 7s&lt;/a&gt;.&lt;/body&gt;&lt;/html&gt;</pre></div>