Reference

Cents to MIDI Pitch Bend Units

Standard MIDI Files use a pitch wheel range of +/-2 semitones = 200 cents. MIDI pitch bend wheel resolution (according to the spec) is +8192/-8191. That means there are 8192/200 = 40.96 pitch bend units to 1 cent. Calculating pitch bend units for retuning SMFs, then, is simply a matter of finding the desired difference in cents from 12 EDO of each note, and multiplying that value by 40.96.

The tables below show only ratios with odd numerators. That keeps the charts half the size they would otherwise be. A ratio with an even numerator takes the same pitch bend value as its inversion, only reversing the sign. For example, 3:2 gets a pitch bend of +80, so 4:3 gets a pitch bend of -80.


Ordered by Ratio
through the 31-limit
RatioCentsNearest
12 EDO
Pitch
Cents
Difference
PB units
N:D
3:2701.967001.9680
5:3884.36900-15.64-641
5:4386.31400-13.69-561
7:4968.831000-31.17-1277
7:5582.51600-17.49-716
7:6266.87300-33.13-1357
9:51017.60100017.60721
9:7435.0840035.081437
9:8203.912003.91160
11:61049.36100049.362022
11:7782.49800-17.51-717
11:8551.32600-48.68-1994
11:9347.4130047.411942
11:10165.00200-35.00-1433
13:71071.701100-28.30-1159
13:8840.5380040.531660
13:9636.6260036.621500
13:10454.21500-45.79-1875
13:11289.21300-10.79-442
13:12138.5710038.571580
15:81088.271100-11.73-481
15:11536.9550036.951514
15:13247.7420047.741955
15:14119.4410019.44796
17:91101.0511001.0543
17:10918.6490018.64764
17:11753.64800-46.36-1899
17:12603.006003.00123
17:13464.43500-35.57-1457
17:14336.1330036.131480
17:15216.6920016.69683
17:16104.961004.96203
19:101111.20110011.20459
19:11946.2090046.201892
19:12795.56800-4.44-182
19:13656.99700-43.01-1762
19:14528.6950028.691175
19:15409.244009.24379
19:16297.51300-2.49-102
19:17192.56200-7.44-305
19:1893.60100-6.40-262
21:111119.46110019.46797
21:13830.2580030.251239
21:16470.78500-29.22-1197
21:17365.83400-34.17-1400
21:19173.27200-26.73-1095
21:2084.47100-15.53-636
23:121126.32110026.321078
23:13987.751000-12.25-502
23:14859.45900-40.55-1661
23:15740.0170040.011639
23:16628.2760028.271158
23:17523.3250023.32955
23:18424.3640024.36998
23:19330.7630030.761260
23:20241.9620041.961719
23:21157.49200-42.51-1741
23:2276.96100-23.04-944
25:131132.10110032.101315
25:141003.8010003.80156
25:16772.63800-27.37-1121
25:17667.67700-32.33-1324
25:18568.72600-31.28-1281
25:19475.11500-24.89-1019
25:21301.853001.8576
25:22221.3120021.31873
25:23144.3510044.351817
25:2470.67100-29.33-1201
27:141137.04110037.041517
27:16905.879005.87240
27:17800.918000.9137
27:19608.356008.35342
27:20519.5550019.55801
27:22354.55400-45.45-1862
27:23277.59300-22.41-918
27:25133.2410033.241361
27:2665.34100-34.66-1420
29:151141.31110041.311692
29:161029.58100029.581211
29:17924.6290024.621009
29:18825.6780025.671051
29:19732.0670032.061313
29:20643.2660043.261772
29:21558.80600-41.20-1688
29:22478.26500-21.74-891
29:23401.304001.3053
29:24327.6230027.621131
29:25256.95300-43.05-1763
29:26189.05200-10.95-449
29:27123.7110023.71971
29:2860.75100-39.25-1608
31:161145.04110045.041845
31:171040.08100040.081642
31:18941.1390041.131685
31:19847.5280047.521947
31:20758.72800-41.28-1691
31:21674.25700-25.75-1055
31:22593.72600-6.28-257
31:23516.7650016.76687
31:24443.0840043.081765
31:25372.41400-27.59-1130
31:26304.513004.51185
31:27239.1720039.171604
31:28176.21200-23.79-974
31:29115.4610015.46633
31:3056.77100-43.23-1771

