The Clavette

>From the Minnesota Composers Forum October newsletter:

The Clavette, a microtonal MIDI keyboard shown at the 1995 International
Computer Music Conference, will be demonstrated by its inventor, composer
Harold Fortuin, on Monday, October 16, at 7 p.m., in the MCF offices in St.
Paul. The instrument was developed for the performance of live microtonal
music in a wide variety of termperaments. It includes a 122-key keyboard,
two 3-D vector pedals, and up to six foot switches. The presentaiton will
feature performances of works by several composers in a range of
non-standard equal and just tunings. For more information, call (612)
228-1407.

Stan Hoffman
stanh@isomedia.com



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Date: Mon, 25 Sep 1995 18:28:51 +0000
Sender: Harpsichords and Related Topics
From: Aleksander Frosztega
Subject: Re: FWD: Bach's tuning

On Mon, 25 Sep 1995 08:21:28 -0700
Johnny Reinhard wrote:

>Re: Kirnberger's saying to Marpurg that "Bach tune each of his major
>thirds sharp." This is true in both equal temperament _and_
>Werckmeister III. The Werckmeister III contains 4 sizes of major third,
>one of which is equivalent to 402 cents, one that is Pythagorean at 408
>cents,one at 396 cents, and the smallest one at 390 - all sharper than
>the just 386 cents.

Yes, you can argue it that way. And yes, you are correct in saying that
both Wm III and ET have major thirds that are larger than just. But the
quote in question still refers to equal temperament. Why? Because of the
context: Most ear-tuning instructions for Circular temperaments in 18th-
century Germany relied on setting the *fifths* in order to temper the scale.
I have never seen (I don't think) 18th-century German ear tuning
instruction that use fifths as a tempering device for Equal Temperament.
They all used rows of MAJOR THIRDS which were to be made wide!
(Sorge gave explicit instructions that each successive third should be
made somewhat *wider* than the last.) Several rows of three successive
major thirds completed the temperament (the idea was to temper the
thirds wide to close the lesser diesis; several of these "third-rows" closed
the Ditonic Comma). On the issue of tuning, C.P.E. Bach even
recommends that his readers buy Barthold Fritz's _Zuverlaessige
Anweisung._, which gives instruction for EQUAL TEMPERAMENT.

Get over it. Bach probably wrote (at least his harpsichord works) for Equal
Temperament or something darn close to it. Not all the revisionism in the
world can alter the *evidence.*


>Further, Kirnberger himself gave directions for the tempered fifth whose
>ratio (10935:16384) is almost exactly 1/12 of a comma smaller than the
>pure fifth in several publications, including his *Von der Temperatur*.

Kirnberger never wrote a book called "Von der Temperatur."


>The method by which he arrived was to take seven pure fifths in
>succession plus one pure major third. This gives the tempered fourth
>8192:10935, which is larger than the pure fourth by 1/12 of a comma, its
>inversion is the tempered fifth 10935:16384.

Yes, this is the F#-C# fifth in Kirnberger I though III. However, it is not
tempered by 1/12 Pythagorean comma; it is tempered by the *schisma.*
Kirnberger was not the best mathematician in the world and Marpurg, in
fact, corrects Kirnberger's calculations in Marpurg's _Versuch._

>According to Kirnberger he showed this discovery to Leonhard Euler in
>1766 and remarked to him that this fifth could be used to determine all
>ratios of equal temperament, an idea subsequently developed by Johann
>Heinrich Lambert and published in the *Memoires de l'academie royale
>des sciences et belle lettres* (Berlin 1774) and used by Marpurg against
>Kirnberger. (See p. 20 of the *Art of Strict Musical Composition* by
>Kirnberger, Yale University Press)

>There is great bitterness against Kirnberger, chief violinist and
>keyboardist at the court in Berlin by Marpurg, the Lottery King Of Berlin.

This is correct. Though I believe that Kirnberger was employed by
Princess Amalie, the sister of Frederick, not Frederick himself, as you
*might* have been implying. If you were not implying this, ignore the last
sentence.


>Clearly, this argument of fifths over thirds is an aesthetic battle of
>historic proportions. Politics enters at every level and success is oft
>measured by clout. What intrigues me most about Prof. Rasch's
>perspective is that the Netherlands has been a leader in performing
>"early music" in historic intonation and as its main musical intellectual
>in this area, Rasch bucked the trend. Perhaps if he were in any one of
>the other countries that had been resistant to historic intonation
>systems, he might have headed the other way.

(1) Dutch HIP players continue to play in historical intonations (although,
frequently without regard to historical framework of period and region);

(2) I find it distressing that historical evidence continues to be ignored and
that the "temperament revisionists," standing on the shakiest of grounds
and often without being really read in the subject, continue to disseminate
disinformation that misleads people and results in performances of
dubious historical accuracy.


Aleksander Frosztega
ignore the evidence>



-------------------------------------------------------
Aleksander Frosztega "Odi summusos; proinde aperte
University of Utrecht dice quid sit quod times."
The Netherlands
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