1ed88c: 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:~~xenwolf~~|~~xenwolf~~]] and made on <tt>2010-09-28 02:46:41 UTC</tt>.

: This revision was by author [[User:Andrew_Heathwaite|Andrew_Heathwaite]] and made on <tt>2010-09-28 16:23:27 UTC</tt>.

: The original revision id was <tt>~~165931725~~</tt>.

: The original revision id was <tt>166174095</tt>.

: The revision comment was: <tt>~~some typo for table, links added (a few only)~~</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.

<h4>Original Wikitext content:</h4>

Line 20:

88cET is considered a very consonant tuning, and you will find that many of its intervals fall very close to simple ratios in 7- and 11-limit just intonation. It is also extremely close to [[41edo]], which is itself extremely close to the 8th root of 3:2 (a perfect fifth divided into exactly 8 logarithmically equal steps). See chart:

||~ Degree ||~ 88cET ||~ 41edo ||~ 8th Root ||~ Some Nearby ||

||~ ||~ ||~ 3-steps ||~ of 3:2 ||~ JI Intervals ||

||||||||||= **//first octave//** ||

|| 0 || 0 || 0 || 0 || 1/1=0 ||

|| 1 || 88 || 87.805 || 87.744 || 22/21=80.537, 21/20=84.467, 20/19=88.801, 19/18=93.603 ||

|| 2 || 176 || 175.610 || 175.489 || [[11_10|11/10]]=165.004, 21/19=173.268, [[10_9|10/9]]=182.404 ||

|| 3 || 264 || 263.415 || 263.233 || [[7_6|7/6]]=266.871 ||

|| 4 || 352 || 351.220 || 350.978 || [[11_9|11/9]]= 347.408, 27/22=354.547, 16/13=359.472 ||

|| 5 || 440 || 439.024 || 438.722 || 32/25=427.373, [[9_7|9/7]]=435.084, 22/17 446.363 ||

|| 6 || 528 || 526.829 || 526.466 || 19/14=528.687, 49/36=533.742, [[15_11|15/11]]=536.95 ||

|| 7 || 616 || 614.634 || 614.211 || [[10_7|10/7]]=617.488 ||

|| 8 || 704 || 702.439 || 701.955 || [[3_2|3/2]]=701.955 ||

|| 9 || 792 || 790.244 || 789.699 || [[11_7|11/7]]=782.492, 30/19=790.756, 128/81=792.180, 19/12=795.558, 27/17=800.910, [[8_5|8/5]]=813.686 ||

|| 10 || 880 || 878.049 || 878.444 || [[5_3|5/3]]=884.359 ||

|| 11 || 968 || 965.854 || 965.188 || [[7_4|7/4]]=968.826 ||

|| 12 || 1056 || 1053.659 || 1052.933 || [[11_6|11/6]]=1049.363, 35/19=1057.627, 24/13=1061.427 ||

|| 13 || 1144 || 1141.463 || 1140.677 || 27/14=1137.039, 31/16=1145.036 ||

||||||||||= **//second octave//** ||

|| 14 || 32 || 29.268 || 28.421 || ||

|| 14 || 32 || 29.268 || 28.421 || 65/64=26.841, 64/63=27.264, 63/62=27.700, 58/57=30.109 ||

|| 15 || 120 || 117.073 || 116.166 || ||

|| 15 || 120 || 117.073 || 116.166 || 16/15=111.731, 15/14=119.443, 14/13=128.298 ||

|| 16 || 208 || 204.878 || 203.910 || ||

|| 16 || 208 || 204.878 || 203.910 || 9/8=203.910 ||

|| 17 || 296 || 292.683 || 291.654 || ||

|| 17 || 296 || 292.683 || 291.654 || 13/11=289.210, 32/27=294.135, 19/16=297.513 ||

|| 18 || 384 || 380.488 || 379.399 || ||

|| 18 || 384 || 380.488 || 379.399 || 5/4=386.314 ||

|| 19 || 472 || 468.293 || 467.143 || ||

|| 19 || 472 || 468.293 || 467.143 || 17/13=464.428, 21/16=470.781 ||

|| 20 || 560 || 556.098 || 554.888 || ||

|| 20 || 560 || 556.098 || 554.888 || 11/8=551.318, 18/13=563.382 ||

|| 21 || 648 || 643.902 || 642.632 || ||

|| 21 || 648 || 643.902 || 642.632 || 16/11=648.682 ||

|| 22 || 736 || 731.707 || 730.376 || ||

|| 22 || 736 || 731.707 || 730.376 || 32/21=729.219, 26/17=735.572, 49/32=737.652 ||

