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| <h2>IMPORTED REVISION FROM WIKISPACES</h2>
| | =Summary= |
| This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br>
| | 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 [[Aaron_Andrew_Hunt|Aaron Andrew Hunt]]. 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]]. |
| : This revision was by author [[User:mbattaglia1|mbattaglia1]] and made on <tt>2018-06-19 16:08:06 UTC</tt>.<br>
| |
| : The original revision id was <tt>630637691</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>
| |
| <h4>Original Wikitext 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;white-space: pre-wrap ! important" class="old-revision-html">=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= | | =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== | | ==3-limit commas== |
| ||~ name(s) ||~ monzo ||~ cents ||
| |
| || 56-syntonic comma || | 225 -224 56 > || 1.431 ||
| |
| || dodifo || | -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== | | {| class="wikitable" |
| ||~ name(s) ||~ ratio ||~ monzo ||~ cents || | | |- |
| || 44-septimal comma || || | -263 88 0 44 > || 0.294 || | | ! | <span style="display: block; text-align: center;">name(s)</span> |
| || horwell || 65625 / 65536 || | -16 1 5 1 > || 2.349 ||
| | ! | <span style="display: block; text-align: center;">monzo</span> |
| || meter || || | -11 2 7 -3 > || 1.628 || | | ! | <span style="display: block; text-align: center;">cents</span> |
| || wizma || || | -6 -8 2 5 > || 1.117 ||
| | |- |
| || breedsma || [[2401_2400|2401 / 2400]] || | -5 -1 -2 4 > || 0.721 ||
| | | | Sasktel comma, 51-Pythagorean comma |
| || ragisma || 4375 / 4374 || | -1 -7 4 1 > || 0.396 || | | | | | 485 -306 > |
| || akjaysma, 5\7 octave comma || || | 47 -7 -7 -7 > || 0.338 || | | | | 1.770 |
| || landscape || || | -4 6 -6 3 > || 0.325 ||
| | |- |
| || starscape || || | -4 17 1 -9 > || 0.116 || | | | | [[Satanic_comma|Satanic comma]] |
| || euzenius || || | 3 -13 10 -2 > || 0.070 || | | | | | -1054 665 > |
| || termite || || | 9 -28 37 -18 > || 1.072 * 10^-3 ||
| | | | 0.076 |
| || 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== | | ==5-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== | | {| class="wikitable" |
| ||~ name(s) ||~ ratio ||~ monzo ||~ cents || | | |- |
| || xenisma || 2058 / 2057 || | 1 1 0 3 -2 0 -1 > || 0.841 || | | ! | name(s) |
| || flashma || 12376 / 12375 || | 3 -2 -3 1 -1 1 1 > || 0.140 || | | ! | monzo |
| || sparkisma || 14400 / 14399 || | 6 2 2 -1 -2 0 -1 > || 0.120 || | | ! | cents |
| || scintillisma || || | -4 4 -1 4 -1 -1 -1 > || 0.009 || | | |- |
| | | | 56-syntonic comma |
| | | | | 225 -224 56 > |
| | | | 1.431 |
| | |- |
| | | | dodifo |
| | | | | -67 -9 35> |
| | | | 3.385 |
| | |- |
| | | | [[vishnuzma|vishnuzma]], semisuper |
