31edo: Difference between revisions
Wikispaces>TallKite **Imported revision 602864796 - Original comment: ** |
Wikispaces>xenwolf **Imported revision 602871964 - Original comment: ** |
||
| Line 1: | Line 1: | ||
<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: | : This revision was by author [[User:xenwolf|xenwolf]] and made on <tt>2016-12-28 11:00:16 UTC</tt>.<br> | ||
: The original revision id was <tt> | : The original revision id was <tt>602871964</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 40: | Line 40: | ||
==Selected just intervals by error== | ==Selected just intervals by error== | ||
The following table shows how [[Just-24|some prominent just intervals]] are represented in 31edo (ordered by absolute error). | The following table shows how [[Just-24|some prominent just intervals]] are represented in 31edo (ordered by absolute error). | ||
|| | ||~ Interval, complement ||~ Error (abs., in [[cent|cents]]) || | ||
||= [[5_4|5/4]], [[8_5|8/5]] ||= 0.783 || | ||= [[5_4|5/4]], [[8_5|8/5]] ||= 0.783 || | ||
||= [[11_9|11/9]], [[18_11|18/11]] ||= 0.979 || | ||= [[11_9|11/9]], [[18_11|18/11]] ||= 0.979 || | ||
| Line 305: | Line 305: | ||
=Commas= | =Commas= | ||
31 EDO tempers out the following commas. (Note: This assumes the val < 31 49 72 87 107 115 |, comma values rounded to 5 significant digits.) | 31 EDO tempers out the following commas. (Note: This assumes the val < 31 49 72 87 107 115 |, comma values rounded to 5 significant digits.) | ||
||~ | ||~ Ratio ||~ Monzo ||~ Value (Cents) ||~ Name 1 ||~ Name 2 ||~ Name 3 || | ||
||= | ||= 9931568/9752117 ||< | -25 7 6 > ||> 31.567 ||= [[ampersand|Ampersand's Comma]] ||= ||= || | ||
||= 81/80 ||< | -4 4 -1 > ||> 21.506 ||= [[Syntonic Comma]] ||= Didymos Comma ||= Meantone Comma || | ||= 81/80 ||< | -4 4 -1 > ||> 21.506 ||= [[Syntonic Comma]] ||= Didymos Comma ||= Meantone Comma || | ||
||= | ||= 393216/390625 ||< | 17 1 -8 > ||> 11.445 ||= [[Würschmidt comma|Würschmidt Comma]] ||= ||= || | ||
||= | ||= 2109375/2097152 ||< | -21 3 7 > ||> 10.061 ||= [[semicomma|Semicomma]] ||= Fokker Comma ||= || | ||
||= | ||= 6719816/6714445 ||< | 38 -2 -15 > ||> 1.3843 ||= Hemithirds Comma ||= ||= || | ||
||= | ||= 9859966/9733137 ||< | -10 7 8 -7 > ||> 22.413 ||= Blackjackisma ||= ||= || | ||
||= 64827/64000 ||< | -9 3 -3 4 > ||> 22.227 ||= Squalentine ||= ||= || | ||= 64827/64000 ||< | -9 3 -3 4 > ||> 22.227 ||= Squalentine ||= ||= || | ||
||= 2430/2401 ||< | 1 5 1 -4 > ||> 20.785 ||= Nuwell ||= ||= || | ||= 2430/2401 ||< | 1 5 1 -4 > ||> 20.785 ||= Nuwell ||= ||= || | ||
| Line 322: | Line 322: | ||
||= 3136/3125 ||< | 6 0 -5 2 > ||> 6.0832 ||= Hemimean ||= ||= || | ||= 3136/3125 ||< | 6 0 -5 2 > ||> 6.0832 ||= Hemimean ||= ||= || | ||
||= 6144/6125 ||< | 11 1 -3 -2 > ||> 5.3621 ||= Porwell ||= ||= || | ||= 6144/6125 ||< | 11 1 -3 -2 > ||> 5.3621 ||= Porwell ||= ||= || | ||
||= | ||= 1065875/1063543 ||< | -26 -1 1 9 > ||> 3.7919 ||= Wadisma ||= ||= || | ||
||= 65625/65536 ||< | -16 1 5 1 > ||> 2.3495 ||= Horwell ||= ||= || | ||= 65625/65536 ||< | -16 1 5 1 > ||> 2.3495 ||= Horwell ||= ||= || | ||
||= | ||= 703125/702464 ||< | -11 2 7 -3 > ||> 1.6283 ||= Meter ||= ||= || | ||
||= 2401/2400 ||< | -5 -1 -2 4 > ||> 0.72120 ||= Breedsma ||= ||= || | ||= 2401/2400 ||< | -5 -1 -2 4 > ||> 0.72120 ||= Breedsma ||= ||= || | ||
||= 99/98 ||< | -1 2 0 -2 1 > ||> 17.576 ||= Mothwellsma ||= ||= || | ||= 99/98 ||< | -1 2 0 -2 1 > ||> 17.576 ||= Mothwellsma ||= ||= || | ||
| Line 619: | Line 619: | ||
<table class="wiki_table"> | <table class="wiki_table"> | ||
<tr> | <tr> | ||
< | <th>Interval, complement<br /> | ||
</ | </th> | ||
< | <th>Error (abs., in <a class="wiki_link" href="/cent">cents</a>)<br /> | ||
</ | </th> | ||
</tr> | </tr> | ||
<tr> | <tr> | ||
| Line 8,058: | Line 8,058: | ||
<table class="wiki_table"> | <table class="wiki_table"> | ||
<tr> | <tr> | ||
<th> | <th>Ratio<br /> | ||
</th> | </th> | ||
<th>Monzo<br /> | <th>Monzo<br /> | ||
| Line 8,072: | Line 8,072: | ||
</tr> | </tr> | ||
<tr> | <tr> | ||
<td style="text-align: center;"><br /> | <td style="text-align: center;">9931568/9752117<br /> | ||
</td> | </td> | ||
<td style="text-align: left;">| -25 7 6 &gt;<br /> | <td style="text-align: left;">| -25 7 6 &gt;<br /> | ||
| Line 8,100: | Line 8,100: | ||
</tr> | </tr> | ||
<tr> | <tr> | ||
<td style="text-align: center;"><br /> | <td style="text-align: center;">393216/390625<br /> | ||
</td> | </td> | ||
<td style="text-align: left;">| 17 1 -8 &gt;<br /> | <td style="text-align: left;">| 17 1 -8 &gt;<br /> | ||
| Line 8,114: | Line 8,114: | ||
</tr> | </tr> | ||
<tr> | <tr> | ||
<td style="text-align: center;"><br /> | <td style="text-align: center;">2109375/2097152<br /> | ||
</td> | </td> | ||
<td style="text-align: left;">| -21 3 7 &gt;<br /> | <td style="text-align: left;">| -21 3 7 &gt;<br /> | ||
| Line 8,128: | Line 8,128: | ||
</tr> | </tr> | ||
<tr> | <tr> | ||
<td style="text-align: center;"><br /> | <td style="text-align: center;">6719816/6714445<br /> | ||
</td> | </td> | ||
<td style="text-align: left;">| 38 -2 -15 &gt;<br /> | <td style="text-align: left;">| 38 -2 -15 &gt;<br /> | ||
| Line 8,142: | Line 8,142: | ||
</tr> | </tr> | ||
<tr> | <tr> | ||
<td style="text-align: center;"><br /> | <td style="text-align: center;">9859966/9733137<br /> | ||
</td> | </td> | ||
<td style="text-align: left;">| -10 7 8 -7 &gt;<br /> | <td style="text-align: left;">| -10 7 8 -7 &gt;<br /> | ||
| Line 8,296: | Line 8,296: | ||
</tr> | </tr> | ||
<tr> | <tr> | ||
<td style="text-align: center;"><br /> | <td style="text-align: center;">1065875/1063543<br /> | ||
</td> | </td> | ||
<td style="text-align: left;">| -26 -1 1 9 &gt;<br /> | <td style="text-align: left;">| -26 -1 1 9 &gt;<br /> | ||
| Line 8,324: | Line 8,324: | ||
</tr> | </tr> | ||
<tr> | <tr> | ||
<td style="text-align: center;"><br /> | <td style="text-align: center;">703125/702464<br /> | ||
</td> | </td> | ||
<td style="text-align: left;">| -11 2 7 -3 &gt;<br /> | <td style="text-align: left;">| -11 2 7 -3 &gt;<br /> | ||