5L 2s: Difference between revisions

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<h2>IMPORTED REVISION FROM WIKISPACES</h2>

This is an imported revision from Wikispaces. The revision metadata is included below for reference:

: This revision was by author [[User:Andrew_Heathwaite|Andrew_Heathwaite]] and made on <tt>2009-11-~~04 16~~:31:20 UTC</tt>.

: This revision was by author [[User:Andrew_Heathwaite|Andrew_Heathwaite]] and made on <tt>2009-11-05 23:25:03 UTC</tt>.

: The original revision id was <tt>~~100233459~~</tt>.

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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">=5L 2s - "diatonic"=

One way of distinguishing the "diatonic" scale is by considering it a [[MOSScales|moment of symmetry]] scale produced by a chain of "fifths". This will include [[12edo]]'s diatonic scale along with the Pythagorean diatonic scale, while excluding just intonation scales that use more than one size of "tone".

One way of distinguishing the "diatonic" scale is by considering it a [[MOSScales|moment of symmetry]] scale produced by a chain of "fifths". This will include [[12edo]]'s diatonic scale along with the Pythagorean diatonic scale and meantone systems, while excluding just intonation scales that use more than one size of "tone".

It may be misleading to call 5L 2s "diatonic," since other scales called diatonic can be arrived at different ways (through just intonation procedures for instance, or with tetrachords). Also, a composer working with a 5L 2s scale may choose to do something very different than typical diatonic music.

==substituting step sizes==

~~This produces a~~ generalized ~~diatonic scale with the~~ form:

The 5L 2s MOS scale has this generalized form.

L L s L L L s

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If we carry this freshman-summing out a little further, new, larger [[edo]]s pop up in our continuum.

