Bach's signet of 1722 & wohltemperirt

Dear members,

For some time I already had been planning to distribute here information on
"dedcoding" the Bach's signet. I put around the circle of fifths, amending thus
Bach's seal. ( See

http://ha.kellner.bei.t-online.de )

I stress, of course that I myself added my interpretation of the seal
in form of the circle of fifths in my webpage. Please note that the seal
does not contain any indication concerning the distribution of perfect
and tempered fifths. The rationale for the graphic art in my website I
shall thus present here, below.

It is striking that the crown of the signet holds 5 identical items of one
sort and and other 7 identical items of another sort.
Those I interpret rspectively as the 5 fifths "wohltemperirt" and the 7 perfect
fifths.

Friedrich Smend suggested his interpretation: 5 rubis and 7 pearls. I feel
this goes very well indeed with those two sorts of fifths. Who would, turned
around, relate perfect fifths with Smend's rubis and tempered fifths with his
pearls? Intuitively, nobody would do that!?

The system "wohltemperirt" of Werckmeister/Bach is based upon a TRIAD,
musical symbol of the Holy Trinity - trias harmonica perfecta, about which
Margot Schulter recently provided pertinent references to historical
authors of writing treatises within the traditions of music-theory.

Below, at mark �����, I take the liberty
to quote Margot Schulter's excellent essay concerning the
trias harmonica perfecta I apprecaite and for which I am grateful.

Returning now to "Bach/wohltemperirt", the beats within the
fundamental C-major triad , C-E and C-G, occur at the unison,
at the perfection of the baroque "unitas"=UNITY. In Werckmeister's
writings the argument about the unity's perfection steadily recurs.

The trefle crowning the seal can be associated with the
TRINITY, the triad.
The sort of lateral symmetry of the signet represents the UNITY
ithe seal; this argument is not very strong, though. The center
of the signet is made up from the letters JSB running from left
top down to right bottom, intertwined with their mirror-image.

JSB utilized this seal - his second(!) one, after abandoning a first and
earlier one - for the first time in 1722. This is at the same time the
only number figuring at the autograph title of Das wohltemperirte Clavier.
The number 1722 may be interpreted as belonging to wohltemperirt,
representing as follows the

1 tempering fifth B-f#
7 perfect fifths and two pairs of fifths "wohltemperirt":
2 fifths c-g-d together with
2 fifths d-a-e.

Juxtaposing, will form 1722; striking!

The first document we posess, upon which Bach has employed his seal, in an
administrative matter on heritages in the family, was found in an Erfurt
archive.
It is dated March 15th, 1722 - again the number of that year.
The context of "wohltemperirt", and written the German way, 15.3. 1722

1=UNITY
5 fifth in thoroughbass
3 third in thoroughbass

This can be interpreted as nothing else than the specification of the beat
properties within the basic welltempered triad c-e-g.

The entire date, 15.3.1722, boldly juxtaposed as 1531722 has an
interesting and surprising factorization - I shall mention later
should nobody else submit it earlier.

The factorization - to whet the appetites - of
1722 reads 1722=3*14*41
3 TRINY
14 BACH
41 J.S. BACH according to Henk dieben's number alphabet
and gematria.

In this context, all the bars, preludes and fugues of WTC I,
altogether 48 numbers, do form a "magic rectangle", 4*12, the sum
of all 12 lines amounts to 174. Discovered by Henk Dieben!
174: 1 tempering fifth B-f#, 7 perfect fifths, 4 ordinary fifths wohltemperirt.

Kellner, H.A.: Le temp�rament in�gal de Werckmeister/Bach et l'alphabet
num�rique de Henk Dieben. Revue de Musicologie Vol. 80/2, 1994, 283-298

I do not enter into more details into the interpretation of
the composer's signet along these lines.

���� I quote Margot Schulter:
"Hello, there, and my first reaction is to recognize the concept of _trias
harmonica_ as being the contribution of Johannes Lippius in his treatises
of 1610 and 1612 where the triad indeed defines a "musico-theological
spirituality." Lippius defines this triad both as the manifestation of the
Trinity in music, and as the key to musical practice.

For Lippius, the triad is expressed in terms of the just intonation system
of Zarlino (based on the syntonic diatonic of Ptolemy) as a string ratio
of 15:12:10 or 6:5:4.

Of course, Lippius defines a concept of _trias harmonica_ which becomes a
feature of German as well as international theory, with both Werckmeister
and Fux making it part of their approach.

While I regard the era of Lippius itself by the recent term of
"Manneristic," including what are often known as the late Renaissance and
early Baroque, I would much agree that the _trias harmonica_ is a vital
feature of the Baroque era we are discussing.

Here my question might be: while the _trias harmonica_ is at the heart
both of the late modal practice around 1600 and the early tonal practice
around 1680-1720 which Werckmeister helps to define, does the concept of
the triad necessarily favor any one well-temperament, given that all are
compromises?

Similarly, while Zarlino's concept of _harmonia perfetta_ is central to
late 16th-century practice, does it necessarily favor one specific
meantone tuning?"
I unquote Margot Schulter.&&&&&&&&&&&&&&&&&

Best regards,
Herbert A. Kellner

--- In tuning@y..., ha.kellner@t... wrote:

> Returning now to "Bach/wohltemperirt", the beats within the
> fundamental C-major triad , C-E and C-G, occur at the unison,

Can you explain what you mean by that? Do you
mean that these beat rates, transposed up several
octaves, would correspond exactly to the
frequency of C?

--- In tuning@y..., ha.kellner@t... wrote:

/tuning/topicId_26161.html#26161

>
> The trefle crowning the seal can be associated with the
> TRINITY, the triad.
> The sort of lateral symmetry of the signet represents the UNITY
> ithe seal; this argument is not very strong, though. The center
> of the signet is made up from the letters JSB running from left
> top down to right bottom, intertwined with their mirror-image.
>

This is really amazing, and I didn't see it at first! This becomes
very "spooky"... almost "supernatural" in a way with all the
connotations!

> JSB utilized this seal - his second(!) one, after abandoning a
first and earlier one - for the first time in 1722. This is at the
same time the only number figuring at the autograph title of Das
wohltemperirte Clavier.
> The number 1722 may be interpreted as belonging to wohltemperirt,
> representing as follows the
>
> 1 tempering fifth B-f#
> 7 perfect fifths and two pairs of fifths "wohltemperirt":
> 2 fifths c-g-d together with
> 2 fifths d-a-e.
>
> Juxtaposing, will form 1722; striking!
>

This is all really incredible... These puzzles are surpirsing,
mysterious and tantalizing!

_______ _______ ______
Joseph Pehrson