41edo: Difference between revisions

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41edo is the 13th [[prime numbers|prime]] edo, following [[37edo]] and coming before [[43edo]].

=Temperaments=

=Commas=

41 EDO tempers out the following commas using its patent val, < 41 65 95 115 142 152 168 174 185 199 203 |.

||~ Name ||~ Monzo ||~ Ratio ||~ Cents ||

|| odiheim || | -1 2 -4 5 -2 > || 151263/151250 || 0.15 ||

|| harmonisma || | 3 -2 0 -1 3 -2 > || 10648/10647 || 0.16 ||

|| tridecimal schisma, Sagittal schismina || | 12 -2 -1 -1 0 -1 > || 4096/4095 || 0.42 ||

|| Lehmerisma || | -4 -3 2 -1 2 > || 3025/3024 || 0.57 ||

|| Breedsma || | -5 -1 -2 4 > || 2401/2400 || 0.72 ||

|| Eratosthenes' comma || | 6 -5 -1 0 0 0 0 1 > || 1216/1215 || 1.42 ||

|| schisma || | -15 8 1 > || 32805/32768 || 1.95 ||

|| squbema || | -3 6 0 -1 0 -1 > || 729/728 || 2.38 ||

|| septendecimal bridge comma || | -1 -1 1 -1 1 1 -1 > || 715/714 || 2.42 ||

|| Swets' comma, swetisma || | 2 3 1 -2 -1 > || 540/539 || 3.21 ||

|| undevicesimal comma, Boethius' comma || | -9 3 0 0 0 0 0 1 > || 513/512 || 3.38 ||

|| moctdel || | -2 0 3 -3 1 > || 1375/1372 || 3.78 ||

|| Beta 2, septimal schisma, garischisma || | 25 -14 0 -1 > || 4994735/4983772 || 3.80 ||

|| Werckmeister's undecimal septenarian schisma, werckisma || | -3 2 -1 2 -1 > || 441/440 || 3.93 ||

|| cuthbert || | 0 0 -1 1 2 -2 > || 847/845 || 4.09 ||

|| undecimal kleisma, keenanisma || | -7 -1 1 1 1 > || 385/384 || 4.50 ||

|| gentle comma || | 2 -1 0 1 -2 1 > || 364/363 || 4.76 ||

|| minthma || | 5 -3 0 0 1 -1 > || 352/351 || 4.93 ||

|| marveltwin || | -2 -4 2 0 0 1 > || 325/324 || 5.34 ||

|| Beta 5, Garibaldi comma, hemifamity || | 10 -6 1 -1 > || 5120/5103 || 5.76 ||

|| hemimage || | 5 -7 -1 3 > || 10976/10935 || 6.48 ||

|| septendecimal kleisma || | 8 -1 -1 0 0 0 -1 > || 256/255 || 6.78 ||

|| small BP diesis, mirkwai || | 0 3 4 -5 > || 16875/16807 || 6.99 ||

|| neutral third comma, rastma || | -1 5 0 0 -2 > || 243/242 || 7.14 ||

|| kestrel comma || | 2 3 0 -1 1 -2 > || 1188/1183 || 7.30 ||

|| septimal kleisma, marvel comma || | -5 2 2 -1 > || 225/224 || 7.71 ||

|| huntma || | 7 0 1 -2 0 -1 > || 640/637 || 8.13 ||

|| spleen comma || | 1 1 1 1 -1 0 0 -1 > || 210/209 || 8.26 ||

|| orgonisma || | 16 0 0 -2 -3 > || 65536/65219 || 8.39 ||

|| gamelan residue, gamelisma || | -10 1 0 3 > || 1029/1024 || 8.43 ||

|| septendecimal comma || | -7 7 0 0 0 0 -1 > || 2187/2176 || 8.73 ||

|| mynucuma || | 2 -1 -1 2 0 -1 > || 196/195 || 8.86 ||

|| quince || | -15 0 -2 7 > || 823543/819200 || 9.15 ||

|| undecimal semicomma, pentacircle (minthma * gentle) || | 7 -4 0 1 -1 > || 896/891 || 9.69 ||

|| 29th-partial chroma || | -4 -2 1 0 0 0 0 0 0 1 > || 145/144 || 11.98 ||

|| grossma || | 4 2 0 0 -1 -1 > || 144/143 || 12.06 ||

|| gassorma || | 0 -1 2 -1 1 -1 > || 275/273 || 12.64 ||

|| septimal semicomma, octagar || | 5 -4 3 -2 > || 4000/3969 || 13.47 ||

|| minor BP diesis, sensamagic || | 0 -5 1 2 > || 245/243 || 14.19 ||

|| secorian || | 12 -7 0 1 0 -1 > || 28672/28431 || 14.61 ||

|| mirwomo comma || | -15 3 2 2 > || 33075/32768 || 16.14 ||

|| vicesimotertial comma || | 5 -6 0 0 0 0 0 0 1 > || 736/729 || 16.54 ||

|| small tridecimal comma, animist || | -3 1 1 1 0 -1 > || 105/104 || 16.57 ||

|| hemimin || | 6 1 0 1 -3 > || 1344/1331 || 16.83 ||

|| Ptolemy's comma, ptolemisma || | 2 -2 2 0 -1 > || 100/99 || 17.40 ||

|| '41-tone' comma || | 65 -41 > || || 19.84 ||

|| tolerma || | 10 -11 2 1 > || 179200/177147 || 19.95 ||

|| major BP diesis, gariboh || | 0 -2 5 -3 > || 3125/3087 || 21.18 ||

|| cassacot || | -1 0 1 2 -2 > || 245/242 || 21.33 ||

|| keema || | -5 -3 3 1 > || 875/864 || 21.90 ||

|| blackjackisma || | -10 7 8 -7 > || 9859966/9733137 || 22.41 ||

|| roda || | 20 -17 3 > || 6122773/6032531 || 25.71 ||

|| minimal diesis, tetracot comma || | 5 -9 4 > || 20000/19683 || 27.66 ||

|| small diesis, magic comma || | -10 -1 5 > || 3125/3072 || 29.61 ||

|| thuja comma || | 15 0 1 0 -5 > || 163840/161051 || 29.72 ||

|| Ampersand's comma || | -25 7 6 > || || 31.57 ||

|| great BP diesis || | 0 -7 6 -1 > || 15625/15309 || 35.37 ||

|| shibboleth || | -5 -10 9 > || 1953125/1889568 || 57.27 ||

=Temperaments=

[[List of edo-distinct 41et rank two temperaments]]

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=Music=

[[http://soundcloud.com/cameron-bobro/eveninghorizon-cbobro|EveningHorizon]] [[http://micro.soonlabel.com/gene_ward_smith/Others/Bobro/EveningHorizon_CBobro.mp3|play]] by Cameron Bobro

[[http://soundcloud.com/cameron-bobro/eveninghorizon-cbobro|EveningHorizon]] //[[http://micro.soonlabel.com/gene_ward_smith/Others/Bobro/EveningHorizon_CBobro.mp3|play]]// by Cameron Bobro

=Links=

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<h4>Original HTML content:</h4>

<div style="width:100%; max-height:400pt; overflow:auto; background-color:#f8f9fa; border: 1px solid #eaecf0; padding:0em"><pre style="margin:0px;border:none;background:none;word-wrap:break-word;width:200%;white-space: pre-wrap ! important" class="old-revision-html"><html><head><title>41edo</title></head><body>41 Tone Equal Temperament

<a href="#Introduction">Introduction</a> | <a href="#Temperaments">Temperaments</a> | <a href="#Intervals">Intervals</a> | <a href="#Instruments">Instruments</a> | <a href="#Harmonic Scale">Harmonic Scale</a> | <a href="#Nonoctave Temperaments">Nonoctave Temperaments</a> | <a href="#Music">Music</a> | <a href="#Links">Links</a>

<a href="#Introduction">Introduction</a> | <a href="#Commas">Commas</a> | <a href="#Temperaments">Temperaments</a> | <a href="#Intervals">Intervals</a> | <a href="#Instruments">Instruments</a> | <a href="#Harmonic Scale">Harmonic Scale</a> | <a href="#Nonoctave Temperaments">Nonoctave Temperaments</a> | <a href="#Music">Music</a> | <a href="#Links">Links</a>

<h1 id="toc0"><a name="Introduction"></a>Introduction</h1>

<h1 id="toc0"><a name="Introduction"></a>Introduction</h1>

The 41-tET, 41-EDO, or 41-ET, is the scale derived by dividing the octave into 41 equally-sized steps. Each step represents a frequency ratio of 29.268 <a class="wiki_link" href="/cent">cent</a>s, an <a class="wiki_link" href="/interval">interval</a> close in size to <a class="wiki_link" href="/64_63">64/63</a>, the <a class="wiki_link" href="/Septimal%20comma">septimal comma</a>. 41-ET can be seen as a tuning of the <a class="wiki_link" href="/Schismatic%20family#Garibaldi">Garibaldi temperament</a> <a href="#cite_note-1">[1]</a> , <a href="#cite_note-2">[2]</a> , <a href="#cite_note-3">[3]</a> the <a class="wiki_link" href="/Magic%20family">Magic temperament</a> <a href="#cite_note-4">[4]</a> and the superkleismic (41&amp;26) temperament. It is the second smallest equal temperament (after <a class="wiki_link" href="/29edo">29edo</a>) whose perfect fifth is closer to just intonation than that of <a class="wiki_link" href="/12edo">12-ET</a>, and is the seventh <a class="wiki_link" href="/The%20Riemann%20Zeta%20Function%20and%20Tuning#Zeta%20EDO%20lists">zeta integral edo</a> after 31; it is not, however, a <a class="wiki_link" href="/The%20Riemann%20Zeta%20Function%20and%20Tuning#Zeta%20EDO%20lists">zeta gap edo</a>. This has to do with the fact that it can deal with the <a class="wiki_link" href="/11-limit">11-limit</a> fairly well, and the <a class="wiki_link" href="/13-limit">13-limit</a> perhaps close enough for government work, though its <a class="wiki_link" href="/13_10">13/10</a> is 14 cents sharp. Various 13-limit <a class="wiki_link" href="/magic%20extensions">magic extensions</a> are supported by 41: 13-limit magic, and less successfully necromancy and witchcraft, all merge into one in 41edo tuning. The 41f val provides a superb tuning for sorcery, giving a less-complex version of the 13-limit, and the 41ef val likewise works well for telepathy; telepathy and sorcery merging into one however not in 41edo but in 22edo.

