Intervals of BP

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, 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