|| 3\7 || || || || || ||

||||||||||||~ generator ||~ in cents ||

|| || || || || || 17\40 ||

|| 3\7 || || || || || || 514.286 ||

|| || || || || 14\33 || ||

|| || || || || || 17\40 || 510.000 ||

|| || || || || || 25\59 ||

|| || || || || 14\33 || || 509.091 ||

|| || || || 11\26 || || ||

|| || || || || || 25\59 || 508.475 ||

|| || || || || || 30\71 ||

|| || || || 11\26 || || || 507.692 ||

|| || || || || 19\45 || ||

|| || || || || || 30\71 || 507.042 ||

|| || || || || || 27\63 ||

|| || || || || 19\45 || || 506.667 ||

|| || || 8\19 || || || ||

|| || || || || || 27\64 || 506.250 ||

|| || || || || || 29\69 ||

|| || || 8\19 || || || || 506.263 ||

|| || || || || 21\50 || ||

|| || || || || || 29\69 || 504.348 ||

|| || || || || || 34\81 ||

|| || || || || 21\50 || || 504.000 ||

|| || || || 13\31 || || ||

|| || || || || || 34\81 || 503.704 ||

|| || || || || || 31\74 ||

|| || || || 13\31 || || || 503.226 ||

|| || || || || 18\43 || ||

|| || || || || || 31\74 || 502.703 ||

|| || || || || || 23\55 ||

|| || || || || 18\43 || || 502.326 ||

|| || 5\12 || || || || ||

|| || || || || || 23\55 || 501.818 ||

|| || || || || || 22\53 ||

|| || 5\12 || || || || || 500.000 ||

|| || || || || 17\41 || ||

|| || || || || || 22\53 || 498.113 ||

|| || || || || || 29\60 ||

|| || || || || 17\41 || || 497.591 ||

|| || || || 12\29 || || ||

|| || || || || || 29\70 || 497.143 ||

|| || || || || || 31\75 ||

|| || || || 12\29 || || || 496.552 ||

|| || || || || 19\46 || ||

|| || || || || || 31\75 || 496.000 ||

|| || || || || || 26\63 ||

|| || || || || 19\46 || || 495.652 ||

|| || || 7\17 || || || ||

|| || || || || || 26\63 || 495.238 ||

|| || || || || || 23\56 ||

|| || || 7\17 || || || || 494.118 ||

|| || || || || 16\39 || ||

|| || || || || || 23\56 || 492.857 ||

|| || || || || || 25\61 ||

|| || || || || 16\39 || || 492.308 ||

|| || || || 9\22 || || ||

|| || || || || || 25\61 || 491.803 ||

|| || || || || || 28\49 ||

|| || || || 9\22 || || || 490.909 ||

|| || || || || 11\27 || ||

|| || || || || || 20\49 || 489.796 ||

|| || || || || || 19\32 ||

|| || || || || 11\27 || || 488.889 ||

|| 2\5 || || || || || ||

|| || || || || || 13\32 || 487.500 ||

|| 2\5 || || || || || || 480.000 ||

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 below 5/12 on this chart are called "positive temperaments" 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.</pre></div>

Temperaments below 5/12 on this chart are called "positive temperaments" 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.

5L 2s contains the pentatonic MOS [[2L 3s]] and (except for that in 12edo) is itself contained in a dodecaphonic MOS: either [[7L 5s]] or [[5L 7s]].</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>5L 2s</title></head><body><h1 id="toc0"><a name="x5L 2s - &quot;diatonic&quot;"></a>5L 2s - &quot;diatonic&quot;</h1>

One way of distinguishing the &quot;diatonic&quot; scale is by considering it a <a class="wiki_link" href="/MOSScales">moment of symmetry</a> scale produced by a chain of &quot;fifths&quot;. This will include <a class="wiki_link" href="/12edo">12edo</a>'s diatonic scale along with the Pythagorean diatonic scale, while excluding just intonation scales that use more than one size of &quot;tone&quot;.

One way of distinguishing the &quot;diatonic&quot; scale is by considering it a <a class="wiki_link" href="/MOSScales">moment of symmetry</a> scale produced by a chain of &quot;fifths&quot;. This will include <a class="wiki_link" href="/12edo">12edo</a>'s diatonic scale along with the Pythagorean diatonic scale and meantone systems, while excluding just intonation scales that use more than one size of &quot;tone&quot;.

It may be misleading to call 5L 2s &quot;diatonic,&quot; since other scales called diatonic can be arrived at different ways (through just intonation procedures for instance, or with tetrachords). Also, a composer working with a 5L 2s scale may choose to do something very different than typical diatonic music.

<h2 id="toc1"><a name="x5L 2s - &quot;diatonic&quot;-substituting step sizes"></a>substituting step sizes</h2>

~~This produces a~~ generalized ~~diatonic scale with the~~ form:

The 5L 2s MOS scale has this generalized form.

L L s L L L s

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<tr>

<th colspan="6">generator

</th>

<th>in cents

</th>

</tr>

<tr>

<td>3\7

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</td>

<td>

</td>

<td>514.286

</td>

</tr>

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Line 212:

</td>

<td>17\40

</td>

<td>510.000

</td>

</tr>

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Line 228:

</td>

<td>

</td>

<td>509.091

</td>

</tr>

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Line 244:

</td>

<td>25\59

</td>

<td>508.475

</td>

</tr>

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</td>

<td>

</td>

<td>507.692

</td>

</tr>

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</td>

<td>30\71

</td>

<td>507.042

</td>

</tr>

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</td>

<td>

</td>

<td>506.667

</td>

</tr>

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<td>

</td>

<td>27\63

<td>27\64

</td>

<td>506.250

</td>

</tr>

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</td>

<td>

</td>

<td>506.263

</td>

</tr>

Line 309:

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</td>

<td>29\69

</td>

<td>504.348

</td>

</tr>

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</td>

<td>

</td>

<td>504.000

</td>

</tr>

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</td>

<td>34\81

</td>

<td>503.704

</td>

</tr>

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</td>

<td>

</td>

<td>503.226

</td>

</tr>

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Line 404:

</td>

<td>31\74

</td>

<td>502.703

</td>

</tr>

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</td>

<td>

</td>

<td>502.326

</td>

</tr>

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Line 436:

</td>

<td>23\55

</td>

<td>501.818

</td>

</tr>

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</td>

<td>

</td>

<td>500.000

</td>

</tr>

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Line 468:

</td>

<td>22\53

</td>

<td>498.113

</td>

</tr>

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</td>

<td>

</td>

<td>497.591

</td>

</tr>

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<td>

</td>

<td>29\60

<td>29\70

</td>

<td>497.143

</td>

</tr>

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</td>

<td>

</td>

<td>496.552

</td>

</tr>

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</td>

<td>31\75

</td>

<td>496.000

</td>

</tr>

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</td>

<td>

</td>

<td>495.652

</td>

</tr>

Line 505:

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</td>

<td>26\63

</td>

<td>495.238

</td>

</tr>

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</td>

<td>

</td>

<td>494.118

</td>

</tr>

Line 533:

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</td>

<td>23\56

</td>

<td>492.857

</td>

</tr>

Line 547:

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</td>

<td>

</td>

<td>492.308

</td>

</tr>

Line 561:

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</td>

<td>25\61

</td>

<td>491.803

</td>

</tr>

Line 575:

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</td>

<td>

</td>

<td>490.909

</td>

</tr>

Line 588:

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<td>

</td>

<td>28\49

<td>20\49

</td>

<td>489.796

</td>

</tr>

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</td>

<td>

</td>

<td>488.889

</td>

</tr>

Line 616:

Line 691:

<td>

</td>

<td>19\32

<td>13\32

</td>

<td>487.500

</td>

</tr>

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Line 708:

</td>

<td>

</td>

<td>480.000

</td>

</tr>

Line 638:

Line 717:

Temperaments above 5\12 on this chart are called &quot;negative temperaments&quot; (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 below 5/12 on this chart are called &quot;positive temperaments&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.</body></html></pre></div>

Temperaments below 5/12 on this chart are called &quot;positive temperaments&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.

5L 2s contains the pentatonic MOS <a class="wiki_link" href="/2L%203s">2L 3s</a> and (except for that in 12edo) is itself contained in a dodecaphonic MOS: either <a class="wiki_link" href="/7L%205s">7L 5s</a> or <a class="wiki_link" href="/5L%207s">5L 7s</a>.</body></html></pre></div>