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41edo is the 13th <a class="wiki_link" href="/prime%20numbers">prime</a> edo, following <a class="wiki_link" href="/37edo">37edo</a> and coming before <a class="wiki_link" href="/43edo">43edo</a>.

<h1 id="toc1"><a name="Temperaments"></a>Temperaments</h1>

<h1 id="toc1"><a name="Commas"></a>Commas</h1>

<a class="wiki_link" href="/List%20of%20edo-distinct%2041et%20rank%20two%20temperaments">List of edo-distinct 41et rank two temperaments</a>

41 EDO tempers out the following commas using its patent val, &lt; 41 65 95 115 142 152 168 174 185 199 203 |.

<tr>

<th>Name

</th>

<th>Monzo

</th>

<th>Ratio

</th>

<th>Cents

</th>

</tr>

<tr>

<td>odiheim

</td>

<td>| -1 2 -4 5 -2 &gt;

</td>

<td>151263/151250

</td>

<td>0.15

</td>

</tr>

<tr>

<td>harmonisma

</td>

<td>| 3 -2 0 -1 3 -2 &gt;

</td>

<td>10648/10647

</td>

<td>0.16

</td>

</tr>

<tr>

<td>tridecimal schisma, Sagittal schismina

</td>

<td>| 12 -2 -1 -1 0 -1 &gt;

</td>

<td>4096/4095

</td>

<td>0.42

</td>

</tr>

<tr>

<td>Lehmerisma

</td>

<td>| -4 -3 2 -1 2 &gt;

</td>

<td>3025/3024

</td>

<td>0.57

</td>

</tr>

<tr>

<td>Breedsma

</td>

<td>| -5 -1 -2 4 &gt;

</td>

<td>2401/2400

</td>

<td>0.72

</td>

</tr>

<tr>

<td>Eratosthenes' comma

</td>

<td>| 6 -5 -1 0 0 0 0 1 &gt;

</td>

<td>1216/1215

</td>

<td>1.42

</td>

</tr>

<tr>

<td>schisma

</td>

<td>| -15 8 1 &gt;

</td>

<td>32805/32768

</td>

<td>1.95

</td>

</tr>

<tr>

<td>squbema

</td>

<td>| -3 6 0 -1 0 -1 &gt;

</td>

<td>729/728

</td>

<td>2.38

</td>

</tr>

<tr>

<td>septendecimal bridge comma

</td>

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

</td>

<td>715/714

</td>

<td>2.42

</td>

</tr>

<tr>

<td>Swets' comma, swetisma

</td>

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

</td>

<td>540/539

</td>

<td>3.21

</td>

</tr>

<tr>

<td>undevicesimal comma, Boethius' comma

</td>

<td>| -9 3 0 0 0 0 0 1 &gt;

</td>

<td>513/512

</td>

<td>3.38

</td>

</tr>

<tr>

<td>moctdel

</td>

<td>| -2 0 3 -3 1 &gt;

</td>

<td>1375/1372

</td>

<td>3.78

</td>

</tr>

<tr>

<td>Beta 2, septimal schisma, garischisma

</td>

<td>| 25 -14 0 -1 &gt;

</td>

<td>4994735/4983772

</td>

<td>3.80

</td>

</tr>

<tr>

<td>Werckmeister's undecimal septenarian schisma, werckisma

</td>

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

</td>

<td>441/440

</td>

<td>3.93

</td>

</tr>

<tr>

<td>cuthbert

</td>

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

</td>

<td>847/845

</td>

<td>4.09

</td>

</tr>

<tr>

<td>undecimal kleisma, keenanisma

</td>

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

</td>

<td>385/384

</td>

<td>4.50

</td>

</tr>

<tr>

<td>gentle comma

</td>

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

</td>

<td>364/363

</td>

<td>4.76

</td>

</tr>

<tr>

<td>minthma

</td>

<td>| 5 -3 0 0 1 -1 &gt;

</td>

<td>352/351

</td>

<td>4.93

</td>

</tr>

<tr>

<td>marveltwin

</td>

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

</td>

<td>325/324

</td>

<td>5.34

</td>

</tr>

<tr>

<td>Beta 5, Garibaldi comma, hemifamity

</td>

<td>| 10 -6 1 -1 &gt;

</td>

<td>5120/5103

</td>

<td>5.76

</td>

</tr>

<tr>

<td>hemimage

</td>

<td>| 5 -7 -1 3 &gt;

</td>

<td>10976/10935

</td>

<td>6.48

</td>

</tr>

<tr>

<td>septendecimal kleisma

</td>

<td>| 8 -1 -1 0 0 0 -1 &gt;

</td>

<td>256/255

</td>

<td>6.78

</td>

</tr>

<tr>

<td>small BP diesis, mirkwai

</td>

<td>| 0 3 4 -5 &gt;

</td>

<td>16875/16807

</td>

<td>6.99

</td>

</tr>

<tr>

<td>neutral third comma, rastma

</td>

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

</td>

<td>243/242

</td>

<td>7.14

</td>

</tr>

<tr>

<td>kestrel comma

</td>

<td>| 2 3 0 -1 1 -2 &gt;

</td>

<td>1188/1183

</td>

<td>7.30

</td>

</tr>

<tr>

<td>septimal kleisma, marvel comma

</td>

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

</td>

<td>225/224

</td>

<td>7.71

</td>

</tr>

<tr>

<td>huntma

</td>

<td>| 7 0 1 -2 0 -1 &gt;

</td>

<td>640/637

</td>

<td>8.13

</td>

</tr>

<tr>

<td>spleen comma

</td>

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

</td>

<td>210/209

</td>

<td>8.26

</td>

</tr>

<tr>

<td>orgonisma

</td>

<td>| 16 0 0 -2 -3 &gt;

</td>

<td>65536/65219

</td>

<td>8.39

</td>

</tr>

<tr>

<td>gamelan residue, gamelisma

</td>

<td>| -10 1 0 3 &gt;

</td>

<td>1029/1024

</td>

<td>8.43

</td>

</tr>

<tr>

<td>septendecimal comma

</td>

<td>| -7 7 0 0 0 0 -1 &gt;

</td>

<td>2187/2176

</td>

<td>8.73

</td>

</tr>

<tr>

<td>mynucuma

</td>

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

</td>

<td>196/195

</td>

<td>8.86

</td>

</tr>

<tr>

<td>quince

</td>

<td>| -15 0 -2 7 &gt;

</td>

<td>823543/819200

</td>

<td>9.15

</td>

</tr>

<tr>

<td>undecimal semicomma, pentacircle (minthma * gentle)

</td>

<td>| 7 -4 0 1 -1 &gt;

</td>

<td>896/891

</td>

<td>9.69

</td>

</tr>

<tr>

<td>29th-partial chroma

</td>

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

</td>

<td>145/144

</td>

<td>11.98

</td>

</tr>

<tr>

<td>grossma

</td>

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

</td>

<td>144/143

</td>

<td>12.06

</td>

</tr>

<tr>

<td>gassorma

</td>

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

</td>

<td>275/273

</td>

<td>12.64

</td>

</tr>

<tr>

<td>septimal semicomma, octagar

</td>

<td>| 5 -4 3 -2 &gt;

</td>

<td>4000/3969

</td>

<td>13.47

</td>

</tr>

<tr>

<td>minor BP diesis, sensamagic

</td>

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

</td>

<td>245/243

</td>

<td>14.19

</td>

</tr>

<tr>

<td>secorian

</td>

<td>| 12 -7 0 1 0 -1 &gt;

</td>

<td>28672/28431

</td>

<td>14.61

</td>

</tr>

<tr>

<td>mirwomo comma

</td>

<td>| -15 3 2 2 &gt;

</td>

<td>33075/32768

</td>

<td>16.14

</td>

</tr>

<tr>

<td>vicesimotertial comma

</td>

<td>| 5 -6 0 0 0 0 0 0 1 &gt;

</td>

<td>736/729

</td>

<td>16.54

</td>

</tr>

<tr>

<td>small tridecimal comma, animist

</td>

<td>| -3 1 1 1 0 -1 &gt;

