Intervals of BP

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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 11/9

27/22

347.4

354.55

+2.8

-3.35

28 496.5 4/3 498.05 +2.05
29 642.8 36/25 631.3 +11.3.
30 789.1 30/19

128/81

19/12

11/7

100/63

790.8

792.2

795.6

782.5

799.9.

-1.7

-3.1

-6.5

+6.6

-10.8

31 935.4 12/7

19/11

933.1

946.2

+2.3

+10.8

32 1081.7 15/8

28/15

13/7

1088.3

1080.6

1071.7

-6.6

+1.1

+10.0

fifth octave...
33 28.0 64/63 27.3 +0.7
34 174.3 11/10

21/19

10/9

165.0

173.3

182.4

+9.3

+1.0

-8.1

35 320.65 6/5 315.6 +5.05
36 466.95 21/16

17/13

98/75

64/49

13/10

470.8

464.4

463.1

462.3

454.2

-3.85

+2.55

+3.85

+4.65

+12.75

37 613.3 10/7

64/45

617.5

609.8

-4.2

+3.5

38 759.6 14/9 764.9 -5.3