65edo: 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:~~JosephRuhf~~|~~JosephRuhf~~]] and made on <tt>2016-12-~~07 11~~:01:08 UTC</tt>.

: This revision was by author [[User:xenwolf|xenwolf]] and made on <tt>2016-12-29 17:51:20 UTC</tt>.

: The original revision id was <tt>~~601622206~~</tt>.

: The original revision id was <tt>602901538</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 10:

=65 tone equal temperament=

**//65edo//** divides the [[octave]] into 65 equal parts of 18.4615 cents each. It can be characterized as the temperament which tempers out the [[schisma]], 32805/32768, the [[sensipent comma]], 78732/78125, and the [[wuerschmidt comma]]. In the [[7-limit]], there are two different maps; the first is <65 103 151/1 182|, [[tempering out]] 126/125, 245/243 and 686/675, so that 65edo supports sensi temperament, and the second is <65 103 151/1 183|, tempering out 225/224, 3125/3097, 4000/3969 and 5120/5103, so that 65edo supports garibaldi temperament. In both cases, the tuning privileges the [[5-limit]] over the 7-limit, as the 5-limit of 65 is quite accurate. The same can be said for the two different versions of 7-limit [[wuerschmidt temperament]] (wurschmidt and worschmidt) these two mappings provide.

**//65edo//** divides the [[octave]] into 65 equal parts of 18.4615 cents each. It can be characterized as the temperament which tempers out the [[schisma]], 32805/32768, the [[sensipent comma]], 78732/78125, and the [[wuerschmidt comma]]. In the [[7-limit]], there are two different maps; the first is <65 103 151 182|, [[tempering out]] 126/125, 245/243 and 686/675, so that 65edo supports sensi temperament, and the second is <65 103 151 183|, tempering out 225/224, 3125/3097, 4000/3969 and 5120/5103, so that 65edo supports garibaldi temperament. In both cases, the tuning privileges the [[5-limit]] over the 7-limit, as the 5-limit of 65 is quite accurate. The same can be said for the two different versions of 7-limit [[wuerschmidt temperament]] (wurschmidt and worschmidt) these two mappings provide.

65edo approximates the intervals [[3_2|3/2]], [[5_4|5/4]], [[11_8|11/8]] and [[19_16|19/16]] well, so that it does a good job representing the 2.3.5.11.19 [[just intonation subgroup]]. To this one may want to add 13/8 and 17/16, giving the [[19-limit]] no-sevens subgroup 2.3.5.11.13.17.19. Also of interest is the 19-limit [[k*N subgroups|2*65 subgroup]] 2.3.5.49.11.91.119.19, on which 65 has the same tuning and commas as [[130edo]].

Line 17:

=Intervals=

|| ~~Degrees of 65-EDO~~ || Cents ~~value~~ ||

||~ [[Degree]] ||~ Size ([[cent|Cents]]) ||

|| 0 || 0 ||

||= 0 ||> 0.0000 ||

|| 1 || 18.4615 ||

||= 1 ||> 18.4615 ||

|| 2 || 36.9231 ||

||= 2 ||> 36.9231 ||

|| 3 || 55.3846 ||

||= 3 ||> 55.3846 ||

|| 4 || 73.8462 ||

||= 4 ||> 73.8462 ||

|| 5 || 92.3077 ||

||= 5 ||> 92.3077 ||

|| 6 || 110.7692/1 ||

||= 6 ||> 110.7692 ||

|| 7 || 129.2308/1 ||

||= 7 ||> 129.2308 ||

|| 8 || 147.6923/1 ||

||= 8 ||> 147.6923 ||

|| 9 || 166.1538/1 ||

||= 9 ||> 166.1538 ||

|| 10 || 184.6154/1 ||

||= 10 ||> 184.6154 ||

|| 11 || 203.0769/1 ||

||= 11 ||> 203.0769 ||

|| 12 || 221.5385/1 ||

||= 12 ||> 221.5385 ||

|| 13 || 240 ||

||= 13 ||> 240.0000 ||

|| 14 || 258.4615/1 ||

||= 14 ||> 258.4615 ||

|| 15 || 276.9231/1 ||

||= 15 ||> 276.9231 ||

|| 16 || 295.3846/1 ||

||= 16 ||> 295.3846 ||

|| 17 || 313.8462/1 ||

||= 17 ||> 313.8462 ||

|| 18 || 332.3077/1 ||

||= 18 ||> 332.3077 ||

|| 19 || 350.7692/1 ||

||= 19 ||> 350.7692 ||

|| 20 || 369.2308/1 ||

||= 20 ||> 369.2308 ||

|| 21 || 387.6923/1 ||

||= 21 ||> 387.6923 ||

|| 22 || 406.1538/1 ||

||= 22 ||> 406.1538 ||

|| 23 || 424.6154/1 ||

||= 23 ||> 424.6154 ||

|| 24 || 443.0769/1 ||

||= 24 ||> 443.0769 ||

|| 25 || 461.5385/1 ||

||= 25 ||> 461.5385 ||

|| 26 || 480 ||

||= 26 ||> 480.0000 ||

|| 27 || 498.4615/1 ||

||= 27 ||> 498.4615 ||

|| 28 || 516.9231/1 ||

||= 28 ||> 516.9231 ||

|| 29 || 535.3846/1 ||

||= 29 ||> 535.3846 ||

|| 30 || 553.8462/1 ||

||= 30 ||> 553.8462 ||

|| 31 || 572.3077/1 ||

||= 31 ||> 572.3077 ||

|| 32 || 590.7692/1 ||

||= 32 ||> 590.7692 ||

|| 33 || 609.2308/1 ||

||= 33 ||> 609.2308 ||

|| 34 || 627.6923/1 ||

||= 34 ||> 627.6923 ||

|| 35 || 646.1538/1 ||

||= 35 ||> 646.1538 ||

|| 36 || 664.6154/1 ||

||= 36 ||> 664.6154 ||

|| 37 || 683.0769/1 ||

||= 37 ||> 683.0769 ||

|| 38 || 701.5385/1 ||

||= 38 ||> 701.5385 ||

|| 39 || 720 ||

||= 39 ||> 720.0000 ||

|| 40 || 738.4615/1 ||

||= 40 ||> 738.4615 ||

|| 41 || 756.9231/1 ||

||= 41 ||> 756.9231 ||

|| 42 || 775.3846/1 ||

||= 42 ||> 775.3846 ||

|| 43 || 793.8462/1 ||

||= 43 ||> 793.8462 ||

|| 44 || 812.3077/1 ||

||= 44 ||> 812.3077 ||

|| 45 || 830.7692/1 ||

||= 45 ||> 830.7692 ||

|| 46 || 849.2308/1 ||

||= 46 ||> 849.2308 ||

|| 47 || 867.6923/1 ||

||= 47 ||> 867.6923 ||

|| 48 || 886.1538/1 ||

||= 48 ||> 886.1538 ||

|| 49 || 904.6154/1 ||

||= 49 ||> 904.6154 ||

|| 50 || 923.0769/1 ||

||= 50 ||> 923.0769 ||

|| 51 || 941.5385/1 ||

||= 51 ||> 941.5385 ||

|| 52 || 960 ||

||= 52 ||> 960.0000 ||

|| 53 || 978.4615/1 ||

||= 53 ||> 978.4615 ||

|| 54 || 996.9231/1 ||

||= 54 ||> 996.9231 ||

|| 55 || 1015.3846 ||

||= 55 ||> 1015.3846 ||

|| 56 || 1033.8462 ||

||= 56 ||> 1033.8462 ||

|| 57 || 1052.3077 ||

||= 57 ||> 1052.3077 ||

|| 58 || 1070.7692 ||

||= 58 ||> 1070.7692 ||

|| 59 || 1089.2308 ||

||= 59 ||> 1089.2308 ||

|| 60 || 1107.6923 ||

||= 60 ||> 1107.6923 ||

|| 61 || 1126.1538 ||

||= 61 ||> 1126.1538 ||

|| 62 || 1144.6154 ||

||= 62 ||> 1144.6154 ||

|| 63 || 1163.0769 ||

||= 63 ||> 1163.0769 ||

|| 64 || 1181.5385 ||

||= 64 ||> 1181.5385 ||

||= 65 ||> 1200.0000 ||

=Scales=

Line 92:

Line 93:

<h1 id="toc0"><a name="x65 tone equal temperament"></a>65 tone equal temperament</h1>

65edo divides the <a class="wiki_link" href="/octave">octave</a> into 65 equal parts of 18.4615 cents each. It can be characterized as the temperament which tempers out the <a class="wiki_link" href="/schisma">schisma</a>, 32805/32768, the <a class="wiki_link" href="/sensipent%20comma">sensipent comma</a>, 78732/78125, and the <a class="wiki_link" href="/wuerschmidt%20comma">wuerschmidt comma</a>. In the <a class="wiki_link" href="/7-limit">7-limit</a>, there are two different maps; the first is &lt;65 103 151/1 182|, <a class="wiki_link" href="/tempering%20out">tempering out</a> 126/125, 245/243 and 686/675, so that 65edo supports sensi temperament, and the second is &lt;65 103 151/1 183|, tempering out 225/224, 3125/3097, 4000/3969 and 5120/5103, so that 65edo supports garibaldi temperament. In both cases, the tuning privileges the <a class="wiki_link" href="/5-limit">5-limit</a> over the 7-limit, as the 5-limit of 65 is quite accurate. The same can be said for the two different versions of 7-limit <a class="wiki_link" href="/wuerschmidt%20temperament">wuerschmidt temperament</a> (wurschmidt and worschmidt) these two mappings provide.

65edo divides the <a class="wiki_link" href="/octave">octave</a> into 65 equal parts of 18.4615 cents each. It can be characterized as the temperament which tempers out the <a class="wiki_link" href="/schisma">schisma</a>, 32805/32768, the <a class="wiki_link" href="/sensipent%20comma">sensipent comma</a>, 78732/78125, and the <a class="wiki_link" href="/wuerschmidt%20comma">wuerschmidt comma</a>. In the <a class="wiki_link" href="/7-limit">7-limit</a>, there are two different maps; the first is &lt;65 103 151 182|, <a class="wiki_link" href="/tempering%20out">tempering out</a> 126/125, 245/243 and 686/675, so that 65edo supports sensi temperament, and the second is &lt;65 103 151 183|, tempering out 225/224, 3125/3097, 4000/3969 and 5120/5103, so that 65edo supports garibaldi temperament. In both cases, the tuning privileges the <a class="wiki_link" href="/5-limit">5-limit</a> over the 7-limit, as the 5-limit of 65 is quite accurate. The same can be said for the two different versions of 7-limit <a class="wiki_link" href="/wuerschmidt%20temperament">wuerschmidt temperament</a> (wurschmidt and worschmidt) these two mappings provide.

65edo approximates the intervals <a class="wiki_link" href="/3_2">3/2</a>, <a class="wiki_link" href="/5_4">5/4</a>, <a class="wiki_link" href="/11_8">11/8</a> and <a class="wiki_link" href="/19_16">19/16</a> well, so that it does a good job representing the 2.3.5.11.19 <a class="wiki_link" href="/just%20intonation%20subgroup">just intonation subgroup</a>. To this one may want to add 13/8 and 17/16, giving the <a class="wiki_link" href="/19-limit">19-limit</a> no-sevens subgroup 2.3.5.11.13.17.19. Also of interest is the 19-limit <a class="wiki_link" href="/k%2AN%20subgroups">2*65 subgroup</a> 2.3.5.49.11.91.119.19, on which 65 has the same tuning and commas as <a class="wiki_link" href="/130edo">130edo</a>.

