Intervals of BP: Difference between revisions
Wikispaces>Andrew_Heathwaite **Imported revision 106266775 - Original comment: ** |
Wikispaces>Andrew_Heathwaite **Imported revision 106270595 - Original comment: ** |
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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:Andrew_Heathwaite|Andrew_Heathwaite]] and made on <tt>2009-11-30 23: | : This revision was by author [[User:Andrew_Heathwaite|Andrew_Heathwaite]] and made on <tt>2009-11-30 23:23:14 UTC</tt>.<br> | ||
: The original revision id was <tt> | : The original revision id was <tt>106270595</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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<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;white-space: pre-wrap ! important" class="old-revision-html">This page gives the intervals of the equal tempered [[BP|Bohlen-Pierce]] scale -- the 13th root of 3, along with some nearby just ratios for comparison. | <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;white-space: pre-wrap ! important" class="old-revision-html">This page gives the intervals of the equal tempered [[BP|Bohlen-Pierce]] scale -- the 13th root of 3, along with some nearby just ratios for comparison. | ||
|| degree || cents value || nearby frequency ratios || cents value || difference between BP interval & just interval || | ||~ degree ||~ cents value ||~ nearby frequency ratios ||~ cents value ||~ difference between BP interval & just interval || | ||
||||||~ first octave and first tritave... || || || | |||
|| 0 || 0 || 1/1 || 0 || 0 || | || 0 || 0 || 1/1 || 0 || 0 || | ||
|| 1 || 146.3 || 12/11 | || 1 || 146.3 || 12/11 | ||
| Line 48: | Line 49: | ||
6.5 || | 6.5 || | ||
|| 8 || 1170.4 || 49/25 || 1165.0 || 5.4 || | || 8 || 1170.4 || 49/25 || 1165.0 || 5.4 || | ||
||||||~ second octave... || || || | |||
|| 9 || 116.7 || 15/14 | || 9 || 116.7 || 15/14 | ||
16/15 || 119.4 | 16/15 || 119.4 | ||
| Line 64: | Line 66: | ||
-7.7 | -7.7 | ||
-13.0 || | -13.0 || | ||
||||||~ second tritave... || || || | |||
|| 13 || 702.0 || 3/2 || 702.0 || 0 || | || 13 || 702.0 || 3/2 || 702.0 || 0 || | ||
|| | || 14 || 848.3 || 18/11 | ||
|| | 13/8 || 852.6 | ||
|| | 840.5 || -4.3 | ||
|| | 7.8 || | ||
|| | || 15 || 994.6 || 16/9 || 996.1 || -1.5 || | ||
|| | || 16 || 1140.9 || 27/14 || 1137.0 || 3.9 || | ||
|| | ||||||~ third octave... || || || | ||
|| | || 17 || 87.2 || 20/19 | ||
|| | 21/20 || 88.8 | ||
|| | 84.5 || -1.6 | ||
|| | 2.7 || | ||
|| | || 18 || 233.5 || 8/7 || 231.2 || 2.3 || | ||
|| | || 19 || 379.8 || 5/4 || 386.3 || -6.5 || | ||
|| 20 || 526.1 || 19/14 | |||
27/20 || 528.7 | |||
519.6 || -2.6 | |||
6.5 || | |||
|| 21 || 672.4 || 28/19 | |||
25/17 || 671.3 | |||
667.7 || 1.1 | |||
4.7 || | |||
|| 22 || 818.7 || 8/5 || 813.7 || 5.0 || | |||
|| 23 || 965.0 || 7/4 || 968.8 || -3.8 || | |||
|| 24 || 1111.3 || 19/10 | |||
40/21 || 1111.2 | |||
1115.5 || 0.1 | |||
-4.2 || | |||
