Unnoticeable comma: Difference between revisions

Revision as of 12:51, 29 December 2016

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=Summary= 
These commas are called "unnoticeable" because, being equal to or less than 3.5 cents, they are smaller than the average peak [[http://musictheory.zentral.zone/huntsystem2.html#2|JND]] (just-noticeable difference) of human pitch perception, as illustrated by the research of <range type="comment" id="597264646_1">[[Aaron Andrew Hunt]].</range id="597264646_1"> It is improbable that even a trained listener would be able to notice these intervals, and as such they a prime target for psychoacoustically informed [[Microtempering|microtempering]].

=List of commas, by prime limit= 
==3-limit commas== 
||~ <span style="display: block; text-align: center;">name(s)</span> ||~ <span style="display: block; text-align: center;">monzo</span> ||~ <span style="display: block; text-align: center;">cents</span> ||
|| Sasktel comma, 51-Pythagorean comma || | 485 -306 > || 1.770 ||
|| [[Satanic comma]] || | -1054 665 > || 0.076 ||

==5-limit commas== 
||~ name(s) ||~ monzo ||~ cents ||
|| 56-syntonic comma || | 225 -224 56 > || 1.431 ||
|| rubidia || | -67 -9 35> || 3.385 ||
|| [[vishnuzma]], semisuper || | 23 6 -14 > || 3.338 ||
|| [[enneadeca]], 19-tone-comma || | -14 -19 19 > || 2.816 ||
|| vavoom || | -68 18 17 > || 2.523 ||
|| tricot comma || | 39 -29 3 > || 2.246 ||
|| schisma || | -15 8 1 > || 1.954 ||
|| counterschisma || | -69 45 -1 > || 1.661 ||
|| septendecima || | -52 -17 34 > || 1.431 ||
|| hemithirds comma, lunama || | 38 -2 -15 > || 1.384 ||
|| minortone comma || | -16 35 -17 > || 1.092 ||
|| [[Ennealimmal|ennealimma]] || | 1 -27 18 > || 0.862 ||
|| astro || | 91 -12 -31 > || 0.815 ||
|| kwazy || | -53 10 16 > || 0.569 ||
|| whoosh || | 37 25 -33 > || 0.522 ||
|| egads || | -36 -52 51 > || 0.339 ||
|| monzisma || | 54 -37 2 > || 0.292 ||
|| fortune || | -107 47 14 > || 0.277 ||
|| gross || | 144 -22 -47 > || 0.245 ||
|| senior || | -17 62 -35 > || 0.230 ||
|| raider || | 71 -99 37 > || 0.062 ||
|| pirate || | -90 -15 49 > || 0.047 ||
|| viking || | -251 69 61 > || 0.032 ||
|| atom || | 161 -84 -12 > || 0.015 ||
|| selenia || | -433 -137 280 > || 0.004764 ||
|| titania || | 2746 -521 -827 > || 0.003183 ||
|| quark || | -573 237 85 > || 0.000884 ||
|| scamp || | -5836 4293 -417 > || 0.000033 ||
|| rover || | 1634 1502 -1729 > || 0.000028 ||
|| rascal || | -7470 2791 1312 > || 0.000006 ||

==7-limit commas== 
||~ name(s) ||~ ratio ||~ monzo ||~ cents ||
|| 44-septimal comma ||   || | -263 88 0 44 > || 0.294 ||
|| horwell || 65625 / 65536 || | -16 1 5 1 > || 2.349 ||
|| meter ||   || | -11 2 7 -3 > || 1.628 ||
|| wizma ||   || | -6 -8 2 5 > || 1.117 ||
|| breedsma || [[2401_2400|2401 / 2400]] || | -5 -1 -2 4 > || 0.721 ||
|| ragisma || 4375 / 4374 || | -1 -7 4 1 > || 0.396 ||
|| akjaysma, 5\7 octave comma ||   || | 47 -7 -7 -7 > || 0.338 ||
|| landscape ||   || | -4 6 -6 3 > || 0.325 ||
|| starscape ||   || | -4 17 1 -9 > || 0.116 ||
|| euzenius ||   || | 3 -13 10 -2 > || 0.070 ||
|| termite ||   || | 9 -28 37 -18 > || 1.072 * 10^-3 ||
|| neutrino ||   || | 1889 -2145 138 424 > || 1.636 * 10^-10 ||
==11-limit commas== 
||~ name(s) ||~ ratio ||~ monzo ||~ cents ||
|| 11-cycle schisma, 37-11-comma ||   || | 128 0 0 0 -37 > || 1.236 ||
|| [[swetismic chords|swetisma]] || 540 / 539 || | 2 3 1 -2 -1 > || 3.209 ||
|| wizardharry || 4000 / 3993 || | 5 -1 3 0 -3 > || 3.032 ||
|| vishdel || 5632 / 5625 || | 9 -2 -4 0 1 > || 2.153 ||
|| sesdecal ||   || | -4 1 7 0 -4 > || 0.879 ||
|| hemigail || 43923 / 43904 || | -7 1 0 -3 4 > || 0.749 ||
|| lehmerisma || 3025 / 3024 || | -4 -3 2 -1 2 > || 0.572 ||
|| kalisma, Gauss' comma || 9801 / 9800 || | -3 4 -2 -2 2 > || 0.177 ||
|| odiheim ||   || | -1 2 -4 5 -2 > || 0.149 ||
|| parimo ||   || | -1 -11 -1 0 6 > || 0.089 ||
|| ultimo ||   || | -2 2 2 -7 4 > || 0.028 ||