Line 103:

Line 104:

<tr>

<td>~~Degrees of 65-EDO~~

<th><a class="wiki_link" href="/Degree">Degree</a>

</th>

<th>Size (<a class="wiki_link" href="/cent">Cents</a>)

</th>

</tr>

<tr>

<td style="text-align: center;">0

</td>

<td>~~Cents value~~

<td style="text-align: right;">0.0000

</td>

</tr>

<tr>

<td>0

<td style="text-align: center;">1

</td>

<td>0

<td style="text-align: right;">18.4615

</td>

</tr>

<tr>

<td>1

<td style="text-align: center;">2

</td>

<td>18.~~4615~~

<td style="text-align: right;">36.9231

</td>

</tr>

<tr>

<td>2

<td style="text-align: center;">3

</td>

<td>36.~~9231~~

<td style="text-align: right;">55.3846

</td>

</tr>

<tr>

<td>3

<td style="text-align: center;">4

</td>

<td>55.~~3846~~

<td style="text-align: right;">73.8462

</td>

</tr>

<tr>

<td>4

<td style="text-align: center;">5

</td>

<td>73.~~8462~~

<td style="text-align: right;">92.3077

</td>

</tr>

<tr>

<td>5

<td style="text-align: center;">6

</td>

<td>92.~~3077~~

<td style="text-align: right;">110.7692

</td>

</tr>

<tr>

<td>6

<td style="text-align: center;">7

</td>

<td>~~110~~.~~7692/1~~

<td style="text-align: right;">129.2308

</td>

</tr>

<tr>

<td>7

<td style="text-align: center;">8

</td>

<td>~~129~~.~~2308/1~~

<td style="text-align: right;">147.6923

</td>

</tr>

<tr>

<td>8

<td style="text-align: center;">9

</td>

<td>~~147~~.~~6923/1~~

<td style="text-align: right;">166.1538

</td>

</tr>

<tr>

<td>9

<td style="text-align: center;">10

</td>

<td>~~166~~.~~1538/1~~

<td style="text-align: right;">184.6154

</td>

</tr>

<tr>

<td>10

<td style="text-align: center;">11

</td>

<td>~~184~~.~~6154/1~~

<td style="text-align: right;">203.0769

</td>

</tr>

<tr>

<td>11

<td style="text-align: center;">12

</td>

<td>~~203~~.~~0769/1~~

<td style="text-align: right;">221.5385

</td>

</tr>

<tr>

<td>12

<td style="text-align: center;">13

</td>

<td>~~221~~.~~5385/1~~

<td style="text-align: right;">240.0000

</td>

</tr>

<tr>

<td>13

<td style="text-align: center;">14

</td>

<td>~~240~~

<td style="text-align: right;">258.4615

</td>

</tr>

<tr>

<td>14

<td style="text-align: center;">15

</td>

<td>~~258~~.~~4615/1~~

<td style="text-align: right;">276.9231

</td>

</tr>

<tr>

<td>15

<td style="text-align: center;">16

</td>

<td>~~276~~.~~9231/1~~

<td style="text-align: right;">295.3846

</td>

</tr>

<tr>

<td>16

<td style="text-align: center;">17

</td>

<td>~~295~~.~~3846/1~~

<td style="text-align: right;">313.8462

</td>

</tr>

<tr>

<td>17

<td style="text-align: center;">18

</td>

<td>~~313~~.~~8462/1~~

<td style="text-align: right;">332.3077

</td>

</tr>

<tr>

<td>18

<td style="text-align: center;">19

</td>

<td>~~332~~.~~3077/1~~

<td style="text-align: right;">350.7692

</td>

</tr>

<tr>

<td>19

<td style="text-align: center;">20

</td>

<td>~~350~~.~~7692/1~~

<td style="text-align: right;">369.2308

</td>

</tr>

<tr>

<td>20

<td style="text-align: center;">21

</td>

<td>~~369~~.~~2308/1~~

<td style="text-align: right;">387.6923

</td>

</tr>

<tr>

<td>21

<td style="text-align: center;">22

</td>

<td>~~387~~.~~6923/1~~

<td style="text-align: right;">406.1538

</td>

</tr>

<tr>

<td>22

<td style="text-align: center;">23

</td>

<td>~~406~~.~~1538/1~~

<td style="text-align: right;">424.6154

</td>

</tr>

<tr>

<td>23

<td style="text-align: center;">24

</td>

<td>~~424~~.~~6154/1~~

<td style="text-align: right;">443.0769

</td>

</tr>

<tr>

<td>24

<td style="text-align: center;">25

</td>

<td>~~443~~.~~0769/1~~

<td style="text-align: right;">461.5385

</td>

</tr>

<tr>

<td>25

<td style="text-align: center;">26

</td>

<td>~~461~~.~~5385/1~~

<td style="text-align: right;">480.0000

</td>

</tr>

<tr>

<td>26

<td style="text-align: center;">27

</td>

<td>~~480~~

<td style="text-align: right;">498.4615

</td>

</tr>

<tr>

<td>27

<td style="text-align: center;">28

</td>

<td>~~498~~.~~4615/1~~

<td style="text-align: right;">516.9231

</td>

</tr>

<tr>

<td>28

<td style="text-align: center;">29

</td>

<td>~~516~~.~~9231/1~~

<td style="text-align: right;">535.3846

</td>

</tr>

<tr>

<td>29

<td style="text-align: center;">30

</td>

<td>~~535~~.~~3846/1~~

<td style="text-align: right;">553.8462

</td>

</tr>

<tr>

<td>30

<td style="text-align: center;">31

</td>

<td>~~553~~.~~8462/1~~

<td style="text-align: right;">572.3077

</td>

</tr>

<tr>

<td>31

<td style="text-align: center;">32

</td>

<td>~~572~~.~~3077/1~~

<td style="text-align: right;">590.7692

</td>

</tr>

<tr>

<td>32

<td style="text-align: center;">33

</td>

<td>~~590~~.~~7692/1~~

<td style="text-align: right;">609.2308

</td>

</tr>

<tr>

<td>33

<td style="text-align: center;">34

</td>

<td>~~609~~.~~2308/1~~

<td style="text-align: right;">627.6923

</td>

</tr>

<tr>

<td>34

<td style="text-align: center;">35

</td>

<td>~~627~~.~~6923/1~~

<td style="text-align: right;">646.1538

</td>

</tr>

<tr>

<td>35

<td style="text-align: center;">36

</td>

<td>~~646~~.~~1538/1~~

<td style="text-align: right;">664.6154

</td>

</tr>

<tr>

<td>36

<td style="text-align: center;">37

</td>

<td>~~664~~.~~6154/1~~

<td style="text-align: right;">683.0769

</td>

</tr>

<tr>

<td>37

<td style="text-align: center;">38

</td>

<td>~~683~~.~~0769/1~~

<td style="text-align: right;">701.5385

</td>

</tr>

<tr>

<td>38

<td style="text-align: center;">39

</td>

<td>~~701~~.~~5385/1~~

<td style="text-align: right;">720.0000

</td>

</tr>

<tr>

<td>39

<td style="text-align: center;">40

</td>

<td>~~720~~

<td style="text-align: right;">738.4615

</td>

</tr>

<tr>

<td>40

<td style="text-align: center;">41

</td>

<td>~~738~~.~~4615/1~~

<td style="text-align: right;">756.9231

</td>

</tr>

<tr>

<td>41

<td style="text-align: center;">42

</td>

<td>~~756~~.~~9231/1~~

<td style="text-align: right;">775.3846

</td>

</tr>

<tr>

<td>42

<td style="text-align: center;">43

</td>

<td>~~775~~.~~3846/1~~

<td style="text-align: right;">793.8462

</td>

</tr>

<tr>

<td>43

<td style="text-align: center;">44

</td>

<td>~~793~~.~~8462/1~~

<td style="text-align: right;">812.3077

</td>

</tr>

<tr>

<td>44

<td style="text-align: center;">45

</td>

<td>~~812~~.~~3077/1~~

<td style="text-align: right;">830.7692

</td>

</tr>

<tr>

<td>45

