From: roger@crux.Princeton.EDU (Roger Lustig)
Subject: Re: Define "Well Tempered"
Originator: news@nimaster
Reply-To: roger@astro.princeton.edu (Roger Lustig)
Organization: Princeton University
Date: Wed, 13 Jan 1993 02:14:30 GMT

In article <C0rnn0.Bu1@comp.vuw.ac.nz> Michael.Norrish@comp.vuw.ac.nz (Michael Norrish) writes:
>>>>>> On Tue, 12 Jan 1993 06:52:25 GMT, roger@crux.Princeton.EDU
>>>>>> (Roger Lustig) said:

>Roger> In article <5170027@hpindda.cup.hp.com> tomm@hpindda.cup.hp.com
>Roger> (Tom McNeal) writes:

>>Does anyone know the difference between 'well-tempered' and
>>'equal-tempered' tuning on a piano?  All I know is that
>>'equal-tempered' is the current tuning style, and has been for some
>>time, and that Bach used 'well-tempered' tuning (Oho, you say, THATS
>>what "Well-tempered Clavier" meant.)

>Roger> Equal temperament means just that: all semitones are the same
>Roger> size, therefore all intervals of the same number of semitones
>Roger> are the same size.

>Roger> Well-tempered means using one of several tunings developed a
>Roger> little before Bach's time.  These are somewhere between
>Roger> mean-tone (most thirds pure) and equal temperament.  There are
>Roger> lots of descriptions of the actual numbers involved; try Easley
>Roger> Blackwood's book on tunings (Princeton, 1985 or so).

>Two questions, (one unashamedly un-r.m.c. :-)

>1. Is that Easley Blackwood the same as the Bridge player of the
>famous ace-asking convention?

His son, also a Life Master.  EB, Sr. died just last year; Jr. is
Professor of Music at  U of Chicago, and a composer.

>and 

>2. Given that the WTC sort of seems to specify the way it should be
>played by title alone, do recordings of it these days use a
>well-tempered tuning or not? 

I'm sure that some do.  Can't tell you which ones, though.

On the other hand, Bach had no control over which tunings 
people used when they played it in his time, either, and not 
everyone used the Werckmeister tunings...

>There have been numerous discussions of this tuning business before on
>r.m.c, but my physics stopped a long time ago and all those
>frequencies, octaves and harmonies are quite confusing. However, I
>have heard that using a tuning that is not well-tempered can make some
>keys sound pretty odd. 

Equal temperament takes care of this, too.

>Now presumably, this sort of effect might have
>been exploited by composers of the time, (and indeed it would explain
>perhaps why keys had various connotations, (D minor is demonic or some
>such? That's the key to Mozart's 20th piano concerto isn't it?)), but

Actually, there's very little evidence linking tunings to affections
related to any but the most extreme (e.g., f sharp minor) keys.

>was it used by Bach? 

Bach was trying to show that the new tonal system, coupled with the 
right tuning, allowed one to play in all keys. 

>I think I may have also read that some of the pieces in WTC were
>originally in other keys and Bach just transposed them, so that
>perhaps in these cases at least, the difference from one key to the
>next was insignificant..

Exactly.  That was Bach's point -- that all 24 keys were available.

>Perhaps the maintainer of the FAQ might like to add a subsection along
>the lines of : 
>  "Tuning : (well-tempered etc), for those who hertz is a dirty word."

So write it!  Give 'til it hertz.

Roger
Newsgroups: rec.music.classical