| | | | | 23 6 -14 > |
| | | | 3.338 |
| | |- |
| | | | [[enneadeca|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 |
| | |} |
|
| |
|
| ==19-limit commas== | | ==7-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 ||</pre></div>
| |
| <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>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">
| | {| class="wikitable" |
| <tr>
| | |- |
| <th><span style="display: block; text-align: center;">name(s)</span><br />
| | ! | name(s) |
| </th>
| | ! | ratio |
| <th><span style="display: block; text-align: center;">monzo</span><br />
| | ! | monzo |
| </th>
| | ! | cents |
| <th><span style="display: block; text-align: center;">cents</span><br />
| | |- |
| </th>
| | | | 44-septimal comma |
| </tr>
| | | | |
| <tr>
| | | | | -263 88 0 44 > |
| <td>Sasktel comma, 51-Pythagorean comma<br />
| | | | 0.294 |
| </td>
| | |- |
| <td>| 485 -306 &gt;<br />
| | | | horwell |
| </td>
| | | | 65625 / 65536 |
| <td>1.770<br />
| | | | | -16 1 5 1 > |
| </td>
| | | | 2.349 |
| </tr>
| | |- |
| <tr>
| | | | meter |
| <td><a class="wiki_link" href="/Satanic%20comma">Satanic comma</a><br />
| | | | |
| </td>
| | | | | -11 2 7 -3 > |
| <td>| -1054 665 &gt;<br />
| | | | 1.628 |
| </td>
| | |- |
| <td>0.076<br />
| | | | wizma |
| </td>
| | | | |
| </tr>
| | | | | -6 -8 2 5 > |
| </table>
| | | | 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 |
| | |} |
|
| |
|
| <br />
| | ==11-limit commas== |
| <!-- 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">
| | {| class="wikitable" |
| <tr>
| | |- |
| <th>name(s)<br />
| | ! | name(s) |
| </th>
| | ! | ratio |
| <th>monzo<br />
| | ! | monzo |
| </th>
| | ! | cents |
| <th>cents<br />
| | |- |
| </th>
| | | | 11-cycle schisma, 37-11-comma |
| </tr>
| | | | |
| <tr>
| | | | | 128 0 0 0 -37 > |
| <td>56-syntonic comma<br />
| | | | 1.236 |
| </td>
| | |- |
| <td>| 225 -224 56 &gt;<br />
| | | | [[swetismic_chords|swetisma]] |
| </td>
| | | | 540 / 539 |
| <td>1.431<br />
| | | | | 2 3 1 -2 -1 > |
| </td>
| | | | 3.209 |
| </tr>
| | |- |
| <tr>
| | | | wizardharry |
| <td>dodifo<br />
| | | | 4000 / 3993 |
| </td>
| | | | | 5 -1 3 0 -3 > |
| <td>| -67 -9 35&gt;<br />
| | | | 3.032 |
| </td>
| | |- |
| <td>3.385<br />
| | | | vishdel |
| </td>
| | | | 5632 / 5625 |
| </tr>
| | | | | 9 -2 -4 0 1 > |
| <tr>
| | | | 2.153 |
| <td><a class="wiki_link" href="/vishnuzma">vishnuzma</a>, semisuper<br />
| | |- |
| </td>
| | | | sesdecal |
| <td>| 23 6 -14 &gt;<br />
| | | | |
| </td>
| | | | | -4 1 7 0 -4 > |
| <td>3.338<br />
| | | | 0.879 |
| </td>
| | |- |
| </tr>
| | | | hemigail |
| <tr>
| | | | 43923 / 43904 |
| <td><a class="wiki_link" href="/enneadeca">enneadeca</a>, 19-tone-comma<br />
| | | | | -7 1 0 -3 4 > |
| </td>
| | | | 0.749 |
| <td>| -14 -19 19 &gt;<br />