<td style="text-align: center;">46

</td>

<td>~~830~~.~~7692/1~~

<td style="text-align: right;">849.2308

</td>

</tr>

<tr>

<td>46

<td style="text-align: center;">47

</td>

<td>~~849~~.~~2308/1~~

<td style="text-align: right;">867.6923

</td>

</tr>

<tr>

<td>47

<td style="text-align: center;">48

</td>

<td>~~867~~.~~6923/1~~

<td style="text-align: right;">886.1538

</td>

</tr>

<tr>

<td>48

<td style="text-align: center;">49

</td>

<td>~~886~~.~~1538/1~~

<td style="text-align: right;">904.6154

</td>

</tr>

<tr>

<td>49

<td style="text-align: center;">50

</td>

<td>~~904~~.~~6154/1~~

<td style="text-align: right;">923.0769

</td>

</tr>

<tr>

<td>50

<td style="text-align: center;">51

</td>

<td>~~923~~.~~0769/1~~

<td style="text-align: right;">941.5385

</td>

</tr>

<tr>

<td>51

<td style="text-align: center;">52

</td>

<td>~~941~~.~~5385/1~~

<td style="text-align: right;">960.0000

</td>

</tr>

<tr>

<td>52

<td style="text-align: center;">53

</td>

<td>~~960~~

<td style="text-align: right;">978.4615

</td>

</tr>

<tr>

<td>53

<td style="text-align: center;">54

</td>

<td>~~978~~.~~4615/1~~

<td style="text-align: right;">996.9231

</td>

</tr>

<tr>

<td>54

<td style="text-align: center;">55

</td>

<td>~~996~~.~~9231/1~~

<td style="text-align: right;">1015.3846

</td>

</tr>

<tr>

<td>55

<td style="text-align: center;">56

</td>

<td>~~1015~~.~~3846~~

<td style="text-align: right;">1033.8462

</td>

</tr>

<tr>

<td>56

<td style="text-align: center;">57

</td>

<td>~~1033~~.~~8462~~

<td style="text-align: right;">1052.3077

</td>

</tr>

<tr>

<td>57

<td style="text-align: center;">58

</td>

<td>~~1052~~.~~3077~~

<td style="text-align: right;">1070.7692

</td>

</tr>

<tr>

<td>58

<td style="text-align: center;">59

</td>

<td>~~1070~~.~~7692~~

<td style="text-align: right;">1089.2308

</td>

</tr>

<tr>

<td>59

<td style="text-align: center;">60

</td>

<td>~~1089~~.~~2308~~

<td style="text-align: right;">1107.6923

</td>

</tr>

<tr>

<td>60

<td style="text-align: center;">61

</td>

<td>~~1107~~.~~6923~~

<td style="text-align: right;">1126.1538

</td>

</tr>

<tr>

<td>61

<td style="text-align: center;">62

</td>

<td>~~1126~~.~~1538~~

<td style="text-align: right;">1144.6154

</td>

</tr>

<tr>

<td>62

<td style="text-align: center;">63

</td>

<td>~~1144~~.~~6154~~

<td style="text-align: right;">1163.0769

</td>

</tr>

<tr>

<td>63

<td style="text-align: center;">64

</td>

<td>~~1163~~.~~0769~~

<td style="text-align: right;">1181.5385

</td>

</tr>

<tr>

<td>64

<td style="text-align: center;">65

</td>

<td>~~1181~~.~~5385~~

<td style="text-align: right;">1200.0000

</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:JosephRuhf|JosephRuhf]] and made on <tt>2016-12-07 11:01:08 UTC</tt>.<br>
+: This revision was by author [[User:xenwolf|xenwolf]] and made on <tt>2016-12-29 17:51:20 UTC</tt>.<br>
-: The original revision id was <tt>601622206</tt>.<br>
+: The original revision id was <tt>602901538</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 10: / Line 10: @@
 =&lt;span style="color: #750063; font-family: 'Times New Roman',Times,serif; font-size: 113%;"&gt;65 tone equal temperament&lt;/span&gt;=
-**//65edo//** divides the [[octave]] into 65 equal parts of 18.4615 cents each. It can be characterized as the temperament which tempers out the [[schisma]], 32805/32768, the [[sensipent comma]], 78732/78125, and the [[wuerschmidt comma]]. In the [[7-limit]], there are two different maps; the first is &lt;65 103 151/1 182|, [[tempering out]] 126/125, 245/243 and 686/675, so that 65edo supports sensi temperament, and the second is &lt;65 103 151/1 183|, tempering out 225/224, 3125/3097, 4000/3969 and 5120/5103, so that 65edo supports garibaldi temperament. In both cases, the tuning privileges the [[5-limit]] over the 7-limit, as the 5-limit of 65 is quite accurate. The same can be said for the two different versions of 7-limit [[wuerschmidt temperament]] (wurschmidt and worschmidt) these two mappings provide.
+**//65edo//** divides the [[octave]] into 65 equal parts of 18.4615 cents each. It can be characterized as the temperament which tempers out the [[schisma]], 32805/32768, the [[sensipent comma]], 78732/78125, and the [[wuerschmidt comma]]. In the [[7-limit]], there are two different maps; the first is &lt;65 103 151 182|, [[tempering out]] 126/125, 245/243 and 686/675, so that 65edo supports sensi temperament, and the second is &lt;65 103 151 183|, tempering out 225/224, 3125/3097, 4000/3969 and 5120/5103, so that 65edo supports garibaldi temperament. In both cases, the tuning privileges the [[5-limit]] over the 7-limit, as the 5-limit of 65 is quite accurate. The same can be said for the two different versions of 7-limit [[wuerschmidt temperament]] (wurschmidt and worschmidt) these two mappings provide.
 edo approximates the intervals [[3_2|3/2]], [[5_4|5/4]], [[11_8|11/8]] and [[19_16|19/16]] well, so that it does a good job representing the 2.3.5.11.19 [[just intonation subgroup]]. To this one may want to add 13/8 and 17/16, giving the [[19-limit]] no-sevens subgroup 2.3.5.11.13.17.19. Also of interest is the 19-limit [[k*N subgroups|2*65 subgroup]] 2.3.5.49.11.91.119.19, on which 65 has the same tuning and commas as [[130edo]].
@@ Line 17: / Line 17: @@
 =Intervals=
-|| Degrees of 65-EDO || Cents value ||
+||~ [[Degree]] ||~ Size ([[cent|Cents]]) ||
-|| 0 || 0 ||
+||=  0 ||&gt;    0.0000 ||
-|| 1 || 18.4615 ||
+||=  1 ||&gt;   18.4615 ||
-|| 2 || 36.9231 ||
+||=  2 ||&gt;   36.9231 ||
-|| 3 || 55.3846 ||
+||=  3 ||&gt;   55.3846 ||
-|| 4 || 73.8462 ||
+||=  4 ||&gt;   73.8462 ||
-|| 5 || 92.3077 ||
+||=  5 ||&gt;   92.3077 ||
-|| 6 || 110.7692/1 ||
+||=  6 ||&gt;  110.7692 ||
-|| 7 || 129.2308/1 ||
+||=  7 ||&gt;  129.2308 ||
-|| 8 || 147.6923/1 ||
+||=  8 ||&gt;  147.6923 ||
-|| 9 || 166.1538/1 ||
+||=  9 ||&gt;  166.1538 ||
-|| 10 || 184.6154/1 ||
+||= 10 ||&gt;  184.6154 ||
-|| 11 || 203.0769/1 ||
+||= 11 ||&gt;  203.0769 ||
-|| 12 || 221.5385/1 ||
+||= 12 ||&gt;  221.5385 ||
-|| 13 || 240 ||
+||= 13 ||&gt;  240.0000 ||
-|| 14 || 258.4615/1 ||
+||= 14 ||&gt;  258.4615 ||
-|| 15 || 276.9231/1 ||
+||= 15 ||&gt;  276.9231 ||
-|| 16 || 295.3846/1 ||
+||= 16 ||&gt;  295.3846 ||
-|| 17 || 313.8462/1 ||
+||= 17 ||&gt;  313.8462 ||