==13-limit commas== 
||~ name(s) ||~ ratio ||~ monzo ||~ cents ||
|| tunbarsma || 625 / 624 || | -4 -1 4 0 0 -1 > || 2.772 ||
|| [[The Archipelago|island comma]] || 676 / 675 || | 2 -3 -2 0 0 2 > || 2.563 ||
|| [[squbemic chords|squbema]] || 729 / 728 || | -3 6 0 -1 0 -1 > || 2.376 ||
|| [[petrmic triad|petrma]] || 2200 / 2197 || | 3 0 2 0 1 -3 > || 2.362 ||
|| [[nicolic tetrad|nicola]] || 1575 / 1573 || | 0 2 2 1 -2 -1 > || 2.200 ||
|| [[sinbadmic tetrad|sinbadma]] || 1001 / 1000 || | -3 0 -3 1 1 1 > || 1.730 ||
|| cantonisma || 10985 / 10976 || | -5 0 1 -3 0 3 > || 1.419 ||
|| lummic || 1716 / 1715 || | 2 1 -1 -3 1 1 > || 1.009 ||
|| ibnsinma || 2080 / 2079 || | 5 -3 1 -1 -1 1 > || 0.833 ||
|| schismina || 4096 / 4095 || | 12 -2 -1 -1 0 -1 > || 0.423 ||
|| leprechaun comma || 4225 / 4224 || | -7 -1 2 0 -1 2 > || 0.410 ||
|| jacobin || 6656 / 6655 || | 9 0 -1 0 -3 1 > || 0.260 ||
|| harmonisma || 10648 / 10647 || | 3 -2 0 -1 3 -2 > || 0.163 ||
|| chalmersima ||   || | -6 6 -2 -1 -1 2 > || 0.014 ||

==17-limit commas== 
||~ name(s) ||~ ratio ||~ monzo ||~ cents ||
|| xenisma || 2058 / 2057 || | 1 1 0 3 -2 0 -1 > || 0.841 ||
|| flashma || 12376 / 12375 || | 3 -2 -3 1 -1 1 1 > || 0.140 ||
|| sparkisma || 14400 / 14399 || | 6 2 2 -1 -2 0 -1 > || 0.120 ||
|| scintillisma ||   || | -4 4 -1 4 -1 -1 -1 > || 0.009 ||

==19-limit commas== 
||~ name(s) ||~ ratio ||~ monzo ||~ cents ||
|| Hunt 19-minor mediant comma || 513 / 512 || | -9 3 0 0 0 0 0 1 > || 3.378 ||
|| password || 1216 / 1215 || | 6 -5 -1 0 0 0 0 1> || 1.424 ||
|| Blumeyer comma || 2432 / 2431 || | 7 0 0 0 -1 -1 -1 1 > || 0.712 ||
|| 19-limit decimill ||   || | 9 -3 -3 -2 0 0 1 1> || 0.010 ||

Original HTML content:

