Tuning systems for qanun: 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:hstraub|hstraub]] and made on <tt>2011-08-~~22 08~~:50:01 UTC</tt>.

: This revision was by author [[User:hstraub|hstraub]] and made on <tt>2011-08-23 06:52:15 UTC</tt>.

: The original revision id was <tt>~~247644081~~</tt>.

: The original revision id was <tt>247878883</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 22:

The whole table covers roughly the range of a fourth (the range where the ajnas - maqam tetrachords - reside). Each row corresponds to one string of the qanun. In the first column stands the basic (relative) tuning of a string while the following columns indicate possible intervals that can be reached via lowering the mandals/orabs.

The first table contains the cent values and the second the just intervals, sometimes differing between ascending and descending ratios.

The first table contains the cent values and the second the just intervals, sometimes differing between ascending and descending ratios. The middle part (which is the one that is mainly varying among the systems) is marked in bold.

Any given configuration of mandal/orab positions, resulting in a certain set of pitches that can be played at a given time

Line 36:

Interval table (cents):

|| 0 || 22 || 35 || 48 || 60 || 76 || 92 || 114 ||

|| 0 || 22 || **35** || **48** || **60** || **76** || 92 || 114 ||

|| 90 || 112 || 125 || 138 || 150 || 166 || 182 || 204 ||

|| 90 || 112 || **125** || **138** || **150** || **166** || 182 || 204 ||

|| 294 || 316 || 330 || 342 || 354 || 370 || 386 || 408 ||

|| 294 || 316 || **330** || **342** || **354** || **370** || 386 || 408 ||

|| 384 || 406 || 420 || 432 || 444 || 460 || 476 || 498 ||

|| 384 || 406 || **420** || **432** || **444** || **460** || 476 || 498 ||

|| 498 || 520 || 533 || 546 || 558 || 574 || 590 || 612 ||

|| 498 || 520 || **533** || **546** || **558** || **574** || 590 || 612 ||

Interval table of just intervals (ascending, descending):

Line 51:

|| 32/27 || 6/5 || 98/81 (asc.)

40/33 (desc.) || 39/32 (asc.)

~~XXX~~ || 27/22 (asc.)

11/9 (desc.) || 27/22 (asc.)

~~XXX~~ || 99/80, 26/21 (asc.)

16/13 (desc.) || 99/80, 26/21 (asc.)

XXX || 5/4 || 81/64 ||

243/196, XXX (desc.) || 5/4 || 81/64 ||

|| 8192/6581 || XXX || 25088/19683 || 104/81 || XXX || 176/135 || 320/243 || 4/3 ||

|| XXX || 27/20 || 351/258 || XXX || 243/176 || 891/640 || 45/32 || 729/512 ||

Line 72:

Mandal positions (cents): 22|16|15|12|13|14|22

Interval table XXX

Interval table (cents):

|| 0 || 22 || **38** || **54** || **66** || **78** || 92 || 114 ||

|| 90 || 112 || **128** || **143** || **156** || **168** || 182 || 204 ||

|| 294 || 316 || **332** || **348** || **360** || **372** || 386 || 408 ||

Interval table of just intervals:

XXX

==Symmetrical and super-symmetrical models==

Line 108:

Line 114:

Interval table(cents):

|| 0 || 22 || 36 || 50 || 64 || 76 || 92 || 114 ||

|| 0 || 22 || **36** || **50** || **64** || **76** || 92 || 114 ||

|| 90 || 112 || 126 || 140 || 154 || 168 || 182 || 204 ||

|| 90 || 112 || **126** || **140** || **154** || **168** || 182 || 204 ||

|| 294 || 316 || 330 || 344 || 358 || 372 || 386 || 408 ||

|| 294 || 316 || **330** || **344** || **358** || **372** || 386 || 408 ||

Interval table of just intervals (ascending, descending):

Line 201:

Line 207:

The whole table covers roughly the range of a fourth (the range where the ajnas - maqam tetrachords - reside). Each row corresponds to one string of the qanun. In the first column stands the basic (relative) tuning of a string while the following columns indicate possible intervals that can be reached via lowering the mandals/orabs.

