Intervals of BP
IMPORTED REVISION FROM WIKISPACES
This is an imported revision from Wikispaces. The revision metadata is included below for reference:
- This revision was by author hstraub and made on 2010-09-28 07:52:53 UTC.
- The original revision id was 165960433.
- The revision comment was: fourth octave completed
The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.
Original Wikitext content:
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 || ||||||~ first octave and first tritave... || || || || 0 || 0 || 1/1 || 0 || 0 || || 1 || 146.3 || 12/11 13/12 27/25 || 150.6 138.6 133.2 || -4.3 7.7 13.1 || || 2 || 292.6 || 32/27 13/11 19/16 25/21 || 294.1 289.2 297.5 301.8 || -1.5 3.4 -4.9 -9.2 || || 3 || 438.9 || 9/7 || 435.1 || 3.8 || || 4 || 585.2 || 7/5 45/32 || 582.5 590.2 || 2.7 -5.0 || || 5 || 731.5 || 32/21 26/17 75/49 49/32 20/13 || 729.2 735.6 736.9 737.7 745.8 || 2.3 -4.1 -5.4 -6.2 -14.3 || || 6 || 877.8 || 5/3 || 884.4 || -6.6 || || 7 || 1024.1 || 38/21 29/16 9/5 20/11 || 1026.7 1029.6 1017.6 1035.0 || -2.6 -5.5 6.5 -10.9 || || 8 || 1170.4 || 49/25 || 1165.0 || 5.4 || ||||||~ second octave... || || || || 9 || 116.7 || 15/14 16/15 14/13 || 119.4 111.7 128.3 || -2.7 5.0 -11.6 || || 10 || 263.0 || 7/6 22/19 || 266.9 253.8 || -3.9 9.2 || || 11 || 409.3 || 19/15 81/64 24/19 14/11 63/50 || 409.2 407.8 404.4 417.5 400.1 || .1 1.5 4.9 -8.2 9.2 || || 12 || 555.7 || 11/8 18/13 26/19 25/18 || 551.3 563.4 543.0 568.7 || 4.4 -7.7 12.7 -13.0 || ||||||~ second tritave... || || || || 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 19/18 22/21 || 88.8 84.5 93.6 80.5 || -1.6 2.7 -6.4 6.7 || || 18 || 233.5 || 8/7 15/13 || 231.2 247.7 || 2.3 -14.2 || || 19 || 379.8 || 5/4 26/21 || 386.3 369.7 || -6.5 10.1 || || 20 || 526.1 || 19/14 27/20 15/11 || 528.7 519.6 537.0 || -2.6 6.5 -10.9 || || 21 || 672.4 || 28/19 25/17 22/15 || 671.3 667.7 663.0 || 1.1 4.7 9.4 || || 22 || 818.7 || 8/5 21/13 || 813.7 830.3 || 5.0 -11.6 || || 23 || 965.0 || 7/4 26/15 || 968.8 952.3 || -3.8 12.7 || || 24 || 1111.3 || 19/10 40/21 36/19 21/11 || 1111.2 1115.5 1106.4 1119.5 || 0.1 -4.2 4.9 -8.2 || ||||||~ fourth octave... || || || || 25 || 57.6 || 33/32 || 53.3 || 4.3 || ||||||~ third tritave... || || || || 26 || 203.9 || 9/8 || 203.9 || 0 || || 27 || 350.2 || || || || || 28 || 496.5 || || || || || 29 || 642.8 || || || || || 30 || 789.1 || || || || || 31 || 935.4 || || || || || 32 || 1081.7 || || || || ||||||= **fifth octave...** || || || || 33 || 28.0 || || || || || || || || || || || || || || || || || || || || || || || || || || || || || || || || || ||
Original HTML content:
<html><head><title>Intervals of BP</title></head><body>This page gives the intervals of the equal tempered <a class="wiki_link" href="/BP">Bohlen-Pierce</a> scale -- the 13th root of 3, along with some nearby just ratios for comparison.<br />
<br />
<table class="wiki_table">
<tr>
<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 & just interval<br />
</th>
</tr>
<tr>
<th colspan="3">first octave and first tritave...<br />