<html><head><title>Unnoticeable commas</title></head><body><!-- ws:start:WikiTextHeadingRule:2:&lt;h1&gt; --><h1 id="toc0"><a name="Summary"></a><!-- ws:end:WikiTextHeadingRule:2 -->Summary</h1>
 These commas are called &quot;unnoticeable&quot; because, being equal to or less than 3.5 cents, they are smaller than the average peak <a class="wiki_link_ext" href="http://musictheory.zentral.zone/huntsystem2.html#2" rel="nofollow">JND</a> (just-noticeable difference) of human pitch perception, as illustrated by the research of <a name="comment-597264646_1-open" class="range"></a><a class="wiki_link" href="/Aaron%20Andrew%20Hunt">Aaron Andrew Hunt</a>.<a name="comment-597264646_1-close" class="range"></a> It is improbable that even a trained listener would be able to notice these intervals, and as such they a prime target for psychoacoustically informed <a class="wiki_link" href="/Microtempering">microtempering</a>.<br />
<br />
<!-- ws:start:WikiTextHeadingRule:4:&lt;h1&gt; --><h1 id="toc1"><a name="List of commas, by prime limit"></a><!-- ws:end:WikiTextHeadingRule:4 -->List of commas, by prime limit</h1>
 <!-- ws:start:WikiTextHeadingRule:6:&lt;h2&gt; --><h2 id="toc2"><a name="List of commas, by prime limit-3-limit commas"></a><!-- ws:end:WikiTextHeadingRule:6 -->3-limit commas</h2>
 

<table class="wiki_table">
    <tr>
        <th><span style="display: block; text-align: center;">name(s)</span><br />
</th>
        <th><span style="display: block; text-align: center;">monzo</span><br />
</th>
        <th><span style="display: block; text-align: center;">cents</span><br />
</th>
    </tr>
    <tr>
        <td>Sasktel comma, 51-Pythagorean comma<br />
</td>
        <td>| 485 -306 &gt;<br />
</td>
        <td>1.770<br />
</td>
    </tr>
    <tr>
        <td><a class="wiki_link" href="/Satanic%20comma">Satanic comma</a><br />
</td>
        <td>| -1054 665 &gt;<br />
</td>
        <td>0.076<br />
</td>
    </tr>
</table>

<br />
<!-- ws:start:WikiTextHeadingRule:8:&lt;h2&gt; --><h2 id="toc3"><a name="List of commas, by prime limit-5-limit commas"></a><!-- ws:end:WikiTextHeadingRule:8 -->5-limit commas</h2>
 

<table class="wiki_table">
    <tr>
        <th>name(s)<br />
</th>
        <th>monzo<br />
</th>
        <th>cents<br />
</th>
    </tr>
    <tr>
        <td>56-syntonic comma<br />
</td>
        <td>| 225 -224 56 &gt;<br />
</td>
        <td>1.431<br />
</td>
    </tr>
    <tr>
        <td>rubidia<br />
</td>
        <td>| -67 -9 35&gt;<br />
</td>
        <td>3.385<br />
</td>
    </tr>
    <tr>
        <td><a class="wiki_link" href="/vishnuzma">vishnuzma</a>, semisuper<br />
</td>
        <td>| 23 6 -14 &gt;<br />
</td>
        <td>3.338<br />
</td>
    </tr>
    <tr>
        <td><a class="wiki_link" href="/enneadeca">enneadeca</a>, 19-tone-comma<br />
</td>
        <td>| -14 -19 19 &gt;<br />
</td>
        <td>2.816<br />
</td>
    </tr>
    <tr>
        <td>vavoom<br />
</td>
        <td>| -68 18 17 &gt;<br />
</td>
        <td>2.523<br />
</td>
    </tr>
    <tr>
        <td>tricot comma<br />
</td>
        <td>| 39 -29 3 &gt;<br />
</td>
        <td>2.246<br />
</td>
    </tr>
    <tr>
        <td>schisma<br />
</td>
        <td>| -15 8 1 &gt;<br />
</td>
        <td>1.954<br />
</td>
    </tr>
    <tr>
        <td>counterschisma<br />
</td>
        <td>| -69 45 -1 &gt;<br />
</td>
        <td>1.661<br />
</td>
    </tr>
    <tr>
        <td>septendecima<br />
</td>
        <td>| -52 -17 34 &gt;<br />
</td>
        <td>1.431<br />
</td>
    </tr>
    <tr>
        <td>hemithirds comma, lunama<br />
</td>
        <td>| 38 -2 -15 &gt;<br />
</td>
        <td>1.384<br />
</td>
    </tr>
    <tr>
        <td>minortone comma<br />
</td>
        <td>| -16 35 -17 &gt;<br />
</td>
        <td>1.092<br />
</td>
    </tr>
    <tr>
        <td><a class="wiki_link" href="/Ennealimmal">ennealimma</a><br />
</td>
        <td>| 1 -27 18 &gt;<br />
</td>
        <td>0.862<br />
</td>
    </tr>
    <tr>
        <td>astro<br />
</td>
        <td>| 91 -12 -31 &gt;<br />
</td>
        <td>0.815<br />
</td>
    </tr>
    <tr>
        <td>kwazy<br />
</td>
        <td>| -53 10 16 &gt;<br />
</td>
        <td>0.569<br />
</td>
    </tr>
    <tr>
        <td>whoosh<br />
</td>
        <td>| 37 25 -33 &gt;<br />
</td>
        <td>0.522<br />
</td>
    </tr>
    <tr>
        <td>egads<br />
</td>
        <td>| -36 -52 51 &gt;<br />
</td>
        <td>0.339<br />
</td>
    </tr>
    <tr>
        <td>monzisma<br />
</td>
        <td>| 54 -37 2 &gt;<br />
</td>
        <td>0.292<br />
</td>
    </tr>
    <tr>
        <td>fortune<br />
</td>
        <td>| -107 47 14 &gt;<br />
</td>
        <td>0.277<br />
</td>
    </tr>
    <tr>
        <td>gross<br />
</td>
        <td>| 144 -22 -47 &gt;<br />
</td>
        <td>0.245<br />
</td>
    </tr>
    <tr>
        <td>senior<br />
</td>
        <td>| -17 62 -35 &gt;<br />
</td>
        <td>0.230<br />
</td>
    </tr>
    <tr>
        <td>raider<br />
</td>
        <td>| 71 -99 37 &gt;<br />
</td>
        <td>0.062<br />
</td>
    </tr>
    <tr>
        <td>pirate<br />
</td>
        <td>| -90 -15 49 &gt;<br />
</td>
        <td>0.047<br />
</td>
    </tr>
    <tr>
        <td>viking<br />
</td>
        <td>| -251 69 61 &gt;<br />
</td>
        <td>0.032<br />
</td>
    </tr>
    <tr>
        <td>atom<br />
</td>
        <td>| 161 -84 -12 &gt;<br />
</td>
        <td>0.015<br />
</td>
    </tr>
    <tr>
        <td>selenia<br />
</td>
        <td>| -433 -137 280 &gt;<br />
</td>
        <td>0.004764<br />
</td>
    </tr>
    <tr>
        <td>titania<br />
</td>
        <td>| 2746 -521 -827 &gt;<br />
</td>
        <td>0.003183<br />
</td>
    </tr>
    <tr>
        <td>quark<br />
</td>
        <td>| -573 237 85 &gt;<br />
</td>
        <td>0.000884<br />
</td>
    </tr>
    <tr>
        <td>scamp<br />
</td>
        <td>| -5836 4293 -417 &gt;<br />
</td>
        <td>0.000033<br />
</td>
    </tr>
    <tr>
        <td>rover<br />
</td>
        <td>| 1634 1502 -1729 &gt;<br />
</td>
        <td>0.000028<br />
</td>
    </tr>
    <tr>
        <td>rascal<br />
</td>
        <td>| -7470 2791 1312 &gt;<br />
</td>
        <td>0.000006<br />
</td>
    </tr>
</table>

<br />
<!-- ws:start:WikiTextHeadingRule:10:&lt;h2&gt; --><h2 id="toc4"><a name="List of commas, by prime limit-7-limit commas"></a><!-- ws:end:WikiTextHeadingRule:10 -->7-limit commas</h2>
 

<table class="wiki_table">
    <tr>
        <th>name(s)<br />
</th>
        <th>ratio<br />
</th>
        <th>monzo<br />
</th>
        <th>cents<br />
</th>
    </tr>
    <tr>
        <td>44-septimal comma<br />
</td>
        <td><br />
</td>
        <td>| -263 88 0 44 &gt;<br />
</td>
        <td>0.294<br />
</td>
    </tr>
    <tr>
        <td>horwell<br />
</td>
        <td>65625 / 65536<br />
</td>
        <td>| -16 1 5 1 &gt;<br />
</td>
        <td>2.349<br />
</td>
    </tr>
    <tr>
        <td>meter<br />
</td>
        <td><br />
</td>
        <td>| -11 2 7 -3 &gt;<br />
</td>
        <td>1.628<br />
</td>
    </tr>
    <tr>
        <td>wizma<br />
</td>
        <td><br />
</td>
        <td>| -6 -8 2 5 &gt;<br />
</td>
        <td>1.117<br />
</td>
    </tr>
    <tr>
        <td>breedsma<br />
</td>
        <td><a class="wiki_link" href="/2401_2400">2401 / 2400</a><br />
</td>
        <td>| -5 -1 -2 4 &gt;<br />
</td>
        <td>0.721<br />
</td>
    </tr>
    <tr>
        <td>ragisma<br />
</td>
        <td>4375 / 4374<br />
</td>
        <td>| -1 -7 4 1 &gt;<br />
</td>
        <td>0.396<br />
</td>
    </tr>
    <tr>
        <td>akjaysma, 5\7 octave comma<br />
</td>
        <td><br />
</td>
        <td>| 47 -7 -7 -7 &gt;<br />
</td>
        <td>0.338<br />
</td>
    </tr>
    <tr>
        <td>landscape<br />
</td>
        <td><br />
</td>
        <td>| -4 6 -6 3 &gt;<br />
</td>
        <td>0.325<br />
</td>
    </tr>
    <tr>
        <td>starscape<br />
</td>
        <td><br />
</td>
        <td>| -4 17 1 -9 &gt;<br />
</td>
        <td>0.116<br />
</td>
    </tr>
    <tr>
        <td>euzenius<br />
</td>
        <td><br />
</td>
        <td>| 3 -13 10 -2 &gt;<br />
</td>
        <td>0.070<br />
</td>
    </tr>
    <tr>
        <td>termite<br />
</td>
        <td><br />
</td>
        <td>| 9 -28 37 -18 &gt;<br />
</td>
        <td>1.072 * 10^-3<br />
</td>
    </tr>
    <tr>
        <td>neutrino<br />
</td>
        <td><br />
</td>
        <td>| 1889 -2145 138 424 &gt;<br />
</td>
        <td>1.636 * 10^-10<br />
</td>
    </tr>
</table>

