3L 4s: 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>2011-09-21 10:27:47 UTC</tt>.

: This revision was by author [[User:Andrew_Heathwaite|Andrew_Heathwaite]] and made on <tt>2011-09-21 10:37:38 UTC</tt>.

: The original revision id was <tt>~~256560528~~</tt>.

: The original revision id was <tt>256565220</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.

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|| 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 ||

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

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

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

|| || || || || || 7\22 || || 381.818 || 763.636 || 1145.455 || 327.273 ||= ||

|| || || || || || || || || 10\31 || 387.097 || 774.194 || 1161.290 || 348.387 ||= [[Wuerschmidt family|Wuerschmidt]] is around here ||

|| || || || || || || 13\41 || 380.488 || 760.976 || 1141.463 || 321.951 ||= Magic is around here ||

|| || || || || || || || 9\28 || || 385.714 || 771.429 || 1157.143 || 342.857 || ||

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

|| || || || || || || 8\25 || || || 384.000 || 768.000 || 1152.000 || 336.000 || ||

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

|| || || || || || 7\22 || || || || 381.818 || 763.636 || 1145.455 || 327.273 ||= ||

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

|| || || || || || || 13\41 || || || 380.488 || 760.976 || 1141.463 || 321.951 ||= Magic is around here ||

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

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

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

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

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

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

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

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

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

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

|| || || || 7\23 || || || || || || 365.217 || 730.435 || 1095.652 || 260.870 ||= Modi Sephiratorum (Kosmorsky) ||

|| || || || || 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 ||= ||

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

|| || || || 8\27 || || || || 355.556 || 711.111 || 1066.667 || 222.222 ||= Beatles is around here ||

|| || || || 8\27 || || || || || || 355.556 || 711.111 || 1066.667 || 222.222 ||= Beatles is around here ||

|| || || || || || 21\71 || || 354.930 || || || ||= ||

|| || || || || || 21\71 || || || || 354.930 || || || ||= ||

|| || || || || || || 34\115 || 354.783 || || || ||= Golden neutral thirds scale ||

|| || || || || || || 34\115 || || || 354.783 || || || ||= Golden neutral thirds scale ||

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

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

|| || || 5\17 || || || || || 352.941 || 705.882 || 1058.824 || 211.765 ||= Optimum rank range (L/s=3/2) ||

|| || || 5\17 || || || || || || || 352.941 || 705.882 || 1058.824 || 211.765 ||= Optimum rank range (L/s=3/2) ||

|| || || || || 12\41 || || || 351.220 || 702.439 || 1053.659 || 204.878 ||= 2.3.11 neutral thirds scale

|| || || || || 12\41 || || || || || 351.220 || 702.439 || 1053.659 || 204.878 ||= 2.3.11 neutral thirds scale

is around here ||

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

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

|| || || || || 9\31 || || || 348.387 || 696.774 || 1045.161 || 193.548 ||= Mohajira is around here ||

|| || || || || 9\31 || || || || || 348.387 || 696.774 || 1045.161 || 193.548 ||= Mohajira is around here ||

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

|| 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").

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<tr>

<th colspan="7">generator

</th>

<th>

</th>

<th>

</th>

<th>g

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<tr>

<td>1\3

</td>

<td>

</td>

<td>

</td>

<td>

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</td>

</td>

</tr>

<tr>

<td>

</td>

<td>

</td>

<td>

</td>

<td>

</td>

<td>

</td>

<td>

</td>

<td>

</td>

<td>

</td>

<td>10\31

</td>

<td>387.097

</td>

<td>774.194

</td>

<td>1161.290

</td>

<td>348.387

</td>

<td style="text-align: center;"><a class="wiki_link" href="/Wuerschmidt%20family">Wuerschmidt</a> is around here

</td>

</tr>

<tr>

<td>

</td>

<td>

</td>

<td>

</td>

<td>

</td>

<td>

</td>

<td>

</td>

<td>

</td>

<td>9\28

</td>

<td>

</td>

<td>385.714

</td>

<td>771.429

</td>

<td>1157.143

</td>

<td>342.857

</td>

<td>

</td>

</tr>

<tr>

<td>

</td>

<td>

</td>

<td>

</td>

<td>

</td>

<td>

</td>

<td>

</td>

<td>8\25

</td>

<td>

</td>

<td>

</td>

<td>384.000

</td>

<td>768.000

</td>

<td>1152.000

</td>

<td>336.000

</td>

<td>

</td>

</tr>

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</td>

<td>7\22

</td>

<td>

</td>

<td>

</td>

<td>

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</td>

<td>13\41

</td>

<td>

</td>

<td>

</td>

<td>380.488

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</td>

<td>6\19

</td>

<td>

</td>

<td>

</td>

<td>

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</td>

<td>5\16

</td>

<td>

</td>

<td>

</td>

<td>

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</td>

<td>9\29

</td>

<td>

</td>

<td>

</td>

<td>

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</td>

<td>4\13

</td>

<td>

</td>

<td>

</td>

<td>

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</td>

<td>11\36

</td>

<td>

</td>

<td>

</td>

<td>

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</td>

<td>7\23

</td>

<td>

</td>

<td>

</td>

<td>

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<td>260.870

</td>

<td style="text-align: center;">Modi Sephiratorum (Kosmorsky)