</th>
<td><br />
</td>
<td><br />
</td>
</tr>
<tr>
<td>0<br />
</td>
<td>0<br />
</td>
<td>1/1<br />
</td>
<td>0<br />
</td>
<td>0<br />
</td>
</tr>
<tr>
<td>1<br />
</td>
<td>146.3<br />
</td>
<td>12/11<br />
13/12<br />
27/25<br />
</td>
<td>150.6<br />
138.6<br />
133.2<br />
</td>
<td>-4.3<br />
7.7<br />
13.1<br />
</td>
</tr>
<tr>
<td>2<br />
</td>
<td>292.6<br />
</td>
<td>32/27<br />
13/11<br />
19/16<br />
25/21<br />
</td>
<td>294.1<br />
289.2<br />
297.5<br />
301.8<br />
</td>
<td>-1.5<br />
3.4<br />
-4.9<br />
-9.2<br />
</td>
</tr>
<tr>
<td>3<br />
</td>
<td>438.9<br />
</td>
<td>9/7<br />
</td>
<td>435.1<br />
</td>
<td>3.8<br />
</td>
</tr>
<tr>
<td>4<br />
</td>
<td>585.2<br />
</td>
<td>7/5<br />
45/32<br />
</td>
<td>582.5<br />
590.2<br />
</td>
<td>2.7<br />
-5.0<br />
</td>
</tr>
<tr>
<td>5<br />
</td>
<td>731.5<br />
</td>
<td>32/21<br />
26/17<br />
75/49<br />
49/32<br />
20/13<br />
</td>
<td>729.2<br />
735.6<br />
736.9<br />
737.7<br />
745.8<br />
</td>
<td>2.3<br />
-4.1<br />
-5.4<br />
-6.2<br />
-14.3<br />
</td>
</tr>
<tr>
<td>6<br />
</td>
<td>877.8<br />
</td>
<td>5/3<br />
</td>
<td>884.4<br />
</td>
<td>-6.6<br />
</td>
</tr>
<tr>
<td>7<br />
</td>
<td>1024.1<br />
</td>
<td>38/21<br />
29/16<br />
9/5<br />
20/11<br />
</td>
<td>1026.7<br />
1029.6<br />
1017.6<br />
1035.0<br />
</td>
<td>-2.6<br />
-5.5<br />
6.5<br />
-10.9<br />
</td>
</tr>
<tr>
<td>8<br />
</td>
<td>1170.4<br />
</td>
<td>49/25<br />
</td>
<td>1165.0<br />
</td>
<td>5.4<br />
</td>
</tr>
<tr>
<th colspan="3">second octave...<br />
</th>
<td><br />
</td>
<td><br />
</td>
</tr>
<tr>
<td>9<br />
</td>
<td>116.7<br />
</td>
<td>15/14<br />
16/15<br />
14/13<br />
</td>
<td>119.4<br />
111.7<br />
128.3<br />
</td>
<td>-2.7<br />
5.0<br />
-11.6<br />
</td>
</tr>
<tr>
<td>10<br />
</td>
<td>263.0<br />
</td>
<td>7/6<br />
22/19<br />
</td>
<td>266.9<br />
253.8<br />
</td>
<td>-3.9<br />
9.2<br />
</td>
</tr>
<tr>
<td>11<br />
</td>
<td>409.3<br />
</td>
<td>19/15<br />
81/64<br />
24/19<br />
14/11<br />
63/50<br />
</td>
<td>409.2<br />
407.8<br />
404.4<br />
417.5<br />
400.1<br />
</td>
<td>.1<br />
1.5<br />
4.9<br />
-8.2<br />
9.2<br />
</td>
</tr>
<tr>
<td>12<br />
</td>
<td>555.7<br />
</td>
<td>11/8<br />
18/13<br />
26/19<br />
25/18<br />
</td>
<td>551.3<br />
563.4<br />
543.0<br />
568.7<br />
</td>
<td>4.4<br />
-7.7<br />
12.7<br />
-13.0<br />
</td>
</tr>
<tr>
<th colspan="3">second tritave...<br />
</th>
<td><br />
</td>
<td><br />
</td>
</tr>
<tr>
<td>13<br />
</td>
<td>702.0<br />
</td>
<td>3/2<br />
</td>
<td>702.0<br />
</td>
<td>0<br />
</td>
</tr>
<tr>
<td>14<br />
</td>
<td>848.3<br />
</td>
<td>18/11<br />
13/8<br />
</td>
<td>852.6<br />
840.5<br />
</td>
<td>-4.3<br />
7.8<br />
</td>
</tr>
<tr>
<td>15<br />
</td>
<td>994.6<br />
</td>
<td>16/9<br />
</td>
<td>996.1<br />
</td>
<td>-1.5<br />
</td>
</tr>
<tr>
<td>16<br />
</td>
<td>1140.9<br />
</td>
<td>27/14<br />
</td>
<td>1137.0<br />
</td>
<td>3.9<br />
</td>
</tr>
<tr>
