Bach frequencies

[Helmut Wabnig]

This is the frequency table for the historical Bach tuning.
Reconstructed by scientific methods. Usable for 24 Keys.
"Das Wohltemperirte Clavier" was composed for this temperament.

A detailed description of how to lay this temperament is
to be found in:
Practical Introduction to Historical Tunings.
by
Herbert Anton Kellner.

(My version is in German).
(Einfuehrung in die Praxis historischer Stimmungen.)
(Der Piano und Fluegelbau, by Herbert Junghans, ISBN 3-923639-60-0)
(C 1984 Verlag Bochinsky, Frankfurt)

                                             Bach centr. A
                                             Difference
                 Bach centr.   Bach centr.   from equal
        equal    equal C       normal A      in cents

C  523.2511306   523.2511306   525.7047253   +8.099
B  493.8833013   491.3261646   493.6300588   -0.888
Bb 466.1637615   465.1121161   467.2930891   +4.189
A  440.0000000   437.9464105   440.0000000    0.000
G# 415.3046976   413.4329921   415.3716348   +0.279
G  391.9954360   391.4007084   393.2360388   +5.470
F# 369.9944227   367.4959930   369.2192310   -3.631
F  349.2282314   348.8340871   350.4698169   +6.144
E  329.6275569   327.5507764   329.0867059   -2.843
D# 311.1269837   310.0747441   311.5287261   +2.234
D  293.6647679   292.7723017   294.1451503   +2.830
C# 277.1826310   275.6219947   276.9144232   -1.676
C  261.6255653   261.6255653   262.8523626   +8.099


A Comparison of some piano temperaments:

Sources:
KORG Multi temperament tuner MT 1200 Owner's Manual.
Bach numbers by Wabnig.
Key is C maj where appropriate

Cent Values:
Temperament      C   .   D   .   E   F   .   G   .   A   .   B
--------------------------------------------------------------
Equal            0   0   0   0   0   0   0   0   0   0   0   0
Just maj        +16 -14 +20 +31 +2  +14 -16 +18 -12  0  +33 +4
Just min        +16 +49 +20 +32 +2  +14 +47 +18 +30  0  +34 +4
Mean            +10 -14 +3  +20 -3  +14 -10 +7  -17  0  +17 -7
Pythagoras      -6  +8  -2  -12 +2  -8  +6  -4  +10  0  -10 +4
Werckmeister 3  +12 +2  +4  +6  +2  +10  0  +8  +4   0  +8  +4
Kirnberger 3    +10 +1  +3  +4  -3  +8  +1  +7  +2   0  +6  -2
Vallotti&Young  +6   0  +2  +4  -2  +8  -2  +4  +2   0  +6  -4
Bach            +8  -2  +3  +2  -3  +6  -4  +6   0   0  +4  -1



Bach is absolutely up-to-date.
Can you see?


Yours,
Helmut Wabnig
wabi@net4you.co.at