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:~~xenwolf~~|~~xenwolf~~]] and made on <tt>2011-06-~~30 17~~:59:56 UTC</tt>.

: This revision was by author [[User:Osmiorisbendi|Osmiorisbendi]] and made on <tt>2011-07-12 01:56:01 UTC</tt>.

: The original revision id was <tt>~~239563915~~</tt>.

: The original revision id was <tt>240945017</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 9:

----

=65 tone equal temperament=

=65 tone equal temperament=

//65edo// divides the [[octave]] into 65 equal parts of 18.~~462~~ 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]], 393216/390625. 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//** 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]], 393216/390625. 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 18:

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

|| 0 || 0 ||

|| 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 ||

|| 6 || 110.7692 ||

|| 7 || 129,2308 ||

|| 7 || 129.2308 ||

|| 8 || 147,6923 ||

|| 8 || 147.6923 ||

|| 9 || 166,1538 ||

|| 9 || 166.1538 ||

|| 10 || 184,6154 ||

|| 10 || 184.6154 ||

|| 11 || 203,0769 ||

|| 11 || 203.0769 ||

|| 12 || 221,5385 ||

|| 12 || 221.5385 ||

|| 13 || 240 ||

|| 14 || 258,4615 ||

|| 14 || 258.4615 ||

|| 15 || 276,9231 ||

|| 15 || 276.9231 ||

|| 16 || 295,3846 ||

|| 16 || 295.3846 ||

|| 17 || 313,8462 ||

|| 17 || 313.8462 ||

|| 18 || 332,3077 ||

|| 18 || 332.3077 ||

|| 19 || 350,7692 ||

|| 19 || 350.7692 ||

|| 20 || 369,2308 ||

|| 20 || 369.2308 ||

|| 21 || 387,6923 ||

|| 21 || 387.6923 ||

|| 22 || 406,1538 ||

|| 22 || 406.1538 ||

|| 23 || 424,6154 ||

|| 23 || 424.6154 ||

|| 24 || 443,0769 ||

|| 24 || 443.0769 ||

|| 25 || 461,5385 ||

|| 25 || 461.5385 ||

|| 26 || 480 ||

|| 27 || 498,4615 ||

|| 27 || 498.4615 ||

|| 28 || 516,9231 ||

|| 28 || 516.9231 ||

|| 29 || 535,3846 ||

|| 29 || 535.3846 ||

|| 30 || 553,8462 ||

|| 30 || 553.8462 ||

|| 31 || 572,3077 ||

|| 31 || 572.3077 ||

|| 32 || 590,7692 ||

|| 32 || 590.7692 ||

|| 33 || 609,2308 ||

|| 33 || 609.2308 ||

|| 34 || 627,6923 ||

|| 34 || 627.6923 ||

|| 35 || 646,1538 ||

|| 35 || 646.1538 ||

|| 36 || 664,6154 ||

|| 36 || 664.6154 ||

|| 37 || 683,0769 ||

|| 37 || 683.0769 ||

|| 38 || 701,5385 ||

|| 38 || 701.5385 ||

|| 39 || 720 ||

|| 40 || 738,4615 ||

|| 40 || 738.4615 ||

|| 41 || 756,9231 ||

|| 41 || 756.9231 ||

|| 42 || 775,3846 ||

|| 42 || 775.3846 ||

|| 43 || 793,8462 ||

|| 43 || 793.8462 ||

|| 44 || 812,3077 ||

|| 44 || 812.3077 ||

|| 45 || 830,7692 ||

|| 45 || 830.7692 ||

|| 46 || 849,2308 ||

|| 46 || 849.2308 ||

|| 47 || 867,6923 ||

|| 47 || 867.6923 ||

|| 48 || 886,1538 ||

|| 48 || 886.1538 ||

|| 49 || 904,6154 ||

|| 49 || 904.6154 ||

|| 50 || 923,0769 ||

|| 50 || 923.0769 ||

|| 51 || 941,5385 ||

|| 51 || 941.5385 ||

|| 52 || 960 ||

|| 53 || 978,4615 ||

|| 53 || 978.4615 ||

|| 54 || 996,9231 ||

|| 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 ||

=Scales=

Line 90:

<hr />

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

<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.~~462~~ 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>, 393216/390625. 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 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>, 393216/390625. 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 115:

<td>1

</td>

<td>18,4615

<td>18.4615

</td>

</tr>

Line 121:

<td>2

</td>

<td>36,9231

<td>36.9231

</td>

</tr>

Line 127:

<td>3

</td>

<td>55,3846

<td>55.3846

</td>

</tr>

Line 133:

<td>4

</td>

<td>73,8462

<td>73.8462

</td>

</tr>

Line 139:

<td>5

</td>

<td>92,3077

<td>92.3077

</td>

</tr>

Line 145:

<td>6

</td>

<td>110,7692

<td>110.7692

</td>

</tr>

Line 151:

<td>7

</td>

<td>129,2308

<td>129.2308

</td>

</tr>

Line 157:

<td>8

</td>

<td>147,6923

<td>147.6923

</td>

</tr>

Line 163:

<td>9

</td>

<td>166,1538

<td>166.1538

</td>

</tr>

Line 169:

<td>10

</td>

<td>184,6154

<td>184.6154

</td>

</tr>

Line 175:

<td>11

</td>

<td>203,0769

<td>203.0769

</td>

</tr>

Line 181:

<td>12

</td>

<td>221,5385

<td>221.5385

</td>

</tr>

Line 193:

<td>14

</td>

<td>258,4615

<td>258.4615

</td>

</tr>

Line 199:

<td>15

</td>

<td>276,9231

<td>276.9231

</td>

</tr>

Line 205:

<td>16

</td>

<td>295,3846

<td>295.3846

</td>

</tr>

Line 211:

<td>17

</td>

<td>313,8462

<td>313.8462

</td>

</tr>

Line 217:

<td>18

</td>

<td>332,3077

<td>332.3077

</td>

</tr>

Line 223:

<td>19

</td>

<td>350,7692

<td>350.7692

</td>

</tr>

Line 229:

<td>20

</td>

<td>369,2308

<td>369.2308

</td>

</tr>

Line 235:

<td>21

</td>

<td>387,6923

<td>387.6923

</td>

</tr>

Line 241:

<td>22

</td>

<td>406,1538

<td>406.1538

</td>

</tr>

Line 247:

<td>23

</td>

<td>424,6154

<td>424.6154

</td>

</tr>

Line 253:

<td>24

</td>

<td>443,0769

<td>443.0769

</td>

</tr>

Line 259:

<td>25

</td>

<td>461,5385

<td>461.5385

</td>

</tr>

Line 271:

<td>27

</td>

<td>498,4615

<td>498.4615

</td>

</tr>

Line 277:

<td>28

</td>

<td>516,9231

<td>516.9231

</td>

</tr>

Line 283:

<td>29

</td>

<td>535,3846

<td>535.3846

</td>

</tr>

Line 289:

<td>30

</td>

<td>553,8462

<td>553.8462

</td>

</tr>

Line 295:

<td>31

</td>

<td>572,3077

<td>572.3077

</td>

</tr>

Line 301:

<td>32

</td>

<td>590,7692

<td>590.7692

</td>

</tr>

Line 307:

<td>33

</td>

<td>609,2308

<td>609.2308

</td>

</tr>

Line 313:

<td>34

</td>

<td>627,6923

<td>627.6923

</td>

</tr>

Line 319:

<td>35

</td>

<td>646,1538

<td>646.1538

</td>

</tr>

Line 325:

<td>36

</td>

<td>664,6154

<td>664.6154

</td>

</tr>

Line 331:

<td>37

</td>

<td>683,0769

<td>683.0769

</td>

</tr>

Line 337:

<td>38

</td>

<td>701,5385

<td>701.5385

</td>

</tr>

Line 349:

<td>40

</td>

<td>738,4615

<td>738.4615

</td>

</tr>

Line 355:

<td>41

</td>

<td>756,9231

<td>756.9231

</td>

</tr>

Line 361:

<td>42

</td>

<td>775,3846

<td>775.3846

</td>

</tr>

Line 367:

<td>43

</td>

<td>793,8462

<td>793.8462

</td>

</tr>

Line 373:

<td>44

</td>

<td>812,3077

<td>812.3077

</td>

</tr>

Line 379:

<td>45

</td>

<td>830,7692

<td>830.7692

</td>

</tr>

Line 385:

<td>46

</td>

<td>849,2308

<td>849.2308

</td>

</tr>

Line 391:

<td>47

</td>

<td>867,6923

<td>867.6923

</td>

</tr>

Line 397:

<td>48

</td>

<td>886,1538

<td>886.1538

</td>

</tr>

Line 403:

<td>49

</td>

<td>904,6154

<td>904.6154

</td>

</tr>

Line 409:

<td>50

</td>

<td>923,0769

<td>923.0769

</td>

</tr>

Line 415:

<td>51

</td>

<td>941,5385

<td>941.5385

</td>

</tr>

Line 427:

<td>53

</td>

<td>978,4615

<td>978.4615

</td>

</tr>

Line 433:

<td>54

</td>

<td>996,9231

<td>996.9231

</td>

</tr>

Line 439:

<td>55

</td>

<td>1015,3846

<td>1015.3846

</td>

</tr>

Line 445:

<td>56

</td>

<td>1033,8462

<td>1033.8462

</td>

</tr>

Line 451:

<td>57

</td>

<td>1052,3077

<td>1052.3077

</td>

</tr>

Line 457:

<td>58

</td>

<td>1070,7692

<td>1070.7692

</td>

</tr>

Line 463:

<td>59

</td>

<td>1089,2308

<td>1089.2308

</td>

</tr>

Line 469:

<td>60

</td>

<td>1107,6923

<td>1107.6923

</td>

</tr>

Line 475:

<td>61

</td>

<td>1126,1538

<td>1126.1538

</td>

</tr>

Line 481:

<td>62

</td>

<td>1144,6154

<td>1144.6154

</td>

</tr>

Line 487:

<td>63

</td>

<td>1163,0769

<td>1163.0769

</td>

</tr>

Line 493:

<td>64

</td>

<td>1181,5385

<td>1181.5385

</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>2011-06-30 17:59:56 UTC</tt>.<br>
+: This revision was by author [[User:Osmiorisbendi|Osmiorisbendi]] and made on <tt>2011-07-12 01:56:01 UTC</tt>.<br>
-: The original revision id was <tt>239563915</tt>.<br>
+: The original revision id was <tt>240945017</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 9: / Line 9: @@
 ----
-=&lt;span style="color: #750063;"&gt;65 tone equal temperament&lt;/span&gt;=
+=&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 18.462 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]], 393216/390625. 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.
+**//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]], 393216/390625. 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 18: / Line 18: @@
 || Degrees of 65-EDO || Cents value ||
 || 0 || 0 ||
-|| 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 ||
+|| 6 || 110.7692 ||
-|| 7 || 129,2308 ||
+|| 7 || 129.2308 ||
-|| 8 || 147,6923 ||
+|| 8 || 147.6923 ||
-|| 9 || 166,1538 ||
+|| 9 || 166.1538 ||
-|| 10 || 184,6154 ||
+|| 10 || 184.6154 ||
-|| 11 || 203,0769 ||
+|| 11 || 203.0769 ||
-|| 12 || 221,5385 ||
+|| 12 || 221.5385 ||
 || 13 || 240 ||
-|| 14 || 258,4615 ||
+|| 14 || 258.4615 ||
-|| 15 || 276,9231 ||
+|| 15 || 276.9231 ||
-|| 16 || 295,3846 ||
+|| 16 || 295.3846 ||
-|| 17 || 313,8462 ||
+|| 17 || 313.8462 ||
-|| 18 || 332,3077 ||
+|| 18 || 332.3077 ||
-|| 19 || 350,7692 ||
+|| 19 || 350.7692 ||
-|| 20 || 369,2308 ||
+|| 20 || 369.2308 ||
-|| 21 || 387,6923 ||
+|| 21 || 387.6923 ||
-|| 22 || 406,1538 ||
+|| 22 || 406.1538 ||
-|| 23 || 424,6154 ||
+|| 23 || 424.6154 ||
-|| 24 || 443,0769 ||
+|| 24 || 443.0769 ||
-|| 25 || 461,5385 ||
+|| 25 || 461.5385 ||
 || 26 || 480 ||
-|| 27 || 498,4615 ||
+|| 27 || 498.4615 ||
-|| 28 || 516,9231 ||
+|| 28 || 516.9231 ||
-|| 29 || 535,3846 ||
+|| 29 || 535.3846 ||
-|| 30 || 553,8462 ||
+|| 30 || 553.8462 ||
-|| 31 || 572,3077 ||
+|| 31 || 572.3077 ||
-|| 32 || 590,7692 ||
+|| 32 || 590.7692 ||
-|| 33 || 609,2308 ||
+|| 33 || 609.2308 ||
-|| 34 || 627,6923 ||
+|| 34 || 627.6923 ||
-|| 35 || 646,1538 ||
+|| 35 || 646.1538 ||
-|| 36 || 664,6154 ||
+|| 36 || 664.6154 ||
-|| 37 || 683,0769 ||
+|| 37 || 683.0769 ||
-|| 38 || 701,5385 ||
+|| 38 || 701.5385 ||
 || 39 || 720 ||
-|| 40 || 738,4615 ||
+|| 40 || 738.4615 ||
-|| 41 || 756,9231 ||
+|| 41 || 756.9231 ||
-|| 42 || 775,3846 ||
+|| 42 || 775.3846 ||
-|| 43 || 793,8462 ||
+|| 43 || 793.8462 ||
-|| 44 || 812,3077 ||
+|| 44 || 812.3077 ||
-|| 45 || 830,7692 ||
+|| 45 || 830.7692 ||
-|| 46 || 849,2308 ||
+|| 46 || 849.2308 ||
-|| 47 || 867,6923 ||
+|| 47 || 867.6923 ||
-|| 48 || 886,1538 ||
+|| 48 || 886.1538 ||
-|| 49 || 904,6154 ||
+|| 49 || 904.6154 ||
-|| 50 || 923,0769 ||
+|| 50 || 923.0769 ||
-|| 51 || 941,5385 ||
+|| 51 || 941.5385 ||
 || 52 || 960 ||
-|| 53 || 978,4615 ||
+|| 53 || 978.4615 ||
-|| 54 || 996,9231 ||
+|| 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 ||
 =Scales=
@@ Line 90: / Line 90: @@
 &lt;!-- ws:end:WikiTextTocRule:10 --&gt;&lt;hr /&gt;
 &lt;br /&gt;
-&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;"&gt;65 tone equal temperament&lt;/span&gt;&lt;/h1&gt;
+&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;em&gt;65edo&lt;/em&gt; divides the &lt;a class="wiki_link" href="/octave"&gt;octave&lt;/a&gt; into 65 equal parts of 18.462 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;, 393216/390625. 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;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;, 393216/390625. 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 115: / Line 115: @@
          &lt;td&gt;1&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;18,4615&lt;br /&gt;
+         &lt;td&gt;18.4615&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
@@ Line 121: / Line 121: @@
          &lt;td&gt;2&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;36,9231&lt;br /&gt;
+         &lt;td&gt;36.9231&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
@@ Line 127: / Line 127: @@
          &lt;td&gt;3&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;55,3846&lt;br /&gt;
+         &lt;td&gt;55.3846&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
@@ Line 133: / Line 133: @@
          &lt;td&gt;4&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;73,8462&lt;br /&gt;
+         &lt;td&gt;73.8462&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
@@ Line 139: / Line 139: @@
          &lt;td&gt;5&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;92,3077&lt;br /&gt;
+         &lt;td&gt;92.3077&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
@@ Line 145: / Line 145: @@
          &lt;td&gt;6&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;110,7692&lt;br /&gt;
+         &lt;td&gt;110.7692&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
@@ Line 151: / Line 151: @@
          &lt;td&gt;7&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;129,2308&lt;br /&gt;
+         &lt;td&gt;129.2308&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
@@ Line 157: / Line 157: @@
          &lt;td&gt;8&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;147,6923&lt;br /&gt;
+         &lt;td&gt;147.6923&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
@@ Line 163: / Line 163: @@
          &lt;td&gt;9&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;166,1538&lt;br /&gt;
