3L 4s: Difference between revisions

Line 1:

<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>2011-02-~~13 17~~:10:22 UTC</tt>.

: This revision was by author [[User:keenanpepper|keenanpepper]] and made on <tt>2011-04-25 05:07:08 UTC</tt>.

: The original revision id was <tt>~~201369348~~</tt>.

: The original revision id was <tt>222633306</tt>.

: The revision comment was: <tt></tt>

The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.

Line 19:

|| L s s L s L s || kleeth ||

|| s s L s L s L || led ||

The two notable harmonic entropy minima with this pattern are neutral third scales ("dicot" / "hemififth" / "mohajira") where two generators make a 3/2, and [[Magic family|magic]], where the generator is a 5/4 but five of them make a 3/1.

||||||||||||||~ generator ||~ g ||~ 2g ||~ 3g ||~ 4g (-1200) ||~ comments ||

|| 1\3 || || || || || || || 400.000 || 800.000 || 1200.000 || 400.000 ||= ||

|| || || || || || 7\22 || || 381.818 || || || ||= ||

|| || || || || || || 13\41 || 380.488 || || || ||= Magic is around here ||

|| || || || || 6\19 || || || 378.947 || 757.895 || 1136.842 || 315.789 ||= ||

|| || || || 5\16 || || || || 375.000 || 750.000 || 1125.000 || 300.000 ||= ||

|| || || || || 9\29 || || || 372.414 || 744.828 || 1117.241 || 289.655 ||= ||

|| || || 4\13 || || || || || 369.231 || 738.462 || 1107.692 || 276.923 ||= ||

|| || || || || 11\36 || || || 366.667 || 733.333 || 1100.000 || 266.667 ||= ||

|| || || || 7\23 || || || || 365.217 || 730.435 || 1095.652 || 260.870 ||= ||

|| || || || || 10\33 || || || 363.636 || 727.272 || 1090.909 || 254.545 ||= ||

|| || 3\10 || || || || || || 360.000 || 720.000 || 1080.000 || 240.000 ||= Boundary of propriety (generators

smaller than this are proper) ||

|| || || || || 11\37 || || || 356.757 || 713.514 || 1080.270 || 227.027 ||= ||

|| || || || 8\27 || || || || 355.556 || 711.111 || 1066.667 || 222.222 ||= ||

|| || || || || 13\44 || || || 354.545 || 709.091 || 1063.636 || 218.182 ||= ||

|| || || 5\17 || || || || || 352.941 || 705.882 || 1058.824 || 211.765 ||= ||

|| || || || || 12\41 || || || 351.220 || 702.439 || 1053.659 || 204.878 ||= Neutral thirds scale /

Mohajira is around here ||

|| || || || 7\24 || || || || 350.000 || 700.000 || 1050.000 || 200.000 ||= ||

|| || || || || 9\31 || || || 348.387 || 696.774 || 1045.161 || 193.548 ||= ||

|| 2\7 || || || || || || || 342.847 || 685.714 || 1028.571 || 171.429 ||= ||

3\10 on this chart represents a dividing line between "neutral third scales" on the bottom (eg. [[17edo neutral scale]]), and something else I don't have a name for yet on the top, with [[10edo]] standing in between. (What do you call this region, dear reader?) Of course, magic is in the top half, but it's a pretty specific scale and doesn't describe the whole range. MOS-wise, the neutral third scales, after three more generations, make MOS [[7L 3s]] ("unfair mosh"); the other scales make MOS [[3L 7s]] ("fair mosh").

~~One can build a continuum of equal-tempered scales between 1\3 and 2\7 by taking "freshman sums," adding together the numerators, then adding together the denominators.~~