</td>

<td>105/104

</td>

<td>16.57

</td>

</tr>

<tr>

<td>hemimin

</td>

<td>| 6 1 0 1 -3 &gt;

</td>

<td>1344/1331

</td>

<td>16.83

</td>

</tr>

<tr>

<td>Ptolemy's comma, ptolemisma

</td>

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

</td>

<td>100/99

</td>

<td>17.40

</td>

</tr>

<tr>

<td>'41-tone' comma

</td>

<td>| 65 -41 &gt;

</td>

<td>

</td>

<td>19.84

</td>

</tr>

<tr>

<td>tolerma

</td>

<td>| 10 -11 2 1 &gt;

</td>

<td>179200/177147

</td>

<td>19.95

</td>

</tr>

<tr>

<td>major BP diesis, gariboh

</td>

<td>| 0 -2 5 -3 &gt;

</td>

<td>3125/3087

</td>

<td>21.18

</td>

</tr>

<tr>

<td>cassacot

</td>

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

</td>

<td>245/242

</td>

<td>21.33

</td>

</tr>

<tr>

<td>keema

</td>

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

</td>

<td>875/864

</td>

<td>21.90

</td>

</tr>

<tr>

<td>blackjackisma

</td>

<td>| -10 7 8 -7 &gt;

</td>

<td>9859966/9733137

</td>

<td>22.41

</td>

</tr>

<tr>

<td>roda

</td>

<td>| 20 -17 3 &gt;

</td>

<td>6122773/6032531

</td>

<td>25.71

</td>

</tr>

<tr>

<td>minimal diesis, tetracot comma

</td>

<td>| 5 -9 4 &gt;

</td>

<td>20000/19683

</td>

<td>27.66

</td>

</tr>

<tr>

<td>small diesis, magic comma

</td>

<td>| -10 -1 5 &gt;

</td>

<td>3125/3072

</td>

<td>29.61

</td>

</tr>

<tr>

<td>thuja comma

</td>

<td>| 15 0 1 0 -5 &gt;

</td>

<td>163840/161051

</td>

<td>29.72

</td>

</tr>

<tr>

<td>Ampersand's comma

</td>

<td>| -25 7 6 &gt;

</td>

<td>

</td>

<td>31.57

</td>

</tr>

<tr>

<td>great BP diesis

</td>

<td>| 0 -7 6 -1 &gt;

</td>

<td>15625/15309

</td>

<td>35.37

</td>

</tr>

<tr>

<td>shibboleth

</td>

<td>| -5 -10 9 &gt;

</td>

<td>1953125/1889568

</td>

<td>57.27

</td>

</tr>

</table>

<h1 id="toc2"><a name="Temperaments"></a>Temperaments</h1>

<a class="wiki_link" href="/List%20of%20edo-distinct%2041et%20rank%20two%20temperaments">List of edo-distinct 41et rank two temperaments</a>

<h1 id="~~toc2~~"><a name="Intervals"></a>Intervals</h1>

<h1 id="toc3"><a name="Intervals"></a>Intervals</h1>

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Line 1,428:

<h1 id="~~toc3~~"><a name="Instruments"></a>Instruments</h1>

<h1 id="toc4"><a name="Instruments"></a>Instruments</h1>

<img src="/file/view/Ron_Sword_with_a_41ET_Guitar.jpg/221056094/Ron_Sword_with_a_41ET_Guitar.jpg" alt="Ron_Sword_with_a_41ET_Guitar.jpg" title="Ron_Sword_with_a_41ET_Guitar.jpg" />

<img src="/file/view/Ron_Sword_with_a_41ET_Guitar.jpg/221056094/Ron_Sword_with_a_41ET_Guitar.jpg" alt="Ron_Sword_with_a_41ET_Guitar.jpg" title="Ron_Sword_with_a_41ET_Guitar.jpg" />

41-EDO Classical guitar, by Ron Sword.

A possible system to tune keyboards in 41EDO is discussed in <a class="wiki_link_ext" href="http://launch.groups.yahoo.com/group/tuning/message/74155" rel="nofollow">http://launch.groups.yahoo.com/group/tuning/message/74155</a>.

<h1 id="~~toc4~~"><a name="Harmonic Scale"></a>Harmonic Scale</h1>

<h1 id="toc5"><a name="Harmonic Scale"></a>Harmonic Scale</h1>

41edo is the first edo to do some justice to Mode 8 of the <a class="wiki_link" href="/OverToneSeries">harmonic series</a>, which Dante Rosati calls the &quot;<a class="wiki_link" href="/overtone%20scales">Diatonic Harmonic Series Scale</a>,&quot; consisting of overtones 8 through 16 (sometimes made to repeat at the octave).

Line 902:

Line 1,562:

The scale in 41, as adjacent steps, thus goes: 7 6 6 5 5 4 4 4.

<h1 id="~~toc5~~"><a name="Nonoctave Temperaments"></a>Nonoctave Temperaments</h1>

<h1 id="toc6"><a name="Nonoctave Temperaments"></a>Nonoctave Temperaments</h1>

Taking every third degree of 41edo produces a scale extremely close to <a class="wiki_link" href="/88cET">88cET</a> or 88-cent equal temperament (or the 8th root of 3:2). Likewise, taking every fifth degree produces a scale very close to the equal-tempered <a class="wiki_link" href="/BP">Bohlen-Pierce</a><a class="wiki_link" href="/BP"> Scale</a> (or the 13th root of 3). See chart:

Line 1,856:

Line 2,516:

<h1 id="~~toc6~~"><a name="Music"></a>Music</h1>

<h1 id="toc7"><a name="Music"></a>Music</h1>

<a class="wiki_link_ext" href="http://soundcloud.com/cameron-bobro/eveninghorizon-cbobro" rel="nofollow">EveningHorizon</a> <a class="wiki_link_ext" href="http://micro.soonlabel.com/gene_ward_smith/Others/Bobro/EveningHorizon_CBobro.mp3" rel="nofollow">play</a> by Cameron Bobro

<a class="wiki_link_ext" href="http://soundcloud.com/cameron-bobro/eveninghorizon-cbobro" rel="nofollow">EveningHorizon</a> <a class="wiki_link_ext" href="http://micro.soonlabel.com/gene_ward_smith/Others/Bobro/EveningHorizon_CBobro.mp3" rel="nofollow">play</a> by Cameron Bobro

<h1 id="~~toc7~~"><a name="Links"></a>Links</h1>

<h1 id="toc8"><a name="Links"></a>Links</h1>

<ul><li><a class="wiki_link_ext" href="http://en.wikipedia.org/wiki/41_equal_temperament" rel="nofollow">Wikipedia article on 41edo</a></li><li><a class="wiki_link" href="/Magic22%20as%20srutis#magic22assrutis">Magic22 as srutis</a> describes a possible use of 41edo for <a class="wiki_link" href="/indian">indian</a> music.</li><li>see also <a class="wiki_link" href="/Magic%20family">Magic family</a></li><li>Sword, Ron.<a class="wiki_link_ext" href="http://www.ronsword.com" rel="nofollow" target="_blank"> &quot;Tetracontamonophonic Scales for Guitar&quot;</a></li></ul><hr class="references" /><ol class="references">

<ul><li><a class="wiki_link_ext" href="http://en.wikipedia.org/wiki/41_equal_temperament" rel="nofollow">Wikipedia article on 41edo</a></li><li><a class="wiki_link" href="/Magic22%20as%20srutis#magic22assrutis">Magic22 as srutis</a> describes a possible use of 41edo for <a class="wiki_link" href="/indian">indian</a> music.</li><li>see also <a class="wiki_link" href="/Magic%20family">Magic family</a></li><li>Sword, Ron.<a class="wiki_link_ext" href="http://www.ronsword.com" rel="nofollow" target="_blank"> &quot;Tetracontamonophonic Scales for Guitar&quot;</a></li></ul><hr class="references" /><ol class="references">

<li id="cite_note-1"><a href="#cite_ref-1">^</a> <a class="wiki_link_ext" href="http://x31eq.com/schismic.htm" rel="nofollow">&quot;Schismic Temperaments&quot;</a> at x31eq.com the websize of <a class="wiki_link" href="/Graham%20Breed">Graham Breed</a></li>

<li id="cite_note-2"><a href="#cite_ref-2">^</a> <a class="wiki_link_ext" href="http://x31eq.com/decimal_lattice.htm" rel="nofollow">&quot;Lattices with Decimal Notation&quot;</a> at x31eq.com</li>

<li id="cite_note-3"><a href="#cite_ref-3">^</a> <a class="wiki_link_ext" href="http://en.wikipedia.org/wiki/Schismatic_temperament" rel="nofollow">Schismatic temperament</a></li>

<li id="cite_note-4"><a href="#cite_ref-4">^</a> <a class="wiki_link_ext" href="http://en.wikipedia.org/wiki/Magic_temperament" rel="nofollow">Magic temperament</a></li>