+         &lt;td&gt;166.1538&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
@@ Line 169: / Line 169: @@
          &lt;td&gt;10&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;184,6154&lt;br /&gt;
+         &lt;td&gt;184.6154&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
@@ Line 175: / Line 175: @@
          &lt;td&gt;11&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;203,0769&lt;br /&gt;
+         &lt;td&gt;203.0769&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
@@ Line 181: / Line 181: @@
          &lt;td&gt;12&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;221,5385&lt;br /&gt;
+         &lt;td&gt;221.5385&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
@@ Line 193: / Line 193: @@
          &lt;td&gt;14&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;258,4615&lt;br /&gt;
+         &lt;td&gt;258.4615&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
@@ Line 199: / Line 199: @@
          &lt;td&gt;15&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;276,9231&lt;br /&gt;
+         &lt;td&gt;276.9231&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
@@ Line 205: / Line 205: @@
          &lt;td&gt;16&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;295,3846&lt;br /&gt;
+         &lt;td&gt;295.3846&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
@@ Line 211: / Line 211: @@
          &lt;td&gt;17&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;313,8462&lt;br /&gt;
+         &lt;td&gt;313.8462&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
@@ Line 217: / Line 217: @@
          &lt;td&gt;18&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;332,3077&lt;br /&gt;
+         &lt;td&gt;332.3077&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
@@ Line 223: / Line 223: @@
          &lt;td&gt;19&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;350,7692&lt;br /&gt;
+         &lt;td&gt;350.7692&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
@@ Line 229: / Line 229: @@
          &lt;td&gt;20&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;369,2308&lt;br /&gt;
+         &lt;td&gt;369.2308&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
@@ Line 235: / Line 235: @@
          &lt;td&gt;21&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;387,6923&lt;br /&gt;
+         &lt;td&gt;387.6923&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
@@ Line 241: / Line 241: @@
          &lt;td&gt;22&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;406,1538&lt;br /&gt;
+         &lt;td&gt;406.1538&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
@@ Line 247: / Line 247: @@
          &lt;td&gt;23&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;424,6154&lt;br /&gt;
+         &lt;td&gt;424.6154&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
@@ Line 253: / Line 253: @@
          &lt;td&gt;24&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;443,0769&lt;br /&gt;
+         &lt;td&gt;443.0769&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
@@ Line 259: / Line 259: @@
          &lt;td&gt;25&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;461,5385&lt;br /&gt;
+         &lt;td&gt;461.5385&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
@@ Line 271: / Line 271: @@
          &lt;td&gt;27&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;498,4615&lt;br /&gt;
+         &lt;td&gt;498.4615&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
@@ Line 277: / Line 277: @@
          &lt;td&gt;28&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;516,9231&lt;br /&gt;
+         &lt;td&gt;516.9231&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
@@ Line 283: / Line 283: @@
          &lt;td&gt;29&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;535,3846&lt;br /&gt;
+         &lt;td&gt;535.3846&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
@@ Line 289: / Line 289: @@
          &lt;td&gt;30&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;553,8462&lt;br /&gt;
+         &lt;td&gt;553.8462&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
@@ Line 295: / Line 295: @@
          &lt;td&gt;31&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;572,3077&lt;br /&gt;
+         &lt;td&gt;572.3077&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
@@ Line 301: / Line 301: @@
          &lt;td&gt;32&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;590,7692&lt;br /&gt;
+         &lt;td&gt;590.7692&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
@@ Line 307: / Line 307: @@
          &lt;td&gt;33&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;609,2308&lt;br /&gt;
+         &lt;td&gt;609.2308&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
@@ Line 313: / Line 313: @@
          &lt;td&gt;34&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;627,6923&lt;br /&gt;
+         &lt;td&gt;627.6923&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
@@ Line 319: / Line 319: @@
          &lt;td&gt;35&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;646,1538&lt;br /&gt;
+         &lt;td&gt;646.1538&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
@@ Line 325: / Line 325: @@
          &lt;td&gt;36&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;664,6154&lt;br /&gt;
+         &lt;td&gt;664.6154&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
@@ Line 331: / Line 331: @@
