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Intervals of BP: Difference between revisions

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


{| class="wikitable"
{| class="wikitable"
! rowspan="2" |degree
! colspan="2" |Just intonation
! colspan="2" |Equal-tempered
! colspan="3" |Nearby JI intervals, [[Octave reduction|octave-reduced]]
|-
|-
!(ratio)
! rowspan="2" | Degree
!([[Cent|¢]])
! colspan="2" | Just intonation
!([[Hekt|hekts]])
! colspan="2" | Equal-tempered
!(¢)
! colspan="3" | Nearby JI intervals, [[Octave reduction|octave-reduced]]
! | (ratio)
! | ([[Cent|¢]])
! | error in 13edt (¢)
|-
|-
| | 0
! Ratio
|1/1
! [[Cent]]s
|0
! [[Hekt]]s
|0
! Cents
| | 0
! Ratio
| | 1/1
! Cents
| | 0
! Error in 13edt (¢)
| | 0
|-
|-
| | 1
| 0
|27/25
| 1/1
|133.238
| 0
|100
| 0
| | 146.304
| 0
| | 12/11
| 1/1
 
| 0
13/12
| 0
 
|-
'''27/25'''
| 1
| | 150.6
| 27/25
 
| 133.238
138.6
| 100
 
| 146.304
'''133.2'''
| 12/11<br />13/12<br />'''27/25'''
| |  -4.3
| 150.6<br />138.6<br />'''133.2'''
 
| −4.3<br />+7.7<br />'''+13.1'''
+7.7
 
'''+13.1'''
|-
|-
| | 2
| 2
|25/21
| 25/21
|301.847
| 301.847
|200
| 200
| | 292.608
| 292.608
| | 32/27
| 32/27<br />13/11<br />19/16<br />'''25/21'''
 
| 294.1<br />289.2<br />297.5<br />'''301.8'''
13/11
| −1.5<br />+3.4<br />−4.9<br />'''−9.2'''
 
19/16
 
'''25/21'''
| | 294.1
 
289.2
 
297.5
 
'''301.8'''
| |  -1.5
 
+3.4
 
-4.9
 
'''-9.2'''
|-
|-
| | 3
| 3
|9/7
| 9/7
|435.084
| 435.084
|300
| 300
| | 438.913
| 438.913
| | '''9/7'''
| '''9/7'''
| | '''435.1'''
| '''435.1'''
| | '''+3.8'''
| '''+3.8'''
|-
|-
| | 4
| 4
|7/5
| 7/5
|582.512
| 582.512
|400
| 400
| | 585.217
| 585.217
| | '''7/5'''
| '''7/5'''<br />45/32
 
| '''582.5'''<br />590.2
45/32
| '''+2.7'''<br />−5.0
| | '''582.5'''
 
590.2
| | '''+2.7'''
 
-5.0
|-
|-
| | 5
| 5
|75/49
| 75/49
|736.931
| 736.931
|500
| 500
| | 731.521
| 731.521
| | 32/21
| 32/21<br />26/17<br />'''75/49'''<br />49/32<br />20/13
 
| 729.2<br />735.6<br />'''736.9'''<br />737.7<br />745.8
26/17
| +2.3<br />−4.1<br />'''−5.4'''<br />−6.2<br />−14.3
 
'''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
| 6
|5/3
| 5/3
|884.359
| 884.359
|600
| 600
| | 877.825
| 877.825
| | '''5/3'''
| '''5/3'''
| | '''884.4'''
| '''884.4'''
| | '''-6.5'''
| '''−6.5'''
|-
|-
| | 7
| 7
|9/5
| 9/5
|1017.596
| 1017.596
|700
| 700
| | 1024.130
| 1024.130
| | 38/21
| 38/21<br />29/16<br />'''9/5'''<br />20/11
 
| 1026.7<br />1029.6<br />'''1017.6'''<br />1035.0
29/16
| −2.6<br />−5.5<br />'''+6.5'''<br />−10.9
 
'''9/5'''
 
20/11
| | 1026.7
 
1029.6
 
'''1017.6'''
 
1035.0
| |  -2.6
 
-5.5
 
'''+6.5'''
 
-10.9
|-
|-
| | 8
| 8
|49/25
| 49/25
|1165.024
| 1165.024
|800
| 800
| | 1170.434
| 1170.434
| | '''49/25'''
| '''49/25'''
| | '''1165.0'''
| '''1165.0'''
| | '''+5.4'''
| '''+5.4'''
|-
|-
| | 9
| 9
|15/7
| 15/7
|1319.443
| 1319.443
|900
| 900
| | 1316.738
| 1316.738
| | '''15/14'''
| '''15/14'''<br />16/15<br />14/13
 
| '''119.4'''<br />111.7<br />128.3
16/15
| '''−2.7'''<br />+5.0<br />−11.6
 
14/13
| | '''119.4'''
 