-|| 18 || 332.3077/1 ||
+||= 18 ||&gt;  332.3077 ||
-|| 19 || 350.7692/1 ||
+||= 19 ||&gt;  350.7692 ||
-|| 20 || 369.2308/1 ||
+||= 20 ||&gt;  369.2308 ||
-|| 21 || 387.6923/1 ||
+||= 21 ||&gt;  387.6923 ||
-|| 22 || 406.1538/1 ||
+||= 22 ||&gt;  406.1538 ||
-|| 23 || 424.6154/1 ||
+||= 23 ||&gt;  424.6154 ||
-|| 24 || 443.0769/1 ||
+||= 24 ||&gt;  443.0769 ||
-|| 25 || 461.5385/1 ||
+||= 25 ||&gt;  461.5385 ||
-|| 26 || 480 ||
+||= 26 ||&gt;  480.0000 ||
-|| 27 || 498.4615/1 ||
+||= 27 ||&gt;  498.4615 ||
-|| 28 || 516.9231/1 ||
+||= 28 ||&gt;  516.9231 ||
-|| 29 || 535.3846/1 ||
+||= 29 ||&gt;  535.3846 ||
-|| 30 || 553.8462/1 ||
+||= 30 ||&gt;  553.8462 ||
-|| 31 || 572.3077/1 ||
+||= 31 ||&gt;  572.3077 ||
-|| 32 || 590.7692/1 ||
+||= 32 ||&gt;  590.7692 ||
-|| 33 || 609.2308/1 ||
+||= 33 ||&gt;  609.2308 ||
-|| 34 || 627.6923/1 ||
+||= 34 ||&gt;  627.6923 ||
-|| 35 || 646.1538/1 ||
+||= 35 ||&gt;  646.1538 ||
-|| 36 || 664.6154/1 ||
+||= 36 ||&gt;  664.6154 ||
-|| 37 || 683.0769/1 ||
+||= 37 ||&gt;  683.0769 ||
-|| 38 || 701.5385/1 ||
+||= 38 ||&gt;  701.5385 ||
-|| 39 || 720 ||
+||= 39 ||&gt;  720.0000 ||
-|| 40 || 738.4615/1 ||
+||= 40 ||&gt;  738.4615 ||
-|| 41 || 756.9231/1 ||
+||= 41 ||&gt;  756.9231 ||
-|| 42 || 775.3846/1 ||
+||= 42 ||&gt;  775.3846 ||
-|| 43 || 793.8462/1 ||
+||= 43 ||&gt;  793.8462 ||
-|| 44 || 812.3077/1 ||
+||= 44 ||&gt;  812.3077 ||
-|| 45 || 830.7692/1 ||
+||= 45 ||&gt;  830.7692 ||
-|| 46 || 849.2308/1 ||
+||= 46 ||&gt;  849.2308 ||
-|| 47 || 867.6923/1 ||
+||= 47 ||&gt;  867.6923 ||
-|| 48 || 886.1538/1 ||
+||= 48 ||&gt;  886.1538 ||
-|| 49 || 904.6154/1 ||
+||= 49 ||&gt;  904.6154 ||
-|| 50 || 923.0769/1 ||
+||= 50 ||&gt;  923.0769 ||
-|| 51 || 941.5385/1 ||
+||= 51 ||&gt;  941.5385 ||
-|| 52 || 960 ||
+||= 52 ||&gt;  960.0000 ||
-|| 53 || 978.4615/1 ||
+||= 53 ||&gt;  978.4615 ||
-|| 54 || 996.9231/1 ||
+||= 54 ||&gt;  996.9231 ||
-|| 55 || 1015.3846 ||
+||= 55 ||&gt; 1015.3846 ||
-|| 56 || 1033.8462 ||
+||= 56 ||&gt; 1033.8462 ||
-|| 57 || 1052.3077 ||
+||= 57 ||&gt; 1052.3077 ||
-|| 58 || 1070.7692 ||
+||= 58 ||&gt; 1070.7692 ||
-|| 59 || 1089.2308 ||
+||= 59 ||&gt; 1089.2308 ||
-|| 60 || 1107.6923 ||
+||= 60 ||&gt; 1107.6923 ||
-|| 61 || 1126.1538 ||
+||= 61 ||&gt; 1126.1538 ||
-|| 62 || 1144.6154 ||
+||= 62 ||&gt; 1144.6154 ||
-|| 63 || 1163.0769 ||
+||= 63 ||&gt; 1163.0769 ||
-|| 64 || 1181.5385 ||
+||= 64 ||&gt; 1181.5385 ||
+||= 65 ||&gt; 1200.0000 ||
 =Scales=
@@ Line 92: / Line 93: @@
 &lt;!-- ws:start:WikiTextHeadingRule:0:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc0"&gt;&lt;a name="x65 tone equal temperament"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:0 --&gt;&lt;span style="color: #750063; font-family: 'Times New Roman',Times,serif; font-size: 113%;"&gt;65 tone equal temperament&lt;/span&gt;&lt;/h1&gt;
   &lt;br /&gt;
-&lt;strong&gt;&lt;em&gt;65edo&lt;/em&gt;&lt;/strong&gt; divides the &lt;a class="wiki_link" href="/octave"&gt;octave&lt;/a&gt; into 65 equal parts of 18.4615 cents each. It can be characterized as the temperament which tempers out the &lt;a class="wiki_link" href="/schisma"&gt;schisma&lt;/a&gt;, 32805/32768, the &lt;a class="wiki_link" href="/sensipent%20comma"&gt;sensipent comma&lt;/a&gt;, 78732/78125, and the &lt;a class="wiki_link" href="/wuerschmidt%20comma"&gt;wuerschmidt comma&lt;/a&gt;. In the &lt;a class="wiki_link" href="/7-limit"&gt;7-limit&lt;/a&gt;, there are two different maps; the first is &amp;lt;65 103 151/1 182|, &lt;a class="wiki_link" href="/tempering%20out"&gt;tempering out&lt;/a&gt; 126/125, 245/243 and 686/675, so that 65edo supports sensi temperament, and the second is &amp;lt;65 103 151/1 183|, tempering out 225/224, 3125/3097, 4000/3969 and 5120/5103, so that 65edo supports garibaldi temperament. In both cases, the tuning privileges the &lt;a class="wiki_link" href="/5-limit"&gt;5-limit&lt;/a&gt; over the 7-limit, as the 5-limit of 65 is quite accurate. The same can be said for the two different versions of 7-limit &lt;a class="wiki_link" href="/wuerschmidt%20temperament"&gt;wuerschmidt temperament&lt;/a&gt; (wurschmidt and worschmidt) these two mappings provide.&lt;br /&gt;
+&lt;strong&gt;&lt;em&gt;65edo&lt;/em&gt;&lt;/strong&gt; divides the &lt;a class="wiki_link" href="/octave"&gt;octave&lt;/a&gt; into 65 equal parts of 18.4615 cents each. It can be characterized as the temperament which tempers out the &lt;a class="wiki_link" href="/schisma"&gt;schisma&lt;/a&gt;, 32805/32768, the &lt;a class="wiki_link" href="/sensipent%20comma"&gt;sensipent comma&lt;/a&gt;, 78732/78125, and the &lt;a class="wiki_link" href="/wuerschmidt%20comma"&gt;wuerschmidt comma&lt;/a&gt;. In the &lt;a class="wiki_link" href="/7-limit"&gt;7-limit&lt;/a&gt;, there are two different maps; the first is &amp;lt;65 103 151 182|, &lt;a class="wiki_link" href="/tempering%20out"&gt;tempering out&lt;/a&gt; 126/125, 245/243 and 686/675, so that 65edo supports sensi temperament, and the second is &amp;lt;65 103 151 183|, tempering out 225/224, 3125/3097, 4000/3969 and 5120/5103, so that 65edo supports garibaldi temperament. In both cases, the tuning privileges the &lt;a class="wiki_link" href="/5-limit"&gt;5-limit&lt;/a&gt; over the 7-limit, as the 5-limit of 65 is quite accurate. The same can be said for the two different versions of 7-limit &lt;a class="wiki_link" href="/wuerschmidt%20temperament"&gt;wuerschmidt temperament&lt;/a&gt; (wurschmidt and worschmidt) these two mappings provide.&lt;br /&gt;
 &lt;br /&gt;
 edo approximates the intervals &lt;a class="wiki_link" href="/3_2"&gt;3/2&lt;/a&gt;, &lt;a class="wiki_link" href="/5_4"&gt;5/4&lt;/a&gt;, &lt;a class="wiki_link" href="/11_8"&gt;11/8&lt;/a&gt; and &lt;a class="wiki_link" href="/19_16"&gt;19/16&lt;/a&gt; well, so that it does a good job representing the 2.3.5.11.19 &lt;a class="wiki_link" href="/just%20intonation%20subgroup"&gt;just intonation subgroup&lt;/a&gt;. To this one may want to add 13/8 and 17/16, giving the &lt;a class="wiki_link" href="/19-limit"&gt;19-limit&lt;/a&gt; no-sevens subgroup 2.3.5.11.13.17.19. Also of interest is the 19-limit &lt;a class="wiki_link" href="/k%2AN%20subgroups"&gt;2*65 subgroup&lt;/a&gt; 2.3.5.49.11.91.119.19, on which 65 has the same tuning and commas as &lt;a class="wiki_link" href="/130edo"&gt;130edo&lt;/a&gt;.&lt;br /&gt;
