Intervals of BP: Difference between revisions

Revision as of 23:23, 30 November 2009

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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 || 729.2
735.6
736.9
737.7 || 2.3
-4.1
-5.4
-6.2 ||
|| 6 || 877.8 || 5/3 || 884.4 || -6.6 ||
|| 7 || 1024.1 || 29/16
9/5 || 1029.6
1017.6 || -5.5
6.5 ||
|| 8 || 1170.4 || 49/25 || 1165.0 || 5.4 ||
||||||~ second octave... ||   ||   ||
|| 9 || 116.7 || 15/14
16/15 || 119.4
111.7 || -2.7
5.0 ||
|| 10 || 263.0 || 7/6 || 266.9 || -3.9 ||
|| 11 || 409.3 || 81/64
14/11 || 407.8
417.5 || 1.5
-8.2 ||
|| 12 || 555.7 || 11/8
18/13
25/18 || 551.3
563.4
568.7 || 4.4
-7.7
-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 || 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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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 &amp; 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 />
</td>
        <td>729.2<br />
735.6<br />
736.9<br />
737.7<br />
</td>
        <td>2.3<br />
-4.1<br />
-5.4<br />
-6.2<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>29/16<br />
9/5<br />
</td>
        <td>1029.6<br />
1017.6<br />
</td>
        <td>-5.5<br />
6.5<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 />
</td>
        <td>119.4<br />
111.7<br />
</td>
        <td>-2.7<br />
5.0<br />
</td>
    </tr>
    <tr>
        <td>10<br />
</td>
        <td>263.0<br />
</td>
        <td>7/6<br />
</td>
        <td>266.9<br />
</td>
        <td>-3.9<br />
</td>
    </tr>
    <tr>
        <td>11<br />
</td>
        <td>409.3<br />
</td>
        <td>81/64<br />
14/11<br />
</td>
        <td>407.8<br />
417.5<br />
</td>
        <td>1.5<br />
-8.2<br />
</td>
    </tr>
    <tr>
        <td>12<br />
</td>
        <td>555.7<br />
</td>
        <td>11/8<br />
18/13<br />
25/18<br />
</td>
        <td>551.3<br />
563.4<br />
568.7<br />
</td>
        <td>4.4<br />
-7.7<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 />
</td>
        <td>88.8<br />
84.5<br />
</td>
        <td>-1.6<br />
2.7<br />
</td>
    </tr>
    <tr>
        <td>18<br />
</td>
        <td>233.5<br />
</td>
        <td>8/7<br />
</td>
        <td>231.2<br />
</td>
        <td>2.3<br />
</td>
    </tr>
    <tr>
        <td>19<br />
</td>
        <td>379.8<br />
</td>
        <td>5/4<br />
</td>
        <td>386.3<br />
</td>
        <td>-6.5<br />
</td>
    </tr>
    <tr>
        <td>20<br />
</td>
        <td>526.1<br />
</td>
        <td>19/14<br />
27/20<br />
</td>
        <td>528.7<br />
519.6<br />
</td>
        <td>-2.6<br />
6.5<br />
</td>
    </tr>
    <tr>
        <td>21<br />
</td>
        <td>672.4<br />
</td>
        <td>28/19<br />
25/17<br />
</td>
        <td>671.3<br />
667.7<br />
</td>
        <td>1.1<br />
4.7<br />
</td>
    </tr>
    <tr>
        <td>22<br />
</td>
        <td>818.7<br />
</td>
        <td>8/5<br />
</td>
        <td>813.7<br />
</td>
        <td>5.0<br />
</td>
    </tr>
    <tr>
        <td>23<br />
</td>
        <td>965.0<br />
</td>
        <td>7/4<br />
</td>
        <td>968.8<br />
</td>
        <td>-3.8<br />
</td>
    </tr>
    <tr>
        <td>24<br />
</td>
        <td>1111.3<br />
</td>
        <td>19/10<br />
40/21<br />
</td>
        <td>1111.2<br />
1115.5<br />
</td>
        <td>0.1<br />
-4.2<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><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>
    <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>
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        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
    </tr>
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        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
    </tr>
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        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
    </tr>
</table>

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Intervals of BP: Difference between revisions

Revision as of 23:23, 30 November 2009

IMPORTED REVISION FROM WIKISPACES

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