</td>

</tr>

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</td>

<td>10\33

</td>

<td>

</td>

<td>

</td>

<td>

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</td>

<td>3\10

</td>

<td>

</td>

<td>

</td>

<td>

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<td>11\37

</td>

<td>

</td>

<td>

</td>

<td>

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<td>8\27

</td>

<td>

</td>

<td>

</td>

<td>

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<td>21\71

</td>

<td>

</td>

<td>

</td>

<td>

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</td>

<td>34\115

</td>

<td>

</td>

<td>

</td>

<td>354.783

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</td>

<td>13\44

</td>

<td>

</td>

<td>

</td>

<td>

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<td>5\17

</td>

<td>

</td>

<td>

</td>

<td>

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</td>

<td>12\41

</td>

<td>

</td>

<td>

</td>

<td>

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</td>

<td>7\24

</td>

<td>

</td>

<td>

</td>

<td>

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</td>

<td>9\31

</td>

<td>

</td>

<td>

</td>

<td>

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<tr>

<td>2\7

</td>

<td>

</td>

<td>

</td>

<td>

@@ 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>2011-09-21 10:27:47 UTC</tt>.<br>
+: This revision was by author [[User:Andrew_Heathwaite|Andrew_Heathwaite]] and made on <tt>2011-09-21 10:37:38 UTC</tt>.<br>
-: The original revision id was <tt>256560528</tt>.<br>
+: The original revision id was <tt>256565220</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 20: / Line 20: @@
 || 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 ||
+||||||||||||||~ generator ||~   ||~   ||~ g ||~ 2g ||~ 3g ||~ 4g (-1200) ||~ comments ||
-|| 1\3 ||   ||   ||   ||   ||   ||   || 400.000 || 800.000 || 1200.000 || 400.000 ||=   ||
+|| 1\3 ||   ||   ||   ||   ||   ||   ||   ||   || 400.000 || 800.000 || 1200.000 || 400.000 ||=   ||
-||   ||   ||   ||   ||   || 7\22 ||   || 381.818 || 763.636 || 1145.455 || 327.273 ||=   ||
+||   ||   ||   ||   ||   ||   ||   ||   || 10\31 || 387.097 || 774.194 || 1161.290 || 348.387 ||= [[Wuerschmidt family|Wuerschmidt]] is around here ||
-||   ||   ||   ||   ||   ||   || 13\41 || 380.488 || 760.976 || 1141.463 || 321.951 ||= Magic is around here ||
+||   ||   ||   ||   ||   ||   ||   || 9\28 ||   || 385.714 || 771.429 || 1157.143 || 342.857 ||   ||
-||   ||   ||   ||   || 6\19 ||   ||   || 378.947 || 757.895 || 1136.842 || 315.789 ||=   ||
+||   ||   ||   ||   ||   ||   || 8\25 ||   ||   || 384.000 || 768.000 || 1152.000 || 336.000 ||   ||
-||   ||   ||   || 5\16 ||   ||   ||   || 375.000 || 750.000 || 1125.000 || 300.000 ||=   ||
+||   ||   ||   ||   ||   || 7\22 ||   ||   ||   || 381.818 || 763.636 || 1145.455 || 327.273 ||=   ||
-||   ||   ||   ||   || 9\29 ||   ||   || 372.414 || 744.828 || 1117.241 || 289.655 ||=   ||
+||   ||   ||   ||   ||   ||   || 13\41 ||   ||   || 380.488 || 760.976 || 1141.463 || 321.951 ||= Magic is around here ||
-||   ||   || 4\13 ||   ||   ||   ||   || 369.231 || 738.462 || 1107.692 || 276.923 ||=   ||
+||   ||   ||   ||   || 6\19 ||   ||   ||   ||   || 378.947 || 757.895 || 1136.842 || 315.789 ||=   ||
-||   ||   ||   ||   || 11\36 ||   ||   || 366.667 || 733.333 || 1100.000 || 266.667 ||=   ||
+||   ||   ||   || 5\16 ||   ||   ||   ||   ||   || 375.000 || 750.000 || 1125.000 || 300.000 ||=   ||
-||   ||   ||   || 7\23 ||   ||   ||   || 365.217 || 730.435 || 1095.652 || 260.870 ||=   ||
+||   ||   ||   ||   || 9\29 ||   ||   ||   ||   || 372.414 || 744.828 || 1117.241 || 289.655 ||=   ||
-||   ||   ||   ||   || 10\33 ||   ||   || 363.636 || 727.272 || 1090.909 || 254.545 ||=   ||
+||   ||   || 4\13 ||   ||   ||   ||   ||   ||   || 369.231 || 738.462 || 1107.692 || 276.923 ||=   ||
-||   || 3\10 ||   ||   ||   ||   ||   || 360.000 || 720.000 || 1080.000 || 240.000 ||= Boundary of propriety (generators
