Small comma: Difference between revisions
Wikispaces>genewardsmith **Imported revision 555733075 - Original comment: ** |
Wikispaces>genewardsmith **Imported revision 555733527 - Original comment: ** |
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<h2>IMPORTED REVISION FROM WIKISPACES</h2> | <h2>IMPORTED REVISION FROM WIKISPACES</h2> | ||
This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br> | 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>2015-07-25 13: | : This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2015-07-25 13:40:02 UTC</tt>.<br> | ||
: The original revision id was <tt> | : The original revision id was <tt>555733527</tt>.<br> | ||
: The revision comment was: <tt></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> | The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.<br> | ||
| Line 17: | Line 17: | ||
||~ name(s) ||~ ratio ||~ monzo ||~ cents || | ||~ name(s) ||~ ratio ||~ monzo ||~ cents || | ||
|| limma, Pythagorean minor second || [[256_243|256 / 243]] || | 8 -5 > || 90.225 || | || limma, Pythagorean minor second || [[256_243|256 / 243]] || | 8 -5 > || 90.225 || | ||
|| [[Pythagorean comma]] || 531441 / 524288 || | -19 12 > || 23.460 || | || [[Pythagorean comma]] || 531441 / 524288 || | -19 12 > || 23.460 || | ||
|| [[17-comma]] || 134217728 / 129140163 || | 27 -17 > || 66.765 || | || [[17-comma]] || 134217728 / 129140163 || | 27 -17 > || 66.765 || | ||
|| [[29-comma]] || [[tel/70368744177664|70368744177664]] / [[tel/68630377364883|68630377364883]] || | 46 -29 > || 43.305 || | || [[29-comma]] || [[tel/70368744177664|70368744177664]] / [[tel/68630377364883|68630377364883]] || | 46 -29 > || 43.305 || | ||
|| [[41-comma]] || 36893488147419103232 / 36472996377170786403 || | 65 -41 > || 19.845 || | || [[41-comma]] || 36893488147419103232 / 36472996377170786403 || | 65 -41 > || 19.845 || | ||
|| Pythagorean Integer cents comma || || | 317 -200 > || 9.000 || | |||
|| [[Mercator's comma]], 53-comma || 19383245667680019896796723 / 19342813113834066795298816 || | -84 53 > || 3.615 || | || [[Mercator's comma]], 53-comma || 19383245667680019896796723 / 19342813113834066795298816 || | -84 53 > || 3.615 || | ||
|| Sasktel comma, <span style="line-height: 1.5;">51-</span>Pythagorean comma || || | 485 -306 > || 1.770 || | || Sasktel comma, <span style="line-height: 1.5;">51-</span>Pythagorean comma || || | 485 -306 > || 1.770 || | ||
|| [[Satanic comma]] || || | -1054 665 > || 0.076 || | || [[Satanic comma]] || || | -1054 665 > || 0.076 || | ||
==5-limit commas== | ==5-limit commas== | ||
||~ name(s) ||~ ratio ||~ monzo ||~ cents || | ||~ name(s) ||~ ratio ||~ monzo ||~ cents || | ||
|| Twenty-two thirds limma || || | -51 0 22 > || 98.902 || | |||
|| Twenty-two thirds limma | |||
|| sibbolet || || | -58 0 25 > || 57.843 || | || sibbolet || || | -58 0 25 > || 57.843 || | ||
|| Hunt 5-cycle comma || || | -65 0 28 > || 16.784 || | || Hunt 5-cycle comma || || | -65 0 28 > || 16.784 || | ||
| Line 45: | Line 34: | ||
|| 34-5-comma || || | 79 0 -34 > || 65.334 || | || 34-5-comma || || | 79 0 -34 > || 65.334 || | ||
|| Schismic thirds chromatic semitone || || | -123 0 53 > || 74.627 || | || Schismic thirds chromatic semitone || || | -123 0 53 > || 74.627 || | ||
|| 10-15-comma || || | -39 10 10 > || 82.687 || | || 10-15-comma || || | -39 10 10 > || 82.687 || | ||
|| 11-15-comma || || | 43 -11 -11 > || 29.044 || | || 11-15-comma || || | 43 -11 -11 > || 29.044 || | ||
|| 21-15-comma || || | 82 -21 -21 > || 53.643 || | || 21-15-comma || || | 82 -21 -21 > || 53.643 || | ||
|| 32-15-comma || || | 125 -32 -32 > || 24.599 || | || 32-15-comma || || | 125 -32 -32 > || 24.599 || | ||
|| Huntian 15-cycle comma || || | -168 43 43 > || 4.445 || | || Huntian 15-cycle comma || || | -168 43 43 > || 4.445 || | ||
| Line 55: | Line 42: | ||
|| 54-15-comma || || | 211 -54 -54 > || 33.489 || | || 54-15-comma || || | 211 -54 -54 > || 33.489 || | ||
|| 76-15-comma || || | 297 -76 -76 > || 91.578 || | || 76-15-comma || || | 297 -76 -76 > || 91.578 || | ||
|| major chroma, major limma, pelogic comma || [[135_128|135 / 128]] || | -7 3 1 > || 92.179 || | || major chroma, major limma, pelogic comma || [[135_128|135 / 128]] || | -7 3 1 > || 92.179 || | ||
|| ripple || 6561 / 6250 || | -1 8 -5 > || 84.071 || | || ripple || 6561 / 6250 || | -1 8 -5 > || 84.071 || | ||
| Line 95: | Line 69: | ||
|| minimal diesis, [[tetracot comma]] || 20000 / 19683 || | 5 -9 4 > || 27.660 || | || minimal diesis, [[tetracot comma]] || 20000 / 19683 || | 5 -9 4 > || 27.660 || | ||
|| roda || 131072000 / 129140163 || | 20 -17 3 > || 25.706 || | || roda || 131072000 / 129140163 || | 20 -17 3 > || 25.706 || | ||
|| maja | | || maja || 762939453125 / 753145430616 || | -3 -23 17 > || 22.368 || | ||
|| syntonic comma, Didymos comma, meantone comma || [[81_80|81 / 80]] || | -4 4 -1 > || 21.506 || | || syntonic comma, Didymos comma, meantone comma || [[81_80|81 / 80]] || | -4 4 -1 > || 21.506 || | ||
|| [[Maquila family|maquila comma]] || 562949953421312 / 556182861328125 || |49 -6 -17> || 20.937 || | || [[Maquila family|maquila comma]] || 562949953421312 / 556182861328125 || |49 -6 -17> || 20.937 || | ||
| Line 110: | Line 84: | ||
|| [[escapade comma]] || || | 32 -7 -9 > || 9.492 || | || [[escapade comma]] || || | 32 -7 -9 > || 9.492 || | ||
|| [[kleisma]], semicomma majeur || 15625 / 15552 || | -6 -5 6 > || 8.107 || | || [[kleisma]], semicomma majeur || 15625 / 15552 || | -6 -5 6 > || 8.107 || | ||
|| unidecma | | || unidecma || 31381059609 / 31250000000 || | -7 22 -12 > || 7.245 || | ||
|| [[mutt comma]] || || | -44 -3 21 > || 6.723 || | || [[mutt comma]] || || | -44 -3 21 > || 6.723 || | ||
|| [[amity comma]] || 1600000 / 1594323 || | 9 -13 5 > || 6.154 || | || [[amity comma]] || 1600000 / 1594323 || | 9 -13 5 > || 6.154 || | ||
| Line 117: | Line 91: | ||
|| [[vulture comma]] || || | 24 -21 4 > || 4.200 || | || [[vulture comma]] || || | 24 -21 4 > || 4.200 || | ||
|| rubidia || || | -67 -9 35> || 3.385 || | || rubidia || || | -67 -9 35> || 3.385 || | ||
|| [[vishnuzma]], semisuper | | || [[vishnuzma]], semisuper || 6115295232]] / 6103515625 || | 23 6 -14 > || 3.338 || | ||
|| 15-3/5-comma || || | -11 -15 15 > || 65.381 || | || 15-3/5-comma || || | -11 -15 15 > || 65.381 || | ||
|| [[enneadeca]], 19-tone-comma || || | -14 -19 19 > || 2.816 || | || [[enneadeca]], 19-tone-comma || || | -14 -19 19 > || 2.816 || | ||
|| 23-3/5-comma || || | 17 23 -23 > || 59.750 || | || 23-3/5-comma || || | 17 23 -23 > || 59.750 || | ||
|| 34-3/5-comma || || | -25 -34 34 > || 68.196 || | || 34-3/5-comma || || | -25 -34 34 > || 68.196 || | ||
|| 53-3/5-comma || || | 39 53 -53 > || 71.012 || | || 53-3/5-comma || || | 39 53 -53 > || 71.012 || | ||
|| vavoom || || | -68 18 17 > || 2.523 || | || vavoom || || | -68 18 17 > || 2.523 || | ||
|| tricot comma || || | 39 -29 3 > || 2.246 || | || tricot comma || || | 39 -29 3 > || 2.246 || | ||
| Line 132: | Line 102: | ||
|| counterschisma || || | -69 45 -1 > || 1.661 || | || counterschisma || || | -69 45 -1 > || 1.661 || | ||
|| septendecima || || | -52 -17 34 > || 1.431 || | || septendecima || || | -52 -17 34 > || 1.431 || | ||
|| hemithirds comma, lunama | | || hemithirds comma, lunama || 274877906944]] / 274658203125]] || | 38 -2 -15 > || 1.384 || | ||
|| minortone comma || || | -16 35 -17 > || 1.092 || | || minortone comma || || | -16 35 -17 > || 1.092 || | ||
|| [[Ennealimmal|ennealimma]] || | || [[Ennealimmal|ennealimma]] || 7629394531250 / 7625597484987]] || | 1 -27 18 > || 0.862 || | ||
|| astro || || | 91 -12 -31 > || 0.815 || | || astro || || | 91 -12 -31 > || 0.815 || | ||
|| kwazy || || | -53 10 16 > || 0.569 || | || kwazy || || | -53 10 16 > || 0.569 || | ||
| Line 150: | Line 120: | ||
|| titania || || | [[tel/2746 -521 -827|2746 -521 -827]] > || 0.003183 || | || titania || || | [[tel/2746 -521 -827|2746 -521 -827]] > || 0.003183 || | ||
|| quark || || | -537 237 85 > || 0.000884 || | || quark || || | -537 237 85 > || 0.000884 || | ||
|| rover || || | | || rover || || | 1634 1502 -1729 > || 0.000028 || | ||
|| rascal || || | -7470 | || rascal || || | -7470 2791 1312 > || 0.000006 || | ||
==7-limit commas== | ==7-limit commas== | ||
| Line 392: | Line 362: | ||
</td> | </td> | ||
<td>90.225<br /> | <td>90.225<br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
| Line 442: | Line 402: | ||
</td> | </td> | ||
<td>19.845<br /> | <td>19.845<br /> | ||
</td> | |||
</tr> | |||
<tr> | |||
<td>Pythagorean Integer cents comma<br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
<td>| 317 -200 &gt;<br /> | |||
</td> | |||
<td>9.000<br /> | |||
</td> | </td> | ||
</tr> | </tr> | ||
| Line 474: | Line 444: | ||
</td> | </td> | ||
</tr> | </tr> | ||
</table> | |||
<br /> | |||
<!-- ws:start:WikiTextHeadingRule:7:&lt;h2&gt; --><h2 id="toc3"><a name="List of commas, by prime limit-5-limit commas"></a><!-- ws:end:WikiTextHeadingRule:7 -->5-limit commas</h2> | |||
<table class="wiki_table"> | |||
<tr> | <tr> | ||
<td> | <th>name(s)<br /> | ||
</th> | |||
<th>ratio<br /> | |||
</th> | |||
<th>monzo<br /> | |||
</th> | |||
<th>cents<br /> | |||
</th> | |||
</tr> | |||
<tr> | |||
<td>Twenty-two thirds limma<br /> | |||
</td> | </td> | ||
<td><br /> | <td><br /> | ||
</td> | </td> | ||
<td>| | <td>| -51 0 22 &gt;<br /> | ||
</td> | </td> | ||
<td> | <td>98.902<br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
<tr> | <tr> | ||
<td> | <td>sibbolet<br /> | ||
</td> | </td> | ||
<td><br /> | <td><br /> | ||
</td> | </td> | ||
<td>| - | <td>| -58 0 25 &gt;<br /> | ||
</td> | </td> | ||
<td> | <td>57.843<br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
<tr> | <tr> | ||
<td> | <td>Hunt 5-cycle comma<br /> | ||
</td> | </td> | ||
<td> | <td><br /> | ||
</td> | </td> | ||
<td>| - | <td>| -65 0 28 &gt;<br /> | ||
</td> | </td> | ||
<td> | <td>16.784<br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
<tr> | <tr> | ||
<td> | <td>acute thirds comma<br /> | ||
</td> | </td> | ||
<td><br /> | <td><br /> | ||
</td> | </td> | ||
<td>| - | <td>| 72 0 -31 &gt;<br /> | ||
</td> | </td> | ||
<td> | <td>24.275<br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
<tr> | <tr> | ||
<td> | <td>34-5-comma<br /> | ||
</td> | </td> | ||
<td><br /> | <td><br /> | ||
</td> | </td> | ||
<td>| | <td>| 79 0 -34 &gt;<br /> | ||
</td> | </td> | ||
<td> | <td>65.334<br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
<tr> | <tr> | ||
<td> | <td>Schismic thirds chromatic semitone<br /> | ||
</td> | </td> | ||
<td><br /> | <td><br /> | ||
</td> | </td> | ||
<td>| | <td>| -123 0 53 &gt;<br /> | ||
</td> | </td> | ||
<td> | <td>74.627<br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
<tr> | <tr> | ||
<td> | <td>10-15-comma<br /> | ||
</td> | </td> | ||
<td><br /> | <td><br /> | ||
</td> | </td> | ||
<td>| | <td>| -39 10 10 &gt;<br /> | ||
</td> | </td> | ||
<td> | <td>82.687<br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
<tr> | <tr> | ||
<td> | <td>11-15-comma<br /> | ||
</td> | </td> | ||
<td><br /> | <td><br /> | ||
</td> | </td> | ||
<td>| | <td>| 43 -11 -11 &gt;<br /> | ||
</td> | </td> | ||
<td> | <td>29.044<br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
<tr> | <tr> | ||
<td> | <td>21-15-comma<br /> | ||
</td> | </td> | ||
<td><br /> | <td><br /> | ||
</td> | </td> | ||
<td>| | <td>| 82 -21 -21 &gt;<br /> | ||
</td> | </td> | ||
<td> | <td>53.643<br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
<tr> | <tr> | ||
< | <td>32-15-comma<br /> | ||
</ | </td> | ||
< | <td><br /> | ||
</ | </td> | ||
< | <td>| 125 -32 -32 &gt;<br /> | ||
</ | </td> | ||
< | <td>24.599<br /> | ||
</ | </td> | ||
</tr> | </tr> | ||
<tr> | <tr> | ||
<td> | <td>Huntian 15-cycle comma<br /> | ||
</td> | </td> | ||
<td><br /> | <td><br /> | ||
</td> | </td> | ||
<td>| - | <td>| -168 43 43 &gt;<br /> | ||
</td> | </td> | ||
<td> | <td>4.445<br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
<tr> | <tr> | ||
<td> | <td>53-15-comma<br /> | ||
</td> | </td> | ||
<td><br /> | <td><br /> | ||
</td> | </td> | ||
<td>| - | <td>| -207 53 53 &gt;<br /> | ||
</td> | </td> | ||
<td> | <td>78.242<br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
<tr> | <tr> | ||
<td> | <td>54-15-comma<br /> | ||
</td> | </td> | ||
<td><br /> | <td><br /> | ||
</td> | </td> | ||
<td>| - | <td>| 211 -54 -54 &gt;<br /> | ||
</td> | </td> | ||
<td> | <td>33.489<br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
<tr> | <tr> | ||
<td> | <td>76-15-comma<br /> | ||
</td> | </td> | ||
<td><br /> | <td><br /> | ||
</td> | </td> | ||
<td>| - | <td>| 297 -76 -76 &gt;<br /> | ||
</td> | </td> | ||
<td>91.578<br /> | |||
<td>91.578 | |||
</td> | </td> | ||
</tr> | </tr> | ||
| Line 1,164: | Line 874: | ||
<td>maja<br /> | <td>maja<br /> | ||
</td> | </td> | ||
<td> | <td>762939453125 / 753145430616<br /> | ||
</td> | </td> | ||
<td>| -3 -23 17 &gt;<br /> | <td>| -3 -23 17 &gt;<br /> | ||
| Line 1,314: | Line 1,024: | ||
<td>unidecma<br /> | <td>unidecma<br /> | ||
</td> | </td> | ||
<td> | <td>31381059609 / 31250000000<br /> | ||
</td> | </td> | ||
<td>| -7 22 -12 &gt;<br /> | <td>| -7 22 -12 &gt;<br /> | ||
| Line 1,384: | Line 1,094: | ||
<td><a class="wiki_link" href="/vishnuzma">vishnuzma</a>, semisuper<br /> | <td><a class="wiki_link" href="/vishnuzma">vishnuzma</a>, semisuper<br /> | ||
</td> | </td> | ||
<td> | <td>6115295232]] / 6103515625<br /> | ||
</td> | </td> | ||
<td>| 23 6 -14 &gt;<br /> | <td>| 23 6 -14 &gt;<br /> | ||
</td> | </td> | ||
<td>3.338<br /> | <td>3.338<br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
| Line 1,429: | Line 1,129: | ||
</td> | </td> | ||
<td>59.750<br /> | <td>59.750<br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
| Line 1,469: | Line 1,149: | ||
</td> | </td> | ||
<td>71.012<br /> | <td>71.012<br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
| Line 1,534: | Line 1,204: | ||
<td>hemithirds comma, lunama<br /> | <td>hemithirds comma, lunama<br /> | ||
</td> | </td> | ||
<td> | <td>274877906944]] / 274658203125]]<br /> | ||
</td> | </td> | ||
<td>| 38 -2 -15 &gt;<br /> | <td>| 38 -2 -15 &gt;<br /> | ||
| Line 1,554: | Line 1,224: | ||
<td><a class="wiki_link" href="/Ennealimmal">ennealimma</a><br /> | <td><a class="wiki_link" href="/Ennealimmal">ennealimma</a><br /> | ||
</td> | </td> | ||
<td> | <td>7629394531250 / 7625597484987]]<br /> | ||
</td> | </td> | ||
<td>| 1 -27 18 &gt;<br /> | <td>| 1 -27 18 &gt;<br /> | ||
| Line 1,716: | Line 1,386: | ||
<td><br /> | <td><br /> | ||
</td> | </td> | ||
<td>| | <td>| 1634 1502 -1729 &gt;<br /> | ||
</td> | </td> | ||
<td>0.000028<br /> | <td>0.000028<br /> | ||
| Line 1,726: | Line 1,396: | ||
<td><br /> | <td><br /> | ||
</td> | </td> | ||
<td>| -7470 | <td>| -7470 2791 1312 &gt;<br /> | ||
</td> | </td> | ||
<td>0.000006<br /> | <td>0.000006<br /> | ||