</ol></body></html></pre></div>

</ol></body></html></pre></div>

@@ 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:genewardsmith|genewardsmith]] and made on <tt>2012-11-17 09:49:57 UTC</tt>.<br>
+: This revision was by author [[User:jdfreivald|jdfreivald]] and made on <tt>2013-01-04 12:39:32 UTC</tt>.<br>
-: The original revision id was <tt>383534998</tt>.<br>
+: The original revision id was <tt>395842790</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 15: / Line 15: @@
 edo is the 13th [[prime numbers|prime]] edo, following [[37edo]] and coming before [[43edo]].
-=Temperaments=
+=Commas=
+EDO tempers out the following commas using its patent val, &lt; 41 65 95 115 142 152 168 174 185 199 203 |.
+||~ Name ||~ Monzo ||~ Ratio ||~ Cents ||
+|| odiheim || | -1 2 -4 5 -2 &gt; || 151263/151250 || 0.15 ||
+|| harmonisma || | 3 -2 0 -1 3 -2 &gt; || 10648/10647 || 0.16 ||
+|| tridecimal schisma, Sagittal schismina || | 12 -2 -1 -1 0 -1 &gt; || 4096/4095 || 0.42 ||
+|| Lehmerisma || | -4 -3 2 -1 2 &gt; || 3025/3024 || 0.57 ||
+|| Breedsma || | -5 -1 -2 4 &gt; || 2401/2400 || 0.72 ||
+|| Eratosthenes' comma || | 6 -5 -1 0 0 0 0 1 &gt; || 1216/1215 || 1.42 ||
+|| schisma || | -15 8 1 &gt; || 32805/32768 || 1.95 ||
+|| squbema || | -3 6 0 -1 0 -1 &gt; || 729/728 || 2.38 ||
+|| septendecimal bridge comma || | -1 -1 1 -1 1 1 -1 &gt; || 715/714 || 2.42 ||
+|| Swets' comma, swetisma || | 2 3 1 -2 -1 &gt; || 540/539 || 3.21 ||
+|| undevicesimal comma, Boethius' comma || | -9 3 0 0 0 0 0 1 &gt; || 513/512 || 3.38 ||
+|| moctdel || | -2 0 3 -3 1 &gt; || 1375/1372 || 3.78 ||
+|| Beta 2, septimal schisma, garischisma || | 25 -14 0 -1 &gt; || 4994735/4983772 || 3.80 ||
+|| Werckmeister's undecimal septenarian schisma, werckisma || | -3 2 -1 2 -1 &gt; || 441/440 || 3.93 ||
+|| cuthbert || | 0 0 -1 1 2 -2 &gt; || 847/845 || 4.09 ||
+|| undecimal kleisma, keenanisma || | -7 -1 1 1 1 &gt; || 385/384 || 4.50 ||
+|| gentle comma || | 2 -1 0 1 -2 1 &gt; || 364/363 || 4.76 ||
+|| minthma || | 5 -3 0 0 1 -1 &gt; || 352/351 || 4.93 ||
+|| marveltwin || | -2 -4 2 0 0 1 &gt; || 325/324 || 5.34 ||
+|| Beta 5, Garibaldi comma, hemifamity || | 10 -6 1 -1 &gt; || 5120/5103 || 5.76 ||
+|| hemimage || | 5 -7 -1 3 &gt; || 10976/10935 || 6.48 ||
+|| septendecimal kleisma || | 8 -1 -1 0 0 0 -1 &gt; || 256/255 || 6.78 ||
+|| small BP diesis, mirkwai || | 0 3 4 -5 &gt; || 16875/16807 || 6.99 ||
+|| neutral third comma, rastma || | -1 5 0 0 -2 &gt; || 243/242 || 7.14 ||
+|| kestrel comma || | 2 3 0 -1 1 -2 &gt; || 1188/1183 || 7.30 ||
+|| septimal kleisma, marvel comma || | -5 2 2 -1 &gt; || 225/224 || 7.71 ||
+|| huntma || | 7 0 1 -2 0 -1 &gt; || 640/637 || 8.13 ||
+|| spleen comma || | 1 1 1 1 -1 0 0 -1 &gt; || 210/209 || 8.26 ||
+|| orgonisma || | 16 0 0 -2 -3 &gt; || 65536/65219 || 8.39 ||
+|| gamelan residue, gamelisma || | -10 1 0 3 &gt; || 1029/1024 || 8.43 ||
+|| septendecimal comma || | -7 7 0 0 0 0 -1 &gt; || 2187/2176 || 8.73 ||
+|| mynucuma || | 2 -1 -1 2 0 -1 &gt; || 196/195 || 8.86 ||
+|| quince || | -15 0 -2 7 &gt; || 823543/819200 || 9.15 ||
+|| undecimal semicomma, pentacircle (minthma * gentle) || | 7 -4 0 1 -1 &gt; || 896/891 || 9.69 ||
+|| 29th-partial chroma || | -4 -2 1 0 0 0 0 0 0 1 &gt; || 145/144 || 11.98 ||
+|| grossma || | 4 2 0 0 -1 -1 &gt; || 144/143 || 12.06 ||
+|| gassorma || | 0 -1 2 -1 1 -1 &gt; || 275/273 || 12.64 ||
+|| septimal semicomma, octagar || | 5 -4 3 -2 &gt; || 4000/3969 || 13.47 ||
+|| minor BP diesis, sensamagic || | 0 -5 1 2 &gt; || 245/243 || 14.19 ||
+|| secorian || | 12 -7 0 1 0 -1 &gt; || 28672/28431 || 14.61 ||
+|| mirwomo comma || | -15 3 2 2 &gt; || 33075/32768 || 16.14 ||
+|| vicesimotertial comma || | 5 -6 0 0 0 0 0 0 1 &gt; || 736/729 || 16.54 ||
+|| small tridecimal comma, animist || | -3 1 1 1 0 -1 &gt; || 105/104 || 16.57 ||
+|| hemimin || | 6 1 0 1 -3 &gt; || 1344/1331 || 16.83 ||
+|| Ptolemy's comma, ptolemisma || | 2 -2 2 0 -1 &gt; || 100/99 || 17.40 ||
+|| '41-tone' comma || | 65 -41 &gt; ||   || 19.84 ||
+|| tolerma || | 10 -11 2 1 &gt; || 179200/177147 || 19.95 ||
+|| major BP diesis, gariboh || | 0 -2 5 -3 &gt; || 3125/3087 || 21.18 ||
+|| cassacot || | -1 0 1 2 -2 &gt; || 245/242 || 21.33 ||
+|| keema || | -5 -3 3 1 &gt; || 875/864 || 21.90 ||
+|| blackjackisma || | -10 7 8 -7 &gt; || 9859966/9733137 || 22.41 ||
+|| roda || | 20 -17 3 &gt; || 6122773/6032531 || 25.71 ||
+|| minimal diesis, tetracot comma || | 5 -9 4 &gt; || 20000/19683 || 27.66 ||
+|| small diesis, magic comma || | -10 -1 5 &gt; || 3125/3072 || 29.61 ||
+|| thuja comma || | 15 0 1 0 -5 &gt; || 163840/161051 || 29.72 ||
+|| Ampersand's comma || | -25 7 6 &gt; ||   || 31.57 ||
+|| great BP diesis || | 0 -7 6 -1 &gt; || 15625/15309 || 35.37 ||
+|| shibboleth || | -5 -10 9 &gt; || 1953125/1889568 || 57.27 ||
+=Temperaments=
 [[List of edo-distinct 41et rank two temperaments]]
@@ Line 153: / Line 215: @@
 =Music=
-[[http://soundcloud.com/cameron-bobro/eveninghorizon-cbobro|EveningHorizon]] [[http://micro.soonlabel.com/gene_ward_smith/Others/Bobro/EveningHorizon_CBobro.mp3|play]] by Cameron Bobro
+[[http://soundcloud.com/cameron-bobro/eveninghorizon-cbobro|EveningHorizon]] //[[http://micro.soonlabel.com/gene_ward_smith/Others/Bobro/EveningHorizon_CBobro.mp3|play]]// by Cameron Bobro
 =Links=
@@ Line 162: / Line 224: @@
 <h4>Original HTML content:</h4>
 <div style="width:100%; max-height:400pt; overflow:auto; background-color:#f8f9fa; border: 1px solid #eaecf0; padding:0em"><pre style="margin:0px;border:none;background:none;word-wrap:break-word;width:200%;white-space: pre-wrap ! important" class="old-revision-html">&lt;html&gt;&lt;head&gt;&lt;title&gt;41edo&lt;/title&gt;&lt;/head&gt;&lt;body&gt;&lt;span style="color: #004d25; font-family: 'Times New Roman',Times,serif; font-size: 20px;"&gt;&lt;strong&gt;41 Tone Equal Temperament&lt;/strong&gt;&lt;/span&gt;&lt;br /&gt;
-&lt;!-- ws:start:WikiTextTocRule:25:&amp;lt;img id=&amp;quot;wikitext@@toc@@flat&amp;quot; class=&amp;quot;WikiMedia WikiMediaTocFlat&amp;quot; title=&amp;quot;Table of Contents&amp;quot; src=&amp;quot;/site/embedthumbnail/toc/flat?w=100&amp;amp;h=16&amp;quot;/&amp;gt; --&gt;&lt;!-- ws:end:WikiTextTocRule:25 --&gt;&lt;!-- ws:start:WikiTextTocRule:26: --&gt;&lt;a href="#Introduction"&gt;Introduction&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:26 --&gt;&lt;!-- ws:start:WikiTextTocRule:27: --&gt; | &lt;a href="#Temperaments"&gt;Temperaments&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:27 --&gt;&lt;!-- ws:start:WikiTextTocRule:28: --&gt; | &lt;a href="#Intervals"&gt;Intervals&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:28 --&gt;&lt;!-- ws:start:WikiTextTocRule:29: --&gt; | &lt;a href="#Instruments"&gt;Instruments&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:29 --&gt;&lt;!-- ws:start:WikiTextTocRule:30: --&gt; | &lt;a href="#Harmonic Scale"&gt;Harmonic Scale&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:30 --&gt;&lt;!-- ws:start:WikiTextTocRule:31: --&gt; | &lt;a href="#Nonoctave Temperaments"&gt;Nonoctave Temperaments&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:31 --&gt;&lt;!-- ws:start:WikiTextTocRule:32: --&gt; | &lt;a href="#Music"&gt;Music&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:32 --&gt;&lt;!-- ws:start:WikiTextTocRule:33: --&gt; | &lt;a href="#Links"&gt;Links&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:33 --&gt;&lt;!-- ws:start:WikiTextTocRule:34: --&gt;
