Re: [tuning] An inferior tuning system satisfies J.S. Bach??

Dear Mr. Paul Erlich,

Could an inferior tuning system satisfy J. S. Bach?

Did Bach prefer a technologically inferior system (=Werckmeister III) to
"wohltemperirt"?

The system of J. S. Bach is called henceforth "wohltemperirt", as the composer
writes himself. It has 5 welltempered and 7 perfect fifths.

REFERENCES:
General reference, my website:
http://ha.kellner.bei.t-online.de
Specific reference:
Kellner, H. A.: Temperaments for all 24 Keys - A Systems Analysis. Acustica,
Vol. 52/2, 1982/83. S. Hirzel, Stuttgart. p. 106-113.
(Publication of the lecture delivered July 1980 at the Bruges 6th International
Harpsichord Week)

Did Bach prefer a technologically inferior system (=Werckmeister III) to
"wohltemperirt" ?

Structure of fifths:
Nominal Werckmeister III:
8+4 perfect resp. tempered; the latter 696,09 c

Bach/Werckmeister "wohltemperirt":
7+5 perfect resp. tempered; the latter 697,28 c

Criteria to be applied:
Size/quality of the basic tonal third C-E
Size/quality of the tempered fifths

The result (in cents) looks as follows:

Fifth Third

697,28 389,11 Bach"wohltemperirt"
696,09 390,22 Werckmeister III

1,2 - 1,1 Differences (rounded)

Bach's 5 tempered fifths "wohltemperirt" are
BETTER by 1,2 cent than the 4 tempered fifths of Werckmeister III

Bach's basic tonal third C-E "wohltemperirt"
is by 1,1 cent BETTER than this third in Werckmeister III

CONCLUSION:

Anybody accepting Werckmeister III as Bach's tempering system for all 24 keys,
ACCEPTS that Bach employed an objectively inferior system - as demonstrated
under the criteria enounced above.

Or else, what OTHER rational and more appropriate criteria should be applied,
for assessing two irregular baroque tuning systems?? (Their fifths being
structured 7+5, respectively 8+4).

REMARKS:
There is no sufficient reason that in Werckmeister III the third C-E is bridged
by 3+1 fifths, tempered, respectively perfect. Rather than by 4 EQUAL fifths
amongst themselves, as in Bach/"wohltemperirt".

To the honor of Andreas Werckmeister it must be stressed that he was already
1691 in possession - and the inventor - of the System "Bach/wohltemperirt", as
his treatise "Musicalische Temperatur"shows!!

TO BE CONTINUED
Herbert Anton Kellner

Johnny Reinhard is sure it is Werckmeister.
Barnes, > van Eck, and others have come to various other conclusions. Perhaps
> you'd care to discuss the _evidence_ behind your deduction that this
> is the temperament Bach intended?
>
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