source file: mills2.txt Date: Sun, 6 Jul 1997 05:38:22 +0200 Subject: Point of Well Temperaments From: A440A@aol.com On Fri, 4 Jul 1997, Gary Morrison wrote: > The original premise of the question was that well temperaments get > farther out of tune as you venture farther from C Major. Although > well-temperaments are not my specialty, I'm not aware of many, if any, > well-temperaments have that property. From what I have experienced and learned, virtually all of the Well Temperaments have the property of ascending dissonance in the tonic thirds as the key signature gains more accidentals. At the same time, since thirds and fifths are in acoustical oppostion, the keys with the most purely tuned thirds have the most highly tempered fifths. This supported the twin capabilities of some keys favoring the harmony, while others, ( the remote keys), provided more "expression" for the melodic line. Also, to the above quote, Joseph Downing replies: In ANY of the frequently used well-tempered >systems, F major is the most in-tune key with C and G close seconds. The >less used keys are much more out-of-tune, yet, as required by the >well-tempered philosophy, usable. This is not quite right, (IMHO), . The Valotti temperament, following the style of the Italians, does tune the F-A third as the purest third in the temperament. However, if we look at a number of other well temperaments, such as the Prinz, Young, D'Alembert, or G.F.Handel, we find the C-E third is the purest, (not always just, but usually very close). Since the common denominator seems to be that additiional accidentals bring about about increases in the tempering of the root tonic thirds, how a temperament allotted the comma was a lively topic of conversation in the 18th century. Some, like the Young, begin with a slightly tempered C-E, and progress in even steps all the way up to F#-A# and Gb-Bb. This is a beautiful temperament in its symmetry,plus the fact that the most highly tempered thirds are exactly 1 syntonic comma wide. This is the idealized well temp. form, according to Jorgensen. There are several temperaments by Stanhope that favor the C-E and G-B equally, and others, (Rousseau), that favor the F-A and C-E as the closest to pure polar keys, so it seems that the C-E was the pivot point around which the maximum purity was normally placed. This makes sense as a legacy of the meantone systems, as the most common meantone systems are, I think, directly aimed at producing the Just C-E first. (A real meantone maven could help us out here, I tread thinner ice when I get to far before Werckmiester). Even though the Prinz is probably my favorite, the Young is the most succesful temperament for initiating the heretofore unexposed12 tet masses into key color recognition. I find that some musicians are most impressed with the added purity in the simpler keys, and others are struck by the edge and brilliance that comes from the more highly tempered keys. Some can't tell the differerence, and others go nuts! A well known piano entertainer, ( he was entertainer of the year in the Country music world once before.......) went for my explanation on the temperaments, and I tuned a very clean Young on his Steinway. He called his studio tuner the next day to come return it to ET. He couldn't stand it!!. This is an easily acquired taste, but it is an acquired one.. Regards, Ed Foote Precision Piano Works Nashville, Tn Received: from ns.ezh.nl [137.174.112.59] by vbv40.ezh.nl with SMTP-OpenVMS via TCP/IP; Sun, 6 Jul 1997 08:10 +0200 Received: by ns.ezh.nl; (5.65v3.2/1.3/10May95) id AA05596; Sun, 6 Jul 1997 08:10:46 +0200 Date: Sun, 6 Jul 1997 08:10:46 +0200 Received: from ella.mills.edu by ns (smtpxd); id XA05576 Received: (qmail 2075 invoked from network); 6 Jul 1997 06:10:41 -0000 Received: from localhost (HELO ella.mills.edu) (127.0.0.1) by localhost with SMTP; 6 Jul 1997 06:10:41 -0000 Message-Id: Errors-To: madole@mills.edu Reply-To: tuning@eartha.mills.edu Originator: tuning@eartha.mills.edu Sender: tuning@eartha.mills.edu