50edo
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//50edo// divides the [[octave]] into 50 equal parts of precisely 24 [[cent]]s each. In the [[5-limit]], it tempers out 81/80, making it a [[meantone]] system, and in that capacity has historically has drawn some notice. In "Harmonics or the Philosophy of Musical Sounds" (1759) by Robert Smith, a musical temperament is described where the octave is divided into 50 equal parts - 50edo, in one word. Later W. S. B. Woolhouse noted it was fairly close to the [[Target tunings|least squares]] tuning for 5-limit meantone. 50, however, is especially interesting from a higher limit point of view. While [[31edo]] extends meantone with a [[7_4|7/4]] which is nearly pure, 50 has a flat 7/4 but both [[11_8|11/8]] and [[13_8|13/8]] are nearly pure. 50 tempers out 126/125 in the [[7-limit]], indicating it supports septimal meantone; 245/242, 385/384 and 540/539 in the [[11-limit]] and 105/104, 144/143 and 196/195 in the [[13-limit]], and can be used for even higher limits. Aside from meantone and its extension meanpop, it can be used to advantage for the 15&50 temperament. It is also the unique equal temperament tempering out both 81/80 and the [[vishnuzma]], 6115295232/6103515625 = |23 6 -14>, so that in 50et seven chromatic semitones are a perfect fourth. In 12et by comparison this gives a fifth, in 31et a doubly diminished fifth, and in 19et a diminished fourth. [[http://www.archive.org/details/harmonicsorphilo00smit|Robert Smith's book online]] [[http://www.music.ed.ac.uk/russell/conference/robertsmithkirckman.html|More information about Robert Smith's temperament]] ==Relations== The 50-edo system is related to [[7edo]], [[12edo]], [[19edo]], [[31edo]] as the next approximation to the "Golden Tone System" ([[Das Goldene Tonsystem]]) of Thorvald Kornerup. ==Intervals== || Degrees of 50-EDO || Cents value || || 0 || 0 || || 1 || 24 || || 2 || 48 || || 3 || 72 || || 4 || 96 || || 5 || 120 || || 6 || 144 || || 7 || 168 || || 8 || 192 || || 9 || 216 || || 10 || 240 || || 11 || 264 || || 12 || 288 || || 13 || 312 || || 14 || 336 || || 15 || 360 || || 16 || 384 || || 17 || 408 || || 18 || 432 || || 19 || 456 || || 20 || 480 || || 21 || 504 || || 22 || 528 || || 23 || 552 || || 24 || 576 || || 25 || 600 || || 26 || 624 || || 27 || 648 || || 28 || 672 || || 29 || 696 || || 30 || 720 || || 31 || 744 || || 32 || 768 || || 33 || 792 || || 34 || 816 || || 35 || 840 || || 36 || 864 || || 37 || 888 || || 38 || 912 || || 39 || 936 || || 40 || 960 || || 41 || 984 || || 42 || 1008 || || 43 || 1032 || || 44 || 1056 || || 45 || 1080 || || 46 || 1104 || || 47 || 1128 || || 48 || 1152 || || 49 || 1176 || ==Commas== 50 EDO tempers out the following commas. (Note: This assumes the val < 50 79 116 140 173 185 204 212 226 |, comma values rounded to 2 decimal places.) This list is not all-inclusive, and is based on the interval table from Scala version 2.2. ||~ ===In bra format=== ||~ ===In cents=== ||~ ===Ratio=== ||~ ===Name 1=== ||~ ===Name2=== || || | -4 4 -1 > ||> 21.51 ||= 81/80 || Syntonic comma || Didymus comma || || | -8 8 -2 > ||> 43.01 ||= 6561/6400 || Mathieu superdiesis || || || | 23 6 -14 > ||> 3.34 ||= 1212717/1210381 || Vishnu comma || || || | 1 2 -3 1 > ||> 13.79 ||= 126/125 || Small septimal comma || || || | -5 2 2 -1 > ||> 7.71 ||= 225/224 || Septimal kleisma || || || | 6 0 -5 2 > ||> 6.08 ||= 3136/3125 || Middle second comma || || || | -6 -8 2 5 > ||> 1.12 ||= 420175/419904 || || || || |-11 2 7 -3 > ||> 1.63 ||= 703125/702464 || || || || | 11 -10 -10 10 > ||> 5.57 ||= 6772805/6751042 || || || || |-13 10 0 -1 > ||> 50.72 ||= 59049/57344 || Harrison's comma || || || | 2 3 1 -2 -1 > ||> 3.21 ||= 540/539 || Swets' comma || || || | -3 4 -2 -2 2 > ||> 0.18 ||= 9801/9800 || Kalisma || Gauss' comma || || | 5 -1 3 0 -3 > ||> 3.03 ||= 4000/3993 || Undecimal schisma || || || | -7 -1 1 1 1 > ||> 4.50 ||= 385/384 || Undecimal kleisma || || || | 2 -1 0 1 -2 1 > ||> 4.76 ||= 364/363 || || || || | 2 3 0 -1 1 -2 > ||> 7.30 ||= 1188/1183 || Kestrel Comma || || || | 3 0 2 0 1 -3 > ||> 2.36 ||= 2200/2197 || Parizek comma || || || | -3 1 1 1 0 -1 > ||> 16.57 ||= 105/104 || Small tridecimal comma || || || | 3 -2 0 1 -1 -1 0 0 1 > ||> 1.34 ||= 1288/1287 || Triaphonisma || || [[http://micro.soonlabel.com/gene_ward_smith/Others/Meneghin/Claudi-Meneghin-Twinkle-canon-50-edo.mp3|Twinkle canon – 50 edo]] by [[http://soonlabel.com/xenharmonic/archives/573|Claudi Meneghin]] <span style="display: block; height: 1px; left: -40px; overflow: hidden; position: absolute; top: 5675.5px; width: 1px;">| -4 4 -1 > 21.51 81/80 syntonic comma, Didymus comma</span> <span style="display: block; height: 1px; left: -40px; overflow: hidden; position: absolute; top: 5675.5px; width: 1px;"> | -8 8 -2 > 43.01 6561/6400 Mathieu superdiesis</span> <span style="display: block; height: 1px; left: -40px; overflow: hidden; position: absolute; top: 5675.5px; width: 1px;"> | 23 6 -14 > 3.34 1212717/1210381 Vishnu comma</span> <span style="display: block; height: 1px; left: -40px; overflow: hidden; position: absolute; top: 5675.5px; width: 1px;"> | 1 2 -3 1 > 13.79 126/125 small septimal comma</span> <span style="display: block; height: 1px; left: -40px; overflow: hidden; position: absolute; top: 5675.5px; width: 1px;"> | -5 2 2 -1 > 7.71 225/224 septimal kleisma</span> <span style="display: block; height: 1px; left: -40px; overflow: hidden; position: absolute; top: 5675.5px; width: 1px;"> | 6 0 -5 2 > 6.08 3136/3125 middle second comma</span> <span style="display: block; height: 1px; left: -40px; overflow: hidden; position: absolute; top: 5675.5px; width: 1px;"> | -6 -8 2 5 > 1.12 420175/419904</span> <span style="display: block; height: 1px; left: -40px; overflow: hidden; position: absolute; top: 5675.5px; width: 1px;"> |-11 2 7 -3 > 1.63 703125/702464</span> <span style="display: block; height: 1px; left: -40px; overflow: hidden; position: absolute; top: 5675.5px; width: 1px;"> | 11 -10 -10 10 > 5.57 6772805/6751042</span> <span style="display: block; height: 1px; left: -40px; overflow: hidden; position: absolute; top: 5675.5px; width: 1px;"> |-13 10 0 -1 > 50.72 59049/57344 Harrison's comma</span> <span style="display: block; height: 1px; left: -40px; overflow: hidden; position: absolute; top: 5675.5px; width: 1px;"> | 2 3 1 -2 -1 > 3.21 540/539 Swets' comma</span> <span style="display: block; height: 1px; left: -40px; overflow: hidden; position: absolute; top: 5675.5px; width: 1px;"> | -3 4 -2 -2 2 > 0.18 9801/9800 kalisma, Gauss' comma</span> <span style="display: block; height: 1px; left: -40px; overflow: hidden; position: absolute; top: 5675.5px; width: 1px;"> | 5 -1 3 0 -3 > 3.03 4000/3993 undecimal schisma</span> <span style="display: block; height: 1px; left: -40px; overflow: hidden; position: absolute; top: 5675.5px; width: 1px;"> | -7 -1 1 1 1 > 4.50 385/384 undecimal kleisma</span> <span style="display: block; height: 1px; left: -40px; overflow: hidden; position: absolute; top: 5675.5px; width: 1px;"> | 2 -1 0 1 -2 1 > 4.76 364/363</span> <span style="display: block; height: 1px; left: -40px; overflow: hidden; position: absolute; top: 5675.5px; width: 1px;"> | 2 3 0 -1 1 -2 > 7.30 1188/1183 Kestrel Comma</span> <span style="display: block; height: 1px; left: -40px; overflow: hidden; position: absolute; top: 5675.5px; width: 1px;"> | 3 0 2 0 1 -3 > 2.36 2200/2197 Parizek comma</span> <span style="display: block; height: 1px; left: -40px; overflow: hidden; position: absolute; top: 5675.5px; width: 1px;"> | -3 1 1 1 0 -1 > 16.57 105/104 small tridecimal comma</span> <span style="display: block; height: 1px; left: -40px; overflow: hidden; position: absolute; top: 5675.5px; width: 1px;"> | 3 -2 0 1 -1 -1 0 0 1 > 1.34 1288/1287 triaphonisma</span>
Original HTML content:
<html><head><title>50edo</title></head><body><em>50edo</em> divides the <a class="wiki_link" href="/octave">octave</a> into 50 equal parts of precisely 24 <a class="wiki_link" href="/cent">cent</a>s each. In the <a class="wiki_link" href="/5-limit">5-limit</a>, it tempers out 81/80, making it a <a class="wiki_link" href="/meantone">meantone</a> system, and in that capacity has historically has drawn some notice. In "Harmonics or the Philosophy of Musical Sounds" (1759) by Robert Smith, a musical temperament is described where the octave is divided into 50 equal parts - 50edo, in one word. Later W. S. B. Woolhouse noted it was fairly close to the <a class="wiki_link" href="/Target%20tunings">least squares</a> tuning for 5-limit meantone. 50, however, is especially interesting from a higher limit point of view. While <a class="wiki_link" href="/31edo">31edo</a> extends meantone with a <a class="wiki_link" href="/7_4">7/4</a> which is nearly pure, 50 has a flat 7/4 but both <a class="wiki_link" href="/11_8">11/8</a> and <a class="wiki_link" href="/13_8">13/8</a> are nearly pure.<br />
<br />
50 tempers out 126/125 in the <a class="wiki_link" href="/7-limit">7-limit</a>, indicating it supports septimal meantone; 245/242, 385/384 and 540/539 in the <a class="wiki_link" href="/11-limit">11-limit</a> and 105/104, 144/143 and 196/195 in the <a class="wiki_link" href="/13-limit">13-limit</a>, and can be used for even higher limits. Aside from meantone and its extension meanpop, it can be used to advantage for the 15&50 temperament. It is also the unique equal temperament tempering out both 81/80 and the <a class="wiki_link" href="/vishnuzma">vishnuzma</a>, 6115295232/6103515625 = |23 6 -14>, so that in 50et seven chromatic semitones are a perfect fourth. In 12et by comparison this gives a fifth, in 31et a doubly diminished fifth, and in 19et a diminished fourth.<br />
