34edo: Difference between revisions

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<h2>IMPORTED REVISION FROM WIKISPACES</h2>

This is an imported revision from Wikispaces. The revision metadata is included below for reference:

: This revision was by author [[User:~~phylingual~~|~~phylingual~~]] and made on <tt>2012-05-~~04 11~~:25:58 UTC</tt>.

: This revision was by author [[User:JosephRuhf|JosephRuhf]] and made on <tt>2012-05-26 18:45:24 UTC</tt>.

: The original revision id was <tt>~~330018202~~</tt>.

: The original revision id was <tt>339770294</tt>.

: The revision comment was: <tt></tt>

The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.

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===Approximations to Just Intonation===

Like [[xenharmonic/17edo|17edo]], 34edo contains good approximations of just intervals involving 13 and 3 -- specifically, 13/8, 13/12, 13/9 and their inversions -- while failing to closely approximate ratios of 7 or 11. 34edo adds ratios of 5 into the mix -- including 5/4, 6/5, 9/5, 15/8, 13/10, 15/13, and their inversions -- as well as 17 -- including 17/16, 17~~/18~~, 17/12, 17/10, 17/13, 17/15 and their inversions. Since it distinguishes between 9/8 and 10/9 (exaggerating the difference between them, the syntonic comma of 81/80, from 21.5 cents to 35.3 cents), it is suitable for 5-limit JI. It is not a [[xenharmonic/meantone|meantone ]]system.

Like [[xenharmonic/17edo|17edo]], 34edo contains good approximations of just intervals involving 13 and 3 -- specifically, 13/8, 13/12, 13/9 and their inversions -- while failing to closely approximate ratios of 7 or 11. 34edo adds ratios of 5 into the mix -- including 5/4, 6/5, 9/5, 15/8, 13/10, 15/13, and their inversions -- as well as 17 -- including 17/16, 18/17, 17/12, 17/10, 17/13, 17/15 and their inversions. Since it distinguishes between 9/8 and 10/9 (exaggerating the difference between them, the syntonic comma of 81/80, from 21.5 cents to 35.3 cents), it is suitable for 5-limit JI. It is not a [[xenharmonic/meantone|meantone ]]system.

//Viewed in light of Western diatonic theory, the three extra steps (of 34-et compared to 31-et) in effect widen the intervals between C and D, F and G, and A and B [that is: 6 5 3 6 5 6 3], thus making a distinction between major tones, ratio 9/8 and minor tones, ratio 10/9.// ([[http://en.wikipedia.org/wiki/34_equal_temperament|Wikipedia]])

Line 41:

===Intervals:===

|| degrees of 34edo || cents || approx. ratios of

2.3.5.13.17 [[xenharmonic/subgroup|subgroup]] || additional ratios

[[tel:2.3.5.13.17|2.3.5.13.17]] [[xenharmonic/subgroup|subgroup]] || additional ratios

of the full [[xenharmonic/17-limit|17-limit]] ||

|| 0 || 0.0 || 1/1 || ||

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==Commas==

34-EDO [[xenharmonic/tempering out|tempers out]] the following [[xenharmonic/comma|comma]]s. (Note: This assumes the [[xenharmonic/val|val]] < 34 54 79 95 118 126 |.)

||~ **Comma** ||~ **Monzo** ||~ **Value (Cents)** ||~ **Name 1** ||~ **Name 2** ||~ **Name 3** ||

||~ **Comma** ||~ **Monzo** ||~ **Value (Cents)** ||~ **Name 1** ||~ **Name 2** ||~ **Name 3** ||

|| 134217728/129140163 || | 27 -17 > || 66.765 || 17-comma || || ||

|| 134217728/129140163 || | 27 -17 > || 66.765 || 17-comma || || ||

|| 20000/19683 || | 5 -9 4 > || 27.660 || Minimal Diesis || Tetracot Comma || ||

|| [[tel:20000/19683|20000/19683]] || | 5 -9 4 > || 27.660 || Minimal Diesis || Tetracot Comma || ||

|| 2048/2025 || | 11 -4 -2 > || 19.553 || Diaschisma || || ||

|| 2048/2025 || | 11 -4 -2 > || 19.553 || Diaschisma || || ||

|| 393216/390625 || | 17 1 -8 > || 11.445 || Würschmidt comma || || ||

|| 393216/390625 || | 17 1 -8 > || 11.445 || Würschmidt comma || || ||

|| 15625/15552 || | -6 -5 6 > || 8.1073 || Kleisma || Semicomma Majeur || ||

|| [[tel:15625/15552|15625/15552]] || | -6 -5 6 > || 8.1073 || Kleisma || Semicomma Majeur || ||

|| 1212717/1210381 || | 23 6 -14 > || 3.338 || Vishnuzma || Semisuper || ||

|| 1212717/1210381 || | 23 6 -14 > || 3.338 || Vishnuzma || Semisuper || ||

|| 1029/1000 || | -3 1 -3 3 > || 49.492 || Keega || || ||

|| 1029/1000 || | -3 1 -3 3 > || 49.492 || Keega || || ||

|| [[xenharmonic/49_48|49/48]]~~~~ || | -4 -1 0 2 > || 35.697 || Slendro Diesis || || ||

|| [[xenharmonic/49_48|49/48]] || | -4 -1 0 2 > || 35.697 || Slendro Diesis || || ||

|| 875/864 || | -5 -3 3 1 > || 21.902 || Keema || || ||

|| 875/864 || | -5 -3 3 1 > || 21.902 || Keema || || ||

|| 126/125 || | 1 2 -3 1 > || 13.795 || Starling comma || Septimal semicomma || ||

|| 126/125 || | 1 2 -3 1 > || 13.795 || Starling comma || Septimal semicomma || ||

|| 100/99 || | 2 -2 2 0 -1> || 17.399 || Ptolemisma || Ptolemy's comma || ||

|| 100/99 || | 2 -2 2 0 -1> || 17.399 || Ptolemisma || Ptolemy's comma || ||

|| 243/242 || | -1 5 0 0 -2 > || 7.1391 || Rastma || Neutral third comma || ||

|| 243/242 || | -1 5 0 0 -2 > || 7.1391 || Rastma || Neutral third comma || ||

|| 385/384 || | -7 -1 1 1 1 > || 4.5026 || Keenanisma || || ||

|| 385/384 || | -7 -1 1 1 1 > || 4.5026 || Keenanisma || || ||

|| 91/90 || | -1 -2 -1 1 0 1 > || 19.120 || Superleap || || ||

|| 91/90 || | -1 -2 -1 1 0 1 > || 19.120 || Superleap || || ||

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<h3 id="toc1"><a name="x--Approximations to Just Intonation"></a>Approximations to Just Intonation</h3>

Like <a class="wiki_link" href="http://xenharmonic.wikispaces.com/17edo">17edo</a>, 34edo contains good approximations of just intervals involving 13 and 3 -- specifically, 13/8, 13/12, 13/9 and their inversions -- while failing to closely approximate ratios of 7 or 11. 34edo adds ratios of 5 into the mix -- including 5/4, 6/5, 9/5, 15/8, 13/10, 15/13, and their inversions -- as well as 17 -- including 17/16, 17~~/18~~, 17/12, 17/10, 17/13, 17/15 and their inversions. Since it distinguishes between 9/8 and 10/9 (exaggerating the difference between them, the syntonic comma of 81/80, from 21.5 cents to 35.3 cents), it is suitable for 5-limit JI. It is not a <a class="wiki_link" href="http://xenharmonic.wikispaces.com/meantone">meantone </a>system.

Like <a class="wiki_link" href="http://xenharmonic.wikispaces.com/17edo">17edo</a>, 34edo contains good approximations of just intervals involving 13 and 3 -- specifically, 13/8, 13/12, 13/9 and their inversions -- while failing to closely approximate ratios of 7 or 11. 34edo adds ratios of 5 into the mix -- including 5/4, 6/5, 9/5, 15/8, 13/10, 15/13, and their inversions -- as well as 17 -- including 17/16, 18/17, 17/12, 17/10, 17/13, 17/15 and their inversions. Since it distinguishes between 9/8 and 10/9 (exaggerating the difference between them, the syntonic comma of 81/80, from 21.5 cents to 35.3 cents), it is suitable for 5-limit JI. It is not a <a class="wiki_link" href="http://xenharmonic.wikispaces.com/meantone">meantone </a>system.

