From: jseboldt@pnet51.orb.mn.org (John Seboldt)
Newsgroups: rec.music.classical
Subject: Re: Define "Well Tempered"
Date: 26 Jan 93 04:45:04 GMT
Organization: People-Net [pnet51], Minneapolis, MN.

hatunen@netcom.com (David W Hatunen) writes:
>Unfortunately, this means that you must retune your instrument
>for each different scale you wish to play. Which is impossible
>with some instruments. In the evenly tempered scale, the octave,
>or 2:1 relationship is divided into twelve geometrically evenly
>spaced intervals. Take the twelfth root of two (approx 1.05946..).
>Each tone bears this relationship to the next lowest tone.
>That way, no matter what scale you play, it will sound harmonically
>the same.
>
>The problem is that a third interval is no longer exactly a third;
>that is, it no longer consists of two tones in a simple integer
>relationship. It's very close, but no cigar, and the difference
>is noticable.
>
>So, an even tempered scale doesn't sound quite as good as a
>diatonic scale. But it makes the piano possible (you don't have
>to retune for each different scale) and it makes music with
>key changes possible.
>
>As I understand it, Bach wrote the Well-tempered Klavier as a
>demonstration of the advantages of an even tempered scale.

A bit overstated.  True equal temperament was known in the 18th century, but
they weren't quite ready to totally deaden their ears to the advantages of
keyboard tuning systems with more pure intervals.

Folks wanted to play in more keys, and modulate further, but they still
apparently preferred purer triads in more frequently used keys.  Systems in
this spirit (which are frequently revived today for early music playing) are
such as the Werckmeister temperaments, and especially Kirnberger, who reflects
Bach's general preferences in this area.

Just because Bach wrote preludes/fugues in all keys doesn't mean he's talking
about playing them all at one sitting on one single tuning.  (This idea of
playing cycles like this in one cosmic sweep is definitely a modern
invention!)  A harpsichord was treated more like a guitar in that it was
frequently retuned, perhaps a few notes retuned on the spot to be more
suitable for a particular piece.  (Bach never called his "klavier tuner" in
for monthly tunings!)  

Saying that even (equal) temperament "makes key changes possible" is rather
overstated.  The drama of the more-or-less unequal temperaments used in Bach's
time made key changes even more interesting -- the "home triads" (most
commonly C, F, and G major) might have almost-pure thirds for a nice,
radar-clean penetrating quality, while triads further afield are a little
fuzzier, more dissonant, emphasizing the tension of the piece as it moves
"forward" in development.  Finally, the piece moves back to the home triads,
resolving again into beautiful, pure (or purER) repose.  

Sorry, but Bach is a bit early to look toward as the "father of equal
temperament".  Think later -- early Romantics.  Probably not until the
chromatic ramblings of Liszt, Wagner, and their followers do we have true
equal temperament firmly established (and the duller-sounding piano, where the
rounder timbre more easily hides what one has lost in equal temperament), as
the tyranny of tonality is slowly but surely undermined.

: John Seboldt...Mpls, MN...As a ham, K0JD...as a human...well,... :
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Newsgroups: rec.music.classical