+&lt;!-- ws:start:WikiTextTocRule:27:&amp;lt;img id=&amp;quot;wikitext@@toc@@flat&amp;quot; class=&amp;quot;WikiMedia WikiMediaTocFlat&amp;quot; title=&amp;quot;Table of Contents&amp;quot; src=&amp;quot;/site/embedthumbnail/toc/flat?w=100&amp;amp;h=16&amp;quot;/&amp;gt; --&gt;&lt;!-- ws:end:WikiTextTocRule:27 --&gt;&lt;!-- ws:start:WikiTextTocRule:28: --&gt;&lt;a href="#Introduction"&gt;Introduction&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:28 --&gt;&lt;!-- ws:start:WikiTextTocRule:29: --&gt; | &lt;a href="#Commas"&gt;Commas&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:29 --&gt;&lt;!-- ws:start:WikiTextTocRule:30: --&gt; | &lt;a href="#Temperaments"&gt;Temperaments&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:30 --&gt;&lt;!-- ws:start:WikiTextTocRule:31: --&gt; | &lt;a href="#Intervals"&gt;Intervals&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:31 --&gt;&lt;!-- ws:start:WikiTextTocRule:32: --&gt; | &lt;a href="#Instruments"&gt;Instruments&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:32 --&gt;&lt;!-- ws:start:WikiTextTocRule:33: --&gt; | &lt;a href="#Harmonic Scale"&gt;Harmonic Scale&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:33 --&gt;&lt;!-- ws:start:WikiTextTocRule:34: --&gt; | &lt;a href="#Nonoctave Temperaments"&gt;Nonoctave Temperaments&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:34 --&gt;&lt;!-- ws:start:WikiTextTocRule:35: --&gt; | &lt;a href="#Music"&gt;Music&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:35 --&gt;&lt;!-- ws:start:WikiTextTocRule:36: --&gt; | &lt;a href="#Links"&gt;Links&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:36 --&gt;&lt;!-- ws:start:WikiTextTocRule:37: --&gt;
-&lt;!-- ws:end:WikiTextTocRule:34 --&gt;&lt;!-- ws:start:WikiTextHeadingRule:9:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc0"&gt;&lt;a name="Introduction"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:9 --&gt;Introduction&lt;/h1&gt;
+&lt;!-- ws:end:WikiTextTocRule:37 --&gt;&lt;!-- ws:start:WikiTextHeadingRule:9:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc0"&gt;&lt;a name="Introduction"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:9 --&gt;Introduction&lt;/h1&gt;
   The 41-tET, 41-EDO, or 41-ET, is the scale derived by dividing the octave into 41 equally-sized steps. Each step represents a frequency ratio of 29.268 &lt;a class="wiki_link" href="/cent"&gt;cent&lt;/a&gt;s, an &lt;a class="wiki_link" href="/interval"&gt;interval&lt;/a&gt; close in size to &lt;a class="wiki_link" href="/64_63"&gt;64/63&lt;/a&gt;, the &lt;a class="wiki_link" href="/Septimal%20comma"&gt;septimal comma&lt;/a&gt;. 41-ET can be seen as a tuning of the &lt;em&gt;&lt;a class="wiki_link" href="/Schismatic%20family#Garibaldi"&gt;Garibaldi temperament&lt;/a&gt;&lt;/em&gt; &lt;!-- ws:start:WikiTextRefRule:2:&amp;amp;lt;ref&amp;amp;gt;&amp;lt;a class=&amp;quot;wiki_link_ext&amp;quot; href=&amp;quot;http://x31eq.com/schismic.htm&amp;quot; rel=&amp;quot;nofollow&amp;quot;&amp;gt;&amp;amp;quot;Schismic Temperaments&amp;amp;quot;&amp;lt;/a&amp;gt; at x31eq.com the websize of &amp;lt;a class=&amp;quot;wiki_link&amp;quot; href=&amp;quot;/Graham%20Breed&amp;quot;&amp;gt;Graham Breed&amp;lt;/a&amp;gt;&amp;amp;lt;/ref&amp;amp;gt; --&gt;&lt;sup id="cite_ref-1" class="reference"&gt;&lt;a href="#cite_note-1"&gt;[1]&lt;/a&gt;&lt;/sup&gt;&lt;!-- ws:end:WikiTextRefRule:2 --&gt; , &lt;!-- ws:start:WikiTextRefRule:4:&amp;amp;lt;ref&amp;amp;gt;&amp;lt;a class=&amp;quot;wiki_link_ext&amp;quot; href=&amp;quot;http://x31eq.com/decimal_lattice.htm&amp;quot; rel=&amp;quot;nofollow&amp;quot;&amp;gt;&amp;amp;quot;Lattices with Decimal Notation&amp;amp;quot;&amp;lt;/a&amp;gt; at x31eq.com&amp;amp;lt;/ref&amp;amp;gt; --&gt;&lt;sup id="cite_ref-2" class="reference"&gt;&lt;a href="#cite_note-2"&gt;[2]&lt;/a&gt;&lt;/sup&gt;&lt;!-- ws:end:WikiTextRefRule:4 --&gt; , &lt;!-- ws:start:WikiTextRefRule:6:&amp;amp;lt;ref&amp;amp;gt;&amp;lt;a class=&amp;quot;wiki_link_ext&amp;quot; href=&amp;quot;http://en.wikipedia.org/wiki/Schismatic_temperament&amp;quot; rel=&amp;quot;nofollow&amp;quot;&amp;gt;Schismatic temperament&amp;lt;/a&amp;gt;&amp;amp;lt;/ref&amp;amp;gt; --&gt;&lt;sup id="cite_ref-3" class="reference"&gt;&lt;a href="#cite_note-3"&gt;[3]&lt;/a&gt;&lt;/sup&gt;&lt;!-- ws:end:WikiTextRefRule:6 --&gt; the &lt;em&gt;&lt;a class="wiki_link" href="/Magic%20family"&gt;Magic temperament&lt;/a&gt;&lt;/em&gt; &lt;!-- ws:start:WikiTextRefRule:8:&amp;amp;lt;ref&amp;amp;gt;&amp;lt;a class=&amp;quot;wiki_link_ext&amp;quot; href=&amp;quot;http://en.wikipedia.org/wiki/Magic_temperament&amp;quot; rel=&amp;quot;nofollow&amp;quot;&amp;gt;Magic temperament&amp;lt;/a&amp;gt;&amp;amp;lt;/ref&amp;amp;gt; --&gt;&lt;sup id="cite_ref-4" class="reference"&gt;&lt;a href="#cite_note-4"&gt;[4]&lt;/a&gt;&lt;/sup&gt;&lt;!-- ws:end:WikiTextRefRule:8 --&gt; and the superkleismic (41&amp;amp;26) temperament. It is the second smallest equal temperament (after &lt;a class="wiki_link" href="/29edo"&gt;29edo&lt;/a&gt;) whose perfect fifth is closer to just intonation than that of &lt;a class="wiki_link" href="/12edo"&gt;12-ET&lt;/a&gt;, and is the seventh &lt;a class="wiki_link" href="/The%20Riemann%20Zeta%20Function%20and%20Tuning#Zeta%20EDO%20lists"&gt;zeta integral edo&lt;/a&gt; after 31; it is not, however, a &lt;a class="wiki_link" href="/The%20Riemann%20Zeta%20Function%20and%20Tuning#Zeta%20EDO%20lists"&gt;zeta gap edo&lt;/a&gt;. This has to do with the fact that it can deal with the &lt;a class="wiki_link" href="/11-limit"&gt;11-limit&lt;/a&gt; fairly well, and the &lt;a class="wiki_link" href="/13-limit"&gt;13-limit&lt;/a&gt; perhaps close enough for government work, though its &lt;a class="wiki_link" href="/13_10"&gt;13/10&lt;/a&gt; is 14 cents sharp. Various 13-limit &lt;a class="wiki_link" href="/magic%20extensions"&gt;magic extensions&lt;/a&gt; are supported by 41: 13-limit magic, and less successfully necromancy and witchcraft, all merge into one in 41edo tuning. The 41f val provides a superb tuning for sorcery, giving a less-complex version of the 13-limit, and the 41ef val likewise works well for telepathy; telepathy and sorcery merging into one however not in 41edo but in 22edo.&lt;br /&gt;
 &lt;br /&gt;
@@ Line 170: / Line 232: @@
 edo is the 13th &lt;a class="wiki_link" href="/prime%20numbers"&gt;prime&lt;/a&gt; edo, following &lt;a class="wiki_link" href="/37edo"&gt;37edo&lt;/a&gt; and coming before &lt;a class="wiki_link" href="/43edo"&gt;43edo&lt;/a&gt;.&lt;br /&gt;
 &lt;br /&gt;
-&lt;!-- ws:start:WikiTextHeadingRule:11:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc1"&gt;&lt;a name="Temperaments"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:11 --&gt;Temperaments&lt;/h1&gt;
+&lt;!-- ws:start:WikiTextHeadingRule:11:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc1"&gt;&lt;a name="Commas"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:11 --&gt;Commas&lt;/h1&gt;
-&lt;a class="wiki_link" href="/List%20of%20edo-distinct%2041et%20rank%20two%20temperaments"&gt;List of edo-distinct 41et rank two temperaments&lt;/a&gt;&lt;br /&gt;
+EDO tempers out the following commas using its patent val, &amp;lt; 41 65 95 115 142 152 168 174 185 199 203 |.&lt;br /&gt;
+&lt;table class="wiki_table"&gt;
+    &lt;tr&gt;
+        &lt;th&gt;Name&lt;br /&gt;
+&lt;/th&gt;
+        &lt;th&gt;Monzo&lt;br /&gt;
+&lt;/th&gt;
+        &lt;th&gt;Ratio&lt;br /&gt;
+&lt;/th&gt;
+        &lt;th&gt;Cents&lt;br /&gt;
+&lt;/th&gt;
+    &lt;/tr&gt;
+    &lt;tr&gt;
+        &lt;td&gt;odiheim&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;| -1 2 -4 5 -2 &amp;gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;151263/151250&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;0.15&lt;br /&gt;
+&lt;/td&gt;
+    &lt;/tr&gt;
+    &lt;tr&gt;
+        &lt;td&gt;harmonisma&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;| 3 -2 0 -1 3 -2 &amp;gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;10648/10647&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;0.16&lt;br /&gt;
+&lt;/td&gt;
+    &lt;/tr&gt;
+    &lt;tr&gt;
+        &lt;td&gt;tridecimal schisma, Sagittal schismina&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;| 12 -2 -1 -1 0 -1 &amp;gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;4096/4095&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;0.42&lt;br /&gt;
+&lt;/td&gt;
+    &lt;/tr&gt;
+    &lt;tr&gt;
+        &lt;td&gt;Lehmerisma&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;| -4 -3 2 -1 2 &amp;gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;3025/3024&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;0.57&lt;br /&gt;
+&lt;/td&gt;
+    &lt;/tr&gt;
+    &lt;tr&gt;