|| 23 || 824 || 819.512 || 818.121 || ||

|| 23 || 824 || 819.512 || 818.121 || 8/5=813.686, 45/28=821.398, 21/13=830.253 ||

|| 24 || 912 || 907.317 || 905.865 || ||

|| 24 || 912 || 907.317 || 905.865 || 42/25=898.153, 32/19=902.487, 27/16=905.865, 22/13=910.790, 17/10=918.642 ||

|| 25 || 1000 || 995.122 || 993.609 || ||

|| 25 || 1000 || 995.122 || 993.609 || 39/22=991.165, 16/9=996.090, 25/14=1003.802, 34/19=1007.442 ||

|| 26 || 1088 || 1082.927 || 1081.354 || ||

|| 26 || 1088 || 1082.927 || 1081.354 || 28/15=1080.557, 15/8=1088.269 ||

|| 27 || 1176 || 1170.732 || 1169.098 || ||

|| 27 || 1176 || 1170.732 || 1169.098 || 63/32=1172.736, 160/81=1178.494 ||

||||||||||= **//third octave//** ||

|| 28 || 64 || 58.537 || 56.843 || ||

|| 28 || 64 || 58.537 || 56.843 || 33/3253.273, 28/27=62.961, 80/77=66.170, 27/26=65.337 ||

|| 29 || 152 || 146.341 || 144.587 || ||

|| 29 || 152 || 146.341 || 144.587 || 49/45=147.428, 12/11=150.637, 35/32=155.140 ||

|| 30 || 240 || 234.146 || 232.331 || ||

|| 30 || 240 || 234.146 || 232.331 || 8/7=231.174, 23/20=241.961, 15/13=247.741 ||

|| 31 || 328 || 321.951 || 320.076 || ||

|| 31 || 328 || 321.951 || 320.076 || 6/5=315.641, 23/19=330.761 ||

|| 32 || 416 || 409.756 || 407.820 || ||

|| 32 || 416 || 409.756 || 407.820 || 81/64=407.820, 33/26=412.745, 14/11=417.508 ||

|| 33 || 504 || 497.561 || 495.564 || ||

|| 33 || 504 || 497.561 || 495.564 || 85/64=491.269, 4/3=498.045, 75/56=505.757 ||

|| 34 || 592 || 585.366 || 583.309 || ||

|| 34 || 592 || 585.366 || 583.309 || 7/5=582.512, 45/32=590.224, 38/27=591.648 ||

|| 35 || 680 || 673.171 || 671.053 || ||

|| 35 || 680 || 673.171 || 671.053 || 28/19=671.313, 40/27=680.449 ||

|| 36 || 768 || 760.976 || 758.798 || ||

|| 36 || 768 || 760.976 || 758.798 || 17/11=753.637, 99/64=755.228, 14/9=764.916, 39/25=769.855, 25/16=772.627 ||

|| 37 || 856 || 848.780 || 846.542 || ||

|| 37 || 856 || 848.780 || 846.542 || 13/8=840.528, 18/11=852.592 ||

|| 38 || 944 || 936.585 || 934.286 || ||

|| 38 || 944 || 936.585 || 934.286 || 12/7=933.129, 19/11=946.195 ||

|| 39 || 1032 || 1024.390 || 1022.031 || ||

|| 39 || 1032 || 1024.390 || 1022.031 || 9/5=1017.596, 49/27=1031.787, 20/11=1034.996 ||

|| 40 || 1120 || 1112.195 || 1109.775 || ||

|| 40 || 1120 || 1112.195 || 1109.775 || 36/19=1106.397, 243/128=1109.775, 19/10=1111.199, 21/11=1119.463 ||

||||||||||= **//fourth octave//** (near match) ||

|| 41 || 8 || 0 || 1197.59 || ||

|| 41 || 8 || 0 || 1197.59 || 1/1=0, 2/1=1200 ||

==Compositions==

Line 189:

<td>438.722

</td>

<td>32/25=427.373, <a class="wiki_link" href="/9_7">9/7</a>=435.084, 22/17 446.363

</td>

</tr>

Line 301:

<td>28.421

</td>

<td>

<td>65/64=26.841, 64/63=27.264, 63/62=27.700, 58/57=30.109

</td>

</tr>

Line 313:

<td>116.166

</td>

<td>

<td>16/15=111.731, 15/14=119.443, 14/13=128.298

</td>

</tr>

Line 325:

<td>203.910

</td>

<td>

<td>9/8=203.910

</td>

</tr>

Line 337:

<td>291.654

</td>

<td>

<td>13/11=289.210, 32/27=294.135, 19/16=297.513

</td>

</tr>

Line 349:

<td>379.399

</td>

<td>

<td>5/4=386.314

</td>

</tr>

Line 361:

<td>467.143

</td>

<td>

<td>17/13=464.428, 21/16=470.781

</td>

</tr>

Line 373:

<td>554.888

</td>

<td>

<td>11/8=551.318, 18/13=563.382

</td>

</tr>

Line 385:

<td>642.632

</td>

<td>

<td>16/11=648.682

</td>

</tr>

Line 397:

<td>730.376

</td>

<td>

<td>32/21=729.219, 26/17=735.572, 49/32=737.652

</td>

</tr>

Line 409:

<td>818.121

</td>

<td>

<td>8/5=813.686, 45/28=821.398, 21/13=830.253

</td>

</tr>

Line 421:

<td>905.865

</td>

<td>

<td>42/25=898.153, 32/19=902.487, 27/16=905.865, 22/13=910.790, 17/10=918.642

</td>

</tr>

Line 433:

<td>993.609

</td>

<td>

<td>39/22=991.165, 16/9=996.090, 25/14=1003.802, 34/19=1007.442

</td>

</tr>

Line 445:

<td>1081.354

</td>

<td>

<td>28/15=1080.557, 15/8=1088.269

</td>

</tr>

Line 457:

<td>1169.098

</td>

<td>

<td>63/32=1172.736, 160/81=1178.494

</td>

</tr>

Line 473:

<td>56.843

</td>

<td>

<td>33/3253.273, 28/27=62.961, 80/77=66.170, 27/26=65.337

</td>

</tr>

Line 485:

<td>144.587

</td>

<td>

<td>49/45=147.428, 12/11=150.637, 35/32=155.140

</td>

</tr>

Line 497:

<td>232.331

</td>

<td>

<td>8/7=231.174, 23/20=241.961, 15/13=247.741

</td>

</tr>

Line 509:

<td>320.076

</td>

<td>

<td>6/5=315.641, 23/19=330.761

</td>

</tr>

Line 521:

<td>407.820

</td>

<td>

<td>81/64=407.820, 33/26=412.745, 14/11=417.508

</td>

</tr>

Line 533:

<td>495.564

</td>

<td>

<td>85/64=491.269, 4/3=498.045, 75/56=505.757

</td>

</tr>

Line 545:

<td>583.309

</td>

<td>

<td>7/5=582.512, 45/32=590.224, 38/27=591.648

</td>

</tr>

Line 557:

<td>671.053

</td>

<td>

<td>28/19=671.313, 40/27=680.449

</td>

</tr>

Line 569:

<td>758.798

</td>

<td>

<td>17/11=753.637, 99/64=755.228, 14/9=764.916, 39/25=769.855, 25/16=772.627

</td>

</tr>

Line 581:

<td>846.542

</td>

<td>

<td>13/8=840.528, 18/11=852.592

</td>

</tr>

Line 593:

<td>934.286

</td>

<td>

<td>12/7=933.129, 19/11=946.195

</td>

</tr>

Line 605:

<td>1022.031

</td>

<td>

<td>9/5=1017.596, 49/27=1031.787, 20/11=1034.996

</td>

</tr>

Line 617:

<td>1109.775

</td>

<td>

<td>36/19=1106.397, 243/128=1109.775, 19/10=1111.199, 21/11=1119.463

</td>

</tr>

Line 633:

<td>1197.59

</td>

<td>

<td>1/1=0, 2/1=1200

</td>

</tr>

@@ 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:xenwolf|xenwolf]] and made on <tt>2010-09-28 02:46:41 UTC</tt>.<br>
+: This revision was by author [[User:Andrew_Heathwaite|Andrew_Heathwaite]] and made on <tt>2010-09-28 16:23:27 UTC</tt>.<br>
-: The original revision id was <tt>165931725</tt>.<br>
+: The original revision id was <tt>166174095</tt>.<br>
-: The revision comment was: <tt>some typo for table, links added (a few only)</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>
 <h4>Original Wikitext content:</h4>
@@ Line 20: / Line 20: @@
 cET is considered a very consonant tuning, and you will find that many of its intervals fall very close to simple ratios in 7- and 11-limit just intonation. It is also extremely close to [[41edo]], which is itself extremely close to the 8th root of 3:2 (a perfect fifth divided into exactly 8 logarithmically equal steps). See chart:
-||~ Degree ||~ 88cET ||~ 41edo  ||~ 8th Root ||~ Some Nearby  ||
+||~ Degree ||~ 88cET ||~ 41edo ||~ 8th Root ||~ Some Nearby ||
-||~        ||~        ||~ 3-steps ||~ of 3:2 ||~ JI Intervals ||
+||~   ||~   ||~ 3-steps ||~ of 3:2 ||~ JI Intervals ||
 ||||||||||= **//first octave//** ||
 || 0 || 0 || 0 || 0 || 1/1=0 ||
 || 1 || 88 || 87.805 || 87.744 || 22/21=80.537, 21/20=84.467, 20/19=88.801, 19/18=93.603 ||
-|| 2 || 176 || 175.610 || 175.489 || [[11_10|11/10]]=165.004, 21/19=173.268, [[10_9|10/9]]=182.404  ||
+|| 2 || 176 || 175.610 || 175.489 || [[11_10|11/10]]=165.004, 21/19=173.268, [[10_9|10/9]]=182.404 ||
-|| 3 || 264 || 263.415 || 263.233 || [[7_6|7/6]]=266.871  ||
+|| 3 || 264 || 263.415 || 263.233 || [[7_6|7/6]]=266.871 ||
-|| 4 || 352 || 351.220 || 350.978 || [[11_9|11/9]]= 347.408, 27/22=354.547, 16/13=359.472  ||
+|| 4 || 352 || 351.220 || 350.978 || [[11_9|11/9]]= 347.408, 27/22=354.547, 16/13=359.472 ||
-|| 5 || 440 || 439.024 || 438.722 || 32/25=427.373, [[9_7|9/7]]=435.084, 22/17	446.363  ||
+|| 5 || 440 || 439.024 || 438.722 || 32/25=427.373, [[9_7|9/7]]=435.084, 22/17 446.363 ||
-|| 6 || 528 || 526.829 || 526.466 || 19/14=528.687, 49/36=533.742, [[15_11|15/11]]=536.95  ||
+|| 6 || 528 || 526.829 || 526.466 || 19/14=528.687, 49/36=533.742, [[15_11|15/11]]=536.95 ||
-|| 7 || 616 || 614.634 || 614.211 ||  [[10_7|10/7]]=617.488 ||
+|| 7 || 616 || 614.634 || 614.211 || [[10_7|10/7]]=617.488 ||
-|| 8 || 704 || 702.439 || 701.955 || [[3_2|3/2]]=701.955  ||
+|| 8 || 704 || 702.439 || 701.955 || [[3_2|3/2]]=701.955 ||
-|| 9 || 792 || 790.244 || 789.699 ||  [[11_7|11/7]]=782.492, 30/19=790.756, 128/81=792.180, 19/12=795.558, 27/17=800.910, [[8_5|8/5]]=813.686 ||
+|| 9 || 792 || 790.244 || 789.699 || [[11_7|11/7]]=782.492, 30/19=790.756, 128/81=792.180, 19/12=795.558, 27/17=800.910, [[8_5|8/5]]=813.686 ||
-|| 10 || 880 || 878.049 || 878.444 || [[5_3|5/3]]=884.359  ||
+|| 10 || 880 || 878.049 || 878.444 || [[5_3|5/3]]=884.359 ||
 || 11 || 968 || 965.854 || 965.188 || [[7_4|7/4]]=968.826 ||
-|| 12 || 1056 || 1053.659 || 1052.933 || [[11_6|11/6]]=1049.363, 35/19=1057.627, 24/13=1061.427  ||
+|| 12 || 1056 || 1053.659 || 1052.933 || [[11_6|11/6]]=1049.363, 35/19=1057.627, 24/13=1061.427 ||
-|| 13 || 1144 || 1141.463 || 1140.677 || 27/14=1137.039, 31/16=1145.036  ||
+|| 13 || 1144 || 1141.463 || 1140.677 || 27/14=1137.039, 31/16=1145.036 ||
 ||||||||||= **//second octave//** ||
-|| 14 || 32 || 29.268 || 28.421 ||   ||
+|| 14 || 32 || 29.268 || 28.421 || 65/64=26.841, 64/63=27.264, 63/62=27.700, 58/57=30.109 ||
