28edo: Difference between revisions
Wikispaces>JinowKeatiuku **Imported revision 163549865 - Original comment: ** |
Wikispaces>Osmiorisbendi **Imported revision 163682775 - Original comment: ** |
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| 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:Osmiorisbendi|Osmiorisbendi]] and made on <tt>2010-09-19 00:23:04 UTC</tt>.<br> | ||
: The original revision id was <tt> | : The original revision id was <tt>163682775</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> | ||
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The following table compares it to potentially useful nearby just intervals. | The following table compares it to potentially useful nearby just intervals. | ||
|| Step # | || Step # || ET Cents || Just Interval || Just Cents || Difference (ET minus Just) || | ||
|| || || || || || | |||
|| 1 | || 1 || 42.86 || || || || | ||
|| 2 | || 2 || 85.71 || 21:20 || 84.47 || 1.24 || | ||
|| 3 | || 3 || 128.57 || 14:13 || 128.30 || 0.27 || | ||
|| 4 | || 4 || 171.43 || 11:10 || 165.00 || 6.43 || | ||
|| 5 | || 5 || 214.29 || 17:15 || 216.69 || -2.40 || | ||
|| 6 | || 6 || 257.14 || 7:6 || 266.87 || -9.73 || | ||
|| 7 | || 7 || 300 || 6:5 || 315.64 || -15.64 || | ||
|| 8 | || 8 || 342.86 || 11:9 || 347.41 || -4.55 || | ||
|| 9 | || 9 || 385.71 || 5:4 || 386.31 || -0.60 || | ||
|| 10 | || 10 || 428.57 || 9:7 || 435.08 || -6.51 || | ||
|| 11 | || 11 || 471.43 || || || || | ||
|| 12 | || 12 || 514.29 || 4:3 || 498.04 || 16.25 || | ||
|| 13 | || 13 || 557.14 || || || || | ||
|| 14 | || 14 || 600 || 7:5 || 582.51 || 17.49 || | ||
|| 15 | || 15 || 642.86 || || || || | ||
|| 16 | || 16 || 685.71 || 3:2 || 701.96 || -16.25 || | ||
|| 17 | || 17 || 728.57 || || || || | ||
|| 18 | || 18 || 771.43 || 14:9 || 764.92 || 6.51 || | ||
|| 19 | || 19 || 814.29 || 5:8 || 813.68 || 0.61 || | ||
|| 20 | || 20 || 857.14 || 18:11 || 852.59 || 4.55 || | ||
|| 21 | || 21 || 900 || 5:3 || 884.36 || 15.64 || | ||
|| 22 | || 22 || 942.86 || 12:7 || 933.13 || 9.73 || | ||
|| 23 | || 23 || 985.71 || 30:17 || 983.31 || 2.40 || | ||
|| 24 | || 24 || 1028.57 || 20:11 || 1035.00 || -6.43 || | ||
|| 25 | || 25 || 1071.42 || 13:7 || 1071.70 || -0.27 || | ||
|| 26 | || 26 || 1114.29 || 40:21 || 1115.53 || -1.24 || | ||
|| 27 | || 27 || 1157.14 || || || || | ||
|| 28 | || 28 || 1200 || 2:1 || 1200 || 0 ||</pre></div> | ||
<h4>Original HTML content:</h4> | <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>28edo</title></head><body>28edo, a multiple of both 7edo and 14edo, has a step size of 42.86 cents. It shares three intervals with 12edo: the 300 cent minor third, the 600 cent tritone, and the 900 cent major sixth. Thus it tempers out the greater diesis 648:625. It does not however temper out the 128:125 lesser diesis, as its major third is less than 1 cent flat (and its inversion the minor sixth less than 1 cent sharp). It has the same perfect fourth and fifth as 14edo. It also has decent approximations of several septimal intervals, most of which are also found in 14edo.<br /> | <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>28edo</title></head><body>28edo, a multiple of both 7edo and 14edo, has a step size of 42.86 cents. It shares three intervals with 12edo: the 300 cent minor third, the 600 cent tritone, and the 900 cent major sixth. Thus it tempers out the greater diesis 648:625. It does not however temper out the 128:125 lesser diesis, as its major third is less than 1 cent flat (and its inversion the minor sixth less than 1 cent sharp). It has the same perfect fourth and fifth as 14edo. It also has decent approximations of several septimal intervals, most of which are also found in 14edo.<br /> | ||
| Line 50: | Line 50: | ||
<tr> | <tr> | ||
<td>Step #<br /> | <td>Step #<br /> | ||
</td> | </td> | ||
<td>ET Cents<br /> | <td>ET Cents<br /> | ||
</td> | </td> | ||
<td>Just Interval<br /> | <td>Just Interval<br /> | ||
| Line 66: | Line 58: | ||
</td> | </td> | ||
<td>Difference (ET minus Just)<br /> | <td>Difference (ET minus Just)<br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
<tr> | <tr> | ||
<td><br /> | <td><br /> | ||
</td> | </td> | ||
| Line 94: | Line 74: | ||
<tr> | <tr> | ||
<td>1<br /> | <td>1<br /> | ||
</td> | </td> | ||
<td>42.86<br /> | <td>42.86<br /> | ||
</td> | </td> | ||
<td><br /> | <td><br /> | ||
| Line 116: | Line 86: | ||
<tr> | <tr> | ||
<td>2<br /> | <td>2<br /> | ||
</td> | </td> | ||
<td>85.71<br /> | <td>85.71<br /> | ||
</td> | </td> | ||
<td>21:20<br /> | <td>21:20<br /> | ||
| Line 132: | Line 94: | ||
</td> | </td> | ||
<td>1.24<br /> | <td>1.24<br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
<tr> | <tr> | ||
<td>3<br /> | <td>3<br /> | ||
</td> | </td> | ||
<td>128.57<br /> | <td>128.57<br /> | ||
</td> | </td> | ||
<td>14:13<br /> | <td>14:13<br /> | ||
| Line 154: | Line 106: | ||
</td> | </td> | ||
<td>0.27<br /> | <td>0.27<br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
<tr> | <tr> | ||
<td>4<br /> | <td>4<br /> | ||
</td> | </td> | ||
<td>171.43<br /> | <td>171.43<br /> | ||
</td> | </td> | ||
<td>11:10<br /> | <td>11:10<br /> | ||
| Line 176: | Line 118: | ||
</td> | </td> | ||
<td>6.43<br /> | <td>6.43<br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
<tr> | <tr> | ||
<td>5<br /> | <td>5<br /> | ||
</td> | </td> | ||
<td>214.29<br /> | <td>214.29<br /> | ||
</td> | </td> | ||
<td>17:15<br /> | <td>17:15<br /> | ||
| Line 198: | Line 130: | ||
</td> | </td> | ||
<td>-2.40<br /> | <td>-2.40<br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
<tr> | <tr> | ||
<td>6<br /> | <td>6<br /> | ||
</td> | </td> | ||
<td>257.14<br /> | <td>257.14<br /> | ||
</td> | </td> | ||
<td>7:6<br /> | <td>7:6<br /> | ||
| Line 220: | Line 142: | ||
</td> | </td> | ||
<td>-9.73<br /> | <td>-9.73<br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
<tr> | <tr> | ||
<td>7<br /> | <td>7<br /> | ||
</td> | </td> | ||
<td>300<br /> | <td>300<br /> | ||
</td> | </td> | ||
<td>6:5<br /> | <td>6:5<br /> | ||
| Line 242: | Line 154: | ||
</td> | </td> | ||
<td>-15.64<br /> | <td>-15.64<br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
<tr> | <tr> | ||
<td>8<br /> | <td>8<br /> | ||
</td> | </td> | ||
<td>342.86<br /> | <td>342.86<br /> | ||
</td> | </td> | ||
<td>11:9<br /> | <td>11:9<br /> | ||
| Line 264: | Line 166: | ||
</td> | </td> | ||
<td>-4.55<br /> | <td>-4.55<br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
<tr> | <tr> | ||
<td>9<br /> | <td>9<br /> | ||
</td> | </td> | ||
<td>385.71<br /> | <td>385.71<br /> | ||
</td> | </td> | ||
<td>5:4<br /> | <td>5:4<br /> | ||
| Line 286: | Line 178: | ||
</td> | </td> | ||
<td>-0.60<br /> | <td>-0.60<br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
<tr> | <tr> | ||
<td>10<br /> | <td>10<br /> | ||
</td> | </td> | ||
<td>428.57<br /> | <td>428.57<br /> | ||
</td> | </td> | ||
<td>9:7<br /> | <td>9:7<br /> | ||
| Line 308: | Line 190: | ||
</td> | </td> | ||
<td>-6.51<br /> | <td>-6.51<br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
<tr> | <tr> | ||
<td>11<br /> | <td>11<br /> | ||
</td> | </td> | ||
<td>471.43<br /> | <td>471.43<br /> | ||
</td> | </td> | ||
<td><br /> | <td><br /> | ||
| Line 336: | Line 206: | ||
<tr> | <tr> | ||
<td>12<br /> | <td>12<br /> | ||
</td> | </td> | ||
<td>514.29<br /> | <td>514.29<br /> | ||
</td> | </td> | ||
<td>4:3<br /> | <td>4:3<br /> | ||
| Line 352: | Line 214: | ||
</td> | </td> | ||
<td>16.25<br /> | <td>16.25<br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
<tr> | <tr> | ||
<td>13<br /> | <td>13<br /> | ||
</td> | </td> | ||
<td>557.14<br /> | <td>557.14<br /> | ||
</td> | </td> | ||
<td><br /> | <td><br /> | ||
| Line 380: | Line 230: | ||
<tr> | <tr> | ||
<td>14<br /> | <td>14<br /> | ||
</td> | </td> | ||
<td>600<br /> | <td>600<br /> | ||
</td> | </td> | ||
<td>7:5<br /> | <td>7:5<br /> | ||
| Line 396: | Line 238: | ||
</td> | </td> | ||
<td>17.49<br /> | <td>17.49<br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
<tr> | <tr> | ||
<td>15<br /> | <td>15<br /> | ||
</td> | </td> | ||
<td>642.86<br /> | <td>642.86<br /> | ||
</td> | </td> | ||
<td><br /> | <td><br /> | ||
| Line 424: | Line 254: | ||
<tr> | <tr> | ||
<td>16<br /> | <td>16<br /> | ||
</td> | </td> | ||
<td>685.71<br /> | <td>685.71<br /> | ||
</td> | </td> | ||
<td>3:2<br /> | <td>3:2<br /> | ||
| Line 440: | Line 262: | ||
</td> | </td> | ||
<td>-16.25<br /> | <td>-16.25<br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
<tr> | <tr> | ||
<td>17<br /> | <td>17<br /> | ||
</td> | </td> | ||
<td>728.57<br /> | <td>728.57<br /> | ||
</td> | </td> | ||
<td><br /> | <td><br /> | ||
| Line 468: | Line 278: | ||
<tr> | <tr> | ||
<td>18<br /> | <td>18<br /> | ||
</td> | </td> | ||
<td>771.43<br /> | <td>771.43<br /> | ||
</td> | </td> | ||
<td>14:9<br /> | <td>14:9<br /> | ||
| Line 484: | Line 286: | ||
</td> | </td> | ||
<td>6.51<br /> | <td>6.51<br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
<tr> | <tr> | ||
<td>19<br /> | <td>19<br /> | ||
</td> | </td> | ||
<td>814.29<br /> | <td>814.29<br /> | ||
</td> | </td> | ||
<td>5:8<br /> | <td>5:8<br /> | ||
| Line 506: | Line 298: | ||
</td> | </td> | ||
<td>0.61<br /> | <td>0.61<br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
<tr> | <tr> | ||
<td>20<br /> | <td>20<br /> | ||
</td> | </td> | ||
<td>857.14<br /> | <td>857.14<br /> | ||
</td> | </td> | ||
<td>18:11<br /> | <td>18:11<br /> | ||
| Line 528: | Line 310: | ||
</td> | </td> | ||
<td>4.55<br /> | <td>4.55<br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
<tr> | <tr> | ||
<td>21<br /> | <td>21<br /> | ||
</td> | </td> | ||
<td>900<br /> | <td>900<br /> | ||
</td> | </td> | ||
<td>5:3<br /> | <td>5:3<br /> | ||
| Line 550: | Line 322: | ||
</td> | </td> | ||
<td>15.64<br /> | <td>15.64<br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
<tr> | <tr> | ||
<td>22<br /> | <td>22<br /> | ||
</td> | </td> | ||
<td>942.86<br /> | <td>942.86<br /> | ||
</td> | </td> | ||
<td>12:7<br /> | <td>12:7<br /> | ||
| Line 572: | Line 334: | ||
</td> | </td> | ||
<td>9.73<br /> | <td>9.73<br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
<tr> | <tr> | ||
<td>23<br /> | <td>23<br /> | ||
</td> | </td> | ||
<td>985.71<br /> | <td>985.71<br /> | ||
</td> | </td> | ||
<td>30:17<br /> | <td>30:17<br /> | ||
| Line 594: | Line 346: | ||
</td> | </td> | ||
<td>2.40<br /> | <td>2.40<br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
<tr> | <tr> | ||
<td>24<br /> | <td>24<br /> | ||
</td> | </td> | ||
<td>1028.57<br /> | <td>1028.57<br /> | ||
</td> | </td> | ||
<td> | <td>20:11<br /> | ||
</td> | </td> | ||
<td>1035.00<br /> | <td>1035.00<br /> | ||
</td> | </td> | ||
<td>-6.43<br /> | <td>-6.43<br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
<tr> | <tr> | ||
<td>25<br /> | <td>25<br /> | ||
</td> | </td> | ||
<td>1071.42<br /> | <td>1071.42<br /> | ||
</td> | </td> | ||
<td>13:7<br /> | <td>13:7<br /> | ||
| Line 638: | Line 370: | ||
</td> | </td> | ||
<td>-0.27<br /> | <td>-0.27<br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
<tr> | <tr> | ||
<td>26<br /> | <td>26<br /> | ||
</td> | </td> | ||
<td>1114.29<br /> | <td>1114.29<br /> | ||
</td> | </td> | ||
<td>40:21<br /> | <td>40:21<br /> | ||
| Line 660: | Line 382: | ||
</td> | </td> | ||
<td>-1.24<br /> | <td>-1.24<br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
<tr> | <tr> | ||
<td>27<br /> | <td>27<br /> | ||
</td> | </td> | ||
<td>1157.14<br /> | <td>1157.14<br /> | ||
</td> | </td> | ||
<td><br /> | <td><br /> | ||
| Line 688: | Line 398: | ||
<tr> | <tr> | ||
<td>28<br /> | <td>28<br /> | ||
</td> | </td> | ||
<td>1200<br /> | <td>1200<br /> | ||
</td> | </td> | ||
<td>2:1<br /> | <td>2:1<br /> | ||
| Line 704: | Line 406: | ||
</td> | </td> | ||
<td>0<br /> | <td>0<br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||