          &lt;td&gt;37&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;683,0769&lt;br /&gt;
+         &lt;td&gt;683.0769&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
@@ Line 337: / Line 337: @@
          &lt;td&gt;38&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;701,5385&lt;br /&gt;
+         &lt;td&gt;701.5385&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
@@ Line 349: / Line 349: @@
          &lt;td&gt;40&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;738,4615&lt;br /&gt;
+         &lt;td&gt;738.4615&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
@@ Line 355: / Line 355: @@
          &lt;td&gt;41&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;756,9231&lt;br /&gt;
+         &lt;td&gt;756.9231&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
@@ Line 361: / Line 361: @@
          &lt;td&gt;42&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;775,3846&lt;br /&gt;
+         &lt;td&gt;775.3846&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
@@ Line 367: / Line 367: @@
          &lt;td&gt;43&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;793,8462&lt;br /&gt;
+         &lt;td&gt;793.8462&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
@@ Line 373: / Line 373: @@
          &lt;td&gt;44&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;812,3077&lt;br /&gt;
+         &lt;td&gt;812.3077&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
@@ Line 379: / Line 379: @@
          &lt;td&gt;45&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;830,7692&lt;br /&gt;
+         &lt;td&gt;830.7692&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
@@ Line 385: / Line 385: @@
          &lt;td&gt;46&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;849,2308&lt;br /&gt;
+         &lt;td&gt;849.2308&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
@@ Line 391: / Line 391: @@
          &lt;td&gt;47&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;867,6923&lt;br /&gt;
+         &lt;td&gt;867.6923&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
@@ Line 397: / Line 397: @@
          &lt;td&gt;48&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;886,1538&lt;br /&gt;
+         &lt;td&gt;886.1538&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
@@ Line 403: / Line 403: @@
          &lt;td&gt;49&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;904,6154&lt;br /&gt;
+         &lt;td&gt;904.6154&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
@@ Line 409: / Line 409: @@
          &lt;td&gt;50&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;923,0769&lt;br /&gt;
+         &lt;td&gt;923.0769&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
@@ Line 415: / Line 415: @@
          &lt;td&gt;51&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;941,5385&lt;br /&gt;
+         &lt;td&gt;941.5385&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
@@ Line 427: / Line 427: @@
          &lt;td&gt;53&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;978,4615&lt;br /&gt;
+         &lt;td&gt;978.4615&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
@@ Line 433: / Line 433: @@
          &lt;td&gt;54&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;996,9231&lt;br /&gt;
+         &lt;td&gt;996.9231&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
@@ Line 439: / Line 439: @@
          &lt;td&gt;55&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;1015,3846&lt;br /&gt;
+         &lt;td&gt;1015.3846&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
@@ Line 445: / Line 445: @@
          &lt;td&gt;56&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;1033,8462&lt;br /&gt;
+         &lt;td&gt;1033.8462&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
@@ Line 451: / Line 451: @@
          &lt;td&gt;57&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;1052,3077&lt;br /&gt;
+         &lt;td&gt;1052.3077&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
@@ Line 457: / Line 457: @@
          &lt;td&gt;58&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;1070,7692&lt;br /&gt;
+         &lt;td&gt;1070.7692&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
@@ Line 463: / Line 463: @@
          &lt;td&gt;59&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;1089,2308&lt;br /&gt;
+         &lt;td&gt;1089.2308&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
@@ Line 469: / Line 469: @@
          &lt;td&gt;60&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;1107,6923&lt;br /&gt;
+         &lt;td&gt;1107.6923&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
@@ Line 475: / Line 475: @@
          &lt;td&gt;61&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;1126,1538&lt;br /&gt;
+         &lt;td&gt;1126.1538&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
@@ Line 481: / Line 481: @@
          &lt;td&gt;62&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;1144,6154&lt;br /&gt;
+         &lt;td&gt;1144.6154&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
@@ Line 487: / Line 487: @@
          &lt;td&gt;63&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;1163,0769&lt;br /&gt;
+         &lt;td&gt;1163.0769&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
@@ Line 493: / Line 493: @@
          &lt;td&gt;64&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;1181,5385&lt;br /&gt;
+         &lt;td&gt;1181.5385&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;