The first table contains the cent values and the second the just intervals, sometimes differing between ascending and descending ratios.

The first table contains the cent values and the second the just intervals, sometimes differing between ascending and descending ratios. The middle part (which is the one that is mainly varying among the systems) is marked in bold.

Any given configuration of mandal/orab positions, resulting in a certain set of pitches that can be played at a given time

Line 223:

Line 229:

<td>22

</td>

<td>35

<td>35

</td>

<td>48

<td>48

</td>

<td>60

<td>60

</td>

<td>76

<td>76

</td>

<td>92

Line 241:

Line 247:

<td>112

</td>

<td>125

<td>125

</td>

<td>138

<td>138

</td>

<td>150

<td>150

</td>

<td>166

<td>166

</td>

<td>182

Line 259:

Line 265:

<td>316

</td>

<td>330

<td>330

</td>

<td>342

<td>342

</td>

<td>354

<td>354

</td>

<td>370

<td>370

</td>

<td>386

Line 277:

Line 283:

<td>406

</td>

<td>420

<td>420

</td>

<td>432

<td>432

</td>

<td>444

<td>444

</td>

<td>460

<td>460

</td>

<td>476

Line 295:

Line 301:

<td>520

</td>

<td>533

<td>533

</td>

<td>546

<td>546

</td>

<td>558

<td>558

</td>

<td>574

<td>574

</td>

<td>590

Line 364:

Line 370:

</td>

<td>39/32 (asc.)

~~XXX~~

11/9 (desc.)

</td>

<td>27/22 (asc.)

~~XXX~~

16/13 (desc.)

</td>

<td>99/80, 26/21 (asc.)

XXX

243/196, XXX (desc.)

</td>

<td>5/4

Line 431:

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Mandal positions (cents): 22|16|15|12|13|14|22

Interval table XXX

Interval table (cents):

<tr>

<td>0

</td>

<td>22

</td>

<td>38

</td>

<td>54

</td>

<td>66

</td>

<td>78

</td>

<td>92

</td>

<td>114

</td>

</tr>

<tr>

<td>90

</td>

<td>112

</td>

<td>128

</td>

<td>143

</td>

<td>156

</td>

<td>168

</td>

<td>182

</td>

<td>204

</td>

</tr>

<tr>

<td>294

</td>

<td>316

</td>

<td>332

</td>

<td>348

</td>

<td>360

</td>

<td>372

</td>

<td>386

</td>

<td>408

</td>

</tr>

</table>

Interval table of just intervals:

XXX

<h2 id="toc8"><a name="Newer systems-Symmetrical and super-symmetrical models"></a>Symmetrical and super-symmetrical models</h2>

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<td>22

</td>

<td>36

<td>36

</td>

<td>50

<td>50

</td>

<td>64

<td>64

</td>

<td>76

<td>76

</td>

<td>92

Line 493:

Line 561:

<td>112

</td>

<td>126

<td>126

</td>

<td>140

<td>140

</td>

<td>154

<td>154

</td>

<td>168

<td>168

</td>

<td>182

Line 511:

Line 579:

<td>316

</td>

<td>330

<td>330

</td>

<td>344

<td>344

</td>

<td>358

<td>358

</td>

<td>372

<td>372

</td>

<td>386

@@ 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:hstraub|hstraub]] and made on <tt>2011-08-22 08:50:01 UTC</tt>.<br>
+: This revision was by author [[User:hstraub|hstraub]] and made on <tt>2011-08-23 06:52:15 UTC</tt>.<br>
-: The original revision id was <tt>247644081</tt>.<br>
+: The original revision id was <tt>247878883</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 22: / Line 22: @@
 The whole table covers roughly the range of a fourth (the range where the ajnas - maqam tetrachords - reside). Each row corresponds to one string of the qanun. In the first column stands the basic (relative) tuning of a string while the following columns indicate possible intervals that can be reached via lowering the mandals/orabs.
-The first table contains the cent values and the second the just intervals, sometimes differing between ascending and descending ratios.
+The first table contains the cent values and the second the just intervals, sometimes differing between ascending and descending ratios. The middle part (which is the one that is mainly varying among the systems) is marked in bold.
 Any given configuration of mandal/orab positions, resulting in a certain set of pitches that can be played at a given time
@@ Line 36: / Line 36: @@
 Interval table (cents):
-|| 0 || 22 || 35 || 48 || 60 || 76 || 92 || 114 ||
+|| 0 || 22 || **35** || **48** || **60** || **76** || 92 || 114 ||
-|| 90 || 112 || 125 || 138 || 150 || 166 || 182 || 204 ||
+|| 90 || 112 || **125** || **138** || **150** || **166** || 182 || 204 ||
-|| 294 || 316 || 330 || 342 || 354 || 370 || 386 || 408 ||
+|| 294 || 316 || **330** || **342** || **354** || **370** || 386 || 408 ||
-|| 384 || 406 || 420 || 432 || 444 || 460 || 476 || 498 ||
+|| 384 || 406 || **420** || **432** || **444** || **460** || 476 || 498 ||
-|| 498 || 520 || 533 || 546 || 558 || 574 || 590 || 612 ||
+|| 498 || 520 || **533** || **546** || **558** || **574** || 590 || 612 ||
 Interval table of just intervals (ascending, descending):
@@ Line 51: / Line 51: @@
 || 32/27 || 6/5 || 98/81 (asc.)
 /33 (desc.) || 39/32 (asc.)
-XXX || 27/22 (asc.)
+/9 (desc.) || 27/22 (asc.)
-XXX || 99/80, 26/21 (asc.)
+/13 (desc.) || 99/80, 26/21 (asc.)
-XXX || 5/4 || 81/64 ||
+/196, XXX (desc.) || 5/4 || 81/64 ||
 || 8192/6581 || XXX || 25088/19683 || 104/81 || XXX || 176/135 || 320/243 || 4/3 ||
 || XXX || 27/20 || 351/258 || XXX || 243/176 || 891/640 || 45/32 || 729/512 ||
@@ Line 72: / Line 72: @@
 Mandal positions (cents): &lt;span style="color: #00000a; font-family: Tahoma;"&gt;22|16|15|12|13|14|22&lt;/span&gt;
-Interval table XXX
+Interval table (cents):
+|| 0 || 22 || **38** || **54** || **66** || **78** || 92 || 114 ||
+|| 90 || 112 || **128** || **143** || **156** || **168** || 182 || 204 ||
+|| 294 || 316 || **332** || **348** || **360** || **372** || 386 || 408 ||
+Interval table of just intervals:
+XXX
 ==Symmetrical and super-symmetrical models==
@@ Line 108: / Line 114: @@
 Interval table(cents):
-|| 0 || 22 || 36 || 50 || 64 || 76 || 92 || 114 ||
+|| 0 || 22 || **36** || **50** || **64** || **76** || 92 || 114 ||
-|| 90 || 112 || 126 || 140 || 154 || 168 || 182 || 204 ||
+|| 90 || 112 || **126** || **140** || **154** || **168** || 182 || 204 ||
-|| 294 || 316 || 330 || 344 || 358 || 372 || 386 || 408 ||
+|| 294 || 316 || **330** || **344** || **358** || **372** || 386 || 408 ||
 Interval table of just intervals (ascending, descending):
@@ Line 201: / Line 207: @@
   The whole table covers roughly the range of a fourth (the range where the ajnas - maqam tetrachords - reside). Each row corresponds to one string of the qanun. In the first column stands the basic (relative) tuning of a string while the following columns indicate possible intervals that can be reached via lowering the mandals/orabs.&lt;br /&gt;
 &lt;br /&gt;
-The first table contains the cent values and the second the just intervals, sometimes differing between ascending and descending ratios.&lt;br /&gt;
