57edo: Difference between revisions
Jump to navigation
Jump to search
Wikispaces>JosephRuhf **Imported revision 601607792 - Original comment: ** |
Wikispaces>xenwolf **Imported revision 602901438 - 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>2016-12-29 17:47:24 UTC</tt>.<br> | ||
: The original revision id was <tt> | : The original revision id was <tt>602901438</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: | ||
==Intervals== | ==Intervals== | ||
|| [[Degree]] | || [[Degree]] || Size ([[cent|Cents]]) || | ||
|| 0 || 0 || | ||= 0 ||> 0.0000 || | ||
|| 1 || 21.0526 || | ||= 1 ||> 21.0526 || | ||
|| 2 || 42.1053 || | ||= 2 ||> 42.1053 || | ||
|| 3 || 63.1579 || | ||= 3 ||> 63.1579 || | ||
|| 4 || 84.2105 || | ||= 4 ||> 84.2105 || | ||
|| 5 || 105.2632 | ||= 5 ||> 105.2632 || | ||
|| 6 || 126.3158 | ||= 6 ||> 126.3158 || | ||
|| 7 || 147.3684 | ||= 7 ||> 147.3684 || | ||
|| 8 || 168.4211 | ||= 8 ||> 168.4211 || | ||
|| 9 || 189.4737 | ||= 9 ||> 189.4737 || | ||
|| 10 || 210.5263 | ||= 10 ||> 210.5263 || | ||
|| 11 || 231.5789 | ||= 11 ||> 231.5789 || | ||
|| 12 || 252.6316 | ||= 12 ||> 252.6316 || | ||
|| 13 || 273.6842 | ||= 13 ||> 273.6842 || | ||
|| 14 || 294.7368 | ||= 14 ||> 294.7368 || | ||
|| 15 || 315.7895 | ||= 15 ||> 315.7895 || | ||
|| 16 || 336.8421 | ||= 16 ||> 336.8421 || | ||
|| 17 || 357.8947 | ||= 17 ||> 357.8947 || | ||
|| 18 || 378.9474 | ||= 18 ||> 378.9474 || | ||
|| 19 || 400 || | ||= 19 ||> 400.0000 || | ||
|| 20 || 421.0526 | ||= 20 ||> 421.0526 || | ||
|| 21 || 442.1053 | ||= 21 ||> 442.1053 || | ||
|| 22 || 463.1579 | ||= 22 ||> 463.1579 || | ||
|| 23 || 484.2105 | ||= 23 ||> 484.2105 || | ||
|| 24 || 505.2632 | ||= 24 ||> 505.2632 || | ||
|| 25 || 526.3158 | ||= 25 ||> 526.3158 || | ||
|| 26 || 547.3684 | ||= 26 ||> 547.3684 || | ||
|| 27 || 568.4211 | ||= 27 ||> 568.4211 || | ||
|| 28 || 589.4737 | ||= 28 ||> 589.4737 || | ||
|| 29 || 610.5263 | ||= 29 ||> 610.5263 || | ||
|| 30 || 631.5789 | ||= 30 ||> 631.5789 || | ||
|| 31 || 652.6316 | ||= 31 ||> 652.6316 || | ||
|| 32 || 673.6842 | ||= 32 ||> 673.6842 || | ||
|| 33 || 694.7368 | ||= 33 ||> 694.7368 || | ||
|| 34 || 715.7895 | ||= 34 ||> 715.7895 || | ||
|| 35 || 736.8421 | ||= 35 ||> 736.8421 || | ||
|| 36 || 757.8947 | ||= 36 ||> 757.8947 || | ||
|| 37 || 778.9474 | ||= 37 ||> 778.9474 || | ||
|| 38 || 800 || | ||= 38 ||> 800.0000 || | ||
|| 39 || 821.0526 | ||= 39 ||> 821.0526 || | ||
|| 40 || 842.1053 | ||= 40 ||> 842.1053 || | ||
|| 41 || 863.1579 | ||= 41 ||> 863.1579 || | ||
|| 42 || 884.2105 | ||= 42 ||> 884.2105 || | ||
|| 43 || 905.2632 | ||= 43 ||> 905.2632 || | ||
|| 44 || 926.3158 | ||= 44 ||> 926.3158 || | ||
|| 45 || 947.3684 | ||= 45 ||> 947.3684 || | ||
|| 46 || 968.4211 | ||= 46 ||> 968.4211 || | ||
|| 47 || 989.4737 | ||= 47 ||> 989.4737 || | ||
|| 48 || 1010.5263 || | ||= 48 ||> 1010.5263 || | ||
|| 49 || 1031.5789 || | ||= 49 ||> 1031.5789 || | ||
|| 50 || 1052.6316 || | ||= 50 ||> 1052.6316 || | ||
|| 51 || 1073.6842 || | ||= 51 ||> 1073.6842 || | ||
|| 52 || 1094.7368 || | ||= 52 ||> 1094.7368 || | ||
|| 53 || 1115.7895 || | ||= 53 ||> 1115.7895 || | ||
|| 54 || 1136.8421 || | ||= 54 ||> 1136.8421 || | ||
|| 55 || 1157.8947 || | ||= 55 ||> 1157.8947 || | ||
|| 56 || 1178.9474 || | ||= 56 ||> 1178.9474 || | ||
||= 57 ||> 1200.0000 || | |||
__**Modes of** **57edo**__ | __**Modes of** **57edo**__ | ||
Line 94: | Line 95: | ||
<table class="wiki_table"> | <table class="wiki_table"> | ||
<tr> | <tr> | ||
<td><a class="wiki_link" href="/Degree">Degree</a> | <td><a class="wiki_link" href="/Degree">Degree</a><br /> | ||
</td> | </td> | ||
<td><a class="wiki_link" href="/ | <td>Size (<a class="wiki_link" href="/cent">Cents</a>)<br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
<tr> | <tr> | ||
<td>0<br /> | <td style="text-align: center;">0<br /> | ||
</td> | </td> | ||
<td>0<br /> | <td style="text-align: right;">0.0000<br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
<tr> | <tr> | ||
<td>1<br /> | <td style="text-align: center;">1<br /> | ||
</td> | </td> | ||
<td>21.0526<br /> | <td style="text-align: right;">21.0526<br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
<tr> | <tr> | ||
<td>2<br /> | <td style="text-align: center;">2<br /> | ||
</td> | </td> | ||
<td>42.1053<br /> | <td style="text-align: right;">42.1053<br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
<tr> | <tr> | ||
<td>3<br /> | <td style="text-align: center;">3<br /> | ||
</td> | </td> | ||
<td>63.1579<br /> | <td style="text-align: right;">63.1579<br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
<tr> | <tr> | ||
<td>4<br /> | <td style="text-align: center;">4<br /> | ||
</td> | </td> | ||
<td>84.2105<br /> | <td style="text-align: right;">84.2105<br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
<tr> | <tr> | ||
<td>5<br /> | <td style="text-align: center;">5<br /> | ||
</td> | </td> | ||
<td>105.2632 | <td style="text-align: right;">105.2632<br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
<tr> | <tr> | ||
<td>6<br /> | <td style="text-align: center;">6<br /> | ||
</td> | </td> | ||
<td>126.3158 | <td style="text-align: right;">126.3158<br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
<tr> | <tr> | ||
<td>7<br /> | <td style="text-align: center;">7<br /> | ||
</td> | </td> | ||
<td>147.3684 | <td style="text-align: right;">147.3684<br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
<tr> | <tr> | ||
<td>8<br /> | <td style="text-align: center;">8<br /> | ||
</td> | </td> | ||
<td>168.4211 | <td style="text-align: right;">168.4211<br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
<tr> | <tr> | ||
<td>9<br /> | <td style="text-align: center;">9<br /> | ||
</td> | </td> | ||
<td>189.4737 | <td style="text-align: right;">189.4737<br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
<tr> | <tr> | ||
<td>10<br /> | <td style="text-align: center;">10<br /> | ||
</td> | </td> | ||
<td>210.5263 | <td style="text-align: right;">210.5263<br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
<tr> | <tr> | ||
<td>11<br /> | <td style="text-align: center;">11<br /> | ||
</td> | </td> | ||
<td>231.5789 | <td style="text-align: right;">231.5789<br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
<tr> | <tr> | ||
<td>12<br /> | <td style="text-align: center;">12<br /> | ||
</td> | </td> | ||
<td>252.6316 | <td style="text-align: right;">252.6316<br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
<tr> | <tr> | ||
<td>13<br /> | <td style="text-align: center;">13<br /> | ||
</td> | </td> | ||
<td>273.6842 | <td style="text-align: right;">273.6842<br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
<tr> | <tr> | ||
<td>14<br /> | <td style="text-align: center;">14<br /> | ||
</td> | </td> | ||
<td>294.7368 | <td style="text-align: right;">294.7368<br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
<tr> | <tr> | ||
<td>15<br /> | <td style="text-align: center;">15<br /> | ||
</td> | </td> | ||
<td>315.7895 | <td style="text-align: right;">315.7895<br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
<tr> | <tr> | ||
<td>16<br /> | <td style="text-align: center;">16<br /> | ||
</td> | </td> | ||
<td>336.8421 | <td style="text-align: right;">336.8421<br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
<tr> | <tr> | ||
<td>17<br /> | <td style="text-align: center;">17<br /> | ||
</td> | </td> | ||
<td>357.8947 | <td style="text-align: right;">357.8947<br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
<tr> | <tr> | ||
<td>18<br /> | <td style="text-align: center;">18<br /> | ||
</td> | </td> | ||
<td>378.9474 | <td style="text-align: right;">378.9474<br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
<tr> | <tr> | ||
<td>19<br /> | <td style="text-align: center;">19<br /> | ||
</td> | </td> | ||
<td>400<br /> | <td style="text-align: right;">400.0000<br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
<tr> | <tr> | ||
<td>20<br /> | <td style="text-align: center;">20<br /> | ||
</td> | </td> | ||
<td>421.0526 | <td style="text-align: right;">421.0526<br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
<tr> | <tr> | ||
<td>21<br /> | <td style="text-align: center;">21<br /> | ||
</td> | </td> | ||
<td>442.1053 | <td style="text-align: right;">442.1053<br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
<tr> | <tr> | ||
<td>22<br /> | <td style="text-align: center;">22<br /> | ||
</td> | </td> | ||
<td>463.1579 | <td style="text-align: right;">463.1579<br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
<tr> | <tr> | ||
<td>23<br /> | <td style="text-align: center;">23<br /> | ||
</td> | </td> | ||
<td>484.2105 | <td style="text-align: right;">484.2105<br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
<tr> | <tr> | ||
<td>24<br /> | <td style="text-align: center;">24<br /> | ||
</td> | </td> | ||
<td>505.2632 | <td style="text-align: right;">505.2632<br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
<tr> | <tr> | ||
<td>25<br /> | <td style="text-align: center;">25<br /> | ||
</td> | </td> | ||
<td>526.3158 | <td style="text-align: right;">526.3158<br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
<tr> | <tr> | ||
<td>26<br /> | <td style="text-align: center;">26<br /> | ||
</td> | </td> | ||
<td>547.3684 | <td style="text-align: right;">547.3684<br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
<tr> | <tr> | ||
<td>27<br /> | <td style="text-align: center;">27<br /> | ||
</td> | </td> | ||
<td>568.4211 | <td style="text-align: right;">568.4211<br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
<tr> | <tr> | ||
<td>28<br /> | <td style="text-align: center;">28<br /> | ||
</td> | </td> | ||
<td>589.4737 | <td style="text-align: right;">589.4737<br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
<tr> | <tr> | ||
<td>29<br /> | <td style="text-align: center;">29<br /> | ||
</td> | </td> | ||
<td>610.5263 | <td style="text-align: right;">610.5263<br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
<tr> | <tr> | ||
<td>30<br /> | <td style="text-align: center;">30<br /> | ||
</td> | </td> | ||
<td>631.5789 | <td style="text-align: right;">631.5789<br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
<tr> | <tr> | ||
<td>31<br /> | <td style="text-align: center;">31<br /> | ||
</td> | </td> | ||
<td>652.6316 | <td style="text-align: right;">652.6316<br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
<tr> | <tr> | ||
<td>32<br /> | <td style="text-align: center;">32<br /> | ||
</td> | </td> | ||
<td>673.6842 | <td style="text-align: right;">673.6842<br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
<tr> | <tr> | ||
<td>33<br /> | <td style="text-align: center;">33<br /> | ||
</td> | </td> | ||
<td>694.7368 | <td style="text-align: right;">694.7368<br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
<tr> | <tr> | ||
<td>34<br /> | <td style="text-align: center;">34<br /> | ||
</td> | </td> | ||
<td>715.7895 | <td style="text-align: right;">715.7895<br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
<tr> | <tr> | ||
<td>35<br /> | <td style="text-align: center;">35<br /> | ||
</td> | </td> | ||
<td>736.8421 | <td style="text-align: right;">736.8421<br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
<tr> | <tr> | ||
<td>36<br /> | <td style="text-align: center;">36<br /> | ||
</td> | </td> | ||
<td>757.8947 | <td style="text-align: right;">757.8947<br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
<tr> | <tr> | ||
<td>37<br /> | <td style="text-align: center;">37<br /> | ||
</td> | </td> | ||
<td>778.9474 | <td style="text-align: right;">778.9474<br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
<tr> | <tr> | ||
<td>38<br /> | <td style="text-align: center;">38<br /> | ||
</td> | </td> | ||
<td>800<br /> | <td style="text-align: right;">800.0000<br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
<tr> | <tr> | ||
<td>39<br /> | <td style="text-align: center;">39<br /> | ||
</td> | </td> | ||
<td>821.0526 | <td style="text-align: right;">821.0526<br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
<tr> | <tr> | ||
<td>40<br /> | <td style="text-align: center;">40<br /> | ||
</td> | </td> | ||
<td>842.1053 | <td style="text-align: right;">842.1053<br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
<tr> | <tr> | ||
<td>41<br /> | <td style="text-align: center;">41<br /> | ||
</td> | </td> | ||
<td>863.1579 | <td style="text-align: right;">863.1579<br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
<tr> | <tr> | ||
<td>42<br /> | <td style="text-align: center;">42<br /> | ||
</td> | </td> | ||
<td>884.2105 | <td style="text-align: right;">884.2105<br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
<tr> | <tr> | ||
<td>43<br /> | <td style="text-align: center;">43<br /> | ||
</td> | </td> | ||
<td>905.2632 | <td style="text-align: right;">905.2632<br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
<tr> | <tr> | ||
<td>44<br /> | <td style="text-align: center;">44<br /> | ||
</td> | </td> | ||
<td>926.3158 | <td style="text-align: right;">926.3158<br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
<tr> | <tr> | ||
<td>45<br /> | <td style="text-align: center;">45<br /> | ||
</td> | </td> | ||
<td>947.3684 | <td style="text-align: right;">947.3684<br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
<tr> | <tr> | ||
<td>46<br /> | <td style="text-align: center;">46<br /> | ||
</td> | </td> | ||
<td>968.4211 | <td style="text-align: right;">968.4211<br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
<tr> | <tr> | ||
<td>47<br /> | <td style="text-align: center;">47<br /> | ||
</td> | </td> | ||
<td>989.4737 | <td style="text-align: right;">989.4737<br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
<tr> | <tr> | ||
<td>48<br /> | <td style="text-align: center;">48<br /> | ||
</td> | </td> | ||
<td>1010.5263<br /> | <td style="text-align: right;">1010.5263<br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
<tr> | <tr> | ||
<td>49<br /> | <td style="text-align: center;">49<br /> | ||
</td> | </td> | ||
<td>1031.5789<br /> | <td style="text-align: right;">1031.5789<br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
<tr> | <tr> | ||
<td>50<br /> | <td style="text-align: center;">50<br /> | ||
</td> | </td> | ||
<td>1052.6316<br /> | <td style="text-align: right;">1052.6316<br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
<tr> | <tr> | ||
<td>51<br /> | <td style="text-align: center;">51<br /> | ||
</td> | </td> | ||
<td>1073.6842<br /> | <td style="text-align: right;">1073.6842<br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
<tr> | <tr> | ||
<td>52<br /> | <td style="text-align: center;">52<br /> | ||
</td> | </td> | ||
<td>1094.7368<br /> | <td style="text-align: right;">1094.7368<br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
<tr> | <tr> | ||
<td>53<br /> | <td style="text-align: center;">53<br /> | ||
</td> | </td> | ||
<td>1115.7895<br /> | <td style="text-align: right;">1115.7895<br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
<tr> | <tr> | ||
<td>54<br /> | <td style="text-align: center;">54<br /> | ||
</td> | </td> | ||
<td>1136.8421<br /> | <td style="text-align: right;">1136.8421<br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
<tr> | <tr> | ||
<td>55<br /> | <td style="text-align: center;">55<br /> | ||
</td> | </td> | ||
<td>1157.8947<br /> | <td style="text-align: right;">1157.8947<br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
<tr> | <tr> | ||
<td>56<br /> | <td style="text-align: center;">56<br /> | ||
</td> | </td> | ||
<td>1178.9474<br /> | <td style="text-align: right;">1178.9474<br /> | ||
</td> | |||
</tr> | |||
<tr> | |||
<td style="text-align: center;">57<br /> | |||
</td> | |||
<td style="text-align: right;">1200.0000<br /> | |||
</td> | </td> | ||
</tr> | </tr> |
Revision as of 17:47, 29 December 2016
IMPORTED REVISION FROM WIKISPACES
This is an imported revision from Wikispaces. The revision metadata is included below for reference:
- This revision was by author xenwolf and made on 2016-12-29 17:47:24 UTC.
- The original revision id was 602901438.
- The revision comment was:
The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.
Original Wikitext content:
=<span style="color: #006118; font-family: 'Times New Roman',Times,serif; font-size: 113%;">57 tone equal temperament</span>= //57edo// divides the [[octave]] into 57 parts of size 21.053. It can be used to tune [[mothra temperament]], and is an excellent tuning for the 2.5/3.7.11.13.17.19 [[just intonation subgroup]]. One way to describe 57 is that it has a [[5-limit]] part consisting of three versions of 19, plus a no-threes no-fives part which is much more accurate. A good generator to exploit the 2.5/3.7.11.13.17.19 aspect of 57 is the approximate 11/8, which is 26\57. This gives the [[19-limit]] 46&57 temperament [[Sensipent family|Heinz]]. [[5-limit]] [[comma]]s: 81/80, 3125/3072 [[7-limit]] commas: 81/80, 3125/3072, 1029/1024 [[11-limit]] commas: 99/98, 385/384, 441/440, 625/616 ==Intervals== || [[Degree]] || Size ([[cent|Cents]]) || ||= 0 ||> 0.0000 || ||= 1 ||> 21.0526 || ||= 2 ||> 42.1053 || ||= 3 ||> 63.1579 || ||= 4 ||> 84.2105 || ||= 5 ||> 105.2632 || ||= 6 ||> 126.3158 || ||= 7 ||> 147.3684 || ||= 8 ||> 168.4211 || ||= 9 ||> 189.4737 || ||= 10 ||> 210.5263 || ||= 11 ||> 231.5789 || ||= 12 ||> 252.6316 || ||= 13 ||> 273.6842 || ||= 14 ||> 294.7368 || ||= 15 ||> 315.7895 || ||= 16 ||> 336.8421 || ||= 17 ||> 357.8947 || ||= 18 ||> 378.9474 || ||= 19 ||> 400.0000 || ||= 20 ||> 421.0526 || ||= 21 ||> 442.1053 || ||= 22 ||> 463.1579 || ||= 23 ||> 484.2105 || ||= 24 ||> 505.2632 || ||= 25 ||> 526.3158 || ||= 26 ||> 547.3684 || ||= 27 ||> 568.4211 || ||= 28 ||> 589.4737 || ||= 29 ||> 610.5263 || ||= 30 ||> 631.5789 || ||= 31 ||> 652.6316 || ||= 32 ||> 673.6842 || ||= 33 ||> 694.7368 || ||= 34 ||> 715.7895 || ||= 35 ||> 736.8421 || ||= 36 ||> 757.8947 || ||= 37 ||> 778.9474 || ||= 38 ||> 800.0000 || ||= 39 ||> 821.0526 || ||= 40 ||> 842.1053 || ||= 41 ||> 863.1579 || ||= 42 ||> 884.2105 || ||= 43 ||> 905.2632 || ||= 44 ||> 926.3158 || ||= 45 ||> 947.3684 || ||= 46 ||> 968.4211 || ||= 47 ||> 989.4737 || ||= 48 ||> 1010.5263 || ||= 49 ||> 1031.5789 || ||= 50 ||> 1052.6316 || ||= 51 ||> 1073.6842 || ||= 52 ||> 1094.7368 || ||= 53 ||> 1115.7895 || ||= 54 ||> 1136.8421 || ||= 55 ||> 1157.8947 || ||= 56 ||> 1178.9474 || ||= 57 ||> 1200.0000 || __**Modes of** **57edo**__ 2 1 2 1 2 1 2 1 2 1 1 2 1 2 1 2 1 2 1 2 1 1 2 1 2 1 2 1 2 1 2 1 1 - 3MOS of type 18L 21s (augene)
Original HTML content:
<html><head><title>57edo</title></head><body><!-- ws:start:WikiTextHeadingRule:0:<h1> --><h1 id="toc0"><a name="x57 tone equal temperament"></a><!-- ws:end:WikiTextHeadingRule:0 --><span style="color: #006118; font-family: 'Times New Roman',Times,serif; font-size: 113%;">57 tone equal temperament</span></h1> <br /> <em>57edo</em> divides the <a class="wiki_link" href="/octave">octave</a> into 57 parts of size 21.053. It can be used to tune <a class="wiki_link" href="/mothra%20temperament">mothra temperament</a>, and is an excellent tuning for the 2.5/3.7.11.13.17.19 <a class="wiki_link" href="/just%20intonation%20subgroup">just intonation subgroup</a>. One way to describe 57 is that it has a <a class="wiki_link" href="/5-limit">5-limit</a> part consisting of three versions of 19, plus a no-threes no-fives part which is much more accurate. A good generator to exploit the 2.5/3.7.11.13.17.19 aspect of 57 is the approximate 11/8, which is 26\57. This gives the <a class="wiki_link" href="/19-limit">19-limit</a> 46&57 temperament <a class="wiki_link" href="/Sensipent%20family">Heinz</a>.<br /> <br /> <a class="wiki_link" href="/5-limit">5-limit</a> <a class="wiki_link" href="/comma">comma</a>s: 81/80, 3125/3072<br /> <br /> <a class="wiki_link" href="/7-limit">7-limit</a> commas: 81/80, 3125/3072, 1029/1024<br /> <br /> <a class="wiki_link" href="/11-limit">11-limit</a> commas: 99/98, 385/384, 441/440, 625/616<br /> <br /> <!-- ws:start:WikiTextHeadingRule:2:<h2> --><h2 id="toc1"><a name="x57 tone equal temperament-Intervals"></a><!-- ws:end:WikiTextHeadingRule:2 -->Intervals</h2> <table class="wiki_table"> <tr> <td><a class="wiki_link" href="/Degree">Degree</a><br /> </td> <td>Size (<a class="wiki_link" href="/cent">Cents</a>)<br /> </td> </tr> <tr> <td style="text-align: center;">0<br /> </td> <td style="text-align: right;">0.0000<br /> </td> </tr> <tr> <td style="text-align: center;">1<br /> </td> <td style="text-align: right;">21.0526<br /> </td> </tr> <tr> <td style="text-align: center;">2<br /> </td> <td style="text-align: right;">42.1053<br /> </td> </tr> <tr> <td style="text-align: center;">3<br /> </td> <td style="text-align: right;">63.1579<br /> </td> </tr> <tr> <td style="text-align: center;">4<br /> </td> <td style="text-align: right;">84.2105<br /> </td> </tr> <tr> <td style="text-align: center;">5<br /> </td> <td style="text-align: right;">105.2632<br /> </td> </tr> <tr> <td style="text-align: center;">6<br /> </td> <td style="text-align: right;">126.3158<br /> </td> </tr> <tr> <td style="text-align: center;">7<br /> </td> <td style="text-align: right;">147.3684<br /> </td> </tr> <tr> <td style="text-align: center;">8<br /> </td> <td style="text-align: right;">168.4211<br /> </td> </tr> <tr> <td style="text-align: center;">9<br /> </td> <td style="text-align: right;">189.4737<br /> </td> </tr> <tr> <td style="text-align: center;">10<br /> </td> <td style="text-align: right;">210.5263<br /> </td> </tr> <tr> <td style="text-align: center;">11<br /> </td> <td style="text-align: right;">231.5789<br /> </td> </tr> <tr> <td style="text-align: center;">12<br /> </td> <td style="text-align: right;">252.6316<br /> </td> </tr> <tr> <td style="text-align: center;">13<br /> </td> <td style="text-align: right;">273.6842<br /> </td> </tr> <tr> <td style="text-align: center;">14<br /> </td> <td style="text-align: right;">294.7368<br /> </td> </tr> <tr> <td style="text-align: center;">15<br /> </td> <td style="text-align: right;">315.7895<br /> </td> </tr> <tr> <td style="text-align: center;">16<br /> </td> <td style="text-align: right;">336.8421<br /> </td> </tr> <tr> <td style="text-align: center;">17<br /> </td> <td style="text-align: right;">357.8947<br /> </td> </tr> <tr> <td style="text-align: center;">18<br /> </td> <td style="text-align: right;">378.9474<br /> </td> </tr> <tr> <td style="text-align: center;">19<br /> </td> <td style="text-align: right;">400.0000<br /> </td> </tr> <tr> <td style="text-align: center;">20<br /> </td> <td style="text-align: right;">421.0526<br /> </td> </tr> <tr> <td style="text-align: center;">21<br /> </td> <td style="text-align: right;">442.1053<br /> </td> </tr> <tr> <td style="text-align: center;">22<br /> </td> <td style="text-align: right;">463.1579<br /> </td> </tr> <tr> <td style="text-align: center;">23<br /> </td> <td style="text-align: right;">484.2105<br /> </td> </tr> <tr> <td style="text-align: center;">24<br /> </td> <td style="text-align: right;">505.2632<br /> </td> </tr> <tr> <td style="text-align: center;">25<br /> </td> <td style="text-align: right;">526.3158<br /> </td> </tr> <tr> <td style="text-align: center;">26<br /> </td> <td style="text-align: right;">547.3684<br /> </td> </tr> <tr> <td style="text-align: center;">27<br /> </td> <td style="text-align: right;">568.4211<br /> </td> </tr> <tr> <td style="text-align: center;">28<br /> </td> <td style="text-align: right;">589.4737<br /> </td> </tr> <tr> <td style="text-align: center;">29<br /> </td> <td style="text-align: right;">610.5263<br /> </td> </tr> <tr> <td style="text-align: center;">30<br /> </td> <td style="text-align: right;">631.5789<br /> </td> </tr> <tr> <td style="text-align: center;">31<br /> </td> <td style="text-align: right;">652.6316<br /> </td> </tr> <tr> <td style="text-align: center;">32<br /> </td> <td style="text-align: right;">673.6842<br /> </td> </tr> <tr> <td style="text-align: center;">33<br /> </td> <td style="text-align: right;">694.7368<br /> </td> </tr> <tr> <td style="text-align: center;">34<br /> </td> <td style="text-align: right;">715.7895<br /> </td> </tr> <tr> <td style="text-align: center;">35<br /> </td> <td style="text-align: right;">736.8421<br /> </td> </tr> <tr> <td style="text-align: center;">36<br /> </td> <td style="text-align: right;">757.8947<br /> </td> </tr> <tr> <td style="text-align: center;">37<br /> </td> <td style="text-align: right;">778.9474<br /> </td> </tr> <tr> <td style="text-align: center;">38<br /> </td> <td style="text-align: right;">800.0000<br /> </td> </tr> <tr> <td style="text-align: center;">39<br /> </td> <td style="text-align: right;">821.0526<br /> </td> </tr> <tr> <td style="text-align: center;">40<br /> </td> <td style="text-align: right;">842.1053<br /> </td> </tr> <tr> <td style="text-align: center;">41<br /> </td> <td style="text-align: right;">863.1579<br /> </td> </tr> <tr> <td style="text-align: center;">42<br /> </td> <td style="text-align: right;">884.2105<br /> </td> </tr> <tr> <td style="text-align: center;">43<br /> </td> <td style="text-align: right;">905.2632<br /> </td> </tr> <tr> <td style="text-align: center;">44<br /> </td> <td style="text-align: right;">926.3158<br /> </td> </tr> <tr> <td style="text-align: center;">45<br /> </td> <td style="text-align: right;">947.3684<br /> </td> </tr> <tr> <td style="text-align: center;">46<br /> </td> <td style="text-align: right;">968.4211<br /> </td> </tr> <tr> <td style="text-align: center;">47<br /> </td> <td style="text-align: right;">989.4737<br /> </td> </tr> <tr> <td style="text-align: center;">48<br /> </td> <td style="text-align: right;">1010.5263<br /> </td> </tr> <tr> <td style="text-align: center;">49<br /> </td> <td style="text-align: right;">1031.5789<br /> </td> </tr> <tr> <td style="text-align: center;">50<br /> </td> <td style="text-align: right;">1052.6316<br /> </td> </tr> <tr> <td style="text-align: center;">51<br /> </td> <td style="text-align: right;">1073.6842<br /> </td> </tr> <tr> <td style="text-align: center;">52<br /> </td> <td style="text-align: right;">1094.7368<br /> </td> </tr> <tr> <td style="text-align: center;">53<br /> </td> <td style="text-align: right;">1115.7895<br /> </td> </tr> <tr> <td style="text-align: center;">54<br /> </td> <td style="text-align: right;">1136.8421<br /> </td> </tr> <tr> <td style="text-align: center;">55<br /> </td> <td style="text-align: right;">1157.8947<br /> </td> </tr> <tr> <td style="text-align: center;">56<br /> </td> <td style="text-align: right;">1178.9474<br /> </td> </tr> <tr> <td style="text-align: center;">57<br /> </td> <td style="text-align: right;">1200.0000<br /> </td> </tr> </table> <br /> <u><strong>Modes of</strong> <strong>57edo</strong></u><br /> 2 1 2 1 2 1 2 1 2 1 1 2 1 2 1 2 1 2 1 2 1 1 2 1 2 1 2 1 2 1 2 1 1 - 3MOS of type 18L 21s (augene)</body></html>