<!-- ws:start:WikiTextHeadingRule:12:&lt;h2&gt; --><h2 id="toc5"><a name="List of commas, by prime limit-11-limit commas"></a><!-- ws:end:WikiTextHeadingRule:12 -->11-limit commas</h2>
 

<table class="wiki_table">
    <tr>
        <th>name(s)<br />
</th>
        <th>ratio<br />
</th>
        <th>monzo<br />
</th>
        <th>cents<br />
</th>
    </tr>
    <tr>
        <td>11-cycle schisma, 37-11-comma<br />
</td>
        <td><br />
</td>
        <td>| 128 0 0 0 -37 &gt;<br />
</td>
        <td>1.236<br />
</td>
    </tr>
    <tr>
        <td><a class="wiki_link" href="/swetismic%20chords">swetisma</a><br />
</td>
        <td>540 / 539<br />
</td>
        <td>| 2 3 1 -2 -1 &gt;<br />
</td>
        <td>3.209<br />
</td>
    </tr>
    <tr>
        <td>wizardharry<br />
</td>
        <td>4000 / 3993<br />
</td>
        <td>| 5 -1 3 0 -3 &gt;<br />
</td>
        <td>3.032<br />
</td>
    </tr>
    <tr>
        <td>vishdel<br />
</td>
        <td>5632 / 5625<br />
</td>
        <td>| 9 -2 -4 0 1 &gt;<br />
</td>
        <td>2.153<br />
</td>
    </tr>
    <tr>
        <td>sesdecal<br />
</td>
        <td><br />
</td>
        <td>| -4 1 7 0 -4 &gt;<br />
</td>
        <td>0.879<br />
</td>
    </tr>
    <tr>
        <td>hemigail<br />
</td>
        <td>43923 / 43904<br />
</td>
        <td>| -7 1 0 -3 4 &gt;<br />
</td>
        <td>0.749<br />
</td>
    </tr>
    <tr>
        <td>lehmerisma<br />
</td>
        <td>3025 / 3024<br />
</td>
        <td>| -4 -3 2 -1 2 &gt;<br />
</td>
        <td>0.572<br />
</td>
    </tr>
    <tr>
        <td>kalisma, Gauss' comma<br />
</td>
        <td>9801 / 9800<br />
</td>
        <td>| -3 4 -2 -2 2 &gt;<br />
</td>
        <td>0.177<br />
</td>
    </tr>
    <tr>
        <td>odiheim<br />
</td>
        <td><br />
</td>
        <td>| -1 2 -4 5 -2 &gt;<br />
</td>
        <td>0.149<br />
</td>
    </tr>
    <tr>
        <td>parimo<br />
</td>
        <td><br />
</td>
        <td>| -1 -11 -1 0 6 &gt;<br />
</td>
        <td>0.089<br />
</td>
    </tr>
    <tr>
        <td>ultimo<br />
</td>
        <td><br />
</td>
        <td>| -2 2 2 -7 4 &gt;<br />
</td>
        <td>0.028<br />
</td>
    </tr>
</table>

<br />
<!-- ws:start:WikiTextHeadingRule:14:&lt;h2&gt; --><h2 id="toc6"><a name="List of commas, by prime limit-13-limit commas"></a><!-- ws:end:WikiTextHeadingRule:14 -->13-limit commas</h2>
 