+        &lt;td&gt;Breedsma&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;| -5 -1 -2 4 &amp;gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;2401/2400&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;0.72&lt;br /&gt;
+&lt;/td&gt;
+    &lt;/tr&gt;
+    &lt;tr&gt;
+        &lt;td&gt;Eratosthenes' comma&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;| 6 -5 -1 0 0 0 0 1 &amp;gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;1216/1215&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;1.42&lt;br /&gt;
+&lt;/td&gt;
+    &lt;/tr&gt;
+    &lt;tr&gt;
+        &lt;td&gt;schisma&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;| -15 8 1 &amp;gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;32805/32768&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;1.95&lt;br /&gt;
+&lt;/td&gt;
+    &lt;/tr&gt;
+    &lt;tr&gt;
+        &lt;td&gt;squbema&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;| -3 6 0 -1 0 -1 &amp;gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;729/728&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;2.38&lt;br /&gt;
+&lt;/td&gt;
+    &lt;/tr&gt;
+    &lt;tr&gt;
+        &lt;td&gt;septendecimal bridge comma&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;| -1 -1 1 -1 1 1 -1 &amp;gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;715/714&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;2.42&lt;br /&gt;
+&lt;/td&gt;
+    &lt;/tr&gt;
+    &lt;tr&gt;
+        &lt;td&gt;Swets' comma, swetisma&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;| 2 3 1 -2 -1 &amp;gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;540/539&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;3.21&lt;br /&gt;
+&lt;/td&gt;
+    &lt;/tr&gt;
+    &lt;tr&gt;
+        &lt;td&gt;undevicesimal comma, Boethius' comma&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;| -9 3 0 0 0 0 0 1 &amp;gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;513/512&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;3.38&lt;br /&gt;
+&lt;/td&gt;
+    &lt;/tr&gt;
+    &lt;tr&gt;
+        &lt;td&gt;moctdel&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;| -2 0 3 -3 1 &amp;gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;1375/1372&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;3.78&lt;br /&gt;
+&lt;/td&gt;
+    &lt;/tr&gt;
+    &lt;tr&gt;
+        &lt;td&gt;Beta 2, septimal schisma, garischisma&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;| 25 -14 0 -1 &amp;gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;4994735/4983772&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;3.80&lt;br /&gt;
+&lt;/td&gt;
+    &lt;/tr&gt;
+    &lt;tr&gt;
+        &lt;td&gt;Werckmeister's undecimal septenarian schisma, werckisma&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;| -3 2 -1 2 -1 &amp;gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;441/440&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;3.93&lt;br /&gt;
+&lt;/td&gt;
+    &lt;/tr&gt;
+    &lt;tr&gt;
+        &lt;td&gt;cuthbert&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;| 0 0 -1 1 2 -2 &amp;gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;847/845&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;4.09&lt;br /&gt;
+&lt;/td&gt;
+    &lt;/tr&gt;
+    &lt;tr&gt;
+        &lt;td&gt;undecimal kleisma, keenanisma&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;385/384&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;4.50&lt;br /&gt;
+&lt;/td&gt;
+    &lt;/tr&gt;
+    &lt;tr&gt;
+        &lt;td&gt;gentle comma&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;| 2 -1 0 1 -2 1 &amp;gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;364/363&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;4.76&lt;br /&gt;
+&lt;/td&gt;
+    &lt;/tr&gt;
+    &lt;tr&gt;
+        &lt;td&gt;minthma&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;| 5 -3 0 0 1 -1 &amp;gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;352/351&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;4.93&lt;br /&gt;
+&lt;/td&gt;
+    &lt;/tr&gt;
+    &lt;tr&gt;
+        &lt;td&gt;marveltwin&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;| -2 -4 2 0 0 1 &amp;gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;325/324&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;5.34&lt;br /&gt;
+&lt;/td&gt;
+    &lt;/tr&gt;
+    &lt;tr&gt;
+        &lt;td&gt;Beta 5, Garibaldi comma, hemifamity&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;| 10 -6 1 -1 &amp;gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;5120/5103&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;5.76&lt;br /&gt;
+&lt;/td&gt;
+    &lt;/tr&gt;
+    &lt;tr&gt;
+        &lt;td&gt;hemimage&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;| 5 -7 -1 3 &amp;gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;10976/10935&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;6.48&lt;br /&gt;
+&lt;/td&gt;
+    &lt;/tr&gt;
+    &lt;tr&gt;
+        &lt;td&gt;septendecimal kleisma&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;| 8 -1 -1 0 0 0 -1 &amp;gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;256/255&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;6.78&lt;br /&gt;
+&lt;/td&gt;
+    &lt;/tr&gt;
+    &lt;tr&gt;
+        &lt;td&gt;small BP diesis, mirkwai&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;| 0 3 4 -5 &amp;gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;16875/16807&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;6.99&lt;br /&gt;
+&lt;/td&gt;
+    &lt;/tr&gt;
+    &lt;tr&gt;
+        &lt;td&gt;neutral third comma, rastma&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;243/242&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;7.14&lt;br /&gt;
+&lt;/td&gt;
+    &lt;/tr&gt;
+    &lt;tr&gt;
+        &lt;td&gt;kestrel comma&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;| 2 3 0 -1 1 -2 &amp;gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;1188/1183&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;7.30&lt;br /&gt;
+&lt;/td&gt;
+    &lt;/tr&gt;
+    &lt;tr&gt;
+        &lt;td&gt;septimal kleisma, marvel comma&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;| -5 2 2 -1 &amp;gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;225/224&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;7.71&lt;br /&gt;
+&lt;/td&gt;
+    &lt;/tr&gt;
+    &lt;tr&gt;
+        &lt;td&gt;huntma&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;| 7 0 1 -2 0 -1 &amp;gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;640/637&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;8.13&lt;br /&gt;
+&lt;/td&gt;
+    &lt;/tr&gt;
+    &lt;tr&gt;
+        &lt;td&gt;spleen comma&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;| 1 1 1 1 -1 0 0 -1 &amp;gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;210/209&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;8.26&lt;br /&gt;
+&lt;/td&gt;
+    &lt;/tr&gt;
+    &lt;tr&gt;
+        &lt;td&gt;orgonisma&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;| 16 0 0 -2 -3 &amp;gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;65536/65219&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;8.39&lt;br /&gt;
+&lt;/td&gt;
+    &lt;/tr&gt;
+    &lt;tr&gt;
+        &lt;td&gt;gamelan residue, gamelisma&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;| -10 1 0 3 &amp;gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;1029/1024&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;8.43&lt;br /&gt;
+&lt;/td&gt;
+    &lt;/tr&gt;
+    &lt;tr&gt;
+        &lt;td&gt;septendecimal comma&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;| -7 7 0 0 0 0 -1 &amp;gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;2187/2176&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;8.73&lt;br /&gt;
+&lt;/td&gt;
+    &lt;/tr&gt;
+    &lt;tr&gt;
+        &lt;td&gt;mynucuma&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;| 2 -1 -1 2 0 -1 &amp;gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;196/195&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;8.86&lt;br /&gt;
+&lt;/td&gt;
+    &lt;/tr&gt;
+    &lt;tr&gt;