111.7
 
128.3
| | '''-2.7'''
 
+5.0
 
-11.6
|-
|-
| | 10
| 10
|7/3
| 7/3
|1466.871
| 1466.871
|1000
| 1000
| | 1463.042
| 1463.042
| | '''7/6'''
| '''7/6'''<br />22/19
 
| '''266.9'''<br />253.8
22/19
| '''−3.8'''<br />+9.2
| | '''266.9'''
 
253.8
| | '''-3.8'''
 
+9.2
|-
|-
| | 11
| 11
|63/25
| 63/25
|1600.108
| 1600.108
|1100
| 1100
| | 1609.347
| 1609.347
| | 19/15
| 19/15<br />81/64<br />24/19<br />14/11<br />'''63/50'''
 
| 409.2<br />407.8<br />404.4<br />417.5<br />'''400.1'''
81/64
| +0.1<br />+1.5<br />+4.9<br />−8.2<br />'''+9.2'''
 
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
| 12
|25/9
| 25/9
|1768.717
| 1768.717
|1200
| 1200
| | 1755.651
| 1755.651
| | 11/8
| 11/8<br />18/13<br />26/19<br />'''25/18'''
 
| 551.3<br />563.4<br />543.0<br />'''568.7'''
18/13
| +4.4<br />−7.7<br />+12.7<br />'''−13.1'''
 
26/19
 
'''25/18'''
| | 551.3
 
563.4
 
543.0
 
'''568.7'''
| |  +4.4
 
-7.7
 
+12.7
 
'''-13.1'''
|-
|-
| | 13
| 13
|3/1
| 3/1
|1901.955
| 1901.955
|1300
| 1300
| | 1901.955
| 1901.955
| | '''3/2'''
| '''3/2'''
| | '''702.0'''
| '''702.0'''
| | '''0'''
| '''0'''
|-
|-
| | 14
| 14
|81/25
| 81/25
|2035.193
| 2035.193
|1400
| 1400
| | 2048.259
| 2048.259
| | 18/11
| 18/11<br />13/8<br />'''81/50'''
 
| 852.6<br />840.5<br />'''835.2'''
13/8
| −4.3<br />+7.8<br />'''+13.1'''
 
'''81/50'''
| | 852.6
 
840.5
 
'''835.2'''
| |  -4.3
 
+7.8
 
'''+13.1'''
|-
|-
| | 15
| 15
|25/7
| 25/7
|2203.802
| 2203.802
|1500
| 1500
| | 2194.563
| 2194.563
| | 16/9
| 16/9<br />'''25/14'''
'''25/14'''
| 996.1<br />'''1003.8'''
| | 996.1
| −1.5<br />'''−9.2'''
'''1003.8'''
| |  -1.5
'''-9.2'''
|-
|-
| | 16
| 16
|27/7
| 27/7
|2337.039
| 2337.039
|1600
| 1600
| | 2340.868
| 2340.868
| | '''27/14'''
| '''27/14'''
| | '''1137.0'''
| '''1137.0'''
| | '''+3.8'''
| '''+3.8'''
|-
|-
| | 17
| 17
|21/5
| 21/5
|2484.467
| 2484.467
|1700
| 1700
| | 2487.172
| 2487.172
| | 20/19
| 20/19<br />'''21/20'''<br />19/18<br />22/21
 
| 88.8<br />'''84.5'''<br />93.6<br />80.5
'''21/20'''
| −1.6<br />'''+2.7'''<br />−6.4<br />+6.7
 
19/18
 
22/21
| | 88.8
 
'''84.5'''
 
93.6
 
80.5
| |  -1.6
 
'''+2.7'''
 
-6.4
 
+6.7
|-
|-
| | 18
| 18
|225/49
| 225/49
|2638.886
| 2638.886
|1800
| 1800
| | 2633.476
| 2633.476
| | 8/7
| 8/7<br />'''225/196'''<br />15/13
'''225/196'''
| 231.2<br />'''238.9'''<br />247.7
 
| +2.3<br />'''−5.4'''<br />−14.2
15/13
| | 231.2
 
'''238.9'''
 
247.7
| |  +2.3
 
'''-5.4'''
 
-14.2
|-
|-
| | 19
| 19
|5/1
| 5/1
|2786.314
| 2786.314
|1900
| 1900
| | 2779.780
| 2779.780
| | '''5/4'''
| '''5/4'''<br />26/21
 
| '''386.3'''<br />369.7
26/21
| '''−6.5'''<br />+10.1
| | '''386.3'''
 
369.7
| | '''-6.5'''
 
