Intervals of BP
This page gives the intervals of the equal tempered 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 | |||