Ratios through the 31-limit
Ordered by Interval Size
RatioCentsNearest
12 EDO
Pitch
Cents
Difference
PB units
N:D
31:3056.77100-43.23-1771
29:2860.75100-39.25-1608
27:2665.34100-34.66-1420
25:2470.67100-29.33-1201
23:2276.96100-23.04-944
21:2084.47100-15.53-636
19:1893.60100-6.40-262
17:16104.961004.96203
31:29115.4610015.46633
15:14119.4410019.44796
29:27123.7110023.71971
27:25133.2410033.241361
13:12138.5710038.571580
25:23144.3510044.351817
23:21157.49200-42.51-1741
11:10165.00200-35.00-1433
21:19173.27200-26.73-1095
31:28176.21200-23.79-974
29:26189.05200-10.95-449
19:17192.56200-7.44-305
9:8203.912003.91160
17:15216.6920016.69683
25:22221.3120021.31873
31:27239.1720039.171604
23:20241.9620041.961719
15:13247.7420047.741955
29:25256.95300-43.05-1763
7:6266.87300-33.13-1357
27:23277.59300-22.41-918
13:11289.21300-10.79-442
19:16297.51300-2.49-102
25:21301.853001.8576
31:26304.513004.51185
29:24327.6230027.621131
23:19330.7630030.761260
17:14336.1330036.131480
11:9347.4130047.411942
27:22354.55400-45.45-1862
21:17365.83400-34.17-1400
31:25372.41400-27.59-1130
5:4386.31400-13.69-561
29:23401.304001.3053
19:15409.244009.24379
23:18424.3640024.36998
9:7435.0840035.081437
31:24443.0840043.081765
13:10454.21500-45.79-1875
17:13464.43500-35.57-1457
21:16470.78500-29.22-1197
25:19475.11500-24.89-1019
29:22478.26500-21.74-891
31:23516.7650016.76687
27:20519.5550019.55801
23:17523.3250023.32955
19:14528.6950028.691175
15:11536.9550036.951514
11:8551.32600-48.68-1994
29:21558.80600-41.20-1688
25:18568.72600-31.28-1281
7:5582.51600-17.49-716
31:22593.72600-6.28-257
17:12603.006003.00123
27:19608.356008.35342
23:16628.2760028.271158
13:9636.6260036.621500
29:20643.2660043.261772
19:13656.99700-43.01-1762
25:17667.67700-32.33-1324
31:21674.25700-25.75-1055
3:2701.967001.9680
29:19732.0670032.061313
23:15740.0170040.011639
17:11753.64800-46.36-1899
31:20758.72800-41.28-1691
25:16772.63800-27.37-1121
11:7782.49800-17.51-717
19:12795.56800-4.44-182
27:17800.918000.9137
29:18825.6780025.671051
21:13830.2580030.251239
13:8840.5380040.531660
31:19847.5280047.521947
23:14859.45900-40.55-1661
5:3884.36900-15.64-641
27:16905.879005.87240
17:10918.6490018.64764
29:17924.6290024.621009
31:18941.1390041.131685
19:11946.2090046.201892
7:4968.831000-31.17-1277
23:13987.751000-12.25-502
25:141003.8010003.80156
9:51017.60100017.60721
29:161029.58100029.581211
31:171040.08100040.081642
11:61049.36100049.362022
13:71071.701100-28.30-1159
15:81088.271100-11.73-481
17:91101.0511001.0543
19:101111.20110011.20459
21:111119.46110019.46797
23:121126.32110026.321078
25:131132.10110032.101315
27:141137.04110037.041517
29:151141.31110041.311692
31:161145.04110045.041845

Copyright 2003-4 by David J. Finnamore
All rights reserved.
tuning@elvenminstrel.com