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Intervals of BP

Revision as of 16:45, 3 March 2025 by ArrowHead294 (talk | contribs)

This page lists the first 42 intervals of the Bohlen-Pierce scale in both its just intonation (JI) version and its equal-tempered (ET) version, which also known as 13edt.

In the "nearby JI intervals, octave-reduced" columns, the intervals from the original just BP scale are in bold. Errors are sorted by ascending absolute value.

Degree Just intonation Equal-tempered Nearby JI intervals, octave-reduced
Ratio Cents Hekts Cents Ratio Cents Error in 13edt (¢)
0 1/1 0 0 0 1/1 0 0
1 27/25 133.238 100 146.304 12/11
13/12
27/25 		150.6
138.6
133.2 		−4.3
+7.7
+13.1
2 25/21 301.847 200 292.608 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 9/7 435.084 300 438.913 9/7 435.1 +3.8
4 7/5 582.512 400 585.217 7/5
45/32 		582.5
590.2 		+2.7
−5.0
5 75/49 736.931 500 731.521 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 5/3 884.359 600 877.825 5/3 884.4 −6.5
7 9/5 1017.596 700 1024.130 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 49/25 1165.024 800 1170.434 49/25 1165.0 +5.4
9 15/7 1319.443 900 1316.738 15/14
16/15
14/13 		119.4
111.7
128.3 		−2.7
+5.0
−11.6
10 7/3 1466.871 1000 1463.042 7/6
22/19 		266.9
253.8 		−3.8
+9.2
11 63/25 1600.108 1100 1609.347 19/15
81/64
24/19
14/11
63/50 		409.2
407.8
404.4
417.5
400.1 		+0.1
+1.5
+4.9
−8.2
+9.2
12 25/9 1768.717 1200 1755.651 11/8
18/13
26/19
25/18 		551.3
563.4
543.0
568.7 		+4.4
−7.7
+12.7
−13.1
13 3/1 1901.955 1300 1901.955 3/2 702.0 0
14 81/25 2035.193 1400 2048.259 18/11
13/8
81/50 		852.6
840.5
835.2 		−4.3
+7.8
+13.1
15 25/7 2203.802 1500 2194.563 16/9
25/14 		996.1
1003.8 		−1.5
−9.2
16 27/7 2337.039 1600 2340.868 27/14 1137.0 +3.8
17 21/5 2484.467 1700 2487.172 20/19
21/20
19/18
22/21 		88.8
84.5
93.6
80.5 		−1.6
+2.7
−6.4
+6.7
18 225/49 2638.886 1800 2633.476 8/7
225/196
15/13 		231.2
238.9
247.7 		+2.3
−5.4
−14.2
19 5/1 2786.314 1900 2779.780 5/4
26/21 		386.3
369.7 		−6.5
+10.1
20 27/5 2919.551 2000 2926.085 19/14
27/20
15/11 		528.7
519.6
537.0 		−2.6
+6.5
−10.9
21 147/25 3066.979 2100 3072.389 28/19
25/17
147/100
22/15 		671.3
667.7
667.0
663.0 		+1.1
+4.7
+5.4
+9.4
22 45/7 3221.398 2200 3218.693 45/28
8/5
21/13 		821.4
813.7
830.3 		−2.7
+5.0
−11.6
23 7/1 3368.826 2300 3364.997 7/4
26/15 		968.8
952.3 		−3.8
+12.7
24 189/25 3502.063 2400 3511.302 19/10
40/21
36/19
21/11
189/100 		1111.2
1115.5
1106.4
1119.5
1102.1 		+0.1
−4.2
+4.9
−8.2
+9.2
25 25/3 3670.672 2500 3657.606 33/32
25/24 		53.3
70.7 		+4.3
−13.1
26 9/1 3803.910 2600 3803.910 9/8 203.9 0
27 243/25 3937.148 2700 3950.214 11/9
27/22
243/200 		347.4
354.5
337.1 		+2.8
−4.3
+13.1
28 75/7 4105.757 2800 4096.518 4/3
75/56 		498.0
505.8 		−1.5
−9.2
29 81/7 4238.994 2900 4242.823 81/56
36/25 		639.0
631.3 		+3.8
+11.5
30 63/5 4386.422 3000 4389.127 30/19
63/40
128/81
19/12
11/7
100/63 		790.8
786.4
792.2
795.6
782.5
799.9. 		−1.7
2.7
−3.1
−6.5
+6.6
−10.8
31 675/49 4540.841 3100 4535.431 12/7
675/392
19/11 		933.1
940.8
946.2 		+2.3
−5.4
+10.8
32 15/1 4688.269 3200 4681.735 28/15
15/8
13/7 		1080.6
1088.3
1071.7 		+1.1
−6.5
+10.0
33 81/5 4821.506 3300 4828.040 64/63
81/80 		27.3
21.5 		+0.7
+6.5
34 441/25 4968.934 3400 4974.344 21/19
441/400
10/9
11/10 		173.3
168.9
182.4
165.0 		+1.0
+5.4
−8.1
+9.3
35 135/7 5123.353 3500 5120.648 135/112
6/5 		323.4
315.6 		−2.7
+5.0
36 21/1 5270.781 3600 5266.952 17/13
21/16
98/75
64/49
13/10 		464.4
470.8
463.1
462.3
454.2
 +2.5
−3.8
+3.9
+4.6
+12.7
37 567/25 5404.018 3700 5413.257 64/45
10/7
567/400 		609.8
617.5
604.0 		+3.5
−4.2
+9.2
38 25/1 5572.627 3800 5559.561 14/9
25/16 		764.9
772.6 		−5.3
−13.1
39 27/1 5705.865 3900 5705.865 27/16 905.9 0
40 729/25 5839.103 4000 5852.169 11/6
729/400 		1049.4
1039.1 		+2.8
+13.1
41 225/7 6007.712 4100 5998.473 1/1
225/224 		0.0
7.7 		−1.5
+9.2
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