@@ Line 103: / Line 104: @@
 &lt;table class="wiki_table"&gt;
      &lt;tr&gt;
-         &lt;td&gt;Degrees of 65-EDO&lt;br /&gt;
+        &lt;th&gt;&lt;a class="wiki_link" href="/Degree"&gt;Degree&lt;/a&gt;&lt;br /&gt;
+&lt;/th&gt;
+        &lt;th&gt;Size (&lt;a class="wiki_link" href="/cent"&gt;Cents&lt;/a&gt;)&lt;br /&gt;
+&lt;/th&gt;
+    &lt;/tr&gt;
+    &lt;tr&gt;
+         &lt;td style="text-align: center;"&gt;0&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;Cents value&lt;br /&gt;
+         &lt;td style="text-align: right;"&gt;0.0000&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
      &lt;tr&gt;
-         &lt;td&gt;0&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;1&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;0&lt;br /&gt;
+         &lt;td style="text-align: right;"&gt;18.4615&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
      &lt;tr&gt;
-         &lt;td&gt;1&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;2&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;18.4615&lt;br /&gt;
+         &lt;td style="text-align: right;"&gt;36.9231&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
      &lt;tr&gt;
-         &lt;td&gt;2&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;3&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;36.9231&lt;br /&gt;
+         &lt;td style="text-align: right;"&gt;55.3846&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
      &lt;tr&gt;
-         &lt;td&gt;3&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;4&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;55.3846&lt;br /&gt;
+         &lt;td style="text-align: right;"&gt;73.8462&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
      &lt;tr&gt;
-         &lt;td&gt;4&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;5&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;73.8462&lt;br /&gt;
+         &lt;td style="text-align: right;"&gt;92.3077&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
      &lt;tr&gt;
-         &lt;td&gt;5&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;6&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;92.3077&lt;br /&gt;
+         &lt;td style="text-align: right;"&gt;110.7692&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
      &lt;tr&gt;
-         &lt;td&gt;6&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;7&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;110.7692/1&lt;br /&gt;
+         &lt;td style="text-align: right;"&gt;129.2308&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
      &lt;tr&gt;
-         &lt;td&gt;7&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;8&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;129.2308/1&lt;br /&gt;
+         &lt;td style="text-align: right;"&gt;147.6923&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
      &lt;tr&gt;
-         &lt;td&gt;8&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;9&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;147.6923/1&lt;br /&gt;
+         &lt;td style="text-align: right;"&gt;166.1538&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
      &lt;tr&gt;
-         &lt;td&gt;9&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;10&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;166.1538/1&lt;br /&gt;
+         &lt;td style="text-align: right;"&gt;184.6154&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
      &lt;tr&gt;
-         &lt;td&gt;10&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;11&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;184.6154/1&lt;br /&gt;
+         &lt;td style="text-align: right;"&gt;203.0769&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
      &lt;tr&gt;
-         &lt;td&gt;11&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;12&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;203.0769/1&lt;br /&gt;
+         &lt;td style="text-align: right;"&gt;221.5385&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
      &lt;tr&gt;
-         &lt;td&gt;12&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;13&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;221.5385/1&lt;br /&gt;
+         &lt;td style="text-align: right;"&gt;240.0000&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
      &lt;tr&gt;
-         &lt;td&gt;13&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;14&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;240&lt;br /&gt;
+         &lt;td style="text-align: right;"&gt;258.4615&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
      &lt;tr&gt;
-         &lt;td&gt;14&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;15&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;258.4615/1&lt;br /&gt;
+         &lt;td style="text-align: right;"&gt;276.9231&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
      &lt;tr&gt;
-         &lt;td&gt;15&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;16&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;276.9231/1&lt;br /&gt;
+         &lt;td style="text-align: right;"&gt;295.3846&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
      &lt;tr&gt;
-         &lt;td&gt;16&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;17&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;295.3846/1&lt;br /&gt;
+         &lt;td style="text-align: right;"&gt;313.8462&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
      &lt;tr&gt;
-         &lt;td&gt;17&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;18&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;313.8462/1&lt;br /&gt;
+         &lt;td style="text-align: right;"&gt;332.3077&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
      &lt;tr&gt;
-         &lt;td&gt;18&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;19&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;332.3077/1&lt;br /&gt;
+         &lt;td style="text-align: right;"&gt;350.7692&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
      &lt;tr&gt;
-         &lt;td&gt;19&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;20&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;350.7692/1&lt;br /&gt;
+         &lt;td style="text-align: right;"&gt;369.2308&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
      &lt;tr&gt;
-         &lt;td&gt;20&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;21&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;369.2308/1&lt;br /&gt;
