Belated thoughts on Bach

So I missed the big argument! Probably just as well, or I would spend
too much time making it even more argumentative.

Some more points. As has been pointed out, many Bach pieces use lots
of enharmonic alternatives. The musical reason for this is that they
use constant thematic material to modulate through a wide range of
keys. For example, the Art of Fugue uses A# in a dominant chord in the
key of B, even though the piece begins and ends in one flat.

Although 'wrong' meantone alternatives can be used as local colour if
they occur only for an instant, they won't be acceptable as major
components of the structure of a tonality - particularly when most of
the other tonalities in the piece sound quite normal. Consider that
Bach often transposes a passage into B minor which was in A minor
before. I don't think it would be acceptable for most of the parallel
passages to sound normal - *until* we get to the one which has a
'wrong' enharmonic note - which will stick out like the proverbial
sore thumb. The F# minor Toccata is another good example of this
'durchfuehrung' - taking the same musical idea through many keys -
which looms large in the WTC too.

There is even an early work which ends with a complete trip round the
cycle of fifths - a Fugue in D minor I think.

Next, consider that Bach ordered the pieces in the WTC in this way: C
c C# c# D d ... What sort of retuning would you have to do to go from
C to C minor? Then C minor to C sharp major (alias D flat major)? Then
to C sharp minor? Then to D major? If you were determined to use some
sort of meantone and wanted to play the book through in sequence,
you'd spend more time retuning than playing (at least 2 or 3 notes
have to be retuned each time!), and probably break most of the strings
in the process. Every step in retuning goes to the flatward side,
which means raising the notes by a comma or two.

Next, it was told of Bach that he could make distant modulations sound
as smooth as near modulations. How could this be the case, unless his
tuning (whatever it was on the day!) allowed distant modulations
without glaring differences in intonation?

Also, how can we make sense of the witness statement that Bach
introduced unique subtleties into his tuning, unless it was something
different from the well-known meantone or slightly modified meantone?

Without wishing to go too far into Bach's psychology, why would he
write a book called 'The Well-Tempered Keyboard' if he didn't have
some definite aim in mind and this aim differed from the usual
practice of the time? I think it's fairly clear that the usual
practice did *not* allow you to play in all 24 keys successfully.

For the Werckmeister advocates: what about Werckmeister V, a tuning
which he introduces later than III and specifically says is good for
music with a lot of accidentals? What about the instructions in a
chapter of Musikalische Temperatur (Von der Temperatur Insgemein) when
he says tune all the thirds as sharp as you can stand among the
naturals, with all the fifths 'a little bit flat', and proceed the
same way through the whole keyboard? What about when he calls the
Pythagorean major thirds 'very hard' - can we believe that three long
preludes and fugues were written by Bach to exploit the incessant
jangling of these big major thirds? Can you be satisfied with the
A-flat major Prelude and Fugue in Werckmeister III?

All these considerations leave *some* Werckmeister (maybe not III!),
equal, or some other circulating temp. standing. But equal can be
eliminated, firstly through Barnes' old article in Early Music showing
that Bach composed quite differently in different keys - secondly,
since would be the musical point of deploying exactly the same musical
material in different keys if there were no contrast in intonation
between the keys?

As to Neidhardt, we have to remember that he was a raw novice and
enthusiast of 12-ET in 1706 or whenever this tuning contest took
place. Don't judge his life's work by this youthful mishap.

Now... does this mean we know what Bach's tuning intention was in the
WTC? No, but it exposes some candidates as much less likely than others.

~~~T~~~

Hi Tom,

> But equal can be
> eliminated, firstly through Barnes' old article in Early Music
> showing that Bach composed quite differently in different keys -
> secondly, since would be the musical point of deploying exactly
> the same musical material in different keys if there were no
> contrast in intonation between the keys?

Hiya Tom,

I haven't read the Barnes article but I have read that absolute
pitch was considered to convey colors and emotions through the
time of Mozart, at least. Is that not correct?

It has been shown to my satisfaction that most people have some
degree of absolute pitch sensation, or at least memory. One
experiment had subjects sing modern popular songs and found that
more often than not, they got the key right.

-Carl

--- In tuning@yahoogroups.com, "Tom Dent" <stringph@g...> wrote:

> Also, how can we make sense of the witness statement that Bach
> introduced unique subtleties into his tuning, unless it was
something
> different from the well-known meantone or slightly modified
meantone?

I don't think anyone here is arguing otherwise. I think everyone is
in agreement that most of Bach's music requires a circulating well-
temperament (since he wasn't a split-key man like Handel). Did you
direct this toward someone specifically?

P.S. There's a well-known recording of the WTC that orders the pieces
according to the circle of fifths.

> secondly,
> since would be the musical point of deploying exactly the same
musical
> material in different keys if there were no contrast in intonation
> between the keys?

You could ask that of a jazz musician today, and yet they do do so.
There are many possible "points."

--- In tuning@yahoogroups.com, "Carl Lumma" <clumma@y...> wrote:

> It has been shown to my satisfaction that most people have
> some degree of absolute pitch sensation, or at least memory.
> One experiment had subjects sing modern popular songs and
> found that more often than not, they got the key right.

I've always claimed that i have excellent relative pitch
but not absolute pitch. However, your last statement rings
very true to me:

with my favorite Springsteen album _Born To Run_,
when "Night" ends and there's a long silence after it,
i hear in my mind the opening G-major chord of
"Backstreets" coming next, and sure enough, when
the song starts, what i heard in my head was exactly
the right pitch.

-monz
http://tonalsoft.com
Tonescape microtonal music software