Viewed in light of Western diatonic theory, the three extra steps (of 34-et compared to 31-et) in effect widen the intervals between C and D, F and G, and A and B [that is: 6 5 3 6 5 6 3], thus making a distinction between major tones, ratio 9/8 and minor tones, ratio 10/9. (<a class="wiki_link_ext" href="http://en.wikipedia.org/wiki/34_equal_temperament" rel="nofollow">Wikipedia</a>)

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</td>

<td>approx. ratios of

2.3.5.13.17 <a class="wiki_link" href="http://xenharmonic.wikispaces.com/subgroup">subgroup</a>

<a class="wiki_link" href="http://tel.wikispaces.com/2.3.5.13.17">2.3.5.13.17</a> <a class="wiki_link" href="http://xenharmonic.wikispaces.com/subgroup">subgroup</a>

</td>

<td>additional ratios

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<h2 id="toc5"><a name="x-Commas"></a>Commas</h2>

34-EDO <a class="wiki_link" href="http://xenharmonic.wikispaces.com/tempering%20out">tempers out</a> the following <a class="wiki_link" href="http://xenharmonic.wikispaces.com/comma">comma</a>s. (Note: This assumes the <a class="wiki_link" href="http://xenharmonic.wikispaces.com/val">val</a> &lt; 34 54 79 95 118 126 |.)

34-EDO <a class="wiki_link" href="http://xenharmonic.wikispaces.com/tempering%20out">tempers out</a> the following <a class="wiki_link" href="http://xenharmonic.wikispaces.com/comma">comma</a>s. (Note: This assumes the <a class="wiki_link" href="http://xenharmonic.wikispaces.com/val">val</a> &lt; <a class="wiki_link" href="http://tel.wikispaces.com/34%2054%2079%2095%20118%20126">34 54 79 95 118 126</a> |.)

<tr>

<th>Comma

<th>Comma

</th>

<th>Monzo

<th>Monzo

</th>

<th>Value (Cents)

<th>Value (Cents)

</th>

<th>Name 1

<th>Name 1

</th>

<th>Name 2

<th>Name 2

</th>

<th>Name 3

<th>Name 3

</th>

</tr>

<tr>

<td>134217728/129140163

<td>134217728/129140163

</td>

<td>| 27 -17 &gt;

</td>

<td>66.765

<td>66.765

</td>

<td>17-comma

<td>17-comma

</td>

<td>

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</tr>

<tr>

<td>20000/19683

<td>[[tel:20000/19683|20000/19683]]

</td>

<td>| 5 -9 4 &gt;

</td>

<td>27.660

<td>27.660

</td>

<td>Minimal Diesis

<td>Minimal Diesis

</td>

<td>Tetracot Comma

<td>Tetracot Comma

</td>

<td>

Line 711:

</tr>

<tr>

<td>2048/2025

<td>2048/2025

</td>

<td>| 11 -4 -2 &gt;

</td>

<td>19.553

<td>19.553

</td>

<td>Diaschisma

<td>Diaschisma

</td>

<td>

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</tr>

<tr>

<td>393216/390625

<td>393216/390625

</td>

<td>| 17 1 -8 &gt;

</td>

<td>11.445

<td>11.445

</td>

<td>Würschmidt comma

<td>Würschmidt comma

</td>

<td>

Line 739:

</tr>

<tr>

<td>15625/15552

<td>[[tel:15625/15552|15625/15552]]

</td>

<td>| -6 -5 6 &gt;

</td>

<td>8.1073

<td>8.1073

</td>

<td>Kleisma

<td>Kleisma

</td>

<td>Semicomma Majeur

<td>Semicomma Majeur

</td>

<td>

Line 753:

</tr>

<tr>

<td>1212717/1210381

<td>1212717/1210381

</td>

<td>| 23 6 -14 &gt;

</td>

<td>3.338

<td>3.338

</td>

<td>Vishnuzma

<td>Vishnuzma

</td>

<td>Semisuper

<td>Semisuper

</td>

<td>

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</tr>

<tr>

<td>1029/1000

<td>1029/1000

</td>

<td>| -3 1 -3 3 &gt;

</td>

<td>49.492

<td>49.492

</td>

<td>Keega

<td>Keega

</td>

<td>

Line 781:

</tr>

<tr>

</td>

<td>| -4 -1 0 2 &gt;

</td>

<td>35.697

<td>35.697

</td>

<td>Slendro Diesis

<td>Slendro Diesis

</td>

<td>

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</tr>

<tr>

<td>875/864

<td>875/864

</td>

<td>| -5 -3 3 1 &gt;

</td>

<td>21.902

<td>21.902

</td>

<td>Keema

<td>Keema

</td>

<td>

Line 809:

</tr>

<tr>

<td>126/125

<td>126/125

</td>

<td>| 1 2 -3 1 &gt;

</td>

<td>13.795

<td>13.795

</td>

<td>Starling comma

<td>Starling comma

</td>

<td>Septimal semicomma

<td>Septimal semicomma

</td>

<td>

Line 823:

</tr>

<tr>

<td>100/99

<td>100/99

</td>

<td>| 2 -2 2 0 -1&gt;

</td>

<td>17.399

<td>17.399

</td>

<td>Ptolemisma

<td>Ptolemisma

</td>

<td>Ptolemy's comma

<td>Ptolemy's comma

</td>

<td>

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</tr>

<tr>

<td>243/242

<td>243/242

</td>

<td>| -1 5 0 0 -2 &gt;

</td>

<td>7.1391

<td>7.1391

</td>

<td>Rastma

<td>Rastma

</td>

<td>Neutral third comma

<td>Neutral third comma

</td>

<td>

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</tr>

<tr>

<td>385/384

<td>385/384

</td>

<td>| -7 -1 1 1 1 &gt;

</td>

<td>4.5026

<td>4.5026

</td>

<td>Keenanisma

<td>Keenanisma

</td>

<td>

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</tr>

<tr>

<td>91/90

<td>91/90

</td>

<td>| -1 -2 -1 1 0 1 &gt;

