Re: "well-tempered"?

[r l reid <ro...>]

Robert Cohen wrote:
> 
> I'm puzzled:  The Harvard Dictionary of Music, in its discussion of Bach's 
> "Well-Tempered Clavier," says "the name refers to the then novel system of 
> equal temperament."  So what's the difference?--and Roger, what did you mean 
> by this playful signature?

The Harvard Dictionaryu of Music should know better.  Bach never used
nor advocated equal temperament.  He *did* use well temperament.

To keep it as shors possible, western musical theory comes from
the Greeks, who brought us lots of strange ideas like Christianity.

They understood the 7 notes of the scale to be based on cosmicly
significant small number ratios, whcih are provable by stretching a
string between two points.  All other things being equal, if you
have twop strings an octave apart, they will have a 2:1 length ratio.
The higher string is half the length of the lower string.

A fifth is a 3:2 ratio.  A fourth is a 4:3 ratio. And so forth.

You now have a 7 note system that is only roughly made up of
what we now call half steps and whole steps.  But the actual
distance of those various half and whole half steps are different - 
some a little larger, some a little smaller.

If you try to make an 12 note octave by going up by fifths and
normalizing them into a single octave, if you use those perfect 
fifths with the 3:2 ratio, by the time you get back round to the
octave, you've got an octave that's off by 81:80 from the 2:1.

There's no reason to tune by fifths if you aren't trying to 
play music such as European art music of the last 4 centuries.
Just play in just intonation (with perfect ratios everywhere)
and screw tuning in fifths.

Depending on how much dissonance your ear enjoys, you can even change
keys without retuning.  But in the "old days", a harpsichord player
would actually retune to play in different keys.  The player
of unfretted string instruments could do it by adjusting their intonation.

Doing this with portative organs is also done, but on a great cathedral
organ in a 17th century kirk, that's a fish of a differnt color.

What developed around the time of Bach was the concept of "well temperament".

In well temperament you screwed around and tweeked your intervals so that
most, if not all, keys were usable.  Important point clearly lost
on the Harvard Dictionary (did they *REALLY* say that?  is it an
old edition?  That was conventional wisdom in the 1960's, but not
so by the 1980's) is that although the perfect intervals were no
longer perfect, they were close; and most importantly, EACH KEY
RETAINED A DISTINCTIVE COLOR.  C major was NOT the same exact scale
as Eb major, just a minor third lower.  It still had various sized
whole and half steps, just the variation was less.  The syntonic
comma got spread around.

Anyway, theorists not too long after Bach came up with the idea 
of the 12th root of 2.  They figured out that if you took a
strings length and multiplied it by (1 + (12th root of 2)), you
got a note about a minor second higher, and if you did it twelve times
you got a perfect octave.  And every semitone is the same size.
And you can transpose for conveneince.  In fact, there's no
longer any reason to transpose EXCEPT convenience.  

Its also perfectly bland.  It's the idea of well temperament carried
to an absurd conclusion. Works good for jazz.  It stinks for
Bethoven and Bach.  And it stinks for most traditional musics.

So my piano, and my tsimbl, are tuned in what's known these days
as "Thomas Young's 1800 Well Temperament".  Its major advantage
over equal temperament is that it has wonderful major and minor thirds.
Equal temperament actually has very good fifths.  But the thirds
are so bad that once you experienced real thirds....

If I play a tune in D# Freygish, it is a whole different sound from
playing it in D Freygish.  That's because I'm tuned to favor D and
G as the most consonant keys (closest to just intonation).  D# is
really dark - and lovely for a tune like the Skulener "V'Nafshi".

In other words, Robert, your Harvard dictionary is WRONG.  I'm really
kind of surprised, the mistaken notion that Bach favored equal
temperament is long discredited.

BTW, I am NOT claiming that "Thomas Young's 1800 Well Temperament" is an
authentic tuning for old Jewish music.  Old Jewish musicians didn't
have such nice electronic tuners to help them, for one thing.  About
the only thing I can be sure of is they did NOT tune in equal temperament
until sometime after 1910 or so, and then only if they were tuning to
a professionally tuned piano.

Roger "Just say NO to the Twelth Root of Two!" Reid

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