source file: mills2.txt
Date: Mon, 10 Mar 1997 05:58:16 -0800

Subject: C# and Db:I said KEYS, not PITCHES

From: kollos@cavehill.dnet.co.uk (Jonathan Walker)

Gary Morrison wrote:
> 
>    I'm jumping into this conversation in mid-course, so I may well be
> missing the context.  If so, my apologies.

I'm afraid you are; but this isn't the only problem. 

> A previous writer, quoted by Gary Morrison, wrote:
> 
> "ergo, the distinction between C# and Db makes sense
> _only_ in well temperament. But of course, you can't
> set two different temperaments at once, at least not
> on a piano."

In what we earthlings call "well-temperament", there is no possible 
distinction between C# and Db -- everyone knows this on our planet. The 
well-tempered systems were specifically designed for a 12-note per 
octave keyboard; they were WELL-tempered specifically because they 
removed the wolf of the meantone temperaments, and this was by means of 
closing the "circle" of fifths. No closed temperament offering only 12 
pitch classes can possibly distinguish between and C# and Db -- this is 
a bland truism on planet earth.


Then Gary Morrison himself:

>    Welll...
> 
>    Certainly C# and Db are different in meantone temperaments and just
> intonation as well as in well temperaments.  And also in 17TET, 19TET 
> and 31TET as well.

Meantone, yup.

Just intonation, sure thing. Pythagorean too.

19TET and 31TET, if you treat them as closures of 1/3-comma and 
1/4-comma meantone, yessir. 17TET, I suppose, can also be regarded as 
the closure of a chain of fifths.

But well-temperament? NO! (in 72-point Gothic font)

What's going on here? Has someone just devised an all new well-tempered 
scheme for >12 pitch classes?

>    But even if they are tuned exactly the same as they are in 12TET or
> 24TET, the two notes are functionally different.  C# is nominally the
> leading tone in the key of D, and Db ... well, Db could be a number of
> formulations, like the seventh of a dominant seventh in the key of Ab, 
> or the root of a Neapolitan in C.
 
For the record, when I introduced this Beethoven example, I said that he 
was talking about KEYS and not single pitches. I was saying that 
Beethoven distinguished various keys, assigning them characteristics of 
their own, and that we might be tempted to guess that well-temperament 
was the main or sole cause of Beethoven's distinctions. But then I said 
that we cannot simply ignore one of his distinctions, namely between C# 
major and Db major; since this distinction cannot arise in any 
well-temperament, Beethoven's thinking must have been motivated, at 
least in part by less concrete considerations, such as the accumulated 
associations of certain keys with certain pieces, or the association of 
certain instruments with their most congenial keys, or relational 
associations depending on the difference between modulating in a 
flat-wards direction and in a sharp-wards direction. This is only a 
paraphrase of what I said in two earlier messages.

-- 
Jonathan Walker
Queen's University Belfast
mailto:kollos@cavehill.dnet.co.uk
http://www.music.qub.ac.uk/~walker/



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