<table class="wiki_table">
    <tr>
        <th>name(s)<br />
</th>
        <th>ratio<br />
</th>
        <th>monzo<br />
</th>
        <th>cents<br />
</th>
    </tr>
    <tr>
        <td>tunbarsma<br />
</td>
        <td>625 / 624<br />
</td>
        <td>| -4 -1 4 0 0 -1 &gt;<br />
</td>
        <td>2.772<br />
</td>
    </tr>
    <tr>
        <td><a class="wiki_link" href="/The%20Archipelago">island comma</a><br />
</td>
        <td>676 / 675<br />
</td>
        <td>| 2 -3 -2 0 0 2 &gt;<br />
</td>
        <td>2.563<br />
</td>
    </tr>
    <tr>
        <td><a class="wiki_link" href="/squbemic%20chords">squbema</a><br />
</td>
        <td>729 / 728<br />
</td>
        <td>| -3 6 0 -1 0 -1 &gt;<br />
</td>
        <td>2.376<br />
</td>
    </tr>
    <tr>
        <td><a class="wiki_link" href="/petrmic%20triad">petrma</a><br />
</td>
        <td>2200 / 2197<br />
</td>
        <td>| 3 0 2 0 1 -3 &gt;<br />
</td>
        <td>2.362<br />
</td>
    </tr>
    <tr>
        <td><a class="wiki_link" href="/nicolic%20tetrad">nicola</a><br />
</td>
        <td>1575 / 1573<br />
</td>
        <td>| 0 2 2 1 -2 -1 &gt;<br />
</td>
        <td>2.200<br />
</td>
    </tr>
    <tr>
        <td><a class="wiki_link" href="/sinbadmic%20tetrad">sinbadma</a><br />
</td>
        <td>1001 / 1000<br />
</td>
        <td>| -3 0 -3 1 1 1 &gt;<br />
</td>
        <td>1.730<br />
</td>
    </tr>
    <tr>
        <td>cantonisma<br />
</td>
        <td>10985 / 10976<br />
</td>
        <td>| -5 0 1 -3 0 3 &gt;<br />
</td>
        <td>1.419<br />
</td>
    </tr>
    <tr>
        <td>lummic<br />
</td>
        <td>1716 / 1715<br />
</td>
        <td>| 2 1 -1 -3 1 1 &gt;<br />
</td>
        <td>1.009<br />
</td>
    </tr>
    <tr>
        <td>ibnsinma<br />
</td>
        <td>2080 / 2079<br />
</td>
        <td>| 5 -3 1 -1 -1 1 &gt;<br />
</td>
        <td>0.833<br />
</td>
    </tr>
    <tr>
        <td>schismina<br />
</td>
        <td>4096 / 4095<br />
</td>
        <td>| 12 -2 -1 -1 0 -1 &gt;<br />
</td>
        <td>0.423<br />
</td>
    </tr>
    <tr>
        <td>leprechaun comma<br />
</td>
        <td>4225 / 4224<br />
</td>
        <td>| -7 -1 2 0 -1 2 &gt;<br />
</td>
        <td>0.410<br />
</td>
    </tr>
    <tr>
        <td>jacobin<br />
</td>
        <td>6656 / 6655<br />
</td>
        <td>| 9 0 -1 0 -3 1 &gt;<br />
</td>
        <td>0.260<br />
</td>
    </tr>
    <tr>
        <td>harmonisma<br />
</td>
        <td>10648 / 10647<br />
</td>
        <td>| 3 -2 0 -1 3 -2 &gt;<br />
</td>
        <td>0.163<br />
</td>
    </tr>
    <tr>
        <td>chalmersima<br />
</td>
        <td><br />
</td>
        <td>| -6 6 -2 -1 -1 2 &gt;<br />
</td>
        <td>0.014<br />
</td>
    </tr>
</table>

<br />
<!-- ws:start:WikiTextHeadingRule:16:&lt;h2&gt; --><h2 id="toc7"><a name="List of commas, by prime limit-17-limit commas"></a><!-- ws:end:WikiTextHeadingRule:16 -->17-limit commas</h2>
 

