The temperament which Dr Bradley Lehman discovered (Early Music, February
2005) solves all of the previously outstanding problems of finding a
temperament suitable for playing all of Bach's keyboard works, and it is
also proving useful for other music when a temperament is required which is
suitable for playing in all keys, but with the advantages over Equal
Temperament of purer intervals and differing key colours.
There is quite a divide between those who find electronic tuners useful and
those who consider them a useless abomination, but I know both beginners
and people with hearing impairments who find them useful.
At present there are no tuners available with the Bach/Lehman temperament
installed, and only a few have provision for new temperaments to be added.
Lehman provided a table which includes cents deviations from Equal
Temperament, but it isn't easy to judge when a meter needle is 2, 3.5, 5.9
or 7.8 cents away from an ET setting, and the table is of no use to those
who tune by listening to the tones generated by a tuner.
A close approximation to the Bach/Lehmann temperament at A=415 can be
achieved using a Korg-OT12 or a similar tuner which provides for ET and the
Pythagorean, Werkmeister III and Vallotti temperaments. This method
produces 8 notes exactly in tune, one with an error of 0.09 cents, and
three with errors of 0.26 cents. This should be precise enough for many
purposes, but, if necessary, two of these can be checked and corrected
easily, as they are pure fifths with notes which have already been
Set the tuner to Pythagorean at A=414. Tune F#.
Set the tuner to Werkmeister III at A=415. Tune G#.
Set the tuner to Vallotti at A=415. Tune C, D, D#, E, F, G and A.
Set the tuner to Equal Temperament at A=415. Tune B.
Set the tuner to Equal Temperament at A=416 Tune C# and A#.
Step 7 (if necessary)
Adjust F# to be a pure fifth with B.
Adjust C# to be a pure fifth with F#.
Finally check by ear that:
E B F#C# are perfect fifths
F C G D A E (which are 1/6 comma fifths) sound similar in quality
C# G# D# A# (which are 1/12 comma fifths) sound similar in quality.