<th colspan="3">third octave...<br />
</th>
<td><br />
</td>
<td><br />
</td>
</tr>
<tr>
<td>17<br />
</td>
<td>87.2<br />
</td>
<td>20/19<br />
21/20<br />
19/18<br />
22/21<br />
</td>
<td>88.8<br />
84.5<br />
93.6<br />
80.5<br />
</td>
<td>-1.6<br />
2.7<br />
-6.4<br />
6.7<br />
</td>
</tr>
<tr>
<td>18<br />
</td>
<td>233.5<br />
</td>
<td>8/7<br />
15/13<br />
</td>
<td>231.2<br />
247.7<br />
</td>
<td>2.3<br />
-14.2<br />
</td>
</tr>
<tr>
<td>19<br />
</td>
<td>379.8<br />
</td>
<td>5/4<br />
26/21<br />
</td>
<td>386.3<br />
369.7<br />
</td>
<td>-6.5<br />
10.1<br />
</td>
</tr>
<tr>
<td>20<br />
</td>
<td>526.1<br />
</td>
<td>19/14<br />
27/20<br />
15/11<br />
</td>
<td>528.7<br />
519.6<br />
537.0<br />
</td>
<td>-2.6<br />
6.5<br />
-10.9<br />
</td>
</tr>
<tr>
<td>21<br />
</td>
<td>672.4<br />
</td>
<td>28/19<br />
25/17<br />
22/15<br />
</td>
<td>671.3<br />
667.7<br />
663.0<br />
</td>
<td>1.1<br />
4.7<br />
9.4<br />
</td>
</tr>
<tr>
<td>22<br />
</td>
<td>818.7<br />
</td>
<td>8/5<br />
21/13<br />
</td>
<td>813.7<br />
830.3<br />
</td>
<td>5.0<br />
-11.6<br />
</td>
</tr>
<tr>
<td>23<br />
</td>
<td>965.0<br />
</td>
<td>7/4<br />
26/15<br />
</td>
<td>968.8<br />
952.3<br />
</td>
<td>-3.8<br />
12.7<br />
</td>
</tr>
<tr>
<td>24<br />
</td>
<td>1111.3<br />
</td>
<td>19/10<br />
40/21<br />
36/19<br />
21/11<br />
</td>
<td>1111.2<br />
1115.5<br />
1106.4<br />
1119.5<br />
</td>
<td>0.1<br />
-4.2<br />
4.9<br />
-8.2<br />
</td>
</tr>
<tr>
<th colspan="3">fourth octave...<br />
</th>
<td><br />
</td>
<td><br />
</td>
</tr>
<tr>
<td>25<br />
</td>
<td>57.6<br />
</td>
<td>33/32<br />
</td>
<td>53.3<br />
</td>
<td>4.3<br />
</td>
</tr>
<tr>
<th colspan="3">third tritave...<br />
</th>
<td><br />
</td>
<td><br />
</td>
</tr>
<tr>
<td>26<br />
</td>
<td>203.9<br />
</td>
<td>9/8<br />
</td>
<td>203.9<br />
</td>
<td>0<br />
</td>
</tr>
<tr>
<td>27<br />
</td>
<td>350.2<br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
</tr>
<tr>
<td>28<br />
</td>
<td>496.5<br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
</tr>
<tr>
<td>29<br />
</td>
<td>642.8<br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
</tr>
<tr>
<td>30<br />
</td>
<td>789.1<br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
</tr>
<tr>
<td>31<br />
</td>
<td>935.4<br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
</tr>
<tr>
<td>32<br />
</td>
<td>1081.7<br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
</tr>
<tr>
<td colspan="3" style="text-align: center;"><strong>fifth octave...</strong><br />
</td>
<td><br />
</td>
<td><br />
</td>
</tr>
<tr>
<td>33<br />
</td>
<td>28.0<br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
</tr>
<tr>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
</tr>
<tr>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
</tr>
<tr>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
</tr>
<tr>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
</tr>
<tr>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
</tr>
</table>
</body></html>