source file: mills2.txt Date: Thu, 21 Sep 1995 20:47:16 -0700 Subject: Re: BACH'S TUNING From: Johnny Reinhard Manuel recently posted from the harpsichord list several points of view on Bach's Tuning, one of which commented on Prof. Rudolf Rasch's opinion that J.S. Bach composed in equal temperament. I will quote part of my article *Bach's Tuning* from PITCH I:2 pp. 31-32 in reference to Rudolf Rasch's position on the equal temperament factor and Bach, a position with which I disagree: In a recently published essay, Rudolf Rasch of the Netherlands asks the question "Does 'Well-Tempered' mean 'Equal-Temperament'?" Rasch defines qualification of a tunng in which all tonalities can be performed. Rasch believes, however, that Bach's *The Well-Tempered Clavier* was conceived in equal temperament. He attributes this to Werckmeister's later works which explicitly describe equal temperament. Werckmeister wrote in his *Hypomnemata musica* of 1697 that: Who, however, asks for a temperament in which all consonant intervals are equal, must take care that all fifths beat 1/12th of a comma downward, so that all major thirds beat 2/3 of a comma and the minor third 3/4 of a comma... So far I have not been able to agree with this view, because I prefer to keep the diatonic notes which are used most often with the diatonic tonalities, as pure as possible in tuning. Werckmeister clearly does not fully support equal temperament at this point in his life. Yet in Werckmeister's *Harmonologie musica* of 1702, Rasch has determined that there is "a direct pleading for equal temperament, based on the possibilities of unlimited transportation and enharmonic changes." One problem with this interpretation is that all circular keyboard tunings are, by definition, capable of unlimited transposition and enharmonic changes. In this sense, equal temperament fits well within the larger category of well-tempered tunings. Werckmeister's last opus *Musicalische Paradoxal-Discourse* of 1707 was published posthumously. Based on Rasch's translated excerpts, it would appear to the point of offering an apology "for his earlier propaganda for unequal temperaments. Werckmeister's attitude at the end of his life is summarized in a book published posthumously (1707) where in effect he apologized for not having included equal temperament among the various circulating temperaments for which he had earlier published a monochord diagram. (The incompetent engraver, he said, had complained about dividing the narrow space of a comma into 12 parts.) He quite approved of equal temperament, yet was willing "to have the diatonic 3rds left somewhat purer than the other, less often used ones," a procedure for which he had expressed clear preference in his earlier writings. What can be deduced for certain is that Werckmeister wrote about equal temperament usage with increasing frequency in his later years. This need not be interpreted as a dogmatic insistence on equal temperament, nor as a preference, since Werckmeister was merely cataloging. Manuel, please forward the above to the harpsichord list. Thank you. Johnny Reinhard Director American Festival of Microtonal Music 318 East 70th Street, Suite 5FW New York, New York 10021 USA (212)517-3550/fax (212) 517-5495 reinhard@ios.com Received: from eartha.mills.edu [144.91.3.20] by vbv40.ezh.nl with SMTP-OpenVMS via TCP/IP; Fri, 22 Sep 1995 11:57 +0100 Received: from by eartha.mills.edu via SMTP (940816.SGI.8.6.9/930416.SGI) for id CAA12001; Fri, 22 Sep 1995 02:56:58 -0700 Date: Fri, 22 Sep 1995 02:56:58 -0700 Message-Id: <00996C6AA951A214.1F2C@ezh.nl> Errors-To: madole@ella.mills.edu Reply-To: tuning@eartha.mills.edu Originator: tuning@eartha.mills.edu Sender: tuning@eartha.mills.edu