+         &lt;td style="text-align: right;"&gt;387.6923&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
      &lt;tr&gt;
-         &lt;td&gt;21&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;22&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;387.6923/1&lt;br /&gt;
+         &lt;td style="text-align: right;"&gt;406.1538&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
      &lt;tr&gt;
-         &lt;td&gt;22&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;23&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;406.1538/1&lt;br /&gt;
+         &lt;td style="text-align: right;"&gt;424.6154&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
      &lt;tr&gt;
-         &lt;td&gt;23&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;24&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;424.6154/1&lt;br /&gt;
+         &lt;td style="text-align: right;"&gt;443.0769&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
      &lt;tr&gt;
-         &lt;td&gt;24&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;25&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;443.0769/1&lt;br /&gt;
+         &lt;td style="text-align: right;"&gt;461.5385&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
      &lt;tr&gt;
-         &lt;td&gt;25&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;26&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;461.5385/1&lt;br /&gt;
+         &lt;td style="text-align: right;"&gt;480.0000&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
      &lt;tr&gt;
-         &lt;td&gt;26&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;27&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;480&lt;br /&gt;
+         &lt;td style="text-align: right;"&gt;498.4615&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
      &lt;tr&gt;
-         &lt;td&gt;27&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;28&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;498.4615/1&lt;br /&gt;
+         &lt;td style="text-align: right;"&gt;516.9231&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
      &lt;tr&gt;
-         &lt;td&gt;28&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;29&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;516.9231/1&lt;br /&gt;
+         &lt;td style="text-align: right;"&gt;535.3846&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
      &lt;tr&gt;
-         &lt;td&gt;29&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;30&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;535.3846/1&lt;br /&gt;
+         &lt;td style="text-align: right;"&gt;553.8462&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
      &lt;tr&gt;
-         &lt;td&gt;30&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;31&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;553.8462/1&lt;br /&gt;
+         &lt;td style="text-align: right;"&gt;572.3077&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
      &lt;tr&gt;
-         &lt;td&gt;31&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;32&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;572.3077/1&lt;br /&gt;
+         &lt;td style="text-align: right;"&gt;590.7692&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
      &lt;tr&gt;
-         &lt;td&gt;32&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;33&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;590.7692/1&lt;br /&gt;
+         &lt;td style="text-align: right;"&gt;609.2308&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
      &lt;tr&gt;
-         &lt;td&gt;33&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;34&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;609.2308/1&lt;br /&gt;
+         &lt;td style="text-align: right;"&gt;627.6923&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
      &lt;tr&gt;
-         &lt;td&gt;34&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;35&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;627.6923/1&lt;br /&gt;
+         &lt;td style="text-align: right;"&gt;646.1538&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
      &lt;tr&gt;
-         &lt;td&gt;35&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;36&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;646.1538/1&lt;br /&gt;
+         &lt;td style="text-align: right;"&gt;664.6154&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
      &lt;tr&gt;
-         &lt;td&gt;36&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;37&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;664.6154/1&lt;br /&gt;
+         &lt;td style="text-align: right;"&gt;683.0769&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
      &lt;tr&gt;
-         &lt;td&gt;37&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;38&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;683.0769/1&lt;br /&gt;
+         &lt;td style="text-align: right;"&gt;701.5385&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
      &lt;tr&gt;
-         &lt;td&gt;38&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;39&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;701.5385/1&lt;br /&gt;
+         &lt;td style="text-align: right;"&gt;720.0000&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
      &lt;tr&gt;
-         &lt;td&gt;39&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;40&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;720&lt;br /&gt;
+         &lt;td style="text-align: right;"&gt;738.4615&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
      &lt;tr&gt;
-         &lt;td&gt;40&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;41&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;738.4615/1&lt;br /&gt;
+         &lt;td style="text-align: right;"&gt;756.9231&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
      &lt;tr&gt;
-         &lt;td&gt;41&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;42&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;756.9231/1&lt;br /&gt;
+         &lt;td style="text-align: right;"&gt;775.3846&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
      &lt;tr&gt;
-         &lt;td&gt;42&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;43&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;775.3846/1&lt;br /&gt;
