88cET: Difference between revisions
Wikispaces>Andrew_Heathwaite **Imported revision 165888445 - Original comment: ** |
Wikispaces>xenwolf **Imported revision 165931725 - Original comment: some typo for table, links added (a few only)** |
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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: | : This revision was by author [[User:xenwolf|xenwolf]] and made on <tt>2010-09-28 02:46:41 UTC</tt>.<br> | ||
: The original revision id was <tt> | : The original revision id was <tt>165931725</tt>.<br> | ||
: The revision comment was: <tt></tt><br> | : The revision comment was: <tt>some typo for table, links added (a few only)</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> | ||
<h4>Original Wikitext content:</h4> | <h4>Original Wikitext content:</h4> | ||
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88cET is considered a very consonant tuning, and you will find that many of its intervals fall very close to simple ratios in 7- and 11-limit just intonation. It is also extremely close to [[41edo]], which is itself extremely close to the 8th root of 3:2 (a perfect fifth divided into exactly 8 logarithmically equal steps). See chart: | 88cET is considered a very consonant tuning, and you will find that many of its intervals fall very close to simple ratios in 7- and 11-limit just intonation. It is also extremely close to [[41edo]], which is itself extremely close to the 8th root of 3:2 (a perfect fifth divided into exactly 8 logarithmically equal steps). See chart: | ||
||~ Degree ||~ 88cET ||~ 41edo ||~ 8th Root of 3:2 ||~ | ||~ Degree ||~ 88cET ||~ 41edo ||~ 8th Root ||~ Some Nearby || | ||
|||||||||| | ||~ ||~ ||~ 3-steps ||~ of 3:2 ||~ JI Intervals || | ||
||||||||||= **//first octave//** || | |||
|| 0 || 0 || 0 || 0 || 1/1=0 || | || 0 || 0 || 0 || 0 || 1/1=0 || | ||
|| 1 || 88 || 87.805 || 87.744 || 22/21=80.537, 21/20=84.467, 20/19=88.801, 19/18=93.603 || | || 1 || 88 || 87.805 || 87.744 || 22/21=80.537, 21/20=84.467, 20/19=88.801, 19/18=93.603 || | ||
|| 2 || 176 || 175.610 || 175.489 || 11/10=165.004, 21/19=173.268, 10/9=182.404 || | || 2 || 176 || 175.610 || 175.489 || [[11_10|11/10]]=165.004, 21/19=173.268, [[10_9|10/9]]=182.404 || | ||
|| 3 || 264 || 263.415 || 263.233 || 7/6 266.871 || | || 3 || 264 || 263.415 || 263.233 || [[7_6|7/6]]=266.871 || | ||
|| 4 || 352 || 351.220 || 350.978 || 11/9= 347.408, 27/22=354.547, 16/13=359.472 || | || 4 || 352 || 351.220 || 350.978 || [[11_9|11/9]]= 347.408, 27/22=354.547, 16/13=359.472 || | ||
|| 5 || 440 || 439.024 || 438.722 || 32/25=427.373, 9/7=435.084, 22/17 446.363 || | || 5 || 440 || 439.024 || 438.722 || 32/25=427.373, [[9_7|9/7]]=435.084, 22/17 446.363 || | ||
|| 6 || 528 || 526.829 || 526.466 || 19/14 528.687, 49/36=533.742, 15/11=536.95 || | || 6 || 528 || 526.829 || 526.466 || 19/14=528.687, 49/36=533.742, [[15_11|15/11]]=536.95 || | ||
|| 7 || 616 || 614.634 || 614.211 || 10/7=617.488 || | || 7 || 616 || 614.634 || 614.211 || [[10_7|10/7]]=617.488 || | ||
|| 8 || 704 || 702.439 || 701.955 || 3/2=701.955 || | || 8 || 704 || 702.439 || 701.955 || [[3_2|3/2]]=701.955 || | ||
|| 9 || 792 || 790.244 || 789.699 || 11/7=782.492, 30/19=790.756, 128/81=792.180, 19/12=795.558, 27/17=800.910, 8/5=813.686 || | || 9 || 792 || 790.244 || 789.699 || [[11_7|11/7]]=782.492, 30/19=790.756, 128/81=792.180, 19/12=795.558, 27/17=800.910, [[8_5|8/5]]=813.686 || | ||
|| 10 || 880 || 878.049 || 878.444 || 5/3=884.359 || | || 10 || 880 || 878.049 || 878.444 || [[5_3|5/3]]=884.359 || | ||
|| 11 || 968 || 965.854 || 965.188 || 7/4 968.826 || | || 11 || 968 || 965.854 || 965.188 || [[7_4|7/4]]=968.826 || | ||
|| 12 || 1056 || 1053.659 || 1052.933 || 11/6=1049.363, 35/19=1057.627, 24/13=1061.427 || | || 12 || 1056 || 1053.659 || 1052.933 || [[11_6|11/6]]=1049.363, 35/19=1057.627, 24/13=1061.427 || | ||
|| 13 || 1144 || 1141.463 || 1140.677 || 27/14=1137.039, 31/16=1145.036 || | || 13 || 1144 || 1141.463 || 1140.677 || 27/14=1137.039, 31/16=1145.036 || | ||
|||||||||| | ||||||||||= **//second octave//** || | ||
|| 14 || 32 || 29.268 || 28.421 || || | || 14 || 32 || 29.268 || 28.421 || || | ||
|| 15 || 120 || 117.073 || 116.166 || || | || 15 || 120 || 117.073 || 116.166 || || | ||
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|| 26 || 1088 || 1082.927 || 1081.354 || || | || 26 || 1088 || 1082.927 || 1081.354 || || | ||
|| 27 || 1176 || 1170.732 || 1169.098 || || | || 27 || 1176 || 1170.732 || 1169.098 || || | ||
|||||||||| | ||||||||||= **//third octave//** || | ||
|| 28 || 64 || 58.537 || 56.843 || || | || 28 || 64 || 58.537 || 56.843 || || | ||
|| 29 || 152 || 146.341 || 144.587 || || | || 29 || 152 || 146.341 || 144.587 || || | ||
| Line 65: | Line 66: | ||
|| 39 || 1032 || 1024.390 || 1022.031 || || | || 39 || 1032 || 1024.390 || 1022.031 || || | ||
|| 40 || 1120 || 1112.195 || 1109.775 || || | || 40 || 1120 || 1112.195 || 1109.775 || || | ||
|||||||||| | ||||||||||= **//fourth octave//** (near match) || | ||
|| 41 || 8 || 0 || 1197.59 || || | || 41 || 8 || 0 || 1197.59 || || | ||
| Line 98: | Line 99: | ||
<th>41edo<br /> | <th>41edo<br /> | ||
</th> | </th> | ||
<th>8th Root | <th>8th Root<br /> | ||
</th> | </th> | ||
<th>Some Nearby | <th>Some Nearby<br /> | ||
</th> | </th> | ||
</tr> | </tr> | ||
<tr> | <tr> | ||
<th | <th><br /> | ||
</th> | |||
<th><br /> | |||
</th> | |||
<th>3-steps<br /> | |||
</th> | |||
<th>of 3:2<br /> | |||
</th> | |||
<th>JI Intervals<br /> | |||
</th> | </th> | ||
</tr> | |||
<tr> | |||
<td colspan="5" style="text-align: center;"><strong><em>first octave</em></strong><br /> | |||
</td> | |||
</tr> | </tr> | ||
<tr> | <tr> | ||
| Line 140: | Line 153: | ||
<td>175.489<br /> | <td>175.489<br /> | ||
</td> | </td> | ||
<td>11/10=165.004, 21/19=173.268, 10/9=182.404<br /> | <td><a class="wiki_link" href="/11_10">11/10</a>=165.004, 21/19=173.268, <a class="wiki_link" href="/10_9">10/9</a>=182.404<br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
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<td>263.233<br /> | <td>263.233<br /> | ||
</td> | </td> | ||
<td>7/6 | <td><a class="wiki_link" href="/7_6">7/6</a>=266.871<br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
| Line 164: | Line 177: | ||
<td>350.978<br /> | <td>350.978<br /> | ||
</td> | </td> | ||
<td>11/9= 347.408, 27/22=354.547, 16/13=359.472<br /> | <td><a class="wiki_link" href="/11_9">11/9</a>= 347.408, 27/22=354.547, 16/13=359.472<br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
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<td>438.722<br /> | <td>438.722<br /> | ||
</td> | </td> | ||
<td>32/25=427.373, 9/7=435.084, 22/17 446.363<br /> | <td>32/25=427.373, <a class="wiki_link" href="/9_7">9/7</a>=435.084, 22/17 446.363<br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
| Line 188: | Line 201: | ||
<td>526.466<br /> | <td>526.466<br /> | ||
</td> | </td> | ||
<td>19/14 | <td>19/14=528.687, 49/36=533.742, <a class="wiki_link" href="/15_11">15/11</a>=536.95<br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
| Line 200: | Line 213: | ||
<td>614.211<br /> | <td>614.211<br /> | ||
</td> | </td> | ||
<td>10/7=617.488<br /> | <td><a class="wiki_link" href="/10_7">10/7</a>=617.488<br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
| Line 212: | Line 225: | ||
<td>701.955<br /> | <td>701.955<br /> | ||
</td> | </td> | ||
<td>3/2=701.955<br /> | <td><a class="wiki_link" href="/3_2">3/2</a>=701.955<br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
| Line 224: | Line 237: | ||
<td>789.699<br /> | <td>789.699<br /> | ||
</td> | </td> | ||
<td>11/7=782.492, 30/19=790.756, 128/81=792.180, 19/12=795.558, 27/17=800.910, 8/5=813.686<br /> | <td><a class="wiki_link" href="/11_7">11/7</a>=782.492, 30/19=790.756, 128/81=792.180, 19/12=795.558, 27/17=800.910, <a class="wiki_link" href="/8_5">8/5</a>=813.686<br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
| Line 236: | Line 249: | ||
<td>878.444<br /> | <td>878.444<br /> | ||
</td> | </td> | ||
<td>5/3=884.359<br /> | <td><a class="wiki_link" href="/5_3">5/3</a>=884.359<br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
| Line 248: | Line 261: | ||
<td>965.188<br /> | <td>965.188<br /> | ||
</td> | </td> | ||
<td>7/4 | <td><a class="wiki_link" href="/7_4">7/4</a>=968.826<br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
| Line 260: | Line 273: | ||
<td>1052.933<br /> | <td>1052.933<br /> | ||
</td> | </td> | ||
<td>11/6=1049.363, 35/19=1057.627, 24/13=1061.427<br /> | <td><a class="wiki_link" href="/11_6">11/6</a>=1049.363, 35/19=1057.627, 24/13=1061.427<br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
| Line 276: | Line 289: | ||
</tr> | </tr> | ||
<tr> | <tr> | ||
< | <td colspan="5" style="text-align: center;"><strong><em>second octave</em></strong><br /> | ||
</ | </td> | ||
</tr> | </tr> | ||
<tr> | <tr> | ||
| Line 448: | Line 461: | ||
</tr> | </tr> | ||
<tr> | <tr> | ||
< | <td colspan="5" style="text-align: center;"><strong><em>third octave</em></strong><br /> | ||
</ | </td> | ||
</tr> | </tr> | ||
<tr> | <tr> | ||
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</tr> | </tr> | ||
<tr> | <tr> | ||
< | <td colspan="5" style="text-align: center;"><strong><em>fourth octave</em></strong> (near match)<br /> | ||
</ | </td> | ||
</tr> | </tr> | ||
<tr> | <tr> | ||