~~||||||||||~ generator || g || 2g || 3g || 4g (-1200) ||~~

~~|| 1\3 || || || || || 400.000 || 800.000 || 1200.000 || 400.000 || ||~~

~~|| || || || || 6\19 || 378.947 || 757.895 || 1136.842 || 315.789 || ||~~

~~|| || || || 5\16 || || 375.000 || 750.000 || 1125.000 || 300.000 || ||~~

~~|| || || || || 9\29 || 372.414 || 744.828 || 1117.241 || 289.655 || ||~~

~~|| || || 4\13 || || || 369.231 || 738.462 || 1107.692 || 276.923 || ||~~

~~|| || || || || 11\36 || 366.667 || 733.333 || 1100.000 || 266.667 || ||~~

~~|| || || || 7\23 || || 365.217 || 730.435 || 1095.652 || 260.870 || ||~~

~~|| || || || || 10\33 || 363.636 || 727.272 || 1090.909 || 254.545 || ||~~

~~|| || 3\10 || || || || 360.000 || 720.000 || 1080.000 || 240.000 || ||~~

~~|| || || || || 11\37 || 356.757 || 713.514 || 1080.270 || 227.027 || ||~~

~~|| || || || 8\27 || || 355.556 || 711.111 || 1066.667 || 222.222 || ||~~

~~|| || || || || 13\44 || 354.545 || 709.091 || 1063.636 || 218.182 || ||~~

~~|| || || 5\17 || || || 352.941 || 705.882 || 1058.824 || 211.765 || ||~~

~~|| || || || || 12\41 || 351.220 || 702.439 || 1053.659 || 204.878 || ||~~

~~|| || || || 7\24 || || 350.000 || 700.000 || 1050.000 || 200.000 || ||~~

~~|| || || || || 9\31 || 348.387 || 696.774 || 1045.161 || 193.548 || ||~~

~~|| 2\7 || || || || || 342.847 || 685.714 || 1028.571 || 171.429 || ||~~

3\10 on this chart represents a dividing line between "neutral third scales" on the bottom (eg. [[17edo neutral scale]]), and something else I don't have a name for yet on the top, with [[10edo]] standing in between. (What do you call this region, dear reader?) MOS-wise, the neutral third scales, after three more generations, make MOS [[7L 3s]] ("unfair mosh"); the other scales make MOS [[3L 7s]] ("fair mosh").

In "neural third scale territory," the generators are all "neutral thirds," and two of them make an approximation of the "perfect fifth." Additionally, the L of the scale is somewhere around a "whole tone" and the s of the scale is somewhere around a "neutral tone".

Line 103:

Line 102:

</table>

<~~br /~~>

The two notable harmonic entropy minima with this pattern are neutral third scales (&quot;dicot&quot; / &quot;hemififth&quot; / &quot;mohajira&quot;) where two generators make a 3/2, and <a class="wiki_link" href="/Magic%20family">magic</a>, where the generator is a 5/4 but five of them make a 3/1.

~~&lt~~;br />

~~One can build a continuum of equal-tempered scales between 1\3 and 2\7 by taking~~ &quot;~~freshman sums,~~&quot; ~~adding together the numerators, then adding together the denominators.~~ 

<tr>

<th colspan="5">generator

<th colspan="7">generator

</th>

<th>g

</th>

<th>2g

</th>

<th>3g

</th>

<th>4g (-1200)

</th>

<th>comments

</th>

~~<td>g ~~

~~</td>~~

~~<td>2g ~~

~~</td>~~

~~<td>3g ~~

~~</td>~~

~~<td>4g (-1200) ~~

~~</td>~~

</tr>

<tr>

<td>1\3

</td>

<td>

</td>

<td>

</td>

<td>

Line 142:

</td>

<td>400.000

</td>

</td>

</tr>

<tr>

<td>

</td>

<td>

</td>

<td>

</td>

<td>

</td>

<td>

</td>

<td>7\22

</td>

<td>

</td>

<td>381.818

</td>

<td>

</td>

<td>

</td>

<td>

</td>

</td>

</tr>

<tr>

<td>

</td>

<td>

</td>

<td>

</td>

<td>

</td>

<td>

</td>

<td>

</td>

<td>13\41

</td>

<td>380.488

</td>

<td>

</td>

<td>

</td>

<td>

</td>

<td style="text-align: center;">Magic is around here

</td>

</tr>

Line 156:

Line 208:

</td>

<td>6\19

</td>

<td>

</td>

<td>

</td>

<td>378.947

Line 165:

Line 221:

<td>315.789

</td>

<td>

</td>

</tr>

Line 176:

Line 232:

</td>

<td>5\16

</td>

<td>

</td>

<td>

</td>

<td>

Line 187:

Line 247:

<td>300.000

</td>

<td>

</td>

</tr>

Line 200:

Line 260:

</td>

<td>9\29

</td>

<td>

</td>

<td>

</td>

<td>372.414

Line 209:

Line 273:

<td>289.655

</td>

<td>

</td>

</tr>

Line 218:

Line 282:

</td>

<td>4\13

</td>

<td>

</td>

<td>

</td>

<td>

Line 231:

Line 299:

<td>276.923

</td>

<td>

</td>

</tr>

Line 244:

Line 312:

</td>

<td>11\36

</td>

<td>

</td>

<td>

</td>

<td>366.667

Line 253:

Line 325:

<td>266.667

</td>

<td>

</td>

</tr>

Line 264:

Line 336:

</td>

<td>7\23

</td>

<td>

</td>

<td>

</td>

<td>

Line 275:

Line 351:

<td>260.870

</td>

<td>

</td>

</tr>

Line 288:

Line 364:

</td>

<td>10\33

</td>

<td>

</td>

<td>

</td>

<td>363.636

Line 297:

Line 377:

<td>254.545

</td>

<td>

</td>

</tr>

Line 304:

Line 384:

</td>

<td>3\10

</td>

<td>

</td>

<td>

</td>

<td>

Line 319:

Line 403:

<td>240.000

</td>

<td>

<td style="text-align: center;">Boundary of propriety (generators

smaller than this are proper)

</td>

</tr>

Line 332:

Line 417:

</td>

<td>11\37

</td>

<td>

</td>

<td>

</td>

<td>356.757

Line 341:

Line 430:

<td>227.027

</td>

<td>

</td>

</tr>

Line 352:

Line 441:

</td>

<td>8\27

</td>

<td>

</td>

<td>

</td>

<td>

Line 363:

Line 456:

<td>222.222

</td>

<td>

</td>

</tr>

Line 376:

Line 469:

</td>

<td>13\44

</td>

<td>

</td>

<td>

</td>

<td>354.545

Line 385:

Line 482:

<td>218.182

</td>

<td>

</td>

</tr>

Line 394:

Line 491:

</td>

<td>5\17

</td>

<td>

</td>

<td>

</td>

<td>

Line 407:

Line 508:

<td>211.765

</td>

<td>

</td>

</tr>

Line 420:

Line 521:

</td>

<td>12\41

</td>

<td>

</td>

<td>

</td>

<td>351.220

Line 429:

Line 534:

<td>204.878

</td>

<td>

<td style="text-align: center;">Neutral thirds scale

Mohajira is around here

</td>

</tr>

Line 440:

Line 546:

</td>

<td>7\24

</td>

<td>

</td>

<td>

</td>

<td>

Line 451:

Line 561:

<td>200.000

</td>

<td>

</td>

</tr>

Line 464:

Line 574:

</td>

<td>9\31

</td>

<td>

</td>

<td>

</td>

<td>348.387

Line 473:

Line 587:

<td>193.548

</td>

<td>

</td>

</tr>

<tr>

<td>2\7

</td>

<td>

</td>

<td>

</td>

<td>

Line 495:

Line 613:

<td>171.429

</td>

<td>

</td>

</tr>

Line 501:

Line 619:

3\10 on this chart represents a dividing line between &quot;neutral third scales&quot; on the bottom (eg. <a class="wiki_link" href="/17edo%20neutral%20scale">17edo neutral scale</a>), and something else I don't have a name for yet on the top, with <a class="wiki_link" href="/10edo">10edo</a> standing in between. (What do you call this region, dear reader?) MOS-wise, the neutral third scales, after three more generations, make MOS <a class="wiki_link" href="/7L%203s">7L 3s</a> (&quot;unfair mosh&quot;); the other scales make MOS <a class="wiki_link" href="/3L%207s">3L 7s</a> (&quot;fair mosh&quot;).