+         &lt;td style="text-align: right;"&gt;793.8462&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
      &lt;tr&gt;
-         &lt;td&gt;43&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;44&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;793.8462/1&lt;br /&gt;
+         &lt;td style="text-align: right;"&gt;812.3077&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
      &lt;tr&gt;
-         &lt;td&gt;44&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;45&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;812.3077/1&lt;br /&gt;
+         &lt;td style="text-align: right;"&gt;830.7692&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
      &lt;tr&gt;
-         &lt;td&gt;45&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;46&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;830.7692/1&lt;br /&gt;
+         &lt;td style="text-align: right;"&gt;849.2308&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
      &lt;tr&gt;
-         &lt;td&gt;46&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;47&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;849.2308/1&lt;br /&gt;
+         &lt;td style="text-align: right;"&gt;867.6923&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
      &lt;tr&gt;
-         &lt;td&gt;47&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;48&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;867.6923/1&lt;br /&gt;
+         &lt;td style="text-align: right;"&gt;886.1538&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
      &lt;tr&gt;
-         &lt;td&gt;48&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;49&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;886.1538/1&lt;br /&gt;
+         &lt;td style="text-align: right;"&gt;904.6154&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
      &lt;tr&gt;
-         &lt;td&gt;49&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;50&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;904.6154/1&lt;br /&gt;
+         &lt;td style="text-align: right;"&gt;923.0769&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
      &lt;tr&gt;
-         &lt;td&gt;50&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;51&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;923.0769/1&lt;br /&gt;
+         &lt;td style="text-align: right;"&gt;941.5385&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
      &lt;tr&gt;
-         &lt;td&gt;51&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;52&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;941.5385/1&lt;br /&gt;
+         &lt;td style="text-align: right;"&gt;960.0000&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
      &lt;tr&gt;
-         &lt;td&gt;52&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;53&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;960&lt;br /&gt;
+         &lt;td style="text-align: right;"&gt;978.4615&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
      &lt;tr&gt;
-         &lt;td&gt;53&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;54&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;978.4615/1&lt;br /&gt;
+         &lt;td style="text-align: right;"&gt;996.9231&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
      &lt;tr&gt;
-         &lt;td&gt;54&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;55&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;996.9231/1&lt;br /&gt;
+         &lt;td style="text-align: right;"&gt;1015.3846&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
      &lt;tr&gt;
-         &lt;td&gt;55&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;56&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;1015.3846&lt;br /&gt;
+         &lt;td style="text-align: right;"&gt;1033.8462&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
      &lt;tr&gt;
-         &lt;td&gt;56&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;57&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;1033.8462&lt;br /&gt;
+         &lt;td style="text-align: right;"&gt;1052.3077&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
      &lt;tr&gt;
-         &lt;td&gt;57&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;58&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;1052.3077&lt;br /&gt;
+         &lt;td style="text-align: right;"&gt;1070.7692&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
      &lt;tr&gt;
-         &lt;td&gt;58&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;59&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;1070.7692&lt;br /&gt;
+         &lt;td style="text-align: right;"&gt;1089.2308&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
      &lt;tr&gt;
-         &lt;td&gt;59&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;60&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;1089.2308&lt;br /&gt;
+         &lt;td style="text-align: right;"&gt;1107.6923&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
      &lt;tr&gt;
-         &lt;td&gt;60&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;61&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;1107.6923&lt;br /&gt;
+         &lt;td style="text-align: right;"&gt;1126.1538&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
      &lt;tr&gt;
-         &lt;td&gt;61&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;62&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;1126.1538&lt;br /&gt;
+         &lt;td style="text-align: right;"&gt;1144.6154&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
      &lt;tr&gt;
-         &lt;td&gt;62&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;63&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;1144.6154&lt;br /&gt;
+         &lt;td style="text-align: right;"&gt;1163.0769&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
      &lt;tr&gt;
-         &lt;td&gt;63&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;64&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;1163.0769&lt;br /&gt;
+         &lt;td style="text-align: right;"&gt;1181.5385&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
      &lt;tr&gt;
-         &lt;td&gt;64&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;65&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;1181.5385&lt;br /&gt;
+         &lt;td style="text-align: right;"&gt;1200.0000&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;