<table class="wiki_table">
    <tr>
        <th>name(s)<br />
</th>
        <th>ratio<br />
</th>
        <th>monzo<br />
</th>
        <th>cents<br />
</th>
    </tr>
    <tr>
        <td>xenisma<br />
</td>
        <td>2058 / 2057<br />
</td>
        <td>| 1 1 0 3 -2 0 -1 &gt;<br />
</td>
        <td>0.841<br />
</td>
    </tr>
    <tr>
        <td>flashma<br />
</td>
        <td>12376 / 12375<br />
</td>
        <td>| 3 -2 -3 1 -1 1 1 &gt;<br />
</td>
        <td>0.140<br />
</td>
    </tr>
    <tr>
        <td>sparkisma<br />
</td>
        <td>14400 / 14399<br />
</td>
        <td>| 6 2 2 -1 -2 0 -1 &gt;<br />
</td>
        <td>0.120<br />
</td>
    </tr>
    <tr>
        <td>scintillisma<br />
</td>
        <td><br />
</td>
        <td>| -4 4 -1 4 -1 -1 -1 &gt;<br />
</td>
        <td>0.009<br />
</td>
    </tr>
</table>

<br />
<!-- ws:start:WikiTextHeadingRule:18:&lt;h2&gt; --><h2 id="toc8"><a name="List of commas, by prime limit-19-limit commas"></a><!-- ws:end:WikiTextHeadingRule:18 -->19-limit commas</h2>
 

<table class="wiki_table">
    <tr>
        <th>name(s)<br />
</th>
        <th>ratio<br />
</th>
        <th>monzo<br />
</th>
        <th>cents<br />
</th>
    </tr>
    <tr>
        <td>Hunt 19-minor mediant comma<br />
</td>
        <td>513 / 512<br />
</td>
        <td>| -9 3 0 0 0 0 0 1 &gt;<br />
</td>
        <td>3.378<br />
</td>
    </tr>
    <tr>
        <td>password<br />
</td>
        <td>1216 / 1215<br />
</td>
        <td>| 6 -5 -1 0 0 0 0 1&gt;<br />
</td>
        <td>1.424<br />
</td>
    </tr>
    <tr>
        <td>Blumeyer comma<br />
</td>
        <td>2432 / 2431<br />
</td>
        <td>| 7 0 0 0 -1 -1 -1 1 &gt;<br />
</td>
        <td>0.712<br />
</td>
    </tr>
    <tr>
        <td>19-limit decimill<br />
</td>
        <td><br />
</td>
        <td>| 9 -3 -3 -2 0 0 1 1&gt;<br />
</td>
        <td>0.010<br />
</td>
    </tr>
</table>