||||||~ fourth octave... || || || | |||
|| 25 || 57.6 || 33/32 || 53.3 || 4.3 || | |||
||||||~ third tritave... || || || | |||
|| 26 || 203.9 || 9/8 || 203.9 || 0 || | |||
|| || || || || || | || || || || || || | ||
|| || || || || || | || || || || || || | ||
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<table class="wiki_table"> | <table class="wiki_table"> | ||
<tr> | <tr> | ||
<td> | <th>degree<br /> | ||
</th> | |||
<th>cents value<br /> | |||
</th> | |||
<th>nearby frequency ratios<br /> | |||
</th> | |||
<th>cents value<br /> | |||
</th> | |||
<th>difference between BP interval &amp; just interval<br /> | |||
</th> | |||
</tr> | |||
<tr> | |||
<th colspan="3">first octave and first tritave...<br /> | |||
</th> | |||
<td><br /> | |||
</td> | </td> | ||
<td> | <td><br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
| Line 245: | Line 274: | ||
</td> | </td> | ||
<td>5.4<br /> | <td>5.4<br /> | ||
</td> | |||
</tr> | |||
<tr> | |||
<th colspan="3">second octave...<br /> | |||
</th> | |||
<td><br /> | |||
</td> | |||
<td><br /> | |||
</td> | </td> | ||
</tr> | </tr> | ||
| Line 305: | Line 342: | ||
-7.7<br /> | -7.7<br /> | ||
-13.0<br /> | -13.0<br /> | ||
</td> | |||
</tr> | |||
<tr> | |||
<th colspan="3">second tritave...<br /> | |||
</th> | |||
<td><br /> | |||
</td> | |||
<td><br /> | |||
</td> | </td> | ||
</tr> | </tr> | ||
| Line 320: | Line 365: | ||
</tr> | </tr> | ||
<tr> | <tr> | ||
<td><br /> | <td>14<br /> | ||
</td> | </td> | ||
<td><br /> | <td>848.3<br /> | ||
</td> | </td> | ||
<td><br /> | <td>18/11<br /> | ||
13/8<br /> | |||
</td> | </td> | ||
<td><br /> | <td>852.6<br /> | ||
840.5<br /> | |||
</td> | </td> | ||
<td><br /> | <td>-4.3<br /> | ||
7.8<br /> | |||
</td> | </td> | ||
</tr> | </tr> | ||
<tr> | <tr> | ||
<td><br /> | <td>15<br /> | ||
</td> | </td> | ||
<td><br /> | <td>994.6<br /> | ||
</td> | </td> | ||
<td><br /> | <td>16/9<br /> | ||
</td> | </td> | ||
<td><br /> | <td>996.1<br /> | ||
</td> | </td> | ||
<td><br /> | <td>-1.5<br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
<tr> | <tr> | ||
<td><br /> | <td>16<br /> | ||
</td> | |||
<td>1140.9<br /> | |||
</td> | |||
<td>27/14<br /> | |||
</td> | </td> | ||
<td><br /> | <td>1137.0<br /> | ||
</td> | </td> | ||
<td><br /> | <td>3.9<br /> | ||
</td> | </td> | ||
</tr> | |||
<tr> | |||
<th colspan="3">third octave...<br /> | |||
</th> | |||
<td><br /> | <td><br /> | ||
</td> | </td> | ||
| Line 356: | Line 412: | ||
</tr> | </tr> | ||
<tr> | <tr> | ||
<td><br /> | <td>17<br /> | ||
</td> | </td> | ||
<td><br /> | <td>87.2<br /> | ||
</td> | </td> | ||
<td><br /> | <td>20/19<br /> | ||
21/20<br /> | |||
</td> | </td> | ||
<td><br /> | <td>88.8<br /> | ||
84.5<br /> | |||
</td> | </td> | ||
<td><br /> | <td>-1.6<br /> | ||
2.7<br /> | |||
</td> | </td> | ||
</tr> | </tr> | ||
<tr> | <tr> | ||
<td><br /> | <td>18<br /> | ||
</td> | </td> | ||
<td><br /> | <td>233.5<br /> | ||
</td> | </td> | ||
