Tables of Pitch Bends

The particular tuning of a note depends on where it is in the chord, where the chord root is in the scale, and which scale tuning is used.

To find a pitchpend adjustment value for a note in a chord: Pick the just or Pythagorean table, according to the scale tuning you are using. Look up the chord position of the note in the top row; that is your column. Look up the scale position of the chord root in the left column; that is your row. The cell at that column and row contains the pitchbend for that note.

# and b indicate a chromatic inflection of 25/24 in the chord factors and in just scale degrees, and 2187/2048 in the Pythagorean scale degrees. + and - indicate an inflection of a syntonic comma.

Note that the 5-limit 2nd is substituted in the Just Scale to accommodate some chords that require that tuning. The 3-limit 2nd is the identical to the 2nd in the Pythagorean table.

Just Scale

    1 2b17 2 3b 3 5 6 7b7 7b 7
    1/1 17/16 9/8 6/5 5/4 3/2 5/3 7/4 9/5 15/8
1 1/1 0 203 160 641 -561 80 -641 -1277 721 -481
2b 16/15 481 684 641 1122 -80 561 -160 -796 1202 0
2- 10/9 -721 -518 -561 -80 -1282 -641 -1362 -1998 0 -1202
3b 6/5 641 844 801 1282 80 721 0 -636 1362 160
3 5/4 -561 -358 -401 80 -1122 -481 -1202 -1838 160 -1042
4 4/3 -80 123 80 561 -641 0 -721 -1357 641 -561
4# 25/18 -1281 -1078 -1121 -640 -1842 -1201 -1922 -2558 -560 -1762
5b 36/25 1281 1484 1441 1922 720 1361 640 4 2002 800
5 3/2 80 283 240 721 -481 160 -561 -1197 801 -401
6b 8/5 561 764 721 1202 0 641 -80 -716 1282 80
6 5/3 -641 -438 -481 0 -1202 -561 -1282 -1918 80 -1122
7b 9/5 721 924 881 1362 160 801 80 -556 1442 240
7 15/8 -481 -278 -321 160 -1042 -401 -1122 -1758 240 -962

Pythagorean Scale

    1 2b17 2 3b 3 5 6 7b7 7b 7
    1/1 17/16 9/8 6/5 5/4 3/2 5/3 7/4 9/5 15/8
1 1/1 0 203 160 641 -561 80 -641 -1277 721 -481
2b- 256/243 -400 -197 -240 241 -961 -320 -1041 -1677 321 -881
2 9/8 160 363 320 801 -401 240 -481 -1117 881 -321
3b- 32/27 -240 -37 -80 401 -801 -160 -881 -1517 481 -721
3+ 81/64 320 523 480 961 -241 400 -321 -957 1041 -161
4 4/3 -80 123 80 561 -641 0 721 -1357 641 -561
4# 729/512 480 683 640 1121 -81 560 -161 -797 1201 -1
5b 1024/729 -480 -277 -320 161 -1041 -400 -1121 -1757 241 -961
5 3/2 80 283 240 721 -481 160 -561 -1197 801 -401
6b- 128/81 -320 -117 -160 321 -881 -240 -961 -1597 401 -801
6+ 27/16 240 443 400 881 -321 320 -401 -1037 961 -241
7b- 16/9 -160 43 0 481 -721 -80 -801 -1437 561 -641
7+ 243/128 400 603 560 1041 -161 480 -241 -877 1121 -81

Pitch Bend Calculator

This tool calculates the PBA values of a chord tuned to any note in the scale: 1) Write the PBA of the scale note you want to tune the chord to in the first box. 2) Write the PBA values of the chord in the four boxes below. 3) Push the button under the chord part you want to tune to the scale note. The PBA values of the chord in the adjusted position will be displayed. The default values show an example of a dominant 7th chord with its root on scale note 5.





80   -481   160   -1197

Scales
Index of Intervals
Chord Tunings
Chord Progressions
Glossary of Just Intonation
Fun with Vowel Formants
Just Intonation home page
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