Herbert Anton Kellner's Bach tuning

To Tuning list and Harpsichord list:
In Tuning Digest 462 I posted a frequency table for the
Kellner Bach tuning. Now I got hold of Kellner's original work
and found that his numbers are slightly different.

Deviation from Equal temperament:

Kellner wabi

A 0.0 0.0
B 4.3 4.189
H -0.7 -0.888
C 8.2 8.099
Cis -1.6 -1.676
D 2.8 2.830
Es 2.3 2.234
E -2.7 -2.843
F 6.2 6.144
Fis -3.5 -3.631
G 5.5 5.470
As 0.4 0.279
A 0.0 0.0

The numbers differ more than 1/10 cent and I have to
recalculate them. Consider the possibility that I did
a mistake. Or it is due to rounding errors.

My impression is, that Kellner's work is not widely known.
Otherwise it could not happen that some people still think,
Bach was mean tuned. Absolutely impossible.
Some think, Bach was equal tuned. He might have known ET.
But could he possibly tune it in 15 minutes, as some say?
Can you? Can anybody? Bach's tuning can be laid quickly,
easily and very precisely. (Kellner's words).
ET came with the advent of the piano, and is suited for it,
which has less overtones than a harpsichord.

Anyway, the main arguments are of a quite different nature.
Bach was an eminent mathematician and numerologist.
Kellner is mathematician and physicist, built several
harpsichords on his own, received a patent on his Bach tuning,
and analyzed the codes in Bach's music. This had been done before,
but proving that the tuning scheme for the WTC is modeled into the
structure of the music, that's where the evidence comes from,
has to be credited to Mr. Kellner.

The most astonishing discovery, at least to me, is something
quite unexpected, unbelievable surprise:
Bach himself has coded his tuning scheme into his signet!
The seven pure fifths, the five tempered fifths, the
"three-unitarian" tempering are hidden in that graphical emblem.

Luckily, the small introductory booklet "Wie stimme ich selbst
mein Cembalo?" is available in three languages, German, English
and French. It costs about 30 $, give or take some.

Schriftenreihe Das Musikinstrument
Heft 19
Dritte, erweiterte Auflage
ISBN 3-923639-68-6
Verlag Erwin Bochinsky Gmbh&Co. KG
Frankfurt am Main
Germany

If we don't read contemporary publications, we are going
to miss a lot. Can you suggest some further reading on this topic?
Please post it, if it is rather new and modern.
As for me, there is no question how to play Bach and
especially the WTC. The Kellner Bach Tuning
may be inappropriate for other music, but it is worth a try.

My digital piano has 6 temperaments, but the new types have
microtuning capabilities. They can be programmed for any tuning.
Electronic tuners with microtuning are also available.
So, thanks to the Japanese, and Mr. Kellner et al, we can get the
original sound of Bach's music into our living rooms.
Midi files of the WTC are on midi archives in the Internet.
I like listening to midi music, because it is free of "interpretation",
which does not interest me.

Yours
Helmut Wabnig
wabi@net4you.co.at



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On Thu, 2 Nov 1995, Manuel Op de Coul wrote:

> One third, C-E is very close to pure. Five more are smaller than equal
> tempered. Two minor thirds are halfway between pure and equal tempered.

Remind me: are any major thirds Pythagorean?

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On Thu, 2 Nov 1995, Timothy Tikker and Julia Harlow wrote:
> On Thu, 2 Nov 1995, Manuel Op de Coul wrote:
> > One third, C-E is very close to pure. Five more are smaller than equal
> > tempered. Two minor thirds are halfway between pure and equal tempered.
>
> Remind me: are any major thirds Pythagorean?

Three: F#-A#, Db-F, and Ab-C.

--pH (manynote@library.wustl.edu or http://library.wustl.edu/~manynote)
O
/\ "Play it over? When I need one and you need seven?"
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On Thu, 2 Nov 1995, Paul Hahn wrote:

> > Remind me: are any major thirds Pythagorean?
>
> Three: F#-A#, Db-F, and Ab-C.

Hmmm. Sorry if I'm beating (no pun intended) a dead horse, but didn't
Kirnberger say that Bach tuned with all Major 3rds sharp, but none
Pythagorean?