</td>

<td>19.120

<td>19.120

</td>

<td>Superleap

<td>Superleap

</td>

<td>

@@ Line 1: / Line 1: @@
 <h2>IMPORTED REVISION FROM WIKISPACES</h2>
 This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br>
-: This revision was by author [[User:phylingual|phylingual]] and made on <tt>2012-05-04 11:25:58 UTC</tt>.<br>
+: This revision was by author [[User:JosephRuhf|JosephRuhf]] and made on <tt>2012-05-26 18:45:24 UTC</tt>.<br>
-: The original revision id was <tt>330018202</tt>.<br>
+: The original revision id was <tt>339770294</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 11: / Line 11: @@
 ===Approximations to Just Intonation===
-Like [[xenharmonic/17edo|17edo]], 34edo contains good approximations of just intervals involving 13 and 3 -- specifically, 13/8, 13/12, 13/9 and their inversions -- while failing to closely approximate ratios of 7 or 11. 34edo adds ratios of 5 into the mix -- including 5/4, 6/5, 9/5, 15/8, 13/10, 15/13, and their inversions -- as well as 17 -- including 17/16, 17/18, 17/12, 17/10, 17/13, 17/15 and their inversions. Since it distinguishes between 9/8 and 10/9 (exaggerating the difference between them, the syntonic comma of 81/80, from 21.5 cents to 35.3 cents), it is suitable for 5-limit JI. It is not a [[xenharmonic/meantone|meantone ]]system.
+Like [[xenharmonic/17edo|17edo]], 34edo contains good approximations of just intervals involving 13 and 3 -- specifically, 13/8, 13/12, 13/9 and their inversions -- while failing to closely approximate ratios of 7 or 11. 34edo adds ratios of 5 into the mix -- including 5/4, 6/5, 9/5, 15/8, 13/10, 15/13, and their inversions -- as well as 17 -- including 17/16, 18/17, 17/12, 17/10, 17/13, 17/15 and their inversions. Since it distinguishes between 9/8 and 10/9 (exaggerating the difference between them, the syntonic comma of 81/80, from 21.5 cents to 35.3 cents), it is suitable for 5-limit JI. It is not a [[xenharmonic/meantone|meantone ]]system.
 //Viewed in light of Western diatonic theory, the three extra steps (of 34-et compared to 31-et) in effect widen the intervals between C and D, F and G, and A and B [that is: 6 5 3 6 5 6 3], thus making a distinction between major tones, ratio 9/8 and minor tones, ratio 10/9.// ([[http://en.wikipedia.org/wiki/34_equal_temperament|Wikipedia]])
@@ Line 41: / Line 41: @@
 ===Intervals:===
 || degrees of 34edo || cents || approx. ratios of
-.3.5.13.17 [[xenharmonic/subgroup|subgroup]] || additional ratios
+[[tel:2.3.5.13.17|2.3.5.13.17]] [[xenharmonic/subgroup|subgroup]] || additional ratios
 of the full [[xenharmonic/17-limit|17-limit]] ||
 || 0 || 0.0 || 1/1 ||   ||
@@ Line 79: / Line 79: @@
 ==&lt;span style="background-color: #ffffff;"&gt;Commas&lt;/span&gt;==
-&lt;span style="background-color: #ffffff;"&gt;34-EDO [[xenharmonic/tempering out|tempers out]] the following [[xenharmonic/comma|comma]]s. (Note: This assumes the [[xenharmonic/val|val]] &lt; 34 54 79 95 118 126 |.)&lt;/span&gt;
+&lt;span style="background-color: #ffffff;"&gt;34-EDO [[xenharmonic/tempering out|tempers out]] the following [[xenharmonic/comma|comma]]s. (Note: This assumes the [[xenharmonic/val|val]] &lt; [[tel:34 54 79 95 118 126|34 54 79 95 118 126]] |.)&lt;/span&gt;
-||~ &lt;span style="text-align: center;"&gt;&lt;span style="display: block; text-align: center;"&gt;**Comma**&lt;/span&gt;&lt;/span&gt; ||~ &lt;span style="text-align: center;"&gt;&lt;span style="display: block; text-align: center;"&gt;**Monzo**&lt;/span&gt;&lt;/span&gt; ||~ &lt;span style="text-align: center;"&gt;&lt;span style="display: block; text-align: center;"&gt;**Value (Cents)**&lt;/span&gt;&lt;/span&gt; ||~ &lt;span style="text-align: center;"&gt;&lt;span style="display: block; text-align: center;"&gt;**Name 1**&lt;/span&gt;&lt;/span&gt; ||~ &lt;span style="text-align: center;"&gt;&lt;span style="display: block; text-align: center;"&gt;**Name 2**&lt;/span&gt;&lt;/span&gt; ||~ &lt;span style="text-align: center;"&gt;&lt;span style="display: block; text-align: center;"&gt;**Name 3**&lt;/span&gt;&lt;/span&gt; ||
+||~ &lt;span style="display: block; text-align: center;"&gt;&lt;span style="display: block; text-align: center;"&gt;**Comma**&lt;/span&gt;&lt;/span&gt; ||~ &lt;span style="display: block; text-align: center;"&gt;&lt;span style="display: block; text-align: center;"&gt;**Monzo**&lt;/span&gt;&lt;/span&gt; ||~ &lt;span style="display: block; text-align: center;"&gt;&lt;span style="display: block; text-align: center;"&gt;**Value (Cents)**&lt;/span&gt;&lt;/span&gt; ||~ &lt;span style="display: block; text-align: center;"&gt;&lt;span style="display: block; text-align: center;"&gt;**Name 1**&lt;/span&gt;&lt;/span&gt; ||~ &lt;span style="display: block; text-align: center;"&gt;&lt;span style="display: block; text-align: center;"&gt;**Name 2**&lt;/span&gt;&lt;/span&gt; ||~ &lt;span style="display: block; text-align: center;"&gt;&lt;span style="display: block; text-align: center;"&gt;**Name 3**&lt;/span&gt;&lt;/span&gt; ||
-|| &lt;span style="text-align: center;"&gt;&lt;span style="display: block; text-align: center;"&gt;134217728/129140163&lt;/span&gt;&lt;/span&gt; || | 27 -17 &gt; || &lt;span style="text-align: right;"&gt;&lt;span style="display: block; text-align: right;"&gt;66.765&lt;/span&gt;&lt;/span&gt; || &lt;span style="text-align: center;"&gt;&lt;span style="display: block; text-align: center;"&gt;17-comma&lt;/span&gt;&lt;/span&gt; ||   ||   ||
+|| &lt;span style="display: block; text-align: center;"&gt;&lt;span style="display: block; text-align: center;"&gt;134217728/129140163&lt;/span&gt;&lt;/span&gt; || | 27 -17 &gt; || &lt;span style="display: block; text-align: right;"&gt;&lt;span style="display: block; text-align: right;"&gt;66.765&lt;/span&gt;&lt;/span&gt; || &lt;span style="display: block; text-align: center;"&gt;&lt;span style="display: block; text-align: center;"&gt;17-comma&lt;/span&gt;&lt;/span&gt; ||   ||   ||
-|| &lt;span style="text-align: center;"&gt;&lt;span style="display: block; text-align: center;"&gt;20000/19683&lt;/span&gt;&lt;/span&gt; || | 5 -9 4 &gt; || &lt;span style="text-align: right;"&gt;&lt;span style="display: block; text-align: right;"&gt;27.660&lt;/span&gt;&lt;/span&gt; || &lt;span style="text-align: center;"&gt;&lt;span style="display: block; text-align: center;"&gt;Minimal Diesis&lt;/span&gt;&lt;/span&gt; || &lt;span style="text-align: center;"&gt;&lt;span style="display: block; text-align: center;"&gt;Tetracot Comma&lt;/span&gt;&lt;/span&gt; ||   ||
+|| &lt;span style="display: block; text-align: center;"&gt;&lt;span style="display: block; text-align: center;"&gt;[[tel:20000/19683|20000/19683]]&lt;/span&gt;&lt;/span&gt; || | 5 -9 4 &gt; || &lt;span style="display: block; text-align: right;"&gt;&lt;span style="display: block; text-align: right;"&gt;27.660&lt;/span&gt;&lt;/span&gt; || &lt;span style="display: block; text-align: center;"&gt;&lt;span style="display: block; text-align: center;"&gt;Minimal Diesis&lt;/span&gt;&lt;/span&gt; || &lt;span style="display: block; text-align: center;"&gt;&lt;span style="display: block; text-align: center;"&gt;Tetracot Comma&lt;/span&gt;&lt;/span&gt; ||   ||
-|| &lt;span style="text-align: center;"&gt;&lt;span style="display: block; text-align: center;"&gt;2048/2025&lt;/span&gt;&lt;/span&gt; || | 11 -4 -2 &gt; || &lt;span style="text-align: right;"&gt;&lt;span style="display: block; text-align: right;"&gt;19.553&lt;/span&gt;&lt;/span&gt; || &lt;span style="text-align: center;"&gt;&lt;span style="display: block; text-align: center;"&gt;Diaschisma&lt;/span&gt;&lt;/span&gt; ||   ||   ||