-|| 15 || 120 || 117.073 || 116.166 ||   ||
+|| 15 || 120 || 117.073 || 116.166 || 16/15=111.731, 15/14=119.443, 14/13=128.298 ||
-|| 16 || 208 || 204.878 || 203.910 ||   ||
+|| 16 || 208 || 204.878 || 203.910 || 9/8=203.910 ||
-|| 17 || 296 || 292.683 || 291.654 ||   ||
+|| 17 || 296 || 292.683 || 291.654 || 13/11=289.210, 32/27=294.135, 19/16=297.513 ||
-|| 18 || 384 || 380.488 || 379.399 ||   ||
+|| 18 || 384 || 380.488 || 379.399 || 5/4=386.314 ||
-|| 19 || 472 || 468.293 || 467.143 ||   ||
+|| 19 || 472 || 468.293 || 467.143 || 17/13=464.428, 21/16=470.781 ||
-|| 20 || 560 || 556.098 || 554.888 ||   ||
+|| 20 || 560 || 556.098 || 554.888 || 11/8=551.318, 18/13=563.382 ||
-|| 21 || 648 || 643.902 || 642.632 ||   ||
+|| 21 || 648 || 643.902 || 642.632 || 16/11=648.682 ||
-|| 22 || 736 || 731.707 || 730.376 ||   ||
+|| 22 || 736 || 731.707 || 730.376 || 32/21=729.219, 26/17=735.572, 49/32=737.652 ||
-|| 23 || 824 || 819.512 || 818.121 ||   ||
+|| 23 || 824 || 819.512 || 818.121 || 8/5=813.686, 45/28=821.398, 21/13=830.253 ||
-|| 24 || 912 || 907.317 || 905.865 ||   ||
+|| 24 || 912 || 907.317 || 905.865 || 42/25=898.153, 32/19=902.487, 27/16=905.865, 22/13=910.790, 17/10=918.642 ||
-|| 25 || 1000 || 995.122 || 993.609 ||   ||
+|| 25 || 1000 || 995.122 || 993.609 || 39/22=991.165, 16/9=996.090, 25/14=1003.802, 34/19=1007.442 ||
-|| 26 || 1088 || 1082.927 || 1081.354 ||   ||
+|| 26 || 1088 || 1082.927 || 1081.354 || 28/15=1080.557, 15/8=1088.269 ||
-|| 27 || 1176 || 1170.732 || 1169.098 ||   ||
+|| 27 || 1176 || 1170.732 || 1169.098 || 63/32=1172.736, 160/81=1178.494 ||
 ||||||||||= **//third octave//** ||
-|| 28 || 64 || 58.537 || 56.843 ||   ||
+|| 28 || 64 || 58.537 || 56.843 || 33/3253.273, 28/27=62.961, 80/77=66.170, 27/26=65.337 ||
-|| 29 || 152 || 146.341 || 144.587 ||   ||
+|| 29 || 152 || 146.341 || 144.587 || 49/45=147.428, 12/11=150.637, 35/32=155.140 ||
-|| 30 || 240 || 234.146 || 232.331 ||   ||
+|| 30 || 240 || 234.146 || 232.331 || 8/7=231.174, 23/20=241.961, 15/13=247.741 ||
-|| 31 || 328 || 321.951 || 320.076 ||   ||
+|| 31 || 328 || 321.951 || 320.076 || 6/5=315.641, 23/19=330.761 ||
-|| 32 || 416 || 409.756 || 407.820 ||   ||
+|| 32 || 416 || 409.756 || 407.820 || 81/64=407.820, 33/26=412.745, 14/11=417.508 ||
-|| 33 || 504 || 497.561 || 495.564 ||   ||
+|| 33 || 504 || 497.561 || 495.564 || 85/64=491.269, 4/3=498.045, 75/56=505.757 ||
-|| 34 || 592 || 585.366 || 583.309 ||   ||
+|| 34 || 592 || 585.366 || 583.309 || 7/5=582.512, 45/32=590.224, 38/27=591.648 ||
-|| 35 || 680 || 673.171 || 671.053 ||   ||
+|| 35 || 680 || 673.171 || 671.053 || 28/19=671.313, 40/27=680.449 ||
-|| 36 || 768 || 760.976 || 758.798 ||   ||
+|| 36 || 768 || 760.976 || 758.798 || 17/11=753.637, 99/64=755.228, 14/9=764.916, 39/25=769.855, 25/16=772.627 ||
-|| 37 || 856 || 848.780 || 846.542 ||   ||
+|| 37 || 856 || 848.780 || 846.542 || 13/8=840.528, 18/11=852.592 ||
-|| 38 || 944 || 936.585 || 934.286 ||   ||
+|| 38 || 944 || 936.585 || 934.286 || 12/7=933.129, 19/11=946.195 ||
-|| 39 || 1032 || 1024.390 || 1022.031 ||   ||
+|| 39 || 1032 || 1024.390 || 1022.031 || 9/5=1017.596, 49/27=1031.787, 20/11=1034.996 ||
-|| 40 || 1120 || 1112.195 || 1109.775 ||   ||
+|| 40 || 1120 || 1112.195 || 1109.775 || 36/19=1106.397, 243/128=1109.775, 19/10=1111.199, 21/11=1119.463 ||
 ||||||||||= **//fourth octave//** (near match) ||
-|| 41 || 8 || 0 || 1197.59 ||   ||
+|| 41 || 8 || 0 || 1197.59 || 1/1=0, 2/1=1200 ||
 ==Compositions==