+The first table contains the cent values and the second the just intervals, sometimes differing between ascending and descending ratios. The middle part (which is the one that is mainly varying among the systems) is marked in bold.&lt;br /&gt;
 &lt;br /&gt;
 Any given configuration of mandal/orab positions, resulting in a certain set of pitches that can be played at a given time&lt;br /&gt;
@@ Line 223: / Line 229: @@
          &lt;td&gt;22&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;35&lt;br /&gt;
+         &lt;td&gt;&lt;strong&gt;35&lt;/strong&gt;&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;48&lt;br /&gt;
+         &lt;td&gt;&lt;strong&gt;48&lt;/strong&gt;&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;60&lt;br /&gt;
+         &lt;td&gt;&lt;strong&gt;60&lt;/strong&gt;&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;76&lt;br /&gt;
+         &lt;td&gt;&lt;strong&gt;76&lt;/strong&gt;&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;92&lt;br /&gt;
@@ Line 241: / Line 247: @@
          &lt;td&gt;112&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;125&lt;br /&gt;
+         &lt;td&gt;&lt;strong&gt;125&lt;/strong&gt;&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;138&lt;br /&gt;
+         &lt;td&gt;&lt;strong&gt;138&lt;/strong&gt;&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;150&lt;br /&gt;
+         &lt;td&gt;&lt;strong&gt;150&lt;/strong&gt;&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;166&lt;br /&gt;
+         &lt;td&gt;&lt;strong&gt;166&lt;/strong&gt;&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;182&lt;br /&gt;
@@ Line 259: / Line 265: @@
          &lt;td&gt;316&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;330&lt;br /&gt;
+         &lt;td&gt;&lt;strong&gt;330&lt;/strong&gt;&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;342&lt;br /&gt;
+         &lt;td&gt;&lt;strong&gt;342&lt;/strong&gt;&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;354&lt;br /&gt;
+         &lt;td&gt;&lt;strong&gt;354&lt;/strong&gt;&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;370&lt;br /&gt;
+         &lt;td&gt;&lt;strong&gt;370&lt;/strong&gt;&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;386&lt;br /&gt;
@@ Line 277: / Line 283: @@
          &lt;td&gt;406&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;420&lt;br /&gt;
+         &lt;td&gt;&lt;strong&gt;420&lt;/strong&gt;&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;432&lt;br /&gt;
+         &lt;td&gt;&lt;strong&gt;432&lt;/strong&gt;&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;444&lt;br /&gt;
+         &lt;td&gt;&lt;strong&gt;444&lt;/strong&gt;&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;460&lt;br /&gt;
+         &lt;td&gt;&lt;strong&gt;460&lt;/strong&gt;&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;476&lt;br /&gt;
@@ Line 295: / Line 301: @@
          &lt;td&gt;520&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;533&lt;br /&gt;
+         &lt;td&gt;&lt;strong&gt;533&lt;/strong&gt;&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;546&lt;br /&gt;
+         &lt;td&gt;&lt;strong&gt;546&lt;/strong&gt;&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;558&lt;br /&gt;
+         &lt;td&gt;&lt;strong&gt;558&lt;/strong&gt;&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;574&lt;br /&gt;
+         &lt;td&gt;&lt;strong&gt;574&lt;/strong&gt;&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;590&lt;br /&gt;
@@ Line 364: / Line 370: @@
 &lt;/td&gt;
          &lt;td&gt;39/32 (asc.)&lt;br /&gt;
-XXX&lt;br /&gt;
+/9 (desc.)&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;27/22 (asc.)&lt;br /&gt;
-XXX&lt;br /&gt;
+/13 (desc.)&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;99/80, 26/21 (asc.)&lt;br /&gt;
-XXX&lt;br /&gt;
+/196, XXX (desc.)&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;5/4&lt;br /&gt;
@@ Line 431: / Line 437: @@
 Mandal positions (cents): &lt;span style="color: #00000a; font-family: Tahoma;"&gt;22|16|15|12|13|14|22&lt;/span&gt;&lt;br /&gt;