+|| &lt;span style="display: block; text-align: center;"&gt;&lt;span style="display: block; text-align: center;"&gt;2048/2025&lt;/span&gt;&lt;/span&gt; || | 11 -4 -2 &gt; || &lt;span style="display: block; text-align: right;"&gt;&lt;span style="display: block; text-align: right;"&gt;19.553&lt;/span&gt;&lt;/span&gt; || &lt;span style="display: block; text-align: center;"&gt;&lt;span style="display: block; text-align: center;"&gt;Diaschisma&lt;/span&gt;&lt;/span&gt; ||   ||   ||
-|| &lt;span style="text-align: center;"&gt;&lt;span style="display: block; text-align: center;"&gt;393216/390625&lt;/span&gt;&lt;/span&gt; || | 17 1 -8 &gt; || &lt;span style="text-align: right;"&gt;&lt;span style="display: block; text-align: right;"&gt;11.445&lt;/span&gt;&lt;/span&gt; || &lt;span style="text-align: center;"&gt;&lt;span style="display: block; text-align: center;"&gt;Würschmidt comma&lt;/span&gt;&lt;/span&gt; ||   ||   ||
+|| &lt;span style="display: block; text-align: center;"&gt;&lt;span style="display: block; text-align: center;"&gt;393216/390625&lt;/span&gt;&lt;/span&gt; || | 17 1 -8 &gt; || &lt;span style="display: block; text-align: right;"&gt;&lt;span style="display: block; text-align: right;"&gt;11.445&lt;/span&gt;&lt;/span&gt; || &lt;span style="display: block; text-align: center;"&gt;&lt;span style="display: block; text-align: center;"&gt;Würschmidt comma&lt;/span&gt;&lt;/span&gt; ||   ||   ||
-|| &lt;span style="text-align: center;"&gt;&lt;span style="display: block; text-align: center;"&gt;15625/15552&lt;/span&gt;&lt;/span&gt; || | -6 -5 6 &gt; || &lt;span style="text-align: right;"&gt;&lt;span style="display: block; text-align: right;"&gt;8.1073&lt;/span&gt;&lt;/span&gt; || &lt;span style="text-align: center;"&gt;&lt;span style="display: block; text-align: center;"&gt;Kleisma&lt;/span&gt;&lt;/span&gt; || &lt;span style="text-align: center;"&gt;&lt;span style="display: block; text-align: center;"&gt;Semicomma Majeur&lt;/span&gt;&lt;/span&gt; ||   ||
+|| &lt;span style="display: block; text-align: center;"&gt;&lt;span style="display: block; text-align: center;"&gt;[[tel:15625/15552|15625/15552]]&lt;/span&gt;&lt;/span&gt; || | -6 -5 6 &gt; || &lt;span style="display: block; text-align: right;"&gt;&lt;span style="display: block; text-align: right;"&gt;8.1073&lt;/span&gt;&lt;/span&gt; || &lt;span style="display: block; text-align: center;"&gt;&lt;span style="display: block; text-align: center;"&gt;Kleisma&lt;/span&gt;&lt;/span&gt; || &lt;span style="display: block; text-align: center;"&gt;&lt;span style="display: block; text-align: center;"&gt;Semicomma Majeur&lt;/span&gt;&lt;/span&gt; ||   ||
-|| &lt;span style="text-align: center;"&gt;&lt;span style="display: block; text-align: center;"&gt;1212717/1210381&lt;/span&gt;&lt;/span&gt; || | 23 6 -14 &gt; || &lt;span style="text-align: right;"&gt;&lt;span style="display: block; text-align: right;"&gt;3.338&lt;/span&gt;&lt;/span&gt; || &lt;span style="text-align: center;"&gt;&lt;span style="display: block; text-align: center;"&gt;Vishnuzma&lt;/span&gt;&lt;/span&gt; || &lt;span style="text-align: center;"&gt;&lt;span style="display: block; text-align: center;"&gt;Semisuper&lt;/span&gt;&lt;/span&gt; ||   ||
+|| &lt;span style="display: block; text-align: center;"&gt;&lt;span style="display: block; text-align: center;"&gt;1212717/1210381&lt;/span&gt;&lt;/span&gt; || | 23 6 -14 &gt; || &lt;span style="display: block; text-align: right;"&gt;&lt;span style="display: block; text-align: right;"&gt;3.338&lt;/span&gt;&lt;/span&gt; || &lt;span style="display: block; text-align: center;"&gt;&lt;span style="display: block; text-align: center;"&gt;Vishnuzma&lt;/span&gt;&lt;/span&gt; || &lt;span style="display: block; text-align: center;"&gt;&lt;span style="display: block; text-align: center;"&gt;Semisuper&lt;/span&gt;&lt;/span&gt; ||   ||
-|| &lt;span style="text-align: center;"&gt;&lt;span style="display: block; text-align: center;"&gt;1029/1000&lt;/span&gt;&lt;/span&gt; || | -3 1 -3 3 &gt; || &lt;span style="text-align: right;"&gt;&lt;span style="display: block; text-align: right;"&gt;49.492&lt;/span&gt;&lt;/span&gt; || &lt;span style="text-align: center;"&gt;&lt;span style="display: block; text-align: center;"&gt;Keega&lt;/span&gt;&lt;/span&gt; ||   ||   ||
+|| &lt;span style="display: block; text-align: center;"&gt;&lt;span style="display: block; text-align: center;"&gt;1029/1000&lt;/span&gt;&lt;/span&gt; || | -3 1 -3 3 &gt; || &lt;span style="display: block; text-align: right;"&gt;&lt;span style="display: block; text-align: right;"&gt;49.492&lt;/span&gt;&lt;/span&gt; || &lt;span style="display: block; text-align: center;"&gt;&lt;span style="display: block; text-align: center;"&gt;Keega&lt;/span&gt;&lt;/span&gt; ||   ||   ||
-|| &lt;span style="text-align: center;"&gt;&lt;span style="display: block; text-align: center;"&gt;&lt;span style="color: blue;"&gt;[[xenharmonic/49_48|49/48]]&lt;/span&gt;&lt;/span&gt;&lt;/span&gt; || | -4 -1 0 2 &gt; || &lt;span style="text-align: right;"&gt;&lt;span style="display: block; text-align: right;"&gt;35.697&lt;/span&gt;&lt;/span&gt; || &lt;span style="text-align: center;"&gt;&lt;span style="display: block; text-align: center;"&gt;Slendro Diesis&lt;/span&gt;&lt;/span&gt; ||   ||   ||
+|| &lt;span style="display: block; text-align: center;"&gt;&lt;span style="color: blue; display: block; text-align: center;"&gt;[[xenharmonic/49_48|49/48]]&lt;/span&gt;&lt;/span&gt; || | -4 -1 0 2 &gt; || &lt;span style="display: block; text-align: right;"&gt;&lt;span style="display: block; text-align: right;"&gt;35.697&lt;/span&gt;&lt;/span&gt; || &lt;span style="display: block; text-align: center;"&gt;&lt;span style="display: block; text-align: center;"&gt;Slendro Diesis&lt;/span&gt;&lt;/span&gt; ||   ||   ||
-|| &lt;span style="text-align: center;"&gt;&lt;span style="display: block; text-align: center;"&gt;875/864&lt;/span&gt;&lt;/span&gt; || | -5 -3 3 1 &gt; || &lt;span style="text-align: right;"&gt;&lt;span style="display: block; text-align: right;"&gt;21.902&lt;/span&gt;&lt;/span&gt; || &lt;span style="text-align: center;"&gt;&lt;span style="display: block; text-align: center;"&gt;Keema&lt;/span&gt;&lt;/span&gt; ||   ||   ||
+|| &lt;span style="display: block; text-align: center;"&gt;&lt;span style="display: block; text-align: center;"&gt;875/864&lt;/span&gt;&lt;/span&gt; || | -5 -3 3 1 &gt; || &lt;span style="display: block; text-align: right;"&gt;&lt;span style="display: block; text-align: right;"&gt;21.902&lt;/span&gt;&lt;/span&gt; || &lt;span style="display: block; text-align: center;"&gt;&lt;span style="display: block; text-align: center;"&gt;Keema&lt;/span&gt;&lt;/span&gt; ||   ||   ||
-|| &lt;span style="text-align: center;"&gt;&lt;span style="display: block; text-align: center;"&gt;126/125&lt;/span&gt;&lt;/span&gt; || | 1 2 -3 1 &gt; || &lt;span style="text-align: right;"&gt;&lt;span style="display: block; text-align: right;"&gt;13.795&lt;/span&gt;&lt;/span&gt; || &lt;span style="text-align: center;"&gt;&lt;span style="display: block; text-align: center;"&gt;Starling comma&lt;/span&gt;&lt;/span&gt; || &lt;span style="text-align: center;"&gt;&lt;span style="display: block; text-align: center;"&gt;Septimal semicomma&lt;/span&gt;&lt;/span&gt; ||   ||
+|| &lt;span style="display: block; text-align: center;"&gt;&lt;span style="display: block; text-align: center;"&gt;126/125&lt;/span&gt;&lt;/span&gt; || | 1 2 -3 1 &gt; || &lt;span style="display: block; text-align: right;"&gt;&lt;span style="display: block; text-align: right;"&gt;13.795&lt;/span&gt;&lt;/span&gt; || &lt;span style="display: block; text-align: center;"&gt;&lt;span style="display: block; text-align: center;"&gt;Starling comma&lt;/span&gt;&lt;/span&gt; || &lt;span style="display: block; text-align: center;"&gt;&lt;span style="display: block; text-align: center;"&gt;Septimal semicomma&lt;/span&gt;&lt;/span&gt; ||   ||