<br />
<a class="wiki_link_ext" href="http://www.archive.org/details/harmonicsorphilo00smit" rel="nofollow">Robert Smith's book online</a><br />
<a class="wiki_link_ext" href="http://www.music.ed.ac.uk/russell/conference/robertsmithkirckman.html" rel="nofollow">More information about Robert Smith's temperament</a><br />
<br />
<!-- ws:start:WikiTextHeadingRule:0:<h2> --><h2 id="toc0"><a name="x-Relations"></a><!-- ws:end:WikiTextHeadingRule:0 -->Relations</h2>
The 50-edo system is related to <a class="wiki_link" href="/7edo">7edo</a>, <a class="wiki_link" href="/12edo">12edo</a>, <a class="wiki_link" href="/19edo">19edo</a>, <a class="wiki_link" href="/31edo">31edo</a> as the next approximation to the "Golden Tone System" (<a class="wiki_link" href="/Das%20Goldene%20Tonsystem">Das Goldene Tonsystem</a>) of Thorvald Kornerup.<br />
<br />
<!-- ws:start:WikiTextHeadingRule:2:<h2> --><h2 id="toc1"><a name="x-Intervals"></a><!-- ws:end:WikiTextHeadingRule:2 -->Intervals</h2>
<table class="wiki_table">
<tr>
<td>Degrees of 50-EDO<br />
</td>
<td>Cents value<br />
</td>
</tr>
<tr>
<td>0<br />
</td>
<td>0<br />
</td>
</tr>
<tr>
<td>1<br />
</td>
<td>24<br />
</td>
</tr>
<tr>
<td>2<br />
</td>
<td>48<br />
</td>
</tr>
<tr>
<td>3<br />
</td>
<td>72<br />
</td>
</tr>
<tr>
<td>4<br />
</td>
<td>96<br />
</td>
</tr>
<tr>
<td>5<br />
</td>
<td>120<br />
</td>
</tr>
<tr>
<td>6<br />
</td>
<td>144<br />
</td>
</tr>
<tr>
<td>7<br />
</td>
<td>168<br />
</td>
</tr>
<tr>
<td>8<br />
</td>
<td>192<br />
</td>
</tr>
<tr>
<td>9<br />
</td>
<td>216<br />
</td>
</tr>
<tr>
<td>10<br />
</td>
<td>240<br />
</td>
</tr>
<tr>
<td>11<br />
</td>
<td>264<br />
</td>
</tr>
<tr>
<td>12<br />
</td>
<td>288<br />
</td>
</tr>
<tr>
<td>13<br />
</td>
<td>312<br />
</td>
</tr>
<tr>
<td>14<br />
</td>
<td>336<br />
</td>
</tr>
<tr>
<td>15<br />
</td>
<td>360<br />
</td>
</tr>
<tr>
<td>16<br />
</td>
<td>384<br />
</td>
</tr>
<tr>
<td>17<br />
</td>
<td>408<br />
</td>
</tr>
<tr>
<td>18<br />
</td>
<td>432<br />
</td>
</tr>
<tr>
<td>19<br />
</td>
<td>456<br />
</td>
</tr>
<tr>
<td>20<br />
</td>
<td>480<br />
</td>
</tr>
<tr>
<td>21<br />
</td>
<td>504<br />
</td>
</tr>
<tr>
<td>22<br />
</td>
<td>528<br />
</td>
</tr>
<tr>
<td>23<br />
</td>
<td>552<br />
</td>
</tr>
<tr>
<td>24<br />
</td>
<td>576<br />
</td>
</tr>
<tr>
<td>25<br />
</td>
<td>600<br />
</td>
</tr>
<tr>
<td>26<br />
</td>
<td>624<br />
</td>
</tr>
<tr>
<td>27<br />
</td>
<td>648<br />
</td>
</tr>
<tr>
<td>28<br />
</td>
<td>672<br />
</td>
</tr>
<tr>
<td>29<br />
</td>
<td>696<br />
</td>
</tr>
<tr>
<td>30<br />
</td>
<td>720<br />
</td>
</tr>
<tr>
<td>31<br />
</td>
<td>744<br />
</td>
</tr>
<tr>
<td>32<br />
</td>
<td>768<br />
</td>
</tr>
<tr>
<td>33<br />
</td>
<td>792<br />
</td>
</tr>
<tr>
<td>34<br />
</td>