@@ Line 1: / Line 1: @@
 <h2>IMPORTED REVISION FROM WIKISPACES</h2>
 This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br>
-: This revision was by author [[User:Andrew_Heathwaite|Andrew_Heathwaite]] and made on <tt>2009-11-04 16:31:20 UTC</tt>.<br>
+: This revision was by author [[User:Andrew_Heathwaite|Andrew_Heathwaite]] and made on <tt>2009-11-05 23:25:03 UTC</tt>.<br>
-: The original revision id was <tt>100233459</tt>.<br>
+: The original revision id was <tt>100666597</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>
@@ 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">=5L 2s - "diatonic"=
-One way of distinguishing the "diatonic" scale is by considering it a [[MOSScales|moment of symmetry]] scale produced by a chain of "fifths". This will include [[12edo]]'s diatonic scale along with the Pythagorean diatonic scale, while excluding just intonation scales that use more than one size of "tone".
+One way of distinguishing the "diatonic" scale is by considering it a [[MOSScales|moment of symmetry]] scale produced by a chain of "fifths". This will include [[12edo]]'s diatonic scale along with the Pythagorean diatonic scale and meantone systems, while excluding just intonation scales that use more than one size of "tone".
+It may be misleading to call 5L 2s "diatonic," since other scales called diatonic can be arrived at different ways (through just intonation procedures for instance, or with tetrachords). Also, a composer working with a 5L 2s scale may choose to do something very different than typical diatonic music.
 ==substituting step sizes==
-This produces a generalized diatonic scale with the form:
+The 5L 2s MOS scale has this generalized form.
 L L s L L L s
@@ Line 58: / Line 60: @@
 If we carry this freshman-summing out a little further, new, larger [[edo]]s pop up in our continuum.
-|| 3\7 ||   ||   ||   ||   ||   ||
+||||||||||||~ generator ||~ in cents ||
-||   ||   ||   ||   ||   || 17\40 ||
+|| 3\7 ||   ||   ||   ||   ||   || 514.286 ||
-||   ||   ||   ||   || 14\33 ||   ||
+||   ||   ||   ||   ||   || 17\40 || 510.000 ||
-||   ||   ||   ||   ||   || 25\59 ||
+||   ||   ||   ||   || 14\33 ||   || 509.091 ||
-||   ||   ||   || 11\26 ||   ||   ||
+||   ||   ||   ||   ||   || 25\59 || 508.475 ||
-||   ||   ||   ||   ||   || 30\71 ||
+||   ||   ||   || 11\26 ||   ||   || 507.692 ||
-||   ||   ||   ||   || 19\45 ||   ||
+||   ||   ||   ||   ||   || 30\71 || 507.042 ||
-||   ||   ||   ||   ||   || 27\63 ||
+||   ||   ||   ||   || 19\45 ||   || 506.667 ||
-||   ||   || 8\19 ||   ||   ||   ||
+||   ||   ||   ||   ||   || 27\64 || 506.250 ||
-||   ||   ||   ||   ||   || 29\69 ||
+||   ||   || 8\19 ||   ||   ||   || 506.263 ||
-||   ||   ||   ||   || 21\50 ||   ||
+||   ||   ||   ||   ||   || 29\69 || 504.348 ||
-||   ||   ||   ||   ||   || 34\81 ||
+||   ||   ||   ||   || 21\50 ||   || 504.000 ||
-||   ||   ||   || 13\31 ||   ||   ||
+||   ||   ||   ||   ||   || 34\81 || 503.704 ||
-||   ||   ||   ||   ||   || 31\74 ||
+||   ||   ||   || 13\31 ||   ||   || 503.226 ||
-||   ||   ||   ||   || 18\43 ||   ||
+||   ||   ||   ||   ||   || 31\74 || 502.703 ||
-||   ||   ||   ||   ||   || 23\55 ||
+||   ||   ||   ||   || 18\43 ||   || 502.326 ||
-||   || 5\12 ||   ||   ||   ||   ||
+||   ||   ||   ||   ||   || 23\55 || 501.818 ||
-||   ||   ||   ||   ||   || 22\53 ||
+||   || 5\12 ||   ||   ||   ||   || 500.000 ||
-||   ||   ||   ||   || 17\41 ||   ||
+||   ||   ||   ||   ||   || 22\53 || 498.113 ||
-||   ||   ||   ||   ||   || 29\60 ||
+||   ||   ||   ||   || 17\41 ||   || 497.591 ||
-||   ||   ||   || 12\29 ||   ||   ||
+||   ||   ||   ||   ||   || 29\70 || 497.143 ||
-||   ||   ||   ||   ||   || 31\75 ||
+||   ||   ||   || 12\29 ||   ||   || 496.552 ||
-||   ||   ||   ||   || 19\46 ||   ||
+||   ||   ||   ||   ||   || 31\75 || 496.000 ||
-||   ||   ||   ||   ||   || 26\63 ||
+||   ||   ||   ||   || 19\46 ||   || 495.652 ||
-||   ||   || 7\17 ||   ||   ||   ||
+||   ||   ||   ||   ||   || 26\63 || 495.238 ||
-||   ||   ||   ||   ||   || 23\56 ||
+||   ||   || 7\17 ||   ||   ||   || 494.118 ||
-||   ||   ||   ||   || 16\39 ||   ||
+||   ||   ||   ||   ||   || 23\56 || 492.857 ||
-||   ||   ||   ||   ||   || 25\61 ||
+||   ||   ||   ||   || 16\39 ||   || 492.308 ||
-||   ||   ||   || 9\22 ||   ||   ||
+||   ||   ||   ||   ||   || 25\61 || 491.803 ||
-||   ||   ||   ||   ||   || 28\49 ||
+||   ||   ||   || 9\22 ||   ||   || 490.909 ||
-||   ||   ||   ||   || 11\27 ||   ||
+||   ||   ||   ||   ||   || 20\49 || 489.796 ||
-||   ||   ||   ||   ||   || 19\32 ||
+||   ||   ||   ||   || 11\27 ||   || 488.889 ||
-|| 2\5 ||   ||   ||   ||   ||   ||
+||   ||   ||   ||   ||   || 13\32 || 487.500 ||
+|| 2\5 ||   ||   ||   ||   ||   || 480.000 ||