3\10 on this chart represents a dividing line between &quot;neutral third scales&quot; on the bottom (eg. <a class="wiki_link" href="/17edo%20neutral%20scale">17edo neutral scale</a>), and something else I don't have a name for yet on the top, with <a class="wiki_link" href="/10edo">10edo</a> standing in between. (What do you call this region, dear reader?) Of course, magic is in the top half, but it's a pretty specific scale and doesn't describe the whole range. MOS-wise, the neutral third scales, after three more generations, make MOS <a class="wiki_link" href="/7L%203s">7L 3s</a> (&quot;unfair mosh&quot;); the other scales make MOS <a class="wiki_link" href="/3L%207s">3L 7s</a> (&quot;fair mosh&quot;).

In &quot;neural third scale territory,&quot; the generators are all &quot;neutral thirds,&quot; and two of them make an approximation of the &quot;perfect fifth.&quot; Additionally, the L of the scale is somewhere around a &quot;whole tone&quot; and the s of the scale is somewhere around a &quot;neutral tone&quot;.

In the as-yet unnamed northern territory, the generators are major thirds (including some very flat ones), and two generators are definitely sharp of a perfect fifth. L ranges from a &quot;supermajor second&quot; to a &quot;major third&quot; and s is a &quot;semitone&quot; or smaller.</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>2011-02-13 17:10:22 UTC</tt>.<br>
+: This revision was by author [[User:keenanpepper|keenanpepper]] and made on <tt>2011-04-25 05:07:08 UTC</tt>.<br>
-: The original revision id was <tt>201369348</tt>.<br>
+: The original revision id was <tt>222633306</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 19: / Line 19: @@
 || L s s L s L s || kleeth ||
 || s s L s L s L || led ||
+The two notable harmonic entropy minima with this pattern are neutral third scales ("dicot" / "hemififth" / "mohajira") where two generators make a 3/2, and [[Magic family|magic]], where the generator is a 5/4 but five of them make a 3/1.
+||||||||||||||~ generator ||~ g ||~ 2g ||~ 3g ||~ 4g (-1200) ||~ comments ||
+|| 1\3 ||   ||   ||   ||   ||   ||   || 400.000 || 800.000 || 1200.000 || 400.000 ||=   ||
+||   ||   ||   ||   ||   || 7\22 ||   || 381.818 ||   ||   ||   ||=   ||
+||   ||   ||   ||   ||   ||   || 13\41 || 380.488 ||   ||   ||   ||= Magic is around here ||
+||   ||   ||   ||   || 6\19 ||   ||   || 378.947 || 757.895 || 1136.842 || 315.789 ||=   ||
+||   ||   ||   || 5\16 ||   ||   ||   || 375.000 || 750.000 || 1125.000 || 300.000 ||=   ||
+||   ||   ||   ||   || 9\29 ||   ||   || 372.414 || 744.828 || 1117.241 || 289.655 ||=   ||
+||   ||   || 4\13 ||   ||   ||   ||   || 369.231 || 738.462 || 1107.692 || 276.923 ||=   ||
+||   ||   ||   ||   || 11\36 ||   ||   || 366.667 || 733.333 || 1100.000 || 266.667 ||=   ||
+||   ||   ||   || 7\23 ||   ||   ||   || 365.217 || 730.435 || 1095.652 || 260.870 ||=   ||
+||   ||   ||   ||   || 10\33 ||   ||   || 363.636 || 727.272 || 1090.909 || 254.545 ||=   ||
+||   || 3\10 ||   ||   ||   ||   ||   || 360.000 || 720.000 || 1080.000 || 240.000 ||= Boundary of propriety (generators
+smaller than this are proper) ||
+||   ||   ||   ||   || 11\37 ||   ||   || 356.757 || 713.514 || 1080.270 || 227.027 ||=   ||
+||   ||   ||   || 8\27 ||   ||   ||   || 355.556 || 711.111 || 1066.667 || 222.222 ||=   ||
+||   ||   ||   ||   || 13\44 ||   ||   || 354.545 || 709.091 || 1063.636 || 218.182 ||=   ||
+||   ||   || 5\17 ||   ||   ||   ||   || 352.941 || 705.882 || 1058.824 || 211.765 ||=   ||
+||   ||   ||   ||   || 12\41 ||   ||   || 351.220 || 702.439 || 1053.659 || 204.878 ||= Neutral thirds scale /
+Mohajira is around here ||
+||   ||   ||   || 7\24 ||   ||   ||   || 350.000 || 700.000 || 1050.000 || 200.000 ||=   ||
+||   ||   ||   ||   || 9\31 ||   ||   || 348.387 || 696.774 || 1045.161 || 193.548 ||=   ||