-|| &lt;span style="text-align: center;"&gt;&lt;span style="display: block; text-align: center;"&gt;100/99&lt;/span&gt;&lt;/span&gt; || | 2 -2 2 0 -1&gt; || &lt;span style="text-align: right;"&gt;&lt;span style="display: block; text-align: right;"&gt;17.399&lt;/span&gt;&lt;/span&gt; || &lt;span style="text-align: center;"&gt;&lt;span style="display: block; text-align: center;"&gt;Ptolemisma&lt;/span&gt;&lt;/span&gt; || &lt;span style="text-align: center;"&gt;&lt;span style="display: block; text-align: center;"&gt;Ptolemy's comma&lt;/span&gt;&lt;/span&gt; ||   ||
+|| &lt;span style="display: block; text-align: center;"&gt;&lt;span style="display: block; text-align: center;"&gt;100/99&lt;/span&gt;&lt;/span&gt; || | 2 -2 2 0 -1&gt; || &lt;span style="display: block; text-align: right;"&gt;&lt;span style="display: block; text-align: right;"&gt;17.399&lt;/span&gt;&lt;/span&gt; || &lt;span style="display: block; text-align: center;"&gt;&lt;span style="display: block; text-align: center;"&gt;Ptolemisma&lt;/span&gt;&lt;/span&gt; || &lt;span style="display: block; text-align: center;"&gt;&lt;span style="display: block; text-align: center;"&gt;Ptolemy's comma&lt;/span&gt;&lt;/span&gt; ||   ||
-|| &lt;span style="text-align: center;"&gt;&lt;span style="display: block; text-align: center;"&gt;243/242&lt;/span&gt;&lt;/span&gt; || | -1 5 0 0 -2 &gt; || &lt;span style="text-align: right;"&gt;&lt;span style="display: block; text-align: right;"&gt;7.1391&lt;/span&gt;&lt;/span&gt; || &lt;span style="text-align: center;"&gt;&lt;span style="display: block; text-align: center;"&gt;Rastma&lt;/span&gt;&lt;/span&gt; || &lt;span style="text-align: center;"&gt;&lt;span style="display: block; text-align: center;"&gt;Neutral third comma&lt;/span&gt;&lt;/span&gt; ||   ||
+|| &lt;span style="display: block; text-align: center;"&gt;&lt;span style="display: block; text-align: center;"&gt;243/242&lt;/span&gt;&lt;/span&gt; || | -1 5 0 0 -2 &gt; || &lt;span style="display: block; text-align: right;"&gt;&lt;span style="display: block; text-align: right;"&gt;7.1391&lt;/span&gt;&lt;/span&gt; || &lt;span style="display: block; text-align: center;"&gt;&lt;span style="display: block; text-align: center;"&gt;Rastma&lt;/span&gt;&lt;/span&gt; || &lt;span style="display: block; text-align: center;"&gt;&lt;span style="display: block; text-align: center;"&gt;Neutral third comma&lt;/span&gt;&lt;/span&gt; ||   ||
-|| &lt;span style="text-align: center;"&gt;&lt;span style="display: block; text-align: center;"&gt;385/384&lt;/span&gt;&lt;/span&gt; || | -7 -1 1 1 1 &gt; || &lt;span style="text-align: right;"&gt;&lt;span style="display: block; text-align: right;"&gt;4.5026&lt;/span&gt;&lt;/span&gt; || &lt;span style="text-align: center;"&gt;&lt;span style="display: block; text-align: center;"&gt;Keenanisma&lt;/span&gt;&lt;/span&gt; ||   ||   ||
+|| &lt;span style="display: block; text-align: center;"&gt;&lt;span style="display: block; text-align: center;"&gt;385/384&lt;/span&gt;&lt;/span&gt; || | -7 -1 1 1 1 &gt; || &lt;span style="display: block; text-align: right;"&gt;&lt;span style="display: block; text-align: right;"&gt;4.5026&lt;/span&gt;&lt;/span&gt; || &lt;span style="display: block; text-align: center;"&gt;&lt;span style="display: block; text-align: center;"&gt;Keenanisma&lt;/span&gt;&lt;/span&gt; ||   ||   ||
-|| &lt;span style="text-align: center;"&gt;&lt;span style="display: block; text-align: center;"&gt;91/90&lt;/span&gt;&lt;/span&gt; || | -1 -2 -1 1 0 1 &gt; || &lt;span style="text-align: right;"&gt;&lt;span style="display: block; text-align: right;"&gt;19.120&lt;/span&gt;&lt;/span&gt; || &lt;span style="text-align: center;"&gt;&lt;span style="display: block; text-align: center;"&gt;Superleap&lt;/span&gt;&lt;/span&gt; ||   ||   ||
+|| &lt;span style="display: block; text-align: center;"&gt;&lt;span style="display: block; text-align: center;"&gt;91/90&lt;/span&gt;&lt;/span&gt; || | -1 -2 -1 1 0 1 &gt; || &lt;span style="display: block; text-align: right;"&gt;&lt;span style="display: block; text-align: right;"&gt;19.120&lt;/span&gt;&lt;/span&gt; || &lt;span style="display: block; text-align: center;"&gt;&lt;span style="display: block; text-align: center;"&gt;Superleap&lt;/span&gt;&lt;/span&gt; ||   ||   ||
@@ Line 109: / Line 109: @@
 &lt;br /&gt;
 &lt;!-- ws:start:WikiTextHeadingRule:2:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc1"&gt;&lt;a name="x--Approximations to Just Intonation"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:2 --&gt;Approximations to Just Intonation&lt;/h3&gt;
-  Like &lt;a class="wiki_link" href="http://xenharmonic.wikispaces.com/17edo"&gt;17edo&lt;/a&gt;, 34edo contains good approximations of just intervals involving 13 and 3 -- specifically, 13/8, 13/12, 13/9 and their inversions -- while failing to closely approximate ratios of 7 or 11. 34edo adds ratios of 5 into the mix -- including 5/4, 6/5, 9/5, 15/8, 13/10, 15/13, and their inversions -- as well as 17 -- including 17/16, 17/18, 17/12, 17/10, 17/13, 17/15 and their inversions. Since it distinguishes between 9/8 and 10/9 (exaggerating the difference between them, the syntonic comma of 81/80, from 21.5 cents to 35.3 cents), it is suitable for 5-limit JI. It is not a &lt;a class="wiki_link" href="http://xenharmonic.wikispaces.com/meantone"&gt;meantone &lt;/a&gt;system.&lt;br /&gt;
+  Like &lt;a class="wiki_link" href="http://xenharmonic.wikispaces.com/17edo"&gt;17edo&lt;/a&gt;, 34edo contains good approximations of just intervals involving 13 and 3 -- specifically, 13/8, 13/12, 13/9 and their inversions -- while failing to closely approximate ratios of 7 or 11. 34edo adds ratios of 5 into the mix -- including 5/4, 6/5, 9/5, 15/8, 13/10, 15/13, and their inversions -- as well as 17 -- including 17/16, 18/17, 17/12, 17/10, 17/13, 17/15 and their inversions. Since it distinguishes between 9/8 and 10/9 (exaggerating the difference between them, the syntonic comma of 81/80, from 21.5 cents to 35.3 cents), it is suitable for 5-limit JI. It is not a &lt;a class="wiki_link" href="http://xenharmonic.wikispaces.com/meantone"&gt;meantone &lt;/a&gt;system.&lt;br /&gt;
 &lt;br /&gt;
 &lt;em&gt;Viewed in light of Western diatonic theory, the three extra steps (of 34-et compared to 31-et) in effect widen the intervals between C and D, F and G, and A and B [that is: 6 5 3 6 5 6 3], thus making a distinction between major tones, ratio 9/8 and minor tones, ratio 10/9.&lt;/em&gt; (&lt;a class="wiki_link_ext" href="http://en.wikipedia.org/wiki/34_equal_temperament" rel="nofollow"&gt;Wikipedia&lt;/a&gt;)&lt;br /&gt;
@@ Line 314: / Line 314: @@
 &lt;/td&gt;
          &lt;td&gt;approx. ratios of&lt;br /&gt;
-.3.5.13.17 &lt;a class="wiki_link" href="http://xenharmonic.wikispaces.com/subgroup"&gt;subgroup&lt;/a&gt;&lt;br /&gt;
+&lt;a class="wiki_link" href="http://tel.wikispaces.com/2.3.5.13.17"&gt;2.3.5.13.17&lt;/a&gt; &lt;a class="wiki_link" href="http://xenharmonic.wikispaces.com/subgroup"&gt;subgroup&lt;/a&gt;&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;additional ratios&lt;br /&gt;
@@ Line 664: / Line 664: @@
 &lt;br /&gt;
 &lt;!-- ws:start:WikiTextHeadingRule:10:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc5"&gt;&lt;a name="x-Commas"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:10 --&gt;&lt;span style="background-color: #ffffff;"&gt;Commas&lt;/span&gt;&lt;/h2&gt;
-  &lt;span style="background-color: #ffffff;"&gt;34-EDO &lt;a class="wiki_link" href="http://xenharmonic.wikispaces.com/tempering%20out"&gt;tempers out&lt;/a&gt; the following &lt;a class="wiki_link" href="http://xenharmonic.wikispaces.com/comma"&gt;comma&lt;/a&gt;s. (Note: This assumes the &lt;a class="wiki_link" href="http://xenharmonic.wikispaces.com/val"&gt;val&lt;/a&gt; &amp;lt; 34 54 79 95 118 126 |.)&lt;/span&gt;&lt;br /&gt;
+  &lt;span style="background-color: #ffffff;"&gt;34-EDO &lt;a class="wiki_link" href="http://xenharmonic.wikispaces.com/tempering%20out"&gt;tempers out&lt;/a&gt; the following &lt;a class="wiki_link" href="http://xenharmonic.wikispaces.com/comma"&gt;comma&lt;/a&gt;s. (Note: This assumes the &lt;a class="wiki_link" href="http://xenharmonic.wikispaces.com/val"&gt;val&lt;/a&gt; &amp;lt; &lt;a class="wiki_link" href="http://tel.wikispaces.com/34%2054%2079%2095%20118%20126"&gt;34 54 79 95 118 126&lt;/a&gt; |.)&lt;/span&gt;&lt;br /&gt;
 &lt;table class="wiki_table"&gt;
      &lt;tr&gt;
-         &lt;th&gt;&lt;span style="text-align: center;"&gt;&lt;span style="display: block; text-align: center;"&gt;&lt;strong&gt;Comma&lt;/strong&gt;&lt;/span&gt;&lt;/span&gt;&lt;br /&gt;
+         &lt;th&gt;&lt;span style="display: block; text-align: center;"&gt;&lt;span style="display: block; text-align: center;"&gt;&lt;strong&gt;Comma&lt;/strong&gt;&lt;/span&gt;&lt;/span&gt;&lt;br /&gt;
 &lt;/th&gt;
-         &lt;th&gt;&lt;span style="text-align: center;"&gt;&lt;span style="display: block; text-align: center;"&gt;&lt;strong&gt;Monzo&lt;/strong&gt;&lt;/span&gt;&lt;/span&gt;&lt;br /&gt;
+         &lt;th&gt;&lt;span style="display: block; text-align: center;"&gt;&lt;span style="display: block; text-align: center;"&gt;&lt;strong&gt;Monzo&lt;/strong&gt;&lt;/span&gt;&lt;/span&gt;&lt;br /&gt;
 &lt;/th&gt;
-         &lt;th&gt;&lt;span style="text-align: center;"&gt;&lt;span style="display: block; text-align: center;"&gt;&lt;strong&gt;Value (Cents)&lt;/strong&gt;&lt;/span&gt;&lt;/span&gt;&lt;br /&gt;
+         &lt;th&gt;&lt;span style="display: block; text-align: center;"&gt;&lt;span style="display: block; text-align: center;"&gt;&lt;strong&gt;Value (Cents)&lt;/strong&gt;&lt;/span&gt;&lt;/span&gt;&lt;br /&gt;
 &lt;/th&gt;
-         &lt;th&gt;&lt;span style="text-align: center;"&gt;&lt;span style="display: block; text-align: center;"&gt;&lt;strong&gt;Name 1&lt;/strong&gt;&lt;/span&gt;&lt;/span&gt;&lt;br /&gt;
+         &lt;th&gt;&lt;span style="display: block; text-align: center;"&gt;&lt;span style="display: block; text-align: center;"&gt;&lt;strong&gt;Name 1&lt;/strong&gt;&lt;/span&gt;&lt;/span&gt;&lt;br /&gt;
 &lt;/th&gt;
-         &lt;th&gt;&lt;span style="text-align: center;"&gt;&lt;span style="display: block; text-align: center;"&gt;&lt;strong&gt;Name 2&lt;/strong&gt;&lt;/span&gt;&lt;/span&gt;&lt;br /&gt;
+         &lt;th&gt;&lt;span style="display: block; text-align: center;"&gt;&lt;span style="display: block; text-align: center;"&gt;&lt;strong&gt;Name 2&lt;/strong&gt;&lt;/span&gt;&lt;/span&gt;&lt;br /&gt;
 &lt;/th&gt;
-         &lt;th&gt;&lt;span style="text-align: center;"&gt;&lt;span style="display: block; text-align: center;"&gt;&lt;strong&gt;Name 3&lt;/strong&gt;&lt;/span&gt;&lt;/span&gt;&lt;br /&gt;
+         &lt;th&gt;&lt;span style="display: block; text-align: center;"&gt;&lt;span style="display: block; text-align: center;"&gt;&lt;strong&gt;Name 3&lt;/strong&gt;&lt;/span&gt;&lt;/span&gt;&lt;br /&gt;
 &lt;/th&gt;
      &lt;/tr&gt;
      &lt;tr&gt;
-         &lt;td&gt;&lt;span style="text-align: center;"&gt;&lt;span style="display: block; text-align: center;"&gt;134217728/129140163&lt;/span&gt;&lt;/span&gt;&lt;br /&gt;
+         &lt;td&gt;&lt;span style="display: block; text-align: center;"&gt;&lt;span style="display: block; text-align: center;"&gt;134217728/129140163&lt;/span&gt;&lt;/span&gt;&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;| 27 -17 &amp;gt;&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;&lt;span style="text-align: right;"&gt;&lt;span style="display: block; text-align: right;"&gt;66.765&lt;/span&gt;&lt;/span&gt;&lt;br /&gt;
+         &lt;td&gt;&lt;span style="display: block; text-align: right;"&gt;&lt;span style="display: block; text-align: right;"&gt;66.765&lt;/span&gt;&lt;/span&gt;&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;&lt;span style="text-align: center;"&gt;&lt;span style="display: block; text-align: center;"&gt;17-comma&lt;/span&gt;&lt;/span&gt;&lt;br /&gt;
+         &lt;td&gt;&lt;span style="display: block; text-align: center;"&gt;&lt;span style="display: block; text-align: center;"&gt;17-comma&lt;/span&gt;&lt;/span&gt;&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;&lt;br /&gt;
@@ Line 697: / Line 697: @@
      &lt;/tr&gt;
      &lt;tr&gt;
-         &lt;td&gt;&lt;span style="text-align: center;"&gt;&lt;span style="display: block; text-align: center;"&gt;20000/19683&lt;/span&gt;&lt;/span&gt;&lt;br /&gt;
+         &lt;td&gt;&lt;span style="display: block; text-align: center;"&gt;&lt;span style="display: block; text-align: center;"&gt;[[tel:20000/19683|20000/19683]]&lt;/span&gt;&lt;/span&gt;&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;| 5 -9 4 &amp;gt;&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;&lt;span style="text-align: right;"&gt;&lt;span style="display: block; text-align: right;"&gt;27.660&lt;/span&gt;&lt;/span&gt;&lt;br /&gt;
+         &lt;td&gt;&lt;span style="display: block; text-align: right;"&gt;&lt;span style="display: block; text-align: right;"&gt;27.660&lt;/span&gt;&lt;/span&gt;&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;&lt;span style="text-align: center;"&gt;&lt;span style="display: block; text-align: center;"&gt;Minimal Diesis&lt;/span&gt;&lt;/span&gt;&lt;br /&gt;
+         &lt;td&gt;&lt;span style="display: block; text-align: center;"&gt;&lt;span style="display: block; text-align: center;"&gt;Minimal Diesis&lt;/span&gt;&lt;/span&gt;&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;&lt;span style="text-align: center;"&gt;&lt;span style="display: block; text-align: center;"&gt;Tetracot Comma&lt;/span&gt;&lt;/span&gt;&lt;br /&gt;
+         &lt;td&gt;&lt;span style="display: block; text-align: center;"&gt;&lt;span style="display: block; text-align: center;"&gt;Tetracot Comma&lt;/span&gt;&lt;/span&gt;&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;&lt;br /&gt;
@@ Line 711: / Line 711: @@
      &lt;/tr&gt;
      &lt;tr&gt;
-         &lt;td&gt;&lt;span style="text-align: center;"&gt;&lt;span style="display: block; text-align: center;"&gt;2048/2025&lt;/span&gt;&lt;/span&gt;&lt;br /&gt;
+         &lt;td&gt;&lt;span style="display: block; text-align: center;"&gt;&lt;span style="display: block; text-align: center;"&gt;2048/2025&lt;/span&gt;&lt;/span&gt;&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;| 11 -4 -2 &amp;gt;&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;&lt;span style="text-align: right;"&gt;&lt;span style="display: block; text-align: right;"&gt;19.553&lt;/span&gt;&lt;/span&gt;&lt;br /&gt;
+         &lt;td&gt;&lt;span style="display: block; text-align: right;"&gt;&lt;span style="display: block; text-align: right;"&gt;19.553&lt;/span&gt;&lt;/span&gt;&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;&lt;span style="text-align: center;"&gt;&lt;span style="display: block; text-align: center;"&gt;Diaschisma&lt;/span&gt;&lt;/span&gt;&lt;br /&gt;
+         &lt;td&gt;&lt;span style="display: block; text-align: center;"&gt;&lt;span style="display: block; text-align: center;"&gt;Diaschisma&lt;/span&gt;&lt;/span&gt;&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;&lt;br /&gt;
@@ Line 725: / Line 725: @@
      &lt;/tr&gt;
      &lt;tr&gt;
-         &lt;td&gt;&lt;span style="text-align: center;"&gt;&lt;span style="display: block; text-align: center;"&gt;393216/390625&lt;/span&gt;&lt;/span&gt;&lt;br /&gt;
+         &lt;td&gt;&lt;span style="display: block; text-align: center;"&gt;&lt;span style="display: block; text-align: center;"&gt;393216/390625&lt;/span&gt;&lt;/span&gt;&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;| 17 1 -8 &amp;gt;&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;&lt;span style="text-align: right;"&gt;&lt;span style="display: block; text-align: right;"&gt;11.445&lt;/span&gt;&lt;/span&gt;&lt;br /&gt;
+         &lt;td&gt;&lt;span style="display: block; text-align: right;"&gt;&lt;span style="display: block; text-align: right;"&gt;11.445&lt;/span&gt;&lt;/span&gt;&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;&lt;span style="text-align: center;"&gt;&lt;span style="display: block; text-align: center;"&gt;Würschmidt comma&lt;/span&gt;&lt;/span&gt;&lt;br /&gt;
+         &lt;td&gt;&lt;span style="display: block; text-align: center;"&gt;&lt;span style="display: block; text-align: center;"&gt;Würschmidt comma&lt;/span&gt;&lt;/span&gt;&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;&lt;br /&gt;
@@ Line 739: / Line 739: @@
      &lt;/tr&gt;
      &lt;tr&gt;
-         &lt;td&gt;&lt;span style="text-align: center;"&gt;&lt;span style="display: block; text-align: center;"&gt;15625/15552&lt;/span&gt;&lt;/span&gt;&lt;br /&gt;
+         &lt;td&gt;&lt;span style="display: block; text-align: center;"&gt;&lt;span style="display: block; text-align: center;"&gt;[[tel:15625/15552|15625/15552]]&lt;/span&gt;&lt;/span&gt;&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;| -6 -5 6 &amp;gt;&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;&lt;span style="text-align: right;"&gt;&lt;span style="display: block; text-align: right;"&gt;8.1073&lt;/span&gt;&lt;/span&gt;&lt;br /&gt;
+         &lt;td&gt;&lt;span style="display: block; text-align: right;"&gt;&lt;span style="display: block; text-align: right;"&gt;8.1073&lt;/span&gt;&lt;/span&gt;&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;&lt;span style="text-align: center;"&gt;&lt;span style="display: block; text-align: center;"&gt;Kleisma&lt;/span&gt;&lt;/span&gt;&lt;br /&gt;
+         &lt;td&gt;&lt;span style="display: block; text-align: center;"&gt;&lt;span style="display: block; text-align: center;"&gt;Kleisma&lt;/span&gt;&lt;/span&gt;&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;&lt;span style="text-align: center;"&gt;&lt;span style="display: block; text-align: center;"&gt;Semicomma Majeur&lt;/span&gt;&lt;/span&gt;&lt;br /&gt;
+         &lt;td&gt;&lt;span style="display: block; text-align: center;"&gt;&lt;span style="display: block; text-align: center;"&gt;Semicomma Majeur&lt;/span&gt;&lt;/span&gt;&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;&lt;br /&gt;
@@ Line 753: / Line 753: @@
      &lt;/tr&gt;
      &lt;tr&gt;
-         &lt;td&gt;&lt;span style="text-align: center;"&gt;&lt;span style="display: block; text-align: center;"&gt;1212717/1210381&lt;/span&gt;&lt;/span&gt;&lt;br /&gt;
+         &lt;td&gt;&lt;span style="display: block; text-align: center;"&gt;&lt;span style="display: block; text-align: center;"&gt;1212717/1210381&lt;/span&gt;&lt;/span&gt;&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;| 23 6 -14 &amp;gt;&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;&lt;span style="text-align: right;"&gt;&lt;span style="display: block; text-align: right;"&gt;3.338&lt;/span&gt;&lt;/span&gt;&lt;br /&gt;
+         &lt;td&gt;&lt;span style="display: block; text-align: right;"&gt;&lt;span style="display: block; text-align: right;"&gt;3.338&lt;/span&gt;&lt;/span&gt;&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;&lt;span style="text-align: center;"&gt;&lt;span style="display: block; text-align: center;"&gt;Vishnuzma&lt;/span&gt;&lt;/span&gt;&lt;br /&gt;
+         &lt;td&gt;&lt;span style="display: block; text-align: center;"&gt;&lt;span style="display: block; text-align: center;"&gt;Vishnuzma&lt;/span&gt;&lt;/span&gt;&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;&lt;span style="text-align: center;"&gt;&lt;span style="display: block; text-align: center;"&gt;Semisuper&lt;/span&gt;&lt;/span&gt;&lt;br /&gt;
+         &lt;td&gt;&lt;span style="display: block; text-align: center;"&gt;&lt;span style="display: block; text-align: center;"&gt;Semisuper&lt;/span&gt;&lt;/span&gt;&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;&lt;br /&gt;
@@ Line 767: / Line 767: @@
      &lt;/tr&gt;
      &lt;tr&gt;
-         &lt;td&gt;&lt;span style="text-align: center;"&gt;&lt;span style="display: block; text-align: center;"&gt;1029/1000&lt;/span&gt;&lt;/span&gt;&lt;br /&gt;
+         &lt;td&gt;&lt;span style="display: block; text-align: center;"&gt;&lt;span style="display: block; text-align: center;"&gt;1029/1000&lt;/span&gt;&lt;/span&gt;&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;| -3 1 -3 3 &amp;gt;&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;&lt;span style="text-align: right;"&gt;&lt;span style="display: block; text-align: right;"&gt;49.492&lt;/span&gt;&lt;/span&gt;&lt;br /&gt;
+         &lt;td&gt;&lt;span style="display: block; text-align: right;"&gt;&lt;span style="display: block; text-align: right;"&gt;49.492&lt;/span&gt;&lt;/span&gt;&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;&lt;span style="text-align: center;"&gt;&lt;span style="display: block; text-align: center;"&gt;Keega&lt;/span&gt;&lt;/span&gt;&lt;br /&gt;
+         &lt;td&gt;&lt;span style="display: block; text-align: center;"&gt;&lt;span style="display: block; text-align: center;"&gt;Keega&lt;/span&gt;&lt;/span&gt;&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;&lt;br /&gt;
@@ Line 781: / Line 781: @@
      &lt;/tr&gt;
      &lt;tr&gt;
-         &lt;td&gt;&lt;span style="text-align: center;"&gt;&lt;span style="display: block; text-align: center;"&gt;&lt;span style="color: blue;"&gt;&lt;a class="wiki_link" href="http://xenharmonic.wikispaces.com/49_48"&gt;49/48&lt;/a&gt;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;br /&gt;
+         &lt;td&gt;&lt;span style="display: block; text-align: center;"&gt;&lt;span style="color: blue; display: block; text-align: center;"&gt;&lt;a class="wiki_link" href="http://xenharmonic.wikispaces.com/49_48"&gt;49/48&lt;/a&gt;&lt;/span&gt;&lt;/span&gt;&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;| -4 -1 0 2 &amp;gt;&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;&lt;span style="text-align: right;"&gt;&lt;span style="display: block; text-align: right;"&gt;35.697&lt;/span&gt;&lt;/span&gt;&lt;br /&gt;
+         &lt;td&gt;&lt;span style="display: block; text-align: right;"&gt;&lt;span style="display: block; text-align: right;"&gt;35.697&lt;/span&gt;&lt;/span&gt;&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;&lt;span style="text-align: center;"&gt;&lt;span style="display: block; text-align: center;"&gt;Slendro Diesis&lt;/span&gt;&lt;/span&gt;&lt;br /&gt;
+         &lt;td&gt;&lt;span style="display: block; text-align: center;"&gt;&lt;span style="display: block; text-align: center;"&gt;Slendro Diesis&lt;/span&gt;&lt;/span&gt;&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;&lt;br /&gt;
@@ Line 795: / Line 795: @@
      &lt;/tr&gt;
      &lt;tr&gt;
-         &lt;td&gt;&lt;span style="text-align: center;"&gt;&lt;span style="display: block; text-align: center;"&gt;875/864&lt;/span&gt;&lt;/span&gt;&lt;br /&gt;
+         &lt;td&gt;&lt;span style="display: block; text-align: center;"&gt;&lt;span style="display: block; text-align: center;"&gt;875/864&lt;/span&gt;&lt;/span&gt;&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;| -5 -3 3 1 &amp;gt;&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;&lt;span style="text-align: right;"&gt;&lt;span style="display: block; text-align: right;"&gt;21.902&lt;/span&gt;&lt;/span&gt;&lt;br /&gt;
+         &lt;td&gt;&lt;span style="display: block; text-align: right;"&gt;&lt;span style="display: block; text-align: right;"&gt;21.902&lt;/span&gt;&lt;/span&gt;&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;&lt;span style="text-align: center;"&gt;&lt;span style="display: block; text-align: center;"&gt;Keema&lt;/span&gt;&lt;/span&gt;&lt;br /&gt;
+         &lt;td&gt;&lt;span style="display: block; text-align: center;"&gt;&lt;span style="display: block; text-align: center;"&gt;Keema&lt;/span&gt;&lt;/span&gt;&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;&lt;br /&gt;
@@ Line 809: / Line 809: @@
      &lt;/tr&gt;
      &lt;tr&gt;
-         &lt;td&gt;&lt;span style="text-align: center;"&gt;&lt;span style="display: block; text-align: center;"&gt;126/125&lt;/span&gt;&lt;/span&gt;&lt;br /&gt;
+         &lt;td&gt;&lt;span style="display: block; text-align: center;"&gt;&lt;span style="display: block; text-align: center;"&gt;126/125&lt;/span&gt;&lt;/span&gt;&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;| 1 2 -3 1 &amp;gt;&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;&lt;span style="text-align: right;"&gt;&lt;span style="display: block; text-align: right;"&gt;13.795&lt;/span&gt;&lt;/span&gt;&lt;br /&gt;
+         &lt;td&gt;&lt;span style="display: block; text-align: right;"&gt;&lt;span style="display: block; text-align: right;"&gt;13.795&lt;/span&gt;&lt;/span&gt;&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;&lt;span style="text-align: center;"&gt;&lt;span style="display: block; text-align: center;"&gt;Starling comma&lt;/span&gt;&lt;/span&gt;&lt;br /&gt;
+         &lt;td&gt;&lt;span style="display: block; text-align: center;"&gt;&lt;span style="display: block; text-align: center;"&gt;Starling comma&lt;/span&gt;&lt;/span&gt;&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;&lt;span style="text-align: center;"&gt;&lt;span style="display: block; text-align: center;"&gt;Septimal semicomma&lt;/span&gt;&lt;/span&gt;&lt;br /&gt;
+         &lt;td&gt;&lt;span style="display: block; text-align: center;"&gt;&lt;span style="display: block; text-align: center;"&gt;Septimal semicomma&lt;/span&gt;&lt;/span&gt;&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;&lt;br /&gt;
@@ Line 823: / Line 823: @@
      &lt;/tr&gt;
      &lt;tr&gt;
-         &lt;td&gt;&lt;span style="text-align: center;"&gt;&lt;span style="display: block; text-align: center;"&gt;100/99&lt;/span&gt;&lt;/span&gt;&lt;br /&gt;
+         &lt;td&gt;&lt;span style="display: block; text-align: center;"&gt;&lt;span style="display: block; text-align: center;"&gt;100/99&lt;/span&gt;&lt;/span&gt;&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;| 2 -2 2 0 -1&amp;gt;&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;&lt;span style="text-align: right;"&gt;&lt;span style="display: block; text-align: right;"&gt;17.399&lt;/span&gt;&lt;/span&gt;&lt;br /&gt;
+         &lt;td&gt;&lt;span style="display: block; text-align: right;"&gt;&lt;span style="display: block; text-align: right;"&gt;17.399&lt;/span&gt;&lt;/span&gt;&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;&lt;span style="text-align: center;"&gt;&lt;span style="display: block; text-align: center;"&gt;Ptolemisma&lt;/span&gt;&lt;/span&gt;&lt;br /&gt;
+         &lt;td&gt;&lt;span style="display: block; text-align: center;"&gt;&lt;span style="display: block; text-align: center;"&gt;Ptolemisma&lt;/span&gt;&lt;/span&gt;&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;&lt;span style="text-align: center;"&gt;&lt;span style="display: block; text-align: center;"&gt;Ptolemy's comma&lt;/span&gt;&lt;/span&gt;&lt;br /&gt;
+         &lt;td&gt;&lt;span style="display: block; text-align: center;"&gt;&lt;span style="display: block; text-align: center;"&gt;Ptolemy's comma&lt;/span&gt;&lt;/span&gt;&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;&lt;br /&gt;
@@ Line 837: / Line 837: @@
      &lt;/tr&gt;
      &lt;tr&gt;
-         &lt;td&gt;&lt;span style="text-align: center;"&gt;&lt;span style="display: block; text-align: center;"&gt;243/242&lt;/span&gt;&lt;/span&gt;&lt;br /&gt;
+         &lt;td&gt;&lt;span style="display: block; text-align: center;"&gt;&lt;span style="display: block; text-align: center;"&gt;243/242&lt;/span&gt;&lt;/span&gt;&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;| -1 5 0 0 -2 &amp;gt;&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;&lt;span style="text-align: right;"&gt;&lt;span style="display: block; text-align: right;"&gt;7.1391&lt;/span&gt;&lt;/span&gt;&lt;br /&gt;
+         &lt;td&gt;&lt;span style="display: block; text-align: right;"&gt;&lt;span style="display: block; text-align: right;"&gt;7.1391&lt;/span&gt;&lt;/span&gt;&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;&lt;span style="text-align: center;"&gt;&lt;span style="display: block; text-align: center;"&gt;Rastma&lt;/span&gt;&lt;/span&gt;&lt;br /&gt;
+         &lt;td&gt;&lt;span style="display: block; text-align: center;"&gt;&lt;span style="display: block; text-align: center;"&gt;Rastma&lt;/span&gt;&lt;/span&gt;&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;&lt;span style="text-align: center;"&gt;&lt;span style="display: block; text-align: center;"&gt;Neutral third comma&lt;/span&gt;&lt;/span&gt;&lt;br /&gt;
+         &lt;td&gt;&lt;span style="display: block; text-align: center;"&gt;&lt;span style="display: block; text-align: center;"&gt;Neutral third comma&lt;/span&gt;&lt;/span&gt;&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;&lt;br /&gt;
@@ Line 851: / Line 851: @@
      &lt;/tr&gt;
      &lt;tr&gt;
-         &lt;td&gt;&lt;span style="text-align: center;"&gt;&lt;span style="display: block; text-align: center;"&gt;385/384&lt;/span&gt;&lt;/span&gt;&lt;br /&gt;
+         &lt;td&gt;&lt;span style="display: block; text-align: center;"&gt;&lt;span style="display: block; text-align: center;"&gt;385/384&lt;/span&gt;&lt;/span&gt;&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;| -7 -1 1 1 1 &amp;gt;&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;&lt;span style="text-align: right;"&gt;&lt;span style="display: block; text-align: right;"&gt;4.5026&lt;/span&gt;&lt;/span&gt;&lt;br /&gt;
+         &lt;td&gt;&lt;span style="display: block; text-align: right;"&gt;&lt;span style="display: block; text-align: right;"&gt;4.5026&lt;/span&gt;&lt;/span&gt;&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;&lt;span style="text-align: center;"&gt;&lt;span style="display: block; text-align: center;"&gt;Keenanisma&lt;/span&gt;&lt;/span&gt;&lt;br /&gt;
+         &lt;td&gt;&lt;span style="display: block; text-align: center;"&gt;&lt;span style="display: block; text-align: center;"&gt;Keenanisma&lt;/span&gt;&lt;/span&gt;&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;&lt;br /&gt;
@@ Line 865: / Line 865: @@
      &lt;/tr&gt;
      &lt;tr&gt;
-         &lt;td&gt;&lt;span style="text-align: center;"&gt;&lt;span style="display: block; text-align: center;"&gt;91/90&lt;/span&gt;&lt;/span&gt;&lt;br /&gt;
+         &lt;td&gt;&lt;span style="display: block; text-align: center;"&gt;&lt;span style="display: block; text-align: center;"&gt;91/90&lt;/span&gt;&lt;/span&gt;&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;| -1 -2 -1 1 0 1 &amp;gt;&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;&lt;span style="text-align: right;"&gt;&lt;span style="display: block; text-align: right;"&gt;19.120&lt;/span&gt;&lt;/span&gt;&lt;br /&gt;
+         &lt;td&gt;&lt;span style="display: block; text-align: right;"&gt;&lt;span style="display: block; text-align: right;"&gt;19.120&lt;/span&gt;&lt;/span&gt;&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;&lt;span style="text-align: center;"&gt;&lt;span style="display: block; text-align: center;"&gt;Superleap&lt;/span&gt;&lt;/span&gt;&lt;br /&gt;
+         &lt;td&gt;&lt;span style="display: block; text-align: center;"&gt;&lt;span style="display: block; text-align: center;"&gt;Superleap&lt;/span&gt;&lt;/span&gt;&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;&lt;br /&gt;