 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 below 5/12 on this chart are called "positive temperaments" 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.</pre></div>
+Temperaments below 5/12 on this chart are called "positive temperaments" 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.
+L 2s contains the pentatonic MOS [[2L 3s]] and (except for that in 12edo) is itself contained in a dodecaphonic MOS: either [[7L 5s]] or [[5L 7s]].</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">&lt;html&gt;&lt;head&gt;&lt;title&gt;5L 2s&lt;/title&gt;&lt;/head&gt;&lt;body&gt;&lt;!-- ws:start:WikiTextHeadingRule:0:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc0"&gt;&lt;a name="x5L 2s - &amp;quot;diatonic&amp;quot;"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:0 --&gt;5L 2s - &amp;quot;diatonic&amp;quot;&lt;/h1&gt;
   &lt;br /&gt;
-One way of distinguishing the &amp;quot;diatonic&amp;quot; scale is by considering it a &lt;a class="wiki_link" href="/MOSScales"&gt;moment of symmetry&lt;/a&gt; scale produced by a chain of &amp;quot;fifths&amp;quot;. This will include &lt;a class="wiki_link" href="/12edo"&gt;12edo&lt;/a&gt;'s diatonic scale along with the Pythagorean diatonic scale, while excluding just intonation scales that use more than one size of &amp;quot;tone&amp;quot;.&lt;br /&gt;
+One way of distinguishing the &amp;quot;diatonic&amp;quot; scale is by considering it a &lt;a class="wiki_link" href="/MOSScales"&gt;moment of symmetry&lt;/a&gt; scale produced by a chain of &amp;quot;fifths&amp;quot;. This will include &lt;a class="wiki_link" href="/12edo"&gt;12edo&lt;/a&gt;'s diatonic scale along with the Pythagorean diatonic scale and meantone systems, while excluding just intonation scales that use more than one size of &amp;quot;tone&amp;quot;.&lt;br /&gt;
+&lt;br /&gt;
+It may be misleading to call 5L 2s &amp;quot;diatonic,&amp;quot; since other scales called diatonic can be arrived at different ways (through just intonation procedures for instance, or with tetrachords). Also, a composer working with a 5L 2s scale may choose to do something very different than typical diatonic music.&lt;br /&gt;
 &lt;br /&gt;
 &lt;!-- ws:start:WikiTextHeadingRule:2:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc1"&gt;&lt;a name="x5L 2s - &amp;quot;diatonic&amp;quot;-substituting step sizes"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:2 --&gt;substituting step sizes&lt;/h2&gt;
   &lt;br /&gt;
-This produces a generalized diatonic scale with the form:&lt;br /&gt;
+The 5L 2s MOS scale has this generalized form.&lt;br /&gt;
 L L s L L L s&lt;br /&gt;
 &lt;br /&gt;
@@ Line 171: / Line 178: @@
 &lt;table class="wiki_table"&gt;
+    &lt;tr&gt;
+        &lt;th colspan="6"&gt;generator&lt;br /&gt;
+&lt;/th&gt;
+        &lt;th&gt;in cents&lt;br /&gt;
+&lt;/th&gt;
+    &lt;/tr&gt;
      &lt;tr&gt;
          &lt;td&gt;3\7&lt;br /&gt;
@@ Line 183: / Line 196: @@
 &lt;/td&gt;
          &lt;td&gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;514.286&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
@@ Line 197: / Line 212: @@
 &lt;/td&gt;
          &lt;td&gt;17\40&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;510.000&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
@@ Line 211: / Line 228: @@
 &lt;/td&gt;
          &lt;td&gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;509.091&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
@@ Line 225: / Line 244: @@
 &lt;/td&gt;
          &lt;td&gt;25\59&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;508.475&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
@@ Line 239: / Line 260: @@
 &lt;/td&gt;
          &lt;td&gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;507.692&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
@@ Line 253: / Line 276: @@
 &lt;/td&gt;
          &lt;td&gt;30\71&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;507.042&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
@@ Line 267: / Line 292: @@
 &lt;/td&gt;
          &lt;td&gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;506.667&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
@@ Line 280: / Line 307: @@
          &lt;td&gt;&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;27\63&lt;br /&gt;
+         &lt;td&gt;27\64&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;506.250&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
@@ Line 295: / Line 324: @@
 &lt;/td&gt;
          &lt;td&gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;506.263&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
@@ Line 309: / Line 340: @@
 &lt;/td&gt;
          &lt;td&gt;29\69&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;504.348&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
@@ Line 323: / Line 356: @@
 &lt;/td&gt;