@@ Line 189: / Line 189: @@
          &lt;td&gt;438.722&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;32/25=427.373, &lt;a class="wiki_link" href="/9_7"&gt;9/7&lt;/a&gt;=435.084, 22/17    446.363&lt;br /&gt;
+         &lt;td&gt;32/25=427.373, &lt;a class="wiki_link" href="/9_7"&gt;9/7&lt;/a&gt;=435.084, 22/17 446.363&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
@@ Line 301: / Line 301: @@
          &lt;td&gt;28.421&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;&lt;br /&gt;
+         &lt;td&gt;65/64=26.841, 64/63=27.264, 63/62=27.700, 58/57=30.109&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
@@ Line 313: / Line 313: @@
          &lt;td&gt;116.166&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;&lt;br /&gt;
+         &lt;td&gt;16/15=111.731, 15/14=119.443, 14/13=128.298&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
@@ Line 325: / Line 325: @@
          &lt;td&gt;203.910&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;&lt;br /&gt;
+         &lt;td&gt;9/8=203.910&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
@@ Line 337: / Line 337: @@
          &lt;td&gt;291.654&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;&lt;br /&gt;
+         &lt;td&gt;13/11=289.210, 32/27=294.135, 19/16=297.513&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
@@ Line 349: / Line 349: @@
          &lt;td&gt;379.399&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;&lt;br /&gt;
+         &lt;td&gt;5/4=386.314&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
@@ Line 361: / Line 361: @@
          &lt;td&gt;467.143&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;&lt;br /&gt;
+         &lt;td&gt;17/13=464.428, 21/16=470.781&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
@@ Line 373: / Line 373: @@
          &lt;td&gt;554.888&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;&lt;br /&gt;
+         &lt;td&gt;11/8=551.318, 18/13=563.382&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
@@ Line 385: / Line 385: @@
          &lt;td&gt;642.632&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;&lt;br /&gt;
+         &lt;td&gt;16/11=648.682&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
@@ Line 397: / Line 397: @@
          &lt;td&gt;730.376&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;&lt;br /&gt;
+         &lt;td&gt;32/21=729.219, 26/17=735.572, 49/32=737.652&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
@@ Line 409: / Line 409: @@
          &lt;td&gt;818.121&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;&lt;br /&gt;
+         &lt;td&gt;8/5=813.686, 45/28=821.398, 21/13=830.253&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
@@ Line 421: / Line 421: @@
          &lt;td&gt;905.865&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;&lt;br /&gt;
+         &lt;td&gt;42/25=898.153, 32/19=902.487, 27/16=905.865, 22/13=910.790, 17/10=918.642&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
@@ Line 433: / Line 433: @@
          &lt;td&gt;993.609&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;&lt;br /&gt;
+         &lt;td&gt;39/22=991.165, 16/9=996.090, 25/14=1003.802, 34/19=1007.442&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
@@ Line 445: / Line 445: @@
          &lt;td&gt;1081.354&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;&lt;br /&gt;
+         &lt;td&gt;28/15=1080.557, 15/8=1088.269&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
@@ Line 457: / Line 457: @@