<td><br /> | <td>8/7<br /> | ||
</td> | </td> | ||
<td><br /> | <td>231.2<br /> | ||
</td> | </td> | ||
<td><br /> | <td>2.3<br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
<tr> | <tr> | ||
<td><br /> | <td>19<br /> | ||
</td> | </td> | ||
<td><br /> | <td>379.8<br /> | ||
</td> | </td> | ||
<td><br /> | <td>5/4<br /> | ||
</td> | </td> | ||
<td><br /> | <td>386.3<br /> | ||
</td> | </td> | ||
<td><br /> | <td>-6.5<br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
<tr> | <tr> | ||
<td><br /> | <td>20<br /> | ||
</td> | </td> | ||
<td><br /> | <td>526.1<br /> | ||
</td> | </td> | ||
<td><br /> | <td>19/14<br /> | ||
27/20<br /> | |||
</td> | </td> | ||
<td><br /> | <td>528.7<br /> | ||
519.6<br /> | |||
</td> | </td> | ||
<td><br /> | <td>-2.6<br /> | ||
6.5<br /> | |||
</td> | </td> | ||
</tr> | </tr> | ||
<tr> | <tr> | ||
<td><br /> | <td>21<br /> | ||
</td> | </td> | ||
<td><br /> | <td>672.4<br /> | ||
</td> | </td> | ||
<td><br /> | <td>28/19<br /> | ||
25/17<br /> | |||
</td> | </td> | ||
<td><br /> | <td>671.3<br /> | ||
667.7<br /> | |||
</td> | </td> | ||
<td><br /> | <td>1.1<br /> | ||
4.7<br /> | |||
</td> | </td> | ||
</tr> | </tr> | ||
<tr> | <tr> | ||
<td><br /> | <td>22<br /> | ||
</td> | </td> | ||
<td><br /> | <td>818.7<br /> | ||
</td> | </td> | ||
<td><br /> | <td>8/5<br /> | ||
</td> | </td> | ||
<td><br /> | <td>813.7<br /> | ||
</td> | </td> | ||
<td><br /> | <td>5.0<br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
<tr> | <tr> | ||
<td><br /> | <td>23<br /> | ||
</td> | </td> | ||
<td><br /> | <td>965.0<br /> | ||
</td> | </td> | ||
<td><br /> | <td>7/4<br /> | ||
</td> | </td> | ||
<td><br /> | <td>968.8<br /> | ||
</td> | </td> | ||
<td><br /> | <td>-3.8<br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
<tr> | <tr> | ||
<td><br /> | <td>24<br /> | ||
</td> | |||
<td>1111.3<br /> | |||
</td> | |||
<td>19/10<br /> | |||
40/21<br /> | |||
</td> | </td> | ||
<td><br /> | <td>1111.2<br /> | ||
1115.5<br /> | |||
</td> | </td> | ||
<td><br /> | <td>0.1<br /> | ||
-4.2<br /> | |||
</td> | </td> | ||
</tr> | |||
<tr> | |||
<th colspan="3">fourth octave...<br /> | |||
</th> | |||
<td><br /> | <td><br /> | ||
</td> | </td> | ||
| Line 452: | Line 528: | ||
</tr> | </tr> | ||
<tr> | <tr> | ||
<td><br /> | <td>25<br /> | ||
</td> | |||
<td>57.6<br /> | |||
</td> | |||
<td>33/32<br /> | |||
</td> | </td> | ||
<td><br /> | <td>53.3<br /> | ||
</td> | </td> | ||
<td><br /> | <td>4.3<br /> | ||
</td> | </td> | ||
</tr> | |||
<tr> | |||
<th colspan="3">third tritave...<br /> | |||
</th> | |||
<td><br /> | <td><br /> | ||
</td> | </td> | ||
| Line 464: | Line 548: | ||
</tr> | </tr> | ||
<tr> | <tr> | ||
<td><br /> | <td>26<br /> | ||
</td> | </td> | ||
<td><br /> | <td>203.9<br /> | ||
</td> | </td> | ||
<td><br /> | <td>9/8<br /> | ||
</td> | </td> | ||
<td><br /> | <td>203.9<br /> | ||
</td> | </td> | ||
<td><br /> | <td>0<br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||