+10.1
|-
|-
| | 20
| 20
|27/5
| 27/5
|2919.551
| 2919.551
|2000
| 2000
| | 2926.085
| 2926.085
| | 19/14
| 19/14<br />'''27/20'''<br />15/11
 
| 528.7<br />'''519.6'''<br />537.0
'''27/20'''
| −2.6<br />'''+6.5'''<br />−10.9
 
15/11
| | 528.7
 
'''519.6'''
 
537.0
| |  -2.6
 
'''+6.5'''
 
-10.9
|-
|-
| | 21
| 21
|147/25
| 147/25
|3066.979
| 3066.979
|2100
| 2100
| | 3072.389
| 3072.389
| | 28/19
| 28/19<br />25/17<br />'''147/100'''<br />22/15
 
| 671.3<br />667.7<br />'''667.0'''<br />663.0
25/17
| +1.1<br />+4.7<br />'''+5.4'''<br />+9.4
 
'''147/100'''
 
22/15
| | 671.3
 
667.7
 
'''667.0'''
 
663.0
| |  +1.1
 
+4.7
 
'''+5.4'''
 
+9.4
|-
|-
| | 22
| 22
|45/7
| 45/7
|3221.398
| 3221.398
|2200
| 2200
| | 3218.693
| 3218.693
| | '''45/28'''
| '''45/28'''<br />8/5<br />21/13
8/5
| '''821.4'''<br />813.7<br />830.3
 
| '''−2.7'''<br />+5.0<br />−11.6
21/13
| | '''821.4'''
813.7
 
830.3
| | '''-2.7'''
+5.0
 
-11.6
|-
|-
| | 23
| 23
|7/1
| 7/1
|3368.826
| 3368.826
|2300
| 2300
| | 3364.997
| 3364.997
| | '''7/4'''
| '''7/4'''<br />26/15
 
| '''968.8'''<br />952.3
26/15
| '''−3.8'''<br />+12.7
| | '''968.8'''
 
952.3
| | '''-3.8'''
 
+12.7
|-
|-
| | 24
| 24
|189/25
| 189/25
|3502.063
| 3502.063
|2400
| 2400
| | 3511.302
| 3511.302
| | 19/10
| 19/10<br />40/21<br />36/19<br />21/11<br />'''189/100'''
 
| 1111.2<br />1115.5<br />1106.4<br />1119.5<br />'''1102.1'''
40/21
| +0.1<br />−4.2<br />+4.9<br />−8.2<br />'''+9.2'''
 
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
|25/3
| 25/3
|3670.672
| 3670.672
|2500
| 2500
| | 3657.606
| 3657.606
| | 33/32
| 33/32<br />'''25/24'''
'''25/24'''
| 53.3<br />'''70.7'''
| | 53.3
| +4.3<br />'''−13.1'''
'''70.7'''
| |  +4.3
'''-13.1'''
|-
|-
| | 26
| 26
|9/1
| 9/1
|3803.910
| 3803.910
|2600
| 2600
| | 3803.910
| 3803.910
| | '''9/8'''
| '''9/8'''
| | '''203.9'''
| '''203.9'''
| | '''0'''
| '''0'''
|-
|-
| | 27
| 27
|243/25
| 243/25
|3937.148
| 3937.148
|2700
| 2700
| | 3950.214
| 3950.214
| | 11/9
| 11/9<br />27/22<br />'''243/200'''
 
| 347.4<br />354.5<br />337.1
27/22
| +2.8<br />−4.3<br />'''+13.1'''
 
'''243/200'''
| |347.4
354.5
 
337.1
| |  +2.8
-4.3
 
'''+13.1'''
|-
|-
| | 28
| 28
|75/7
| 75/7
|4105.757
| 4105.757
|2800
| 2800
| | 4096.518
| 4096.518
| | 4/3
| 4/3<br />'''75/56'''
'''75/56'''
| 498.0<br />'''505.8'''
| | 498.0
| −1.5<br />'''−9.2'''
'''505.8'''
| |  -1.5
'''-9.2'''
|-
|-
| | 29
| 29
|81/7
| 81/7
|4238.994
| 4238.994
|2900
| 2900
| | 4242.823
| 4242.823
| |'''81/56'''
| '''81/56'''<br />36/25
36/25
| '''639.0'''<br />631.3
| |'''639.0'''
| '''+3.8'''<br />+11.5
631.3
| | '''+3.8'''
+11.5
|-
|-
| | 30
| 30
|63/5
| 63/5
|4386.422
| 4386.422
|3000
| 3000
| | 4389.127
| 4389.127
| |30/19
| 30/19<br />'''63/40'''<br />128/81<br />19/12<br />11/7<br />100/63
'''63/40'''
| 790.8<br />'''786.4'''<br />792.2<br />795.6<br />782.5<br />799.9.
 
