source file: mills2.txt Date: Tue, 26 Sep 1995 04:01:22 -0700 Subject: FWD: Re: Bach's tuning From: COUL@ezh.nl (Manuel Op de Coul) 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 ------------------------------------------------------- Aleksander Frosztega "Odi summusos; proinde aperte University of Utrecht dice quid sit quod times." The Netherlands ------------------------------------------------------- Received: from eartha.mills.edu [144.91.3.20] by vbv40.ezh.nl with SMTP-OpenVMS via TCP/IP; Tue, 26 Sep 1995 13:52 +0100 Received: from by eartha.mills.edu via SMTP (940816.SGI.8.6.9/930416.SGI) for id EAA04531; Tue, 26 Sep 1995 04:51:59 -0700 Date: Tue, 26 Sep 1995 04:51:59 -0700 Message-Id: <950926053059_70461.10_IHD50-1@CompuServe.COM> Errors-To: madole@ella.mills.edu Reply-To: tuning@eartha.mills.edu Originator: tuning@eartha.mills.edu Sender: tuning@eartha.mills.edu