source file: mills2.txt Date: Sat, 5 Jul 1997 02:47:40 +0200 Subject: Re: Point of Well Temperaments From: Joseph Downing On Fri, 4 Jul 1997, Gary Morrison wrote: > >> The entire point of well temperaments is that they are > >> > about equally well in tune in all keys. > >...I believe that the > >development of sonata form in the classic period was directly related to > >the inequality (but acceptability) of the different keys. > Again noting that I said, "about equally well in tune" and not > "identical sounding" in all keys, I'd say that that, and "inequality (but > acceptability) of different keys" are two different ways of saying the same > thing. > 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. I seriously doubt if ol' JS would > have written in F and F# in the same suite if he expected one to sound > wildly more out of tune than the other! He most certainly did use the relative in-out-of-tuneness in his music, and he was not alone! 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. For a revealing exercise, look at cadences on F# major. They nearly always occur at some point where their very weakness has structural import to the piece. For example: Prelude and Fugue in D, BWV532 The opening section is all in D major - fast scales - very light and showy. The second section of the prelude is somewhat whimsical and uses dotted rhythms over a pedal F#. It is usually played on a secondary manual (even on equal-tempered performances) with a lighter registration. This section cadences on F# major. Note that, because F# major is prettymuch on the out-ofne side of the spectrum, the F# major chord is short - only an eighth note long, and followed by a grand pause. The section basically 'falls apart' on such a weak cadence. The grand pause is followed by a two octave scale leading up to a HUGE (usually full organ) chord on D Major - an incredibly bright key. This is followed by one of the most glorious Alla Breves in music - full of joy and light. Further analysis would show how very carefully Bach related the keys of sections to the tension necessary. You could also look at the Toccata and Fugue in F - the one that begins with a long canon between the hands overa sustained pedal note. In the Fugue, there are a number of deceptive cadences that bear analysis. They all proceed from very tame dominant chords (Ex. C Major) to outlandish, very much more out-of-tune chords (such as Db third inversion). This makes the deception even more shocking. Bach used that same technique in many other pieces. I remember two young daughters (under age 10) listening to a performance of the G major "Piece d'Orgue" which also has a glorious All Breve section which concludes with a shocking deceptive cadence to o vii o7 of V. Even though they had been listening complacently, they both gasped audibly (to the performer's delight and amusement) Look at the Prelude in C major from Book One of WTC. Listen to the chords in any standard well-tempered system, and you will hear a rise in tension over a long arc, then a release, than a larger rise which gives way to final release. (It was this piece that made a believer out of me.) Bach was not alone in his use of the relative dissonance/consonance of chords. In the Burkhart anthology, look at the Scarlatti Sonata in E Major. It, too, has an internal cadence on F# major which is marked as a short note followed by a grand pause. he then proceeds to fanfares on open fifths on F# (where we discover that it was the A# third that was causing the out-of-tune F# triads - the fifths are VERY in-tune.) Joe Downing, in Syracuse Received: from ns.ezh.nl [137.174.112.59] by vbv40.ezh.nl with SMTP-OpenVMS via TCP/IP; Sat, 5 Jul 1997 08:27 +0200 Received: by ns.ezh.nl; (5.65v3.2/1.3/10May95) id AA05283; Sat, 5 Jul 1997 08:28:05 +0200 Date: Sat, 5 Jul 1997 08:28:05 +0200 Received: from ella.mills.edu by ns (smtpxd); id XA05258 Received: (qmail 23961 invoked from network); 5 Jul 1997 06:28:02 -0000 Received: from localhost (HELO ella.mills.edu) (127.0.0.1) by localhost with SMTP; 5 Jul 1997 06:28:02 -0000 Message-Id: <199707050224_MC2-1A49-E3DB@compuserve.com> Errors-To: madole@mills.edu Reply-To: tuning@eartha.mills.edu Originator: tuning@eartha.mills.edu Sender: tuning@eartha.mills.edu