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Kellner temperament ©2015 CBH 5K gif There has been much debate over the years about exactly what sort of temperament might have been Bach’s intention for those two immortal volumes of Das wohltemperirte Clavier, let alone his other works. Bach himself had ample opportunity to include any of his thoughts on tunings in the various prefaces to several musical works published in his lifetime, but for me the fact remains he chose not to. (But see the recent Bach/Lehman temperament researched by Dr Bradley Lehman.)

One temperament, however, found some favor with especially European musicians in the last few decades. It was ratified by the late Dr Herbert Anton Kellner in 1975, and first published a year later in German as his book Wie stimme ich selbst mein Cembalo? The English translation The Tuning of my Harpsichord followed in 1980, and it was also translated to several other languages including Japanese.

While Dr Kellner’s thesis goes to great lengths to prove that this is indeed the Bach temperament, citing the arrangement of gems on Bach’s signet ring and other numerological “proofs” to establish that there absolutely must be 5 tempered fifths and 7 pure fifths, you will, I trust, permit me to remain a little scientifically detached, or even somewhat skeptical. Let’s agree, though, that it is a wonderful temperament: I remember tuning it for baroque flautist Barthold Kuijken’s recital with John O’Donnell on the Bill Bright harpsichord at the 1999 Melbourne Autumn Music Festival.

Cover of Kellner’s book ”The Tuning of my Harpsichord” 17K jpeg
Cover of Kellner’s book

Here’s how you go about setting Kellner:

1. Tune your c'' to the tuning fork, and tune down a pure octave to middle c'. Tune down another octave to tenor c as well, because you are going to be mostly working in this octave below middle c' for this temperament.

2. Tune all the fifths from the flat side of C around the circle of keys absolutely pure. Unlike Kirnberger, where for accuracy I asked you to stop half-way at the E, and begin again around the sharp side of E in the opposite direction, this time continue in the one direction from C through F. Keep all these fifths beatless. You know what a real pure fifth sounds like by now, I hope.

3. Temporarily tune your tenor B a pure fifth below f. Now you are ready for the crux of this Kellner temperament. Play the B Major triad, and observe its harshness. After all, its major third is Pythagorean, ie determined by four pure fifths. (You should know this—you’ve just tuned them!) Slowly raise the tenor B until the third Bd beats six times are fast as the fifth Bf. To do this, you will be continually checking the third against the fifth until satisfied. Don’t ask me how many beats per second, just do it! When you have it right, the fifth Bf measures exactly a fifth comma narrow.

4. Tune up the octave to b, and down a pure fifth to determine e. This will leave a slightly wide third from ce.

5. The four remaining fifths around the circle between C and E must now be made equally narrow and rough, but they are only one fifth of a comma narrow, not quite as rapidly beating as your quarter comma fifths of Kirnberger. Remember you have lost the pure third between c-e. In fact, when you are done, the C Major triad is useful as a check: The third ce should beat at the same speed at cg. As always, if you are tuning intervals which are theoretically the same size, the beat speeds increase as the pitch ascends. Therefore, your Bf beats slightly slower than cg, which itself is slightly slower than da. And of course, your eb doesn’t beat at all, because it must be pure in Kellner.

Further discussion
Anonymous [Kayano, Moxzan] Dodecagon — Chi-s akt temo Tokyo 2012, p80
Asselin, Pierre-Yves Musique et Tempérament Éditions Costallat, Paris 1985, p101
Kellner, Herbert Anton The Tuning of my Harpsichord Verlag Das Musikinstrument, Frankfurt am Main 1980
Padgham, Charles The Well-Tempered Organ Positive Press, Oxford 1986, p74

Temperament index:

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