+        &lt;td&gt;quince&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;| -15 0 -2 7 &amp;gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;823543/819200&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;9.15&lt;br /&gt;
+&lt;/td&gt;
+    &lt;/tr&gt;
+    &lt;tr&gt;
+        &lt;td&gt;undecimal semicomma, pentacircle (minthma * gentle)&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;| 7 -4 0 1 -1 &amp;gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;896/891&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;9.69&lt;br /&gt;
+&lt;/td&gt;
+    &lt;/tr&gt;
+    &lt;tr&gt;
+        &lt;td&gt;29th-partial chroma&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;| -4 -2 1 0 0 0 0 0 0 1 &amp;gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;145/144&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;11.98&lt;br /&gt;
+&lt;/td&gt;
+    &lt;/tr&gt;
+    &lt;tr&gt;
+        &lt;td&gt;grossma&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;| 4 2 0 0 -1 -1 &amp;gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;144/143&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;12.06&lt;br /&gt;
+&lt;/td&gt;
+    &lt;/tr&gt;
+    &lt;tr&gt;
+        &lt;td&gt;gassorma&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;| 0 -1 2 -1 1 -1 &amp;gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;275/273&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;12.64&lt;br /&gt;
+&lt;/td&gt;
+    &lt;/tr&gt;
+    &lt;tr&gt;
+        &lt;td&gt;septimal semicomma, octagar&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;| 5 -4 3 -2 &amp;gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;4000/3969&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;13.47&lt;br /&gt;
+&lt;/td&gt;
+    &lt;/tr&gt;
+    &lt;tr&gt;
+        &lt;td&gt;minor BP diesis, sensamagic&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;| 0 -5 1 2 &amp;gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;245/243&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;14.19&lt;br /&gt;
+&lt;/td&gt;
+    &lt;/tr&gt;
+    &lt;tr&gt;
+        &lt;td&gt;secorian&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;| 12 -7 0 1 0 -1 &amp;gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;28672/28431&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;14.61&lt;br /&gt;
+&lt;/td&gt;
+    &lt;/tr&gt;
+    &lt;tr&gt;
+        &lt;td&gt;mirwomo comma&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;| -15 3 2 2 &amp;gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;33075/32768&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;16.14&lt;br /&gt;
+&lt;/td&gt;
+    &lt;/tr&gt;
+    &lt;tr&gt;
+        &lt;td&gt;vicesimotertial comma&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;| 5 -6 0 0 0 0 0 0 1 &amp;gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;736/729&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;16.54&lt;br /&gt;
+&lt;/td&gt;
+    &lt;/tr&gt;
+    &lt;tr&gt;
+        &lt;td&gt;small tridecimal comma, animist&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;| -3 1 1 1 0 -1 &amp;gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;105/104&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;16.57&lt;br /&gt;
+&lt;/td&gt;
+    &lt;/tr&gt;
+    &lt;tr&gt;
+        &lt;td&gt;hemimin&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;| 6 1 0 1 -3 &amp;gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;1344/1331&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;16.83&lt;br /&gt;
+&lt;/td&gt;
+    &lt;/tr&gt;
+    &lt;tr&gt;
+        &lt;td&gt;Ptolemy's comma, ptolemisma&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;100/99&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;17.40&lt;br /&gt;
+&lt;/td&gt;
+    &lt;/tr&gt;
+    &lt;tr&gt;
+        &lt;td&gt;'41-tone' comma&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;| 65 -41 &amp;gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;19.84&lt;br /&gt;
+&lt;/td&gt;
+    &lt;/tr&gt;
+    &lt;tr&gt;
+        &lt;td&gt;tolerma&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;| 10 -11 2 1 &amp;gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;179200/177147&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;19.95&lt;br /&gt;
+&lt;/td&gt;
+    &lt;/tr&gt;
+    &lt;tr&gt;
+        &lt;td&gt;major BP diesis, gariboh&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;| 0 -2 5 -3 &amp;gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;3125/3087&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;21.18&lt;br /&gt;
+&lt;/td&gt;
+    &lt;/tr&gt;
+    &lt;tr&gt;
+        &lt;td&gt;cassacot&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;| -1 0 1 2 -2 &amp;gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;245/242&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;21.33&lt;br /&gt;
+&lt;/td&gt;
+    &lt;/tr&gt;
+    &lt;tr&gt;
+        &lt;td&gt;keema&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;| -5 -3 3 1 &amp;gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;875/864&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;21.90&lt;br /&gt;
+&lt;/td&gt;
+    &lt;/tr&gt;
+    &lt;tr&gt;
+        &lt;td&gt;blackjackisma&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;| -10 7 8 -7 &amp;gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;9859966/9733137&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;22.41&lt;br /&gt;
+&lt;/td&gt;
+    &lt;/tr&gt;
+    &lt;tr&gt;
+        &lt;td&gt;roda&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;| 20 -17 3 &amp;gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;6122773/6032531&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;25.71&lt;br /&gt;
+&lt;/td&gt;
+    &lt;/tr&gt;
+    &lt;tr&gt;
+        &lt;td&gt;minimal diesis, tetracot comma&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;| 5 -9 4 &amp;gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;20000/19683&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;27.66&lt;br /&gt;
+&lt;/td&gt;
+    &lt;/tr&gt;
+    &lt;tr&gt;
+        &lt;td&gt;small diesis, magic comma&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;| -10 -1 5 &amp;gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;3125/3072&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;29.61&lt;br /&gt;
+&lt;/td&gt;
+    &lt;/tr&gt;
+    &lt;tr&gt;
+        &lt;td&gt;thuja comma&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;| 15 0 1 0 -5 &amp;gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;163840/161051&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;29.72&lt;br /&gt;
+&lt;/td&gt;
+    &lt;/tr&gt;
+    &lt;tr&gt;
+        &lt;td&gt;Ampersand's comma&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;| -25 7 6 &amp;gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;31.57&lt;br /&gt;
+&lt;/td&gt;
+    &lt;/tr&gt;
+    &lt;tr&gt;
+        &lt;td&gt;great BP diesis&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;| 0 -7 6 -1 &amp;gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;15625/15309&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;35.37&lt;br /&gt;
+&lt;/td&gt;
+    &lt;/tr&gt;
+    &lt;tr&gt;
+        &lt;td&gt;shibboleth&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;| -5 -10 9 &amp;gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;1953125/1889568&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;57.27&lt;br /&gt;
+&lt;/td&gt;
+    &lt;/tr&gt;
+&lt;/table&gt;
+&lt;br /&gt;
+&lt;!-- ws:start:WikiTextHeadingRule:13:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc2"&gt;&lt;a name="Temperaments"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:13 --&gt;Temperaments&lt;/h1&gt;
+ &lt;a class="wiki_link" href="/List%20of%20edo-distinct%2041et%20rank%20two%20temperaments"&gt;List of edo-distinct 41et rank two temperaments&lt;/a&gt;&lt;br /&gt;
 &lt;br /&gt;
-&lt;!-- ws:start:WikiTextHeadingRule:13:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc2"&gt;&lt;a name="Intervals"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:13 --&gt;Intervals&lt;/h1&gt;
+&lt;!-- ws:start:WikiTextHeadingRule:15:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc3"&gt;&lt;a name="Intervals"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:15 --&gt;Intervals&lt;/h1&gt;