+|| 2\7 ||   ||   ||   ||   ||   ||   || 342.847 || 685.714 || 1028.571 || 171.429 ||=   ||
+\10 on this chart represents a dividing line between "neutral third scales" on the bottom (eg. [[17edo neutral scale]]), and something else I don't have a name for yet on the top, with [[10edo]] standing in between. (What do you call this region, dear reader?) Of course, magic is in the top half, but it's a pretty specific scale and doesn't describe the whole range. MOS-wise, the neutral third scales, after three more generations, make MOS [[7L 3s]] ("unfair mosh"); the other scales make MOS [[3L 7s]] ("fair mosh").
-One can build a continuum of equal-tempered scales between 1\3 and 2\7 by taking "freshman sums," adding together the numerators, then adding together the denominators.
-||||||||||~ generator || g || 2g || 3g || 4g (-1200) ||
-|| 1\3 ||   ||   ||   ||   || 400.000 || 800.000 || 1200.000 || 400.000 ||   ||
-||   ||   ||   ||   || 6\19 || 378.947 || 757.895 || 1136.842 || 315.789 ||   ||
-||   ||   ||   || 5\16 ||   || 375.000 || 750.000 || 1125.000 || 300.000 ||   ||
-||   ||   ||   ||   || 9\29 || 372.414 || 744.828 || 1117.241 || 289.655 ||   ||
-||   ||   || 4\13 ||   ||   || 369.231 || 738.462 || 1107.692 || 276.923 ||   ||
-||   ||   ||   ||   || 11\36 || 366.667 || 733.333 || 1100.000 || 266.667 ||   ||
-||   ||   ||   || 7\23 ||   || 365.217 || 730.435 || 1095.652 || 260.870 ||   ||
-||   ||   ||   ||   || 10\33 || 363.636 || 727.272 || 1090.909 || 254.545 ||   ||
-||   || 3\10 ||   ||   ||   || 360.000 || 720.000 || 1080.000 || 240.000 ||   ||
-||   ||   ||   ||   || 11\37 || 356.757 || 713.514 || 1080.270 || 227.027 ||   ||
-||   ||   ||   || 8\27 ||   || 355.556 || 711.111 || 1066.667 || 222.222 ||   ||
-||   ||   ||   ||   || 13\44 || 354.545 || 709.091 || 1063.636 || 218.182 ||   ||
-||   ||   || 5\17 ||   ||   || 352.941 || 705.882 || 1058.824 || 211.765 ||   ||
-||   ||   ||   ||   || 12\41 || 351.220 || 702.439 || 1053.659 || 204.878 ||   ||
-||   ||   ||   || 7\24 ||   || 350.000 || 700.000 || 1050.000 || 200.000 ||   ||
-||   ||   ||   ||   || 9\31 || 348.387 || 696.774 || 1045.161 || 193.548 ||   ||
-|| 2\7 ||   ||   ||   ||   || 342.847 || 685.714 || 1028.571 || 171.429 ||   ||
-\10 on this chart represents a dividing line between "neutral third scales" on the bottom (eg. [[17edo neutral scale]]), and something else I don't have a name for yet on the top, with [[10edo]] standing in between. (What do you call this region, dear reader?) MOS-wise, the neutral third scales, after three more generations, make MOS [[7L 3s]] ("unfair mosh"); the other scales make MOS [[3L 7s]] ("fair mosh").
 In "neural third scale territory," the generators are all "neutral thirds," and two of them make an approximation of the "perfect fifth." Additionally, the L of the scale is somewhere around a "whole tone" and the s of the scale is somewhere around a "neutral tone".
@@ Line 103: / Line 102: @@
 &lt;/table&gt;
-&lt;br /&gt;
+The two notable harmonic entropy minima with this pattern are neutral third scales (&amp;quot;dicot&amp;quot; / &amp;quot;hemififth&amp;quot; / &amp;quot;mohajira&amp;quot;) where two generators make a 3/2, and &lt;a class="wiki_link" href="/Magic%20family"&gt;magic&lt;/a&gt;, where the generator is a 5/4 but five of them make a 3/1.&lt;br /&gt;
-&lt;br /&gt;
-One can build a continuum of equal-tempered scales between 1\3 and 2\7 by taking &amp;quot;freshman sums,&amp;quot; adding together the numerators, then adding together the denominators.&lt;br /&gt;
-&lt;br /&gt;
-&lt;br /&gt;
-&lt;br /&gt;
 &lt;table class="wiki_table"&gt;
      &lt;tr&gt;
-         &lt;th colspan="5"&gt;generator&lt;br /&gt;
+         &lt;th colspan="7"&gt;generator&lt;br /&gt;
+&lt;/th&gt;
+        &lt;th&gt;g&lt;br /&gt;
+&lt;/th&gt;
+        &lt;th&gt;2g&lt;br /&gt;
+&lt;/th&gt;
+        &lt;th&gt;3g&lt;br /&gt;
+&lt;/th&gt;
+        &lt;th&gt;4g (-1200)&lt;br /&gt;
