Technical Library

TUNING VIII: Cent deviations

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Cent Deviations…

Scientists needed some means of describing accurately the differences in pitch, and the cent is defined to be exactly 1/100 of an equal-tempered semitone, ie 1/1200 of an octave.

Cents enable us to compare various temperaments. The following table shows the cent deviations from Equal Temperment for each note of the temperaments already programmed in the Korg MT-1200 tuner:

TEMPERAMENT c c# d d# e f f# g g# a a# b
1. Equal Temperament 0 0 0 0 0 0 0 0 0 0 0 0
2. Just Intonation (major pitch) +16 -14 +20 +31 +2 +14 -16 +18 -12 0 +33 +4
3. Just Intonation (minor pitch) +16 +49 +20 +32 +2 +14 +47 +18 +30 0 +34 +4
4. Meantone (Aaron, 1523) +10 -14 +3 +20 -3 +14 -10 +7 -17 0 +17 -7
5. Pythagorean -6 +8 -2 -12 +2 -8 +6 -4 +10 0 -10 +4
6. Werkmeister III (1691) +12 +2 +4 +6 +2 +10 0 +8 +4 0 +8 +4
7. Kirnberger III (1779) +10 +1 +3 +4 -3 +8 +1 +7 +2 0 +6 -2
8. Vallotti (Tartini, 1754) +6 0 +2 +4 -2 +8 -2 +4 +2 0 +6 -4

 

Notice that a is taken as the reference point—that’s why it’s the same zero in each temperament. Equal temperament is not necessarily the ideal, but it does have the semitones of equal size, so providing a good means of comparison with the other temperaments.

With this data and an electronic tuner of sufficient accuracy, it is possible to check your tuning of different temperaments. Most tuners measure Equal Temperament. As an example, to tune your c in Kirnberger III, the table shows it must be 10 cents sharp compared to Equal Temperment, so instead of regarding the note as in tune when the needle or lights show it to be spot on, you must deliberately tune the c so the needle points to “10” on the sharp side.

Before the popular Korg MT-1200 tuner was rendered obsolete, all our purchasers of this model used to receive a copy of our world-exclusive temperment card which also includes the specifications of another eight often-requested temperaments. We now make this card available to all harpsichord enthusiasts, no matter where they may have bought their original MT-1200.

The later model Korg OT-12 has a slightly different selection of preprogramed temperaments. This model has been recently superseded by the Korg OT-120, but the temperaments remain the same:
TEMPERAMENT c c# d d# e f f# g g# a a# b
1. Equal Temperament 0 0 0 0 0 0 0 0 0 0 0 0
2. Pythagorean -6 +8 -2 -12 +2 -8 +6 -4 +10 0 -10 +4
3. Meantone – with eb (Aaron, 1523) +10 -14 +3 +20 -3 +14 -10 +7 -17 0 +17 -7
4. Meantone – with d# +10 -14 +3 -21 -3 +14 -10 +7 -17 0 +17 -7
5. Werkmeister III (1691) +12 +2 +4 +6 +2 +10 0 +8 +4 0 +8 +4
6. Kirnberger III (1779) +10 +1 +3 +4 -3 +8 +1 +7 +2 0 +6 -2
7. Kellner (1982) +8 -2 +3 +2 -3 +6 -4 +5 0 0 +4 -1
8. Vallotti (Tartini, 1754) +6 0 +2 +4 -2 +8 -2 +4 +2 0 +6 -4
9. Young (1800) +6 -4 +2 0 -2 +4 -6 +4 -2 0 +2 -4

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