Re: Re: Werckmeister.4-Bach, Kirnberger

So it is with Helmoltz that we have a newly discovered falsity.

"The equal temperament came into use in Germany before it was introduced into
France. In the second volume of Matheson's "Critica Musica," which appeared
in 1752, he mentions Neidhard and Werckmeister as the inventors of this
temperament. Sebastian Bach had already used it for the clavichord
(clavier), as we must conclude from Marpurg's report of Kirnberger's
assertion, that when he was a pupil of the elder Bach he had been made to
tune all the major Thirds too sharp." (p. 321)

What amazes me is that this hearsay of Kirnberger is his only mention in "On
the Sensations of Tone." Berliner Helmoltz missed completely Kirnberger's
eloquent exposition of non-equal well-temperament. We've already seen that
the Orgel-Probe was re-published later on, and that equal temperament for
organs was not the same as with freer keyboards like the clavichord and
harpsichord.

For Kirnberger to say the thirds were high ("too sharp"?) to just would be an
ideal description for both a Werckmeister temperament, as it would for equal
temperament. It was worth Kirnberger's mention precisely because his
temperament (Kirnberger temperament) insisted on the pure just third being
present in the tuning. Matheson calling W. the inventor of ET?

Johnny Reinhard
AFMM

> In the second volume of Matheson's "Critica Musica," which appeared
> in 1752, he mentions Neidhard and Werckmeister as the inventors of this
> temperament.

It appeared in 1725.

> Matheson calling W. the inventor of ET?

Mattheson called equal temperament "Neidhardtischen exacten Temperatur".

The following is also interesting. Neidhardt described in his book
_Sectio canonis harmonici_ four temperaments. The first clearly unequal,
the second a bit less, the third less even, and the fourth was equal
temperament. About the employment of these temperaments, he gave the
following instruction: "Meines Erachten schickt sich die Erste,
mehrentheils, am besten vor ein Dorff, die Andre vor eine kleine Stadt,
die Dritte vor eine grosse, und die Vierdte vor de Hof".
These places from little village to city to court, are metaphors for
the continuum from traditional music (Dorf) to progressive music (Hof)
(like Bach).

Manuel Op de Coul coul@ezh.nl

J.R. writes:
>that equal temperament for
>organs was not the same as with freer keyboards like the clavichord and
>harpsichord.

This is logical for two reasons: organs allowed beat counts long enough to
use a rather demanding system of interval measurement. The transient dose of
spectra delivered by a harpsichord's wire is a much more difficult image to
quantify.
Also, the ease of altering the temperament's wolves (which, according to
Margo, some composers required) let keyboard instruments possess flexibility
through a range of options. This freedom would not be associated with an
organ, whose tunings could be church/political affairs and not done on a per
performance basis.
Jorgensen makes a case that organ temperament departed from a parallel
course with strung keyboards in the early 1700's by remaining on a MT track,
then joining up when everybody went to ET in the late 1800's. This suggests
that organs missed most of the well tempered movement, I dunno.

>For Kirnberger to say the thirds were high ("too sharp"?) to just would
>be an ideal description for both a Werckmeister temperament, as it would for
>equal temperament. It was worth Kirnberger's mention precisely because his
>temperament (Kirnberger temperament) insisted on the pure just third being
> present in the tuning. Matheson calling W. the inventor of ET?

It is easy for me to imagine that what was " ET" in 1700 would not be
acceptable today as an ET. That perhaps it was only equal in relation to
what came before (meantones with wolves over 25 cents). After 2 centuries of
meantone, a few hot thirds was a small price to pay for "equality".
By Werckmiester's time, getting everything in the circle with no third
over 21 cents could have been seen as a temperament that was "equal". The
suggestion that favoritism was shown to the more commonly used keys didn't
change the fact that it was equal, the absence of wolves proved it equal!.
I have customers that don't recognize the inequality of a late 1800's
temperament (a smooth ascension in tempering from C-E@ 7 cents to F#-A# @18
cents). They do recognize and prefer the different "texture" but don't do so
well trying to pin down where the differences lie. They could very easily be
convinced that the tuning was equal temperament, since they can " play in all
the keys.........".
Regards,
Ed Foote
Precision Piano Works
Nashville, Tn.

Ed Foote wrote,

>Jorgensen makes a case that organ temperament departed from a parallel
>course with strung keyboards in the early 1700's by remaining on a MT
track,
>then joining up when everybody went to ET in the late 1800's. This
suggests
>that organs missed most of the well tempered movement, I dunno.

Jorgenson's book deals primarily with tuning in the English-speaking world.
On the Continent, organs left meantone much earlier.