          &lt;td&gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;504.000&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
@@ Line 337: / Line 372: @@
 &lt;/td&gt;
          &lt;td&gt;34\81&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;503.704&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
@@ Line 351: / Line 388: @@
 &lt;/td&gt;
          &lt;td&gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;503.226&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
@@ Line 365: / Line 404: @@
 &lt;/td&gt;
          &lt;td&gt;31\74&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;502.703&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
@@ Line 379: / Line 420: @@
 &lt;/td&gt;
          &lt;td&gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;502.326&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
@@ Line 393: / Line 436: @@
 &lt;/td&gt;
          &lt;td&gt;23\55&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;501.818&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
@@ Line 407: / Line 452: @@
 &lt;/td&gt;
          &lt;td&gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;500.000&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
@@ Line 421: / Line 468: @@
 &lt;/td&gt;
          &lt;td&gt;22\53&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;498.113&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
@@ Line 435: / Line 484: @@
 &lt;/td&gt;
          &lt;td&gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;497.591&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
@@ Line 448: / Line 499: @@
          &lt;td&gt;&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;29\60&lt;br /&gt;
+         &lt;td&gt;29\70&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;497.143&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
@@ Line 463: / Line 516: @@
 &lt;/td&gt;
          &lt;td&gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;496.552&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
@@ Line 477: / Line 532: @@
 &lt;/td&gt;
          &lt;td&gt;31\75&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;496.000&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
@@ Line 491: / Line 548: @@
 &lt;/td&gt;
          &lt;td&gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;495.652&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
@@ Line 505: / Line 564: @@
 &lt;/td&gt;
          &lt;td&gt;26\63&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;495.238&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
@@ Line 519: / Line 580: @@
 &lt;/td&gt;
          &lt;td&gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;494.118&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
@@ Line 533: / Line 596: @@
 &lt;/td&gt;
          &lt;td&gt;23\56&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;492.857&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
@@ Line 547: / Line 612: @@
 &lt;/td&gt;
          &lt;td&gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;492.308&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
@@ Line 561: / Line 628: @@
 &lt;/td&gt;
          &lt;td&gt;25\61&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;491.803&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
@@ Line 575: / Line 644: @@
 &lt;/td&gt;
          &lt;td&gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;490.909&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
@@ Line 588: / Line 659: @@
          &lt;td&gt;&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;28\49&lt;br /&gt;
+         &lt;td&gt;20\49&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;489.796&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
@@ Line 603: / Line 676: @@
 &lt;/td&gt;
          &lt;td&gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;488.889&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
@@ Line 616: / Line 691: @@
          &lt;td&gt;&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;19\32&lt;br /&gt;
+         &lt;td&gt;13\32&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;487.500&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
@@ Line 631: / Line 708: @@
 &lt;/td&gt;
          &lt;td&gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;480.000&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
@@ Line 638: / Line 717: @@
 Temperaments above 5\12 on this chart are called &amp;quot;negative temperaments&amp;quot; (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.&lt;br /&gt;
 &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;/body&gt;&lt;/html&gt;</pre></div>
+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;
+L 2s contains the pentatonic MOS &lt;a class="wiki_link" href="/2L%203s"&gt;2L 3s&lt;/a&gt; and (except for that in 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>