 &lt;br /&gt;
-Interval table XXX&lt;br /&gt;
+Interval table (cents):&lt;br /&gt;
+&lt;table class="wiki_table"&gt;
+    &lt;tr&gt;
+        &lt;td&gt;0&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;22&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;strong&gt;38&lt;/strong&gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;strong&gt;54&lt;/strong&gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;strong&gt;66&lt;/strong&gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;strong&gt;78&lt;/strong&gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;92&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;114&lt;br /&gt;
+&lt;/td&gt;
+    &lt;/tr&gt;
+    &lt;tr&gt;
+        &lt;td&gt;90&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;112&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;strong&gt;128&lt;/strong&gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;strong&gt;143&lt;/strong&gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;strong&gt;156&lt;/strong&gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;strong&gt;168&lt;/strong&gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;182&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;204&lt;br /&gt;
+&lt;/td&gt;
+    &lt;/tr&gt;
+    &lt;tr&gt;
+        &lt;td&gt;294&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;316&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;strong&gt;332&lt;/strong&gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;strong&gt;348&lt;/strong&gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;strong&gt;360&lt;/strong&gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;strong&gt;372&lt;/strong&gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;386&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;408&lt;br /&gt;
+&lt;/td&gt;
+    &lt;/tr&gt;
+&lt;/table&gt;
+&lt;br /&gt;
+Interval table of just intervals:&lt;br /&gt;
+XXX&lt;br /&gt;
 &lt;br /&gt;
 &lt;!-- ws:start:WikiTextHeadingRule:16:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc8"&gt;&lt;a name="Newer systems-Symmetrical and super-symmetrical models"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:16 --&gt;Symmetrical and super-symmetrical models&lt;/h2&gt;
@@ Line 475: / Line 543: @@
          &lt;td&gt;22&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;36&lt;br /&gt;
+         &lt;td&gt;&lt;strong&gt;36&lt;/strong&gt;&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;50&lt;br /&gt;
+         &lt;td&gt;&lt;strong&gt;50&lt;/strong&gt;&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;64&lt;br /&gt;
+         &lt;td&gt;&lt;strong&gt;64&lt;/strong&gt;&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;76&lt;br /&gt;
+         &lt;td&gt;&lt;strong&gt;76&lt;/strong&gt;&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;92&lt;br /&gt;
@@ Line 493: / Line 561: @@
          &lt;td&gt;112&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;126&lt;br /&gt;
+         &lt;td&gt;&lt;strong&gt;126&lt;/strong&gt;&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;140&lt;br /&gt;
+         &lt;td&gt;&lt;strong&gt;140&lt;/strong&gt;&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;154&lt;br /&gt;
+         &lt;td&gt;&lt;strong&gt;154&lt;/strong&gt;&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;168&lt;br /&gt;
+         &lt;td&gt;&lt;strong&gt;168&lt;/strong&gt;&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;182&lt;br /&gt;
@@ Line 511: / Line 579: @@
          &lt;td&gt;316&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;330&lt;br /&gt;
+         &lt;td&gt;&lt;strong&gt;330&lt;/strong&gt;&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;344&lt;br /&gt;
+         &lt;td&gt;&lt;strong&gt;344&lt;/strong&gt;&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;358&lt;br /&gt;
+         &lt;td&gt;&lt;strong&gt;358&lt;/strong&gt;&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;372&lt;br /&gt;
+         &lt;td&gt;&lt;strong&gt;372&lt;/strong&gt;&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;386&lt;br /&gt;