</body></html>

@@ 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:kai.lugheidh|kai.lugheidh]] and made on <tt>2016-11-21 19:30:25 UTC</tt>.<br>
+: This revision was by author [[User:xenwolf|xenwolf]] and made on <tt>2016-12-29 12:51:22 UTC</tt>.<br>
-: The original revision id was <tt>600045648</tt>.<br>
+: The original revision id was <tt>602895860</tt>.<br>
-: The revision comment was: <tt></tt><br>
+: The revision comment was: <tt>removed tel links</tt><br>
 The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.<br>
 <h4>Original Wikitext content:</h4>
@@ Line 17: / Line 17: @@
 ==5-limit commas==
 ||~ name(s) ||~ monzo ||~ cents ||
-|| 56-syntonic comma || | [[tel/225 -224 56|225 -224 56]] &gt; || 1.431 ||
+|| 56-syntonic comma || | 225 -224 56 &gt; || 1.431 ||
 || rubidia || | -67 -9 35&gt; || 3.385 ||
 || [[vishnuzma]], semisuper || | 23 6 -14 &gt; || 3.338 ||
@@ Line 42: / Line 42: @@
 || atom || | 161 -84 -12 &gt; || 0.015 ||
 || selenia || | -433 -137 280 &gt; || 0.004764 ||
-|| titania || | [[tel/2746 -521 -827|2746 -521 -827]] &gt; || 0.003183 ||
+|| titania || | 2746 -521 -827 &gt; || 0.003183 ||
 || quark || | -573 237 85 &gt; || 0.000884 ||
 || scamp || | -5836 4293 -417 &gt; || 0.000033 ||
-|| rover || | [[tel/1634 1502 -1729|1634 1502 -1729]] &gt; || 0.000028 ||
+|| rover || | 1634 1502 -1729 &gt; || 0.000028 ||
-|| rascal || | -7470 [[tel/2791 1312|2791 1312]] &gt; || 0.000006 ||
+|| rascal || | -7470 2791 1312 &gt; || 0.000006 ||
 ==7-limit commas==
@@ Line 61: / Line 61: @@
 || euzenius ||   || | 3 -13 10 -2 &gt; || 0.070 ||
 || termite ||   || | 9 -28 37 -18 &gt; || 1.072 * 10^-3 ||
-|| neutrino ||   || | [[tel/1889 -2145 138 424|1889 -2145 138 424]] &gt; || 1.636 * 10^-10 ||
+|| neutrino ||   || | 1889 -2145 138 424 &gt; || 1.636 * 10^-10 ||
 ==11-limit commas==
 ||~ name(s) ||~ ratio ||~ monzo ||~ cents ||
-|| 11-cycle schisma, 37-11-comma ||   || | [[tel/128 0 0 0 -37|128 0 0 0 -37]] &gt; || 1.236 ||
+|| 11-cycle schisma, 37-11-comma ||   || | 128 0 0 0 -37 &gt; || 1.236 ||
 || [[swetismic chords|swetisma]] || 540 / 539 || | 2 3 1 -2 -1 &gt; || 3.209 ||
 || wizardharry || 4000 / 3993 || | 5 -1 3 0 -3 &gt; || 3.032 ||
@@ Line 87: / Line 87: @@
 || lummic || 1716 / 1715 || | 2 1 -1 -3 1 1 &gt; || 1.009 ||
 || ibnsinma || 2080 / 2079 || | 5 -3 1 -1 -1 1 &gt; || 0.833 ||
-|| schismina || 4096 / 4095 || | [[tel/12 -2 -1 -1 0 -1|12 -2 -1 -1 0 -1]] &gt; || 0.423 ||
+|| schismina || 4096 / 4095 || | 12 -2 -1 -1 0 -1 &gt; || 0.423 ||
 || leprechaun comma || 4225 / 4224 || | -7 -1 2 0 -1 2 &gt; || 0.410 ||
 || jacobin || 6656 / 6655 || | 9 0 -1 0 -3 1 &gt; || 0.260 ||
@@ Line 157: / Line 157: @@
          &lt;td&gt;56-syntonic comma&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;| &lt;a class="wiki_link" href="http://tel.wikispaces.com/225%20-224%2056"&gt;225 -224 56&lt;/a&gt; &amp;gt;&lt;br /&gt;
+         &lt;td&gt;| 225 -224 56 &amp;gt;&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;1.431&lt;br /&gt;
@@ Line 357: / Line 357: @@
          &lt;td&gt;titania&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;| &lt;a class="wiki_link" href="http://tel.wikispaces.com/2746%20-521%20-827"&gt;2746 -521 -827&lt;/a&gt; &amp;gt;&lt;br /&gt;
+         &lt;td&gt;| 2746 -521 -827 &amp;gt;&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;0.003183&lt;br /&gt;
@@ Line 381: / Line 381: @@
          &lt;td&gt;rover&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;| &lt;a class="wiki_link" href="http://tel.wikispaces.com/1634%201502%20-1729"&gt;1634 1502 -1729&lt;/a&gt; &amp;gt;&lt;br /&gt;
+         &lt;td&gt;| 1634 1502 -1729 &amp;gt;&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;0.000028&lt;br /&gt;
@@ Line 389: / Line 389: @@
          &lt;td&gt;rascal&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;| -7470 &lt;a class="wiki_link" href="http://tel.wikispaces.com/2791%201312"&gt;2791 1312&lt;/a&gt; &amp;gt;&lt;br /&gt;
+         &lt;td&gt;| -7470 2791 1312 &amp;gt;&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;0.000006&lt;br /&gt;
@@ Line 526: / Line 526: @@
          &lt;td&gt;&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;| &lt;a class="wiki_link" href="http://tel.wikispaces.com/1889%20-2145%20138%20424"&gt;1889 -2145 138 424&lt;/a&gt; &amp;gt;&lt;br /&gt;
+         &lt;td&gt;| 1889 -2145 138 424 &amp;gt;&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;1.636 * 10^-10&lt;br /&gt;
@@ Line 552: / Line 552: @@
          &lt;td&gt;&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;| &lt;a class="wiki_link" href="http://tel.wikispaces.com/128%200%200%200%20-37"&gt;128 0 0 0 -37&lt;/a&gt; &amp;gt;&lt;br /&gt;
+         &lt;td&gt;| 128 0 0 0 -37 &amp;gt;&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;1.236&lt;br /&gt;
@@ Line 769: / Line 769: @@
          &lt;td&gt;4096 / 4095&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;| &lt;a class="wiki_link" href="http://tel.wikispaces.com/12%20-2%20-1%20-1%200%20-1"&gt;12 -2 -1 -1 0 -1&lt;/a&gt; &amp;gt;&lt;br /&gt;
+         &lt;td&gt;| 12 -2 -1 -1 0 -1 &amp;gt;&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;0.423&lt;br /&gt;

Unnoticeable comma: Difference between revisions

Revision as of 12:51, 29 December 2016

IMPORTED REVISION FROM WIKISPACES

Original Wikitext content:

Original HTML content:

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