Bach tuning-mathematics

Dear John Starett,

To answer your question: there exists a little booklet, called
"Kleine Chronik der Anna Magdalena Bach" by a certain Esther Meynell.

This booklet is sort of kitsch-legend-writing, as seen from the viewpoint
of Bach's wife about her husband.
Clearly, there can be nothing wrong about that, as long it facilitates the
approach to the biography, the life and music of the master. And as long
as it does not proffer pretended musicological statements.

However, I'm a mathematician (=theoretical physics by formation) with
certain expectations along this line. What do you think I feel when
reading in that "Chronik" the assertion, JSB has never thought a moment
about maths when composing??

On that very question I have been working for 26 years by now -
as a mathematician. In order to find the original method for tempering
the system "Werckmeister/Bach/wohltemperirt" I needed about 3 months.
Thereafter I set out to write - utilizing my result - "Wie stimme
ich selbst mein Cembalo?" (Out of print in English and in 3rd
Edition in German language). Checking into "Das wohltemperirte Clavier",
B-major pieces, proves that Bach must have hat at his disposal the method
of the beat rates third:fifth=6:1 in B-major; see below.

For instance, the prelude measures 19 bars: 12 fifths and 7 octaves
in the opposite direction - 19 intervals - close the circle.

The prelude has 417 keystrokes:
4 fifths c-g-d-a-e
1 tempering fifth B-f#
7 perfect fifths.

The B-major prelude comprises 19 bars, the fugue 34. The total of
B-major, bar-wise, thus 19+34=53 bars,
5= fifth in basso continuo
3= third in basso continuo.
In the basic C-major triad of "wohltemperirt", third and fifth (3 and 5)
must beat at the same speed: UNISON.

The B-major prelude starts at bar 1913 within the OVERALL (!) bar count
through "Das wohltemperirte Clavier" and ends at bar 1931.

You recognize that 1+9+1+3 = 1+9+3+1 = 14.
Genatria converts BACH just into 14 : Bach signs his method.
Re 1913 and 1931: 19 is the closure of the circle of fifths
1=UNITAS of the baroque musico-theological perfection
3=TRINITAS
13 and 31 are tri-unitary juxtapositions

It is by now generally known that a triad was considered a
musical tri-unitary Christian symbol.

In the C-major triad you have UNISON of beats;
in the B-major triad you temper third to fifth 6:1 for the correct beats.

All that I have published already a long time ago and in a much more
elaborated fashion.

In the graphic interpretation of Bach's signet of my site
http://ha.kellner.bei.t-online.de
the distribution of perfect and tempered fifths is described.

The tempering method, to reduce the first fifth by 1/5 of P (Pyth. Comma)
requires that in the B-major triad, the third B-d# beats 6 times faster than
the fifth B-f#. The first reduced fifth will thus be B-f#.

Perhaps I should post here one day the mathematical proof (short) in case
I feel there is sufficient interest foir that specific tuning method for
"wohltemperirt" on the harpsichord.

Kind regards,
Herbert Anton Kellner

P.S.:
You may look by means of any suitable machine, like AltaVista, for
"Kleine Chronik der Anna Magdalena Bach".

John Starrett schrieb:
> --- In tuning@y..., ha.kellner@t... wrote:
> > Dear Mr. Neil Haverstick,
> > I appreciate that you despise tackling matters of "intellectual
> interest".
> > The same principle holds for the Little Chronicle of Anna Magdalena
> Bach!!
> >
> > Best regards,
> > Herbert Anton Kellner
>
> I am unfamiliar with this reference. Can you elaborate on "The
> Little..."?
>
> John Starrett
>
>
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--- In tuning@y..., ha.kellner@t... wrote:
> Dear John Starett,
>
> To answer your question: there exists a little booklet, called
> "Kleine Chronik der Anna Magdalena Bach" by a certain Esther
> Meynell.
>
> This booklet is sort of kitsch-legend-writing, as seen from the
> viewpoint
> of Bach's wife about her husband.
<snip>
> Herbert Anton Kellner

Thanks for clearing this up for me.

John Starrett