+&lt;/th&gt;
+        &lt;th&gt;comments&lt;br /&gt;
 &lt;/th&gt;
-        &lt;td&gt;g&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td&gt;2g&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td&gt;3g&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td&gt;4g (-1200)&lt;br /&gt;
-&lt;/td&gt;
      &lt;/tr&gt;
      &lt;tr&gt;
          &lt;td&gt;1\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;br /&gt;
@@ Line 142: / Line 142: @@
 &lt;/td&gt;
          &lt;td&gt;400.000&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;&lt;br /&gt;
+&lt;/td&gt;
+    &lt;/tr&gt;
+    &lt;tr&gt;
+        &lt;td&gt;&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;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;7\22&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;381.818&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;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;&lt;br /&gt;
+&lt;/td&gt;
+    &lt;/tr&gt;
+    &lt;tr&gt;
+        &lt;td&gt;&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;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;13\41&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;380.488&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;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;Magic is around here&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
@@ Line 156: / Line 208: @@
 &lt;/td&gt;
          &lt;td&gt;6\19&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;378.947&lt;br /&gt;
@@ Line 165: / Line 221: @@
          &lt;td&gt;315.789&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
@@ Line 176: / Line 232: @@
 &lt;/td&gt;
          &lt;td&gt;5\16&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;br /&gt;
@@ Line 187: / Line 247: @@
          &lt;td&gt;300.000&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
@@ Line 200: / Line 260: @@
 &lt;/td&gt;
          &lt;td&gt;9\29&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;372.414&lt;br /&gt;
@@ Line 209: / Line 273: @@
          &lt;td&gt;289.655&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
@@ Line 218: / Line 282: @@
 &lt;/td&gt;
          &lt;td&gt;4\13&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;br /&gt;
@@ Line 231: / Line 299: @@
          &lt;td&gt;276.923&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
@@ Line 244: / Line 312: @@
 &lt;/td&gt;
          &lt;td&gt;11\36&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;366.667&lt;br /&gt;
@@ Line 253: / Line 325: @@
          &lt;td&gt;266.667&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
@@ Line 264: / Line 336: @@
 &lt;/td&gt;
          &lt;td&gt;7\23&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;br /&gt;
@@ Line 275: / Line 351: @@
          &lt;td&gt;260.870&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
@@ Line 288: / Line 364: @@
 &lt;/td&gt;
          &lt;td&gt;10\33&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;363.636&lt;br /&gt;
@@ Line 297: / Line 377: @@
          &lt;td&gt;254.545&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
@@ Line 304: / Line 384: @@
 &lt;/td&gt;
          &lt;td&gt;3\10&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;br /&gt;
@@ Line 319: / Line 403: @@
          &lt;td&gt;240.000&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;Boundary of propriety (generators&lt;br /&gt;
+smaller than this are proper)&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
@@ Line 332: / Line 417: @@
 &lt;/td&gt;
          &lt;td&gt;11\37&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;356.757&lt;br /&gt;
@@ Line 341: / Line 430: @@
          &lt;td&gt;227.027&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
@@ Line 352: / Line 441: @@
 &lt;/td&gt;
          &lt;td&gt;8\27&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;br /&gt;
@@ Line 363: / Line 456: @@