<td>816<br />
</td>
</tr>
<tr>
<td>35<br />
</td>
<td>840<br />
</td>
</tr>
<tr>
<td>36<br />
</td>
<td>864<br />
</td>
</tr>
<tr>
<td>37<br />
</td>
<td>888<br />
</td>
</tr>
<tr>
<td>38<br />
</td>
<td>912<br />
</td>
</tr>
<tr>
<td>39<br />
</td>
<td>936<br />
</td>
</tr>
<tr>
<td>40<br />
</td>
<td>960<br />
</td>
</tr>
<tr>
<td>41<br />
</td>
<td>984<br />
</td>
</tr>
<tr>
<td>42<br />
</td>
<td>1008<br />
</td>
</tr>
<tr>
<td>43<br />
</td>
<td>1032<br />
</td>
</tr>
<tr>
<td>44<br />
</td>
<td>1056<br />
</td>
</tr>
<tr>
<td>45<br />
</td>
<td>1080<br />
</td>
</tr>
<tr>
<td>46<br />
</td>
<td>1104<br />
</td>
</tr>
<tr>
<td>47<br />
</td>
<td>1128<br />
</td>
</tr>
<tr>
<td>48<br />
</td>
<td>1152<br />
</td>
</tr>
<tr>
<td>49<br />
</td>
<td>1176<br />
</td>
</tr>
</table>
<br />
<!-- ws:start:WikiTextHeadingRule:4:<h2> --><h2 id="toc2"><a name="x-Commas"></a><!-- ws:end:WikiTextHeadingRule:4 -->Commas</h2>
50 EDO tempers out the following commas. (Note: This assumes the val < 50 79 116 140 173 185 204 212 226 |, comma values rounded to 2 decimal places.) This list is not all-inclusive, and is based on the interval table from Scala version 2.2.<br />
<table class="wiki_table">
<tr>
<th><!-- ws:start:WikiTextHeadingRule:6:<h3> --><h3 id="toc3"><a name="x-Commas-In bra format"></a><!-- ws:end:WikiTextHeadingRule:6 -->In bra format</h3>
</th>
<th><!-- ws:start:WikiTextHeadingRule:8:<h3> --><h3 id="toc4"><a name="x-Commas-In cents"></a><!-- ws:end:WikiTextHeadingRule:8 -->In cents</h3>
</th>
<th><!-- ws:start:WikiTextHeadingRule:10:<h3> --><h3 id="toc5"><a name="x-Commas-Ratio"></a><!-- ws:end:WikiTextHeadingRule:10 -->Ratio</h3>
</th>
<th><!-- ws:start:WikiTextHeadingRule:12:<h3> --><h3 id="toc6"><a name="x-Commas-Name 1"></a><!-- ws:end:WikiTextHeadingRule:12 -->Name 1</h3>
</th>
<th><!-- ws:start:WikiTextHeadingRule:14:<h3> --><h3 id="toc7"><a name="x-Commas-Name2"></a><!-- ws:end:WikiTextHeadingRule:14 -->Name2</h3>
</th>
</tr>
<tr>
<td>| -4 4 -1 ><br />
</td>
<td style="text-align: right;">21.51<br />
</td>
<td style="text-align: center;">81/80<br />
</td>
<td>Syntonic comma<br />
</td>
<td>Didymus comma<br />
</td>
</tr>
<tr>
<td>| -8 8 -2 ><br />
</td>
<td style="text-align: right;">43.01<br />
</td>
<td style="text-align: center;">6561/6400<br />
</td>
<td>Mathieu superdiesis<br />
</td>
<td><br />
</td>
</tr>
<tr>
<td>| 23 6 -14 ><br />
</td>
<td style="text-align: right;">3.34<br />
</td>
<td style="text-align: center;">1212717/1210381<br />
</td>
<td>Vishnu comma<br />
</td>
<td><br />
</td>
</tr>
<tr>
<td>| 1 2 -3 1 ><br />
</td>
<td style="text-align: right;">13.79<br />
</td>
<td style="text-align: center;">126/125<br />
</td>
<td>Small septimal comma<br />
</td>
<td><br />
</td>
</tr>
<tr>
<td>| -5 2 2 -1 ><br />
</td>
<td style="text-align: right;">7.71<br />
</td>
<td style="text-align: center;">225/224<br />
</td>
<td>Septimal kleisma<br />
</td>
<td><br />
</td>
</tr>
<tr>
<td>| 6 0 -5 2 ><br />
</td>
<td style="text-align: right;">6.08<br />
</td>
<td style="text-align: center;">3136/3125<br />
</td>
<td>Middle second comma<br />
</td>
<td><br />
</td>