Mind you, I like the Kellner temperament - a local organ is tuned in it -
but I just wonder if one of Neidhardt's temperaments is more what Bach
had in mind (if Kirnberger is right - odd that K himself devised
temperaments which didn't fit this description).

- Tim Tikker

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On Thu, 2 Nov 1995, Timothy Tikker and Julia Harlow wrote:
> > > Remind me: are any major thirds Pythagorean?
> >
> > Three: F#-A#, Db-F, and Ab-C.
>
> Hmmm. Sorry if I'm beating (no pun intended) a dead horse, but didn't
> Kirnberger say that Bach tuned with all Major 3rds sharp, but none
> Pythagorean?

This is what Aleksander Frosztega and I got into that big tiff over a
few weeks ago. I hope not to reopen wounds, but here's a brief summary
of my position:

(1) All major thirds sharp, yes. Kirnberger admits that.

(2) None Pythagorean? Nope. Mattheson claims that (1) implies (2),
but he is in error.

OTOH, if you can cite a passage in which Kirnberger admits (2), I'd be
most curious to see it.

--pH (manynote@library.wustl.edu or http://library.wustl.edu/~manynote)
O
/\ "Well, so far, every time I break he runs out.
-\-\-- o But he's gotta slip up sometime . . . "

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Kirnberger never claimed that JS Bach prohibited Pythagorean thirds, only
through a third party that JS Bach tuned all of his thirds sharp (which I
take to mean sharper than just and not necessarily sharped the same amount).

Johnny Reinhard
American Festival of Microtonal Music
318 East 70th Street, Suite 5FW
New York, New York 10021 USA
(212)517-3550/fax (212) 517-5495
reinhard@ios.com

On Thu, 2 Nov 1995, Timothy Tikker and Julia Harlow wrote:

>
> On Thu, 2 Nov 1995, Paul Hahn wrote:
>
> > > Remind me: are any major thirds Pythagorean?
> >
> > Three: F#-A#, Db-F, and Ab-C.
>
> Hmmm. Sorry if I'm beating (no pun intended) a dead horse, but didn't
> Kirnberger say that Bach tuned with all Major 3rds sharp, but none
> Pythagorean?
>
> Mind you, I like the Kellner temperament - a local organ is tuned in it -
> but I just wonder if one of Neidhardt's temperaments is more what Bach
> had in mind (if Kirnberger is right - odd that K himself devised
> temperaments which didn't fit this description).
>
> - Tim Tikker
>

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On Fri, 3 Nov 1995, Paul Hahn wrote:

> This is what Aleksander Frosztega and I got into that big tiff over a
> few weeks ago.

Sorry I didn't take the time to read that in detail. I appreciate your
succinct summary!

> (2) None Pythagorean? Nope. Mattheson claims that (1) implies (2),
> but he is in error.
>
> OTOH, if you can cite a passage in which Kirnberger admits (2), I'd be
> most curious to see it.

I can't... but as I said, I was puzzled that K's temperaments didn't live
up to his own description of JSB's. However, my explanation was that by
K's time taste was shifting towards the classical style, for which K's
temperaments might really be better suited.

Organbuilder John Brombaugh, located here in Eugene, OR, now uses Kellner
regularly (except for the occasional meantone organ with subsemitonia!).
Bach's music is a first priority in his organ designs. He started using
Werckmeister, then Kirnberger, then a modified version of same, use 1/6
comma Valotti in at least one organ (Ames, Iowa), but has now settled on
Kellner. His organ at Eugene's Central Lutheran church is now in
Kellner, previously being in Kirnberger III then a modified Kirnberger.

My house organ was last tuned in Kellner, and I found it quite
satisfactory. I'm considering one of Neidhardt's, though. I asked
Brombaugh's opinion of N's temperaments, and he called them "monkey
business."

- Tim Tikker


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On Fri, 3 Nov 1995, I wrote:
> (2) None Pythagorean? Nope. Mattheson claims that (1) implies (2),
^^^^^^^^^
> but he is in error.

D'oh! I meant Marpurg, of course.

--pH (manynote@library.wustl.edu or http://library.wustl.edu/~manynote)
O
/\ "Well, so far, every time I break he runs out.
-\-\-- o But he's gotta slip up sometime . . . "

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