          &lt;td&gt;222.222&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
@@ Line 376: / Line 469: @@
 &lt;/td&gt;
          &lt;td&gt;13\44&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;354.545&lt;br /&gt;
@@ Line 385: / Line 482: @@
          &lt;td&gt;218.182&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
@@ Line 394: / Line 491: @@
 &lt;/td&gt;
          &lt;td&gt;5\17&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;br /&gt;
@@ Line 407: / Line 508: @@
          &lt;td&gt;211.765&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
@@ Line 420: / Line 521: @@
 &lt;/td&gt;
          &lt;td&gt;12\41&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;351.220&lt;br /&gt;
@@ Line 429: / Line 534: @@
          &lt;td&gt;204.878&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;Neutral thirds scale&lt;br /&gt;
+Mohajira is around here&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
@@ Line 440: / Line 546: @@
 &lt;/td&gt;
          &lt;td&gt;7\24&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;br /&gt;
@@ Line 451: / Line 561: @@
          &lt;td&gt;200.000&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
@@ Line 464: / Line 574: @@
 &lt;/td&gt;
          &lt;td&gt;9\31&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;348.387&lt;br /&gt;
@@ Line 473: / Line 587: @@
          &lt;td&gt;193.548&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
      &lt;tr&gt;
          &lt;td&gt;2\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;br /&gt;
@@ Line 495: / Line 613: @@
          &lt;td&gt;171.429&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
@@ Line 501: / Line 619: @@
 &lt;br /&gt;
-\10 on this chart represents a dividing line between &amp;quot;neutral third scales&amp;quot; on the bottom (eg. &lt;a class="wiki_link" href="/17edo%20neutral%20scale"&gt;17edo neutral scale&lt;/a&gt;), and something else I don't have a name for yet on the top, with &lt;a class="wiki_link" href="/10edo"&gt;10edo&lt;/a&gt; standing in between. (What do you call this region, dear reader?) MOS-wise, the neutral third scales, after three more generations, make MOS &lt;a class="wiki_link" href="/7L%203s"&gt;7L 3s&lt;/a&gt; (&amp;quot;unfair mosh&amp;quot;); the other scales make MOS &lt;a class="wiki_link" href="/3L%207s"&gt;3L 7s&lt;/a&gt; (&amp;quot;fair mosh&amp;quot;).&lt;br /&gt;
+\10 on this chart represents a dividing line between &amp;quot;neutral third scales&amp;quot; on the bottom (eg. &lt;a class="wiki_link" href="/17edo%20neutral%20scale"&gt;17edo neutral scale&lt;/a&gt;), and something else I don't have a name for yet on the top, with &lt;a class="wiki_link" href="/10edo"&gt;10edo&lt;/a&gt; standing in between. (What do you call this region, dear reader?) Of course, magic is in the top half, but it's a pretty specific scale and doesn't describe the whole range. MOS-wise, the neutral third scales, after three more generations, make MOS &lt;a class="wiki_link" href="/7L%203s"&gt;7L 3s&lt;/a&gt; (&amp;quot;unfair mosh&amp;quot;); the other scales make MOS &lt;a class="wiki_link" href="/3L%207s"&gt;3L 7s&lt;/a&gt; (&amp;quot;fair mosh&amp;quot;).&lt;br /&gt;
 &lt;br /&gt;
 In &amp;quot;neural third scale territory,&amp;quot; the generators are all &amp;quot;neutral thirds,&amp;quot; and two of them make an approximation of the &amp;quot;perfect fifth.&amp;quot; Additionally, the L of the scale is somewhere around a &amp;quot;whole tone&amp;quot; and the s of the scale is somewhere around a &amp;quot;neutral tone&amp;quot;.&lt;br /&gt;
 &lt;br /&gt;
 In the as-yet unnamed northern territory, the generators are major thirds (including some very flat ones), and two generators are definitely sharp of a perfect fifth. L ranges from a &amp;quot;supermajor second&amp;quot; to a &amp;quot;major third&amp;quot; and s is a &amp;quot;semitone&amp;quot; or smaller.&lt;/body&gt;&lt;/html&gt;</pre></div>