| −1.7<br />'''2.7'''<br />−3.1<br />−6.5<br />+6.6<br />−10.8
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
| 31
|675/49
| 675/49
|4540.841
| 4540.841
|3100
| 3100
| | 4535.431
| 4535.431
| |12/7
| 12/7<br />'''675/392'''<br />19/11
'''675/392'''
| 933.1<br />'''940.8'''<br />946.2
 
| +2.3<br />'''−5.4'''<br />+10.8
19/11
| |933.1
'''940.8'''
 
946.2
| |  +2.3
'''-5.4'''
 
+10.8
|-
|-
| | 32
| 32
|15/1
| 15/1
|4688.269
| 4688.269
|3200
| 3200
| | 4681.735
| 4681.735
| |28/15
| 28/15<br />'''15/8'''<br />13/7
'''15/8'''
| 1080.6<br />'''1088.3'''<br />1071.7
 
| +1.1<br />'''−6.5'''<br />+10.0
13/7
| |1080.6
'''1088.3'''
 
1071.7
| |  +1.1
'''-6.5'''
 
+10.0
|-
|-
| | 33
| 33
|81/5
| 81/5
|4821.506
| 4821.506
|3300
| 3300
| | 4828.040
| 4828.040
| |64/63
| 64/63<br />'''81/80'''
'''81/80'''
| 27.3<br />'''21.5'''
| |27.3
| +0.7<br />'''+6.5'''
'''21.5'''
| |  +0.7
'''+6.5'''
|-
|-
| |34
| 34
|441/25
| 441/25
|4968.934
| 4968.934
|3400
| 3400
| |4974.344
| 4974.344
| |21/19
| 21/19<br />'''441/400'''<br />10/9<br />11/10
'''441/400'''
| 173.3<br />'''168.9'''<br />182.4<br />165.0
 
| +1.0<br />'''+5.4'''<br />−8.1<br />+9.3
10/9
 
11/10
| |173.3
'''168.9'''
 
182.4
 
165.0
| |  +1.0
'''+5.4'''
 
-8.1
 
+9.3
|-
|-
| |35
| 35
|135/7
| 135/7
|5123.353
| 5123.353
|3500
| 3500
| |5120.648
| 5120.648
| |'''135/112'''
| '''135/112'''<br />6/5
6/5
| '''323.4'''<br />315.6
| |'''323.4'''
| '''−2.7'''<br />+5.0
315.6
| | '''-2.7'''
+5.0
|-
|-
| |36
| 36
|21/1
| 21/1
|5270.781
| 5270.781
|3600
| 3600
| |5266.952
| 5266.952
| |17/13
| 17/13<br />'''21/16'''<br />98/75<br />64/49<br />13/10
'''21/16'''
| 464.4<br />'''470.8'''<br />463.1<br />462.3<br />454.2<br />
 
| +2.5<br />'''−3.8'''<br />+3.9<br />+4.6<br />+12.7
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
| 37
|567/25
| 567/25
|5404.018
| 5404.018
|3700
| 3700
| |5413.257
| 5413.257
| |64/45
| 64/45<br />10/7<br />567/400
10/7
| 609.8<br />617.5<br />'''604.0'''
567/400
| +3.5<br />−4.2<br />'''+9.2'''
| |609.8
617.5
'''604.0'''
| |  +3.5
-4.2
'''+9.2'''
|-
|-
| |38
| 38
|25/1
| 25/1
|5572.627
| 5572.627
|3800
| 3800
| |5559.561
| 5559.561
| |14/9
| 14/9<br />'''25/16'''
'''25/16'''
| 764.9<br />'''772.6'''
| |764.9
| −5.3<br />'''−13.1'''
'''772.6'''
| |  -5.3
'''-13.1'''
|-
|-
|39
| 39
|27/1
| 27/1
|5705.865
| 5705.865
|3900
| 3900
|5705.865
| 5705.865
|'''27/16'''
| '''27/16'''
|'''905.9'''
| '''905.9'''
|'''0'''
| '''0'''
|-
|-
|40
| 40
|729/25
| 729/25
|5839.103
| 5839.103
|4000
| 4000
|5852.169
| 5852.169
|11/6
| 11/6<br />'''729/400'''
'''729/400'''
| 1049.4<br />'''1039.1'''
|1049.4
| +2.8<br />'''+13.1'''
'''1039.1'''
| +2.8
'''+13.1'''
|-
|-
|41
| 41
|225/7
| 225/7
|6007.712
| 6007.712
|4100
| 4100
|5998.473
| 5998.473
|1/1
| 1/1<br />'''225/224'''
'''225/224'''
| 0.0<br />'''7.7'''
|0.0
| −1.5<br />'''+9.2'''
'''7.7'''
| -1.5
'''+9.2'''
|}
|}
[[Category:Bohlen–Pierce]]
[[Category:Lists of intervals]]
[[Category:Tables]]
Retrieved from "https://en.xen.wiki/w/Intervals_of_BP"