C# and Db:I said KEYS, not PITCHES

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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William Sethares wrote:

>A few years ago, Tom Staley and I wrote an article called "Sounds of
>Crystals" in Experimental Musical Instruments (EMI) that did
>something very similar (ref. below). We looked at x-ray diffraction
>patterns (spectra) and mapped them into the audio spectra. Many of
>the resulting sounds were exceedingly complex (*very* many
>nonharmonic partials), but there were some real standouts. One of
>our favorites was the sound of the morphine crystal, which we used
>for a piece titled "Duet for Morphine and Crystal" that appeared in
>the EMI compilation cassette that year.

Neat!

William, can you please explain how you determined what frequencies to
play at what time. I imagine that the crystal output (slowed down) is a
bit like sitting on the keyboard and staying there so you need a way to
seperate the notes.

If any of you composer types want data on this sort of thing then I have
the CRC handbook which has 3600 pages of physical and chemical
constants. It includes the spectra of all elements and heaps of other
similar stuff. I also have a scanner that can do OCR (although it is
behaving weirdly at present) which allows lots of numbers to be put in
with little effort and good accuracy.

*** All my posts to the list seem to suffer from numbers being inserted
after certain characters. For example an equal sign "=" gets the
treatment as did some recent capital f's "F". This does not appear to
happen to other people's posts and it doesn't happen to me on any other
list or in usenet or email. Does anyone have a clue about this? