28edo
IMPORTED REVISION FROM WIKISPACES
This is an imported revision from Wikispaces. The revision metadata is included below for reference:
- This revision was by author Osmiorisbendi and made on 2010-09-19 00:23:04 UTC.
- The original revision id was 163682775.
- 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:
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. The following table compares it to potentially useful nearby just intervals. || Step # || ET Cents || Just Interval || Just Cents || Difference (ET minus Just) || || || || || || || || 1 || 42.86 || || || || || 2 || 85.71 || 21:20 || 84.47 || 1.24 || || 3 || 128.57 || 14:13 || 128.30 || 0.27 || || 4 || 171.43 || 11:10 || 165.00 || 6.43 || || 5 || 214.29 || 17:15 || 216.69 || -2.40 || || 6 || 257.14 || 7:6 || 266.87 || -9.73 || || 7 || 300 || 6:5 || 315.64 || -15.64 || || 8 || 342.86 || 11:9 || 347.41 || -4.55 || || 9 || 385.71 || 5:4 || 386.31 || -0.60 || || 10 || 428.57 || 9:7 || 435.08 || -6.51 || || 11 || 471.43 || || || || || 12 || 514.29 || 4:3 || 498.04 || 16.25 || || 13 || 557.14 || || || || || 14 || 600 || 7:5 || 582.51 || 17.49 || || 15 || 642.86 || || || || || 16 || 685.71 || 3:2 || 701.96 || -16.25 || || 17 || 728.57 || || || || || 18 || 771.43 || 14:9 || 764.92 || 6.51 || || 19 || 814.29 || 5:8 || 813.68 || 0.61 || || 20 || 857.14 || 18:11 || 852.59 || 4.55 || || 21 || 900 || 5:3 || 884.36 || 15.64 || || 22 || 942.86 || 12:7 || 933.13 || 9.73 || || 23 || 985.71 || 30:17 || 983.31 || 2.40 || || 24 || 1028.57 || 20:11 || 1035.00 || -6.43 || || 25 || 1071.42 || 13:7 || 1071.70 || -0.27 || || 26 || 1114.29 || 40:21 || 1115.53 || -1.24 || || 27 || 1157.14 || || || || || 28 || 1200 || 2:1 || 1200 || 0 ||
Original HTML content:
<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 />
<br />
The following table compares it to potentially useful nearby just intervals.<br />
<br />
<table class="wiki_table">
<tr>
<td>Step #<br />
</td>
<td>ET Cents<br />
</td>
<td>Just Interval<br />
</td>
<td>Just Cents<br />
</td>
<td>Difference (ET minus Just)<br />
</td>
</tr>
<tr>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
</tr>
<tr>
<td>1<br />
</td>
<td>42.86<br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
</tr>
<tr>
<td>2<br />
</td>
<td>85.71<br />
</td>
<td>21:20<br />
</td>
<td>84.47<br />
</td>
<td>1.24<br />
</td>
</tr>
<tr>
<td>3<br />
</td>
<td>128.57<br />
</td>
<td>14:13<br />
</td>
<td>128.30<br />
</td>
<td>0.27<br />
</td>
</tr>
<tr>
<td>4<br />
</td>
<td>171.43<br />
</td>
<td>11:10<br />
</td>
<td>165.00<br />
</td>
<td>6.43<br />
</td>
</tr>
<tr>
<td>5<br />
</td>
<td>214.29<br />
</td>
<td>17:15<br />
</td>
<td>216.69<br />
</td>
<td>-2.40<br />
</td>
</tr>
<tr>
<td>6<br />
</td>
<td>257.14<br />
</td>
<td>7:6<br />
</td>
<td>266.87<br />
</td>
<td>-9.73<br />
</td>
</tr>
<tr>
<td>7<br />
</td>
<td>300<br />
</td>
<td>6:5<br />
</td>
<td>315.64<br />
</td>
<td>-15.64<br />
</td>
</tr>
<tr>
<td>8<br />
</td>
<td>342.86<br />
</td>
<td>11:9<br />
</td>
<td>347.41<br />
</td>
<td>-4.55<br />
</td>
</tr>
<tr>
<td>9<br />
</td>
<td>385.71<br />
</td>
<td>5:4<br />
</td>
<td>386.31<br />
</td>
<td>-0.60<br />
</td>
</tr>
<tr>
<td>10<br />
</td>
<td>428.57<br />
</td>
<td>9:7<br />
</td>
<td>435.08<br />
</td>
<td>-6.51<br />
</td>
</tr>
<tr>
<td>11<br />
</td>
<td>471.43<br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
</tr>
<tr>
<td>12<br />
</td>
<td>514.29<br />
</td>
<td>4:3<br />
</td>
<td>498.04<br />
</td>
<td>16.25<br />
</td>
</tr>
<tr>
<td>13<br />
</td>
<td>557.14<br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
</tr>
<tr>
<td>14<br />
</td>
<td>600<br />
</td>
<td>7:5<br />
</td>
<td>582.51<br />
</td>
<td>17.49<br />
</td>
</tr>
<tr>
<td>15<br />
</td>
<td>642.86<br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
</tr>
<tr>
<td>16<br />
</td>
<td>685.71<br />
</td>
<td>3:2<br />
</td>
<td>701.96<br />
</td>
<td>-16.25<br />
</td>
</tr>
<tr>
<td>17<br />
</td>
<td>728.57<br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
</tr>
<tr>
<td>18<br />
</td>
<td>771.43<br />
</td>
<td>14:9<br />
</td>
<td>764.92<br />
</td>
<td>6.51<br />
</td>
</tr>
<tr>
<td>19<br />
</td>
<td>814.29<br />
</td>
<td>5:8<br />
</td>
<td>813.68<br />
</td>
<td>0.61<br />
</td>
</tr>
<tr>
<td>20<br />
</td>
<td>857.14<br />
</td>
<td>18:11<br />
</td>
<td>852.59<br />
</td>
<td>4.55<br />
</td>
</tr>
<tr>
<td>21<br />
</td>
<td>900<br />
</td>
<td>5:3<br />
</td>
<td>884.36<br />
</td>
<td>15.64<br />
</td>
</tr>
<tr>
<td>22<br />
</td>
<td>942.86<br />
</td>
<td>12:7<br />
</td>
<td>933.13<br />
</td>
<td>9.73<br />
</td>
</tr>
<tr>
<td>23<br />
</td>
<td>985.71<br />
</td>
<td>30:17<br />
</td>
<td>983.31<br />
</td>
<td>2.40<br />
</td>
</tr>
<tr>
<td>24<br />
</td>
<td>1028.57<br />
</td>
<td>20:11<br />
</td>
<td>1035.00<br />
</td>
<td>-6.43<br />
</td>
</tr>
<tr>
<td>25<br />
</td>
<td>1071.42<br />
</td>
<td>13:7<br />
</td>
<td>1071.70<br />
</td>
<td>-0.27<br />
</td>
</tr>
<tr>
<td>26<br />
</td>
<td>1114.29<br />
</td>
<td>40:21<br />
</td>
<td>1115.53<br />
</td>
<td>-1.24<br />
</td>
</tr>
<tr>
<td>27<br />
</td>
<td>1157.14<br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
</tr>
<tr>
<td>28<br />
</td>
<td>1200<br />
</td>
<td>2:1<br />
</td>
<td>1200<br />
</td>
<td>0<br />
</td>
</tr>
</table>
</body></html>