          &lt;td&gt;1169.098&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;&lt;br /&gt;
+         &lt;td&gt;63/32=1172.736, 160/81=1178.494&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
@@ Line 473: / Line 473: @@
          &lt;td&gt;56.843&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;&lt;br /&gt;
+         &lt;td&gt;33/3253.273, 28/27=62.961, 80/77=66.170, 27/26=65.337&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
@@ Line 485: / Line 485: @@
          &lt;td&gt;144.587&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;&lt;br /&gt;
+         &lt;td&gt;49/45=147.428, 12/11=150.637, 35/32=155.140&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
@@ Line 497: / Line 497: @@
          &lt;td&gt;232.331&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;&lt;br /&gt;
+         &lt;td&gt;8/7=231.174, 23/20=241.961, 15/13=247.741&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
@@ Line 509: / Line 509: @@
          &lt;td&gt;320.076&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;&lt;br /&gt;
+         &lt;td&gt;6/5=315.641, 23/19=330.761&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
@@ Line 521: / Line 521: @@
          &lt;td&gt;407.820&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;&lt;br /&gt;
+         &lt;td&gt;81/64=407.820, 33/26=412.745, 14/11=417.508&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
@@ Line 533: / Line 533: @@
          &lt;td&gt;495.564&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;&lt;br /&gt;
+         &lt;td&gt;85/64=491.269, 4/3=498.045, 75/56=505.757&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
@@ Line 545: / Line 545: @@
          &lt;td&gt;583.309&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;&lt;br /&gt;
+         &lt;td&gt;7/5=582.512, 45/32=590.224, 38/27=591.648&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
@@ Line 557: / Line 557: @@
          &lt;td&gt;671.053&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;&lt;br /&gt;
+         &lt;td&gt;28/19=671.313, 40/27=680.449&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
@@ Line 569: / Line 569: @@
          &lt;td&gt;758.798&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;&lt;br /&gt;
+         &lt;td&gt;17/11=753.637, 99/64=755.228, 14/9=764.916, 39/25=769.855, 25/16=772.627&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
@@ Line 581: / Line 581: @@
          &lt;td&gt;846.542&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;&lt;br /&gt;
+         &lt;td&gt;13/8=840.528, 18/11=852.592&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
@@ Line 593: / Line 593: @@
          &lt;td&gt;934.286&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;&lt;br /&gt;
+         &lt;td&gt;12/7=933.129, 19/11=946.195&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
@@ Line 605: / Line 605: @@
          &lt;td&gt;1022.031&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;&lt;br /&gt;
+         &lt;td&gt;9/5=1017.596, 49/27=1031.787, 20/11=1034.996&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
@@ Line 617: / Line 617: @@
          &lt;td&gt;1109.775&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;&lt;br /&gt;
+         &lt;td&gt;36/19=1106.397, 243/128=1109.775, 19/10=1111.199, 21/11=1119.463&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
@@ Line 633: / Line 633: @@
          &lt;td&gt;1197.59&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;&lt;br /&gt;
+         &lt;td&gt;1/1=0, 2/1=1200&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;