+||   ||   ||   ||   || 11\36 ||   ||   ||   ||   || 366.667 || 733.333 || 1100.000 || 266.667 ||=   ||
+||   ||   ||   || 7\23 ||   ||   ||   ||   ||   || 365.217 || 730.435 || 1095.652 || 260.870 ||= Modi Sephiratorum (Kosmorsky) ||
+||   ||   ||   ||   || 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 ||=   ||
+||   ||   ||   ||   || 11\37 ||   ||   ||   ||   || 356.757 || 713.514 || 1080.270 || 227.027 ||=   ||
-||   ||   ||   || 8\27 ||   ||   ||   || 355.556 || 711.111 || 1066.667 || 222.222 ||= Beatles is around here ||
+||   ||   ||   || 8\27 ||   ||   ||   ||   ||   || 355.556 || 711.111 || 1066.667 || 222.222 ||= Beatles is around here ||
-||   ||   ||   ||   ||   || 21\71 ||   || 354.930 ||   ||   ||   ||=   ||
+||   ||   ||   ||   ||   || 21\71 ||   ||   ||   || 354.930 ||   ||   ||   ||=   ||
-||   ||   ||   ||   ||   ||   || 34\115 || 354.783 ||   ||   ||   ||= Golden neutral thirds scale ||
+||   ||   ||   ||   ||   ||   || 34\115 ||   ||   || 354.783 ||   ||   ||   ||= Golden neutral thirds scale ||
-||   ||   ||   ||   || 13\44 ||   ||   || 354.545 || 709.091 || 1063.636 || 218.182 ||=   ||
+||   ||   ||   ||   || 13\44 ||   ||   ||   ||   || 354.545 || 709.091 || 1063.636 || 218.182 ||=   ||
-||   ||   || 5\17 ||   ||   ||   ||   || 352.941 || 705.882 || 1058.824 || 211.765 ||= Optimum rank range (L/s=3/2) ||
+||   ||   || 5\17 ||   ||   ||   ||   ||   ||   || 352.941 || 705.882 || 1058.824 || 211.765 ||= Optimum rank range (L/s=3/2) ||
-||   ||   ||   ||   || 12\41 ||   ||   || 351.220 || 702.439 || 1053.659 || 204.878 ||= 2.3.11 neutral thirds scale
+||   ||   ||   ||   || 12\41 ||   ||   ||   ||   || 351.220 || 702.439 || 1053.659 || 204.878 ||= 2.3.11 neutral thirds scale
 is around here ||
-||   ||   ||   || 7\24 ||   ||   ||   || 350.000 || 700.000 || 1050.000 || 200.000 ||=   ||
+||   ||   ||   || 7\24 ||   ||   ||   ||   ||   || 350.000 || 700.000 || 1050.000 || 200.000 ||=   ||
-||   ||   ||   ||   || 9\31 ||   ||   || 348.387 || 696.774 || 1045.161 || 193.548 ||= Mohajira is around here ||
+||   ||   ||   ||   || 9\31 ||   ||   ||   ||   || 348.387 || 696.774 || 1045.161 || 193.548 ||= Mohajira is around here ||
-|| 2\7 ||   ||   ||   ||   ||   ||   || 342.847 || 685.714 || 1028.571 || 171.429 ||=   ||
+|| 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").
@@ Line 110: / Line 113: @@
      &lt;tr&gt;
          &lt;th colspan="7"&gt;generator&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;g&lt;br /&gt;
@@ Line 124: / Line 131: @@
      &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 146: / Line 157: @@
 &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;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;10\31&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;387.097&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;774.194&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;1161.290&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;348.387&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;&lt;a class="wiki_link" href="/Wuerschmidt%20family"&gt;Wuerschmidt&lt;/a&gt; is around here&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;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;9\28&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;385.714&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;771.429&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;1157.143&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;342.857&lt;br /&gt;
+&lt;/td&gt;
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+        &lt;td&gt;768.000&lt;br /&gt;
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+        &lt;td&gt;1152.000&lt;br /&gt;
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+        &lt;td&gt;336.000&lt;br /&gt;
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-         &lt;td style="text-align: center;"&gt;&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;Modi Sephiratorum (Kosmorsky)&lt;br /&gt;
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@@ Line 366: / Line 499: @@
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