</tr>
<tr>
<td>| -6 -8 2 5 ><br />
</td>
<td style="text-align: right;">1.12<br />
</td>
<td style="text-align: center;">420175/419904<br />
</td>
<td><br />
</td>
<td><br />
</td>
</tr>
<tr>
<td>|-11 2 7 -3 ><br />
</td>
<td style="text-align: right;">1.63<br />
</td>
<td style="text-align: center;">703125/702464<br />
</td>
<td><br />
</td>
<td><br />
</td>
</tr>
<tr>
<td>| 11 -10 -10 10 ><br />
</td>
<td style="text-align: right;">5.57<br />
</td>
<td style="text-align: center;">6772805/6751042<br />
</td>
<td><br />
</td>
<td><br />
</td>
</tr>
<tr>
<td>|-13 10 0 -1 ><br />
</td>
<td style="text-align: right;">50.72<br />
</td>
<td style="text-align: center;">59049/57344<br />
</td>
<td>Harrison's comma<br />
</td>
<td><br />
</td>
</tr>
<tr>
<td>| 2 3 1 -2 -1 ><br />
</td>
<td style="text-align: right;">3.21<br />
</td>
<td style="text-align: center;">540/539<br />
</td>
<td>Swets' comma<br />
</td>
<td><br />
</td>
</tr>
<tr>
<td>| -3 4 -2 -2 2 ><br />
</td>
<td style="text-align: right;">0.18<br />
</td>
<td style="text-align: center;">9801/9800<br />
</td>
<td>Kalisma<br />
</td>
<td>Gauss' comma<br />
</td>
</tr>
<tr>
<td>| 5 -1 3 0 -3 ><br />
</td>
<td style="text-align: right;">3.03<br />
</td>
<td style="text-align: center;">4000/3993<br />
</td>
<td>Undecimal schisma<br />
</td>
<td><br />
</td>
</tr>
<tr>
<td>| -7 -1 1 1 1 ><br />
</td>
<td style="text-align: right;">4.50<br />
</td>
<td style="text-align: center;">385/384<br />
</td>
<td>Undecimal kleisma<br />
</td>
<td><br />
</td>
</tr>
<tr>
<td>| 2 -1 0 1 -2 1 ><br />
</td>
<td style="text-align: right;">4.76<br />
</td>
<td style="text-align: center;">364/363<br />
</td>
<td><br />
</td>
<td><br />
</td>
</tr>
<tr>
<td>| 2 3 0 -1 1 -2 ><br />
</td>
<td style="text-align: right;">7.30<br />
</td>
<td style="text-align: center;">1188/1183<br />
</td>
<td>Kestrel Comma<br />
</td>
<td><br />
</td>
</tr>
<tr>
<td>| 3 0 2 0 1 -3 ><br />
</td>
<td style="text-align: right;">2.36<br />
</td>
<td style="text-align: center;">2200/2197<br />
</td>
<td>Parizek comma<br />
</td>
<td><br />
</td>
</tr>
<tr>
<td>| -3 1 1 1 0 -1 ><br />
</td>
<td style="text-align: right;">16.57<br />
</td>
<td style="text-align: center;">105/104<br />
</td>
<td>Small tridecimal comma<br />
</td>
<td><br />
</td>
</tr>
<tr>
<td>| 3 -2 0 1 -1 -1 0 0 1 ><br />
</td>
<td style="text-align: right;">1.34<br />
</td>
<td style="text-align: center;">1288/1287<br />
</td>
<td>Triaphonisma<br />
</td>
<td><br />
</td>
</tr>
</table>
<br />
<a class="wiki_link_ext" href="http://micro.soonlabel.com/gene_ward_smith/Others/Meneghin/Claudi-Meneghin-Twinkle-canon-50-edo.mp3" rel="nofollow">Twinkle canon – 50 edo</a> by <a class="wiki_link_ext" href="http://soonlabel.com/xenharmonic/archives/573" rel="nofollow">Claudi Meneghin</a><br />
<span style="display: block; height: 1px; left: -40px; overflow: hidden; position: absolute; top: 5675.5px; width: 1px;">| -4 4 -1 > 21.51 81/80 syntonic comma, Didymus comma</span><br />
<span style="display: block; height: 1px; left: -40px; overflow: hidden; position: absolute; top: 5675.5px; width: 1px;"> | -8 8 -2 > 43.01 6561/6400 Mathieu superdiesis</span><br />