@@ Line 768: / Line 1,428: @@
 &lt;br /&gt;
-&lt;!-- ws:start:WikiTextHeadingRule:15:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc3"&gt;&lt;a name="Instruments"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:15 --&gt;Instruments&lt;/h1&gt;
+&lt;!-- ws:start:WikiTextHeadingRule:17:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc4"&gt;&lt;a name="Instruments"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:17 --&gt;Instruments&lt;/h1&gt;
-  &lt;!-- ws:start:WikiTextLocalImageRule:1693:&amp;lt;img src=&amp;quot;/file/view/Ron_Sword_with_a_41ET_Guitar.jpg/221056094/Ron_Sword_with_a_41ET_Guitar.jpg&amp;quot; alt=&amp;quot;&amp;quot; title=&amp;quot;&amp;quot; /&amp;gt; --&gt;&lt;img src="/file/view/Ron_Sword_with_a_41ET_Guitar.jpg/221056094/Ron_Sword_with_a_41ET_Guitar.jpg" alt="Ron_Sword_with_a_41ET_Guitar.jpg" title="Ron_Sword_with_a_41ET_Guitar.jpg" /&gt;&lt;!-- ws:end:WikiTextLocalImageRule:1693 --&gt;&lt;br /&gt;
+  &lt;!-- ws:start:WikiTextLocalImageRule:2288:&amp;lt;img src=&amp;quot;/file/view/Ron_Sword_with_a_41ET_Guitar.jpg/221056094/Ron_Sword_with_a_41ET_Guitar.jpg&amp;quot; alt=&amp;quot;&amp;quot; title=&amp;quot;&amp;quot; /&amp;gt; --&gt;&lt;img src="/file/view/Ron_Sword_with_a_41ET_Guitar.jpg/221056094/Ron_Sword_with_a_41ET_Guitar.jpg" alt="Ron_Sword_with_a_41ET_Guitar.jpg" title="Ron_Sword_with_a_41ET_Guitar.jpg" /&gt;&lt;!-- ws:end:WikiTextLocalImageRule:2288 --&gt;&lt;br /&gt;
 &lt;em&gt;41-EDO Classical guitar, by Ron Sword.&lt;/em&gt;&lt;br /&gt;
 &lt;br /&gt;
 A possible system to tune keyboards in 41EDO is discussed in &lt;a class="wiki_link_ext" href="http://launch.groups.yahoo.com/group/tuning/message/74155" rel="nofollow"&gt;http://launch.groups.yahoo.com/group/tuning/message/74155&lt;/a&gt;.&lt;br /&gt;
 &lt;br /&gt;
-&lt;!-- ws:start:WikiTextHeadingRule:17:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc4"&gt;&lt;a name="Harmonic Scale"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:17 --&gt;Harmonic Scale&lt;/h1&gt;
+&lt;!-- ws:start:WikiTextHeadingRule:19:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc5"&gt;&lt;a name="Harmonic Scale"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:19 --&gt;Harmonic Scale&lt;/h1&gt;
 edo is the first edo to do some justice to Mode 8 of the &lt;a class="wiki_link" href="/OverToneSeries"&gt;harmonic series&lt;/a&gt;, which Dante Rosati calls the &amp;quot;&lt;a class="wiki_link" href="/overtone%20scales"&gt;Diatonic Harmonic Series Scale&lt;/a&gt;,&amp;quot; consisting of overtones 8 through 16 (sometimes made to repeat at the octave).&lt;br /&gt;
 &lt;br /&gt;
@@ Line 902: / Line 1,562: @@
 The scale in 41, as adjacent steps, thus goes: 7 6 6 5 5 4 4 4.&lt;br /&gt;
 &lt;br /&gt;
-&lt;!-- ws:start:WikiTextHeadingRule:19:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc5"&gt;&lt;a name="Nonoctave Temperaments"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:19 --&gt;Nonoctave Temperaments&lt;/h1&gt;
+&lt;!-- ws:start:WikiTextHeadingRule:21:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc6"&gt;&lt;a name="Nonoctave Temperaments"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:21 --&gt;Nonoctave Temperaments&lt;/h1&gt;
   Taking every third degree of 41edo produces a scale extremely close to &lt;a class="wiki_link" href="/88cET"&gt;88cET&lt;/a&gt; or 88-cent equal temperament (or the 8th root of 3:2). Likewise, taking every fifth degree produces a scale very close to the equal-tempered &lt;span class="wiki_link_new"&gt;&lt;a class="wiki_link" href="/BP"&gt;Bohlen-Pierce&lt;/a&gt;&lt;/span&gt;&lt;a class="wiki_link" href="/BP"&gt; Scale&lt;/a&gt; (or the 13th root of 3). See chart:&lt;br /&gt;
 &lt;br /&gt;
@@ Line 1,856: / Line 2,516: @@
 &lt;br /&gt;
 &lt;br /&gt;
-&lt;!-- ws:start:WikiTextHeadingRule:21:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc6"&gt;&lt;a name="Music"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:21 --&gt;Music&lt;/h1&gt;
+&lt;!-- ws:start:WikiTextHeadingRule:23:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc7"&gt;&lt;a name="Music"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:23 --&gt;Music&lt;/h1&gt;
-  &lt;a class="wiki_link_ext" href="http://soundcloud.com/cameron-bobro/eveninghorizon-cbobro" rel="nofollow"&gt;EveningHorizon&lt;/a&gt; &lt;a class="wiki_link_ext" href="http://micro.soonlabel.com/gene_ward_smith/Others/Bobro/EveningHorizon_CBobro.mp3" rel="nofollow"&gt;play&lt;/a&gt; by Cameron Bobro&lt;br /&gt;
+  &lt;a class="wiki_link_ext" href="http://soundcloud.com/cameron-bobro/eveninghorizon-cbobro" rel="nofollow"&gt;EveningHorizon&lt;/a&gt; &lt;em&gt;&lt;a class="wiki_link_ext" href="http://micro.soonlabel.com/gene_ward_smith/Others/Bobro/EveningHorizon_CBobro.mp3" rel="nofollow"&gt;play&lt;/a&gt;&lt;/em&gt; by Cameron Bobro&lt;br /&gt;
 &lt;br /&gt;
-&lt;!-- ws:start:WikiTextHeadingRule:23:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc7"&gt;&lt;a name="Links"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:23 --&gt;Links&lt;/h1&gt;
+&lt;!-- ws:start:WikiTextHeadingRule:25:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc8"&gt;&lt;a name="Links"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:25 --&gt;Links&lt;/h1&gt;
-  &lt;ul&gt;&lt;li&gt;&lt;a class="wiki_link_ext" href="http://en.wikipedia.org/wiki/41_equal_temperament" rel="nofollow"&gt;Wikipedia article on 41edo&lt;/a&gt;&lt;/li&gt;&lt;li&gt;&lt;a class="wiki_link" href="/Magic22%20as%20srutis#magic22assrutis"&gt;Magic22 as srutis&lt;/a&gt; describes a possible use of 41edo for &lt;a class="wiki_link" href="/indian"&gt;indian&lt;/a&gt; music.&lt;/li&gt;&lt;li&gt;see also &lt;a class="wiki_link" href="/Magic%20family"&gt;Magic family&lt;/a&gt;&lt;/li&gt;&lt;li&gt;Sword, Ron.&lt;a class="wiki_link_ext" href="http://www.ronsword.com" rel="nofollow" target="_blank"&gt; &amp;quot;Tetracontamonophonic Scales for Guitar&amp;quot;&lt;/a&gt;&lt;/li&gt;&lt;/ul&gt;&lt;!-- ws:start:WikiTextReferencesRule:2568: --&gt;&lt;hr class="references" /&gt;&lt;ol class="references"&gt;
+  &lt;ul&gt;&lt;li&gt;&lt;a class="wiki_link_ext" href="http://en.wikipedia.org/wiki/41_equal_temperament" rel="nofollow"&gt;Wikipedia article on 41edo&lt;/a&gt;&lt;/li&gt;&lt;li&gt;&lt;a class="wiki_link" href="/Magic22%20as%20srutis#magic22assrutis"&gt;Magic22 as srutis&lt;/a&gt; describes a possible use of 41edo for &lt;a class="wiki_link" href="/indian"&gt;indian&lt;/a&gt; music.&lt;/li&gt;&lt;li&gt;see also &lt;a class="wiki_link" href="/Magic%20family"&gt;Magic family&lt;/a&gt;&lt;/li&gt;&lt;li&gt;Sword, Ron.&lt;a class="wiki_link_ext" href="http://www.ronsword.com" rel="nofollow" target="_blank"&gt; &amp;quot;Tetracontamonophonic Scales for Guitar&amp;quot;&lt;/a&gt;&lt;/li&gt;&lt;/ul&gt;&lt;!-- ws:start:WikiTextReferencesRule:3403: --&gt;&lt;hr class="references" /&gt;&lt;ol class="references"&gt;
 &lt;li id="cite_note-1"&gt;&lt;a href="#cite_ref-1"&gt;^&lt;/a&gt; &lt;a class="wiki_link_ext" href="http://x31eq.com/schismic.htm" rel="nofollow"&gt;&amp;quot;Schismic Temperaments&amp;quot;&lt;/a&gt; at x31eq.com the websize of &lt;a class="wiki_link" href="/Graham%20Breed"&gt;Graham Breed&lt;/a&gt;&lt;/li&gt;
 &lt;li id="cite_note-2"&gt;&lt;a href="#cite_ref-2"&gt;^&lt;/a&gt; &lt;a class="wiki_link_ext" href="http://x31eq.com/decimal_lattice.htm" rel="nofollow"&gt;&amp;quot;Lattices with Decimal Notation&amp;quot;&lt;/a&gt; at x31eq.com&lt;/li&gt;
 &lt;li id="cite_note-3"&gt;&lt;a href="#cite_ref-3"&gt;^&lt;/a&gt; &lt;a class="wiki_link_ext" href="http://en.wikipedia.org/wiki/Schismatic_temperament" rel="nofollow"&gt;Schismatic temperament&lt;/a&gt;&lt;/li&gt;
 &lt;li id="cite_note-4"&gt;&lt;a href="#cite_ref-4"&gt;^&lt;/a&gt; &lt;a class="wiki_link_ext" href="http://en.wikipedia.org/wiki/Magic_temperament" rel="nofollow"&gt;Magic temperament&lt;/a&gt;&lt;/li&gt;
-&lt;/ol&gt;&lt;!-- ws:end:WikiTextReferencesRule:2568 --&gt;&lt;/body&gt;&lt;/html&gt;</pre></div>
+&lt;/ol&gt;&lt;!-- ws:end:WikiTextReferencesRule:3403 --&gt;&lt;/body&gt;&lt;/html&gt;</pre></div>