| | |- |
| </td>
| | | | lehmerisma |
| <td>2.816<br />
| | | | 3025 / 3024 |
| </td>
| | | | | -4 -3 2 -1 2 > |
| </tr>
| | | | 0.572 |
| <tr>
| | |- |
| <td>vavoom<br />
| | | | kalisma, Gauss' comma |
| </td>
| | | | 9801 / 9800 |
| <td>| -68 18 17 &gt;<br />
| | | | | -3 4 -2 -2 2 > |
| </td>
| | | | 0.177 |
| <td>2.523<br />
| | |- |
| </td>
| | | | odiheim |
| </tr>
| | | | |
| <tr>
| | | | | -1 2 -4 5 -2 > |
| <td>tricot comma<br />
| | | | 0.149 |
| </td>
| | |- |
| <td>| 39 -29 3 &gt;<br />
| | | | parimo |
| </td>
| | | | |
| <td>2.246<br />
| | | | | -1 -11 -1 0 6 > |
| </td>
| | | | 0.089 |
| </tr>
| | |- |
| <tr>
| | | | ultimo |
| <td>schisma<br />
| | | | |
| </td>
| | | | | -2 2 2 -7 4 > |
| <td>| -15 8 1 &gt;<br />
| | | | 0.028 |
| </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 />
| | ==13-limit commas== |
| <!-- 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">
| | {| class="wikitable" |
| <tr>
| | |- |
| <th>name(s)<br />
| | ! | name(s) |
| </th>
| | ! | ratio |
| <th>ratio<br />
| | ! | monzo |
| </th>
| | ! | cents |
| <th>monzo<br />
| | |- |
| </th>
| | | | tunbarsma |
| <th>cents<br />
| | | | 625 / 624 |
| </th>
| | | | | -4 -1 4 0 0 -1 > |
| </tr>
| | | | 2.772 |
| <tr>
| | |- |
| <td>44-septimal comma<br />
| | | | [[The_Archipelago|island comma]] |
| </td>
| | | | 676 / 675 |
| <td><br />
| | | | | 2 -3 -2 0 0 2 > |
| </td>
| | | | 2.563 |
| <td>| -263 88 0 44 &gt;<br />
| | |- |
| </td>
| | | | [[squbemic_chords|squbema]] |
| <td>0.294<br />
| | | | 729 / 728 |
| </td>
| | | | | -3 6 0 -1 0 -1 > |
| </tr>
| | | | 2.376 |
| <tr>
| | |- |
| <td>horwell<br />
| | | | [[petrmic_triad|petrma]] |
| </td>
| | | | 2200 / 2197 |
| <td>65625 / 65536<br />
| | | | | 3 0 2 0 1 -3 > |
| </td>
| | | | 2.362 |
| <td>| -16 1 5 1 &gt;<br />
| | |- |
| </td>
| | | | [[nicolic_tetrad|nicola]] |
| <td>2.349<br />
| | | | 1575 / 1573 |
| </td>
| | | | | 0 2 2 1 -2 -1 > |
| </tr>
| | | | 2.200 |
| <tr>
| | |- |
| <td>meter<br />
| | | | [[sinbadmic_tetrad|sinbadma]] |
| </td>
| | | | 1001 / 1000 |
| <td><br />
| | | | | -3 0 -3 1 1 1 > |
| </td>
| | | | 1.730 |
| <td>| -11 2 7 -3 &gt;<br />
| | |- |
| </td>
| | | | cantonisma |
| <td>1.628<br />
| | | | 10985 / 10976 |
| </td>
| | | | | -5 0 1 -3 0 3 > |
| </tr>
| | | | 1.419 |
| <tr>
| | |- |
| <td>wizma<br />
| | | | lummic |
| </td>
| | | | 1716 / 1715 |
| <td><br />
| | | | | 2 1 -1 -3 1 1 > |
| </td>
| | | | 1.009 |
| <td>| -6 -8 2 5 &gt;<br />
| | |- |
| </td>
| | | | ibnsinma |
| <td>1.117<br />
| | | | 2080 / 2079 |
| </td>
| | | | | 5 -3 1 -1 -1 1 > |
| </tr>
| | | | 0.833 |
| <tr>
| | |- |
| <td>breedsma<br />
| | | | schismina |
| </td>
| | | | 4096 / 4095 |
| <td><a class="wiki_link" href="/2401_2400">2401 / 2400</a><br />
| | | | | 12 -2 -1 -1 0 -1 > |
| </td>
| | | | 0.423 |
| <td>| -5 -1 -2 4 &gt;<br />
| | |- |
| </td>
| | | | leprechaun comma |
| <td>0.721<br />
| | | | 4225 / 4224 |
| </td>
| | | | | -7 -1 2 0 -1 2 > |
| </tr>
| | | | 0.410 |
| <tr>
| | |- |
| <td>ragisma<br />
| | | | jacobin |
| </td>
| | | | 6656 / 6655 |
| <td>4375 / 4374<br />
| | | | | 9 0 -1 0 -3 1 > |
| </td>
| | | | 0.260 |
| <td>| -1 -7 4 1 &gt;<br />
| | |- |
| </td>
| | | | harmonisma |
| <td>0.396<br />
| | | | 10648 / 10647 |
| </td>
| | | | | 3 -2 0 -1 3 -2 > |
| </tr>
| | | | 0.163 |
| <tr>
| | |- |
| <td>akjaysma, 5\7 octave comma<br />
| | | | chalmersima |
| </td>
| | | | |
| <td><br />
| | | | | -6 6 -2 -1 -1 2 > |
| </td>
| | | | 0.014 |
| <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>
| | ==17-limit commas== |
|
| |
|
| |
|
| <table class="wiki_table">
| | {| class="wikitable" |
| <tr>
| | |- |
| <th>name(s)<br />
| | ! | name(s) |
| </th>
| | ! | ratio |
| <th>ratio<br />
| | ! | monzo |
| </th>
| | ! | cents |
| <th>monzo<br />
| | |- |
| </th>
| | | | xenisma |
| <th>cents<br />
| | | | 2058 / 2057 |
| </th>
| | | | | 1 1 0 3 -2 0 -1 > |
| </tr>
| | | | 0.841 |
| <tr>
| | |- |
| <td>11-cycle schisma, 37-11-comma<br />
| | | | flashma |
| </td>
| | | | 12376 / 12375 |
| <td><br />
| | | | | 3 -2 -3 1 -1 1 1 > |
| </td>
| | | | 0.140 |
| <td>| 128 0 0 0 -37 &gt;<br />
| | |- |
| </td>
| | | | sparkisma |
| <td>1.236<br />
| | | | 14400 / 14399 |
| </td>
| | | | | 6 2 2 -1 -2 0 -1 > |
| </tr>
| | | | 0.120 |
| <tr>
| | |- |
| <td><a class="wiki_link" href="/swetismic%20chords">swetisma</a><br />
| | | | scintillisma |
| </td>
| | | | |
| <td>540 / 539<br />
| | | | | -4 4 -1 4 -1 -1 -1 > |
| </td>
| | | | 0.009 |
| <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 />
| | ==19-limit commas== |
| <!-- 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">
| | {| class="wikitable" |
| <tr>
| | |- |
| <th>name(s)<br />
| | ! | name(s) |
| </th>
| | ! | ratio |
| <th>ratio<br />
| | ! | monzo |
| </th>
| | ! | cents |
| <th>monzo<br />
| | |- |
| </th>
| | | | Hunt 19-minor mediant comma |
| <th>cents<br />
| | | | 513 / 512 |
| </th>
| | | | | -9 3 0 0 0 0 0 1 > |
| </tr>
| | | | 3.378 |
| <tr>
| | |- |
| <td>tunbarsma<br />
| | | | password |
| </td>
| | | | 1216 / 1215 |
| <td>625 / 624<br />
| | | | | 6 -5 -1 0 0 0 0 1> |
| </td>
| | | | 1.424 |
| <td>| -4 -1 4 0 0 -1 &gt;<br />
| | |- |
| </td>
| | | | Blumeyer comma |
| <td>2.772<br />
| | | | 2432 / 2431 |
| </td>
| | | | | 7 0 0 0 -1 -1 -1 1 > |
| </tr>
| | | | 0.712 |
| <tr>
| | |- |
| <td><a class="wiki_link" href="/The%20Archipelago">island comma</a><br />
| | | | 19-limit decimill |
| </td>
| | | | |
| <td>676 / 675<br />
| | | | | 9 -3 -3 -2 0 0 1 1> |
| </td>
| | | | 0.010 |
| <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></pre></div>
| |