<span style="display: block; height: 1px; left: -40px; overflow: hidden; position: absolute; top: 5675.5px; width: 1px;"> | 23 6 -14 > 3.34 1212717/1210381 Vishnu comma</span><br />
<span style="display: block; height: 1px; left: -40px; overflow: hidden; position: absolute; top: 5675.5px; width: 1px;"> | 1 2 -3 1 > 13.79 126/125 small septimal comma</span><br />
<span style="display: block; height: 1px; left: -40px; overflow: hidden; position: absolute; top: 5675.5px; width: 1px;"> | -5 2 2 -1 > 7.71 225/224 septimal kleisma</span><br />
<span style="display: block; height: 1px; left: -40px; overflow: hidden; position: absolute; top: 5675.5px; width: 1px;"> | 6 0 -5 2 > 6.08 3136/3125 middle second comma</span><br />
<span style="display: block; height: 1px; left: -40px; overflow: hidden; position: absolute; top: 5675.5px; width: 1px;"> | -6 -8 2 5 > 1.12 420175/419904</span><br />
<span style="display: block; height: 1px; left: -40px; overflow: hidden; position: absolute; top: 5675.5px; width: 1px;"> |-11 2 7 -3 > 1.63 703125/702464</span><br />
<span style="display: block; height: 1px; left: -40px; overflow: hidden; position: absolute; top: 5675.5px; width: 1px;"> | 11 -10 -10 10 > 5.57 6772805/6751042</span><br />
<span style="display: block; height: 1px; left: -40px; overflow: hidden; position: absolute; top: 5675.5px; width: 1px;"> |-13 10 0 -1 > 50.72 59049/57344 Harrison's comma</span><br />
<span style="display: block; height: 1px; left: -40px; overflow: hidden; position: absolute; top: 5675.5px; width: 1px;"> | 2 3 1 -2 -1 > 3.21 540/539 Swets' comma</span><br />
<span style="display: block; height: 1px; left: -40px; overflow: hidden; position: absolute; top: 5675.5px; width: 1px;"> | -3 4 -2 -2 2 > 0.18 9801/9800 kalisma, Gauss' comma</span><br />
<span style="display: block; height: 1px; left: -40px; overflow: hidden; position: absolute; top: 5675.5px; width: 1px;"> | 5 -1 3 0 -3 > 3.03 4000/3993 undecimal schisma</span><br />
<span style="display: block; height: 1px; left: -40px; overflow: hidden; position: absolute; top: 5675.5px; width: 1px;"> | -7 -1 1 1 1 > 4.50 385/384 undecimal kleisma</span><br />
<span style="display: block; height: 1px; left: -40px; overflow: hidden; position: absolute; top: 5675.5px; width: 1px;"> | 2 -1 0 1 -2 1 > 4.76 364/363</span><br />
<span style="display: block; height: 1px; left: -40px; overflow: hidden; position: absolute; top: 5675.5px; width: 1px;"> | 2 3 0 -1 1 -2 > 7.30 1188/1183 Kestrel Comma</span><br />
<span style="display: block; height: 1px; left: -40px; overflow: hidden; position: absolute; top: 5675.5px; width: 1px;"> | 3 0 2 0 1 -3 > 2.36 2200/2197 Parizek comma</span><br />
<span style="display: block; height: 1px; left: -40px; overflow: hidden; position: absolute; top: 5675.5px; width: 1px;"> | -3 1 1 1 0 -1 > 16.57 105/104 small tridecimal comma</span><br />
<span style="display: block; height: 1px; left: -40px; overflow: hidden; position: absolute; top: 5675.5px; width: 1px;"> | 3 -2 0 1 -1 -1 0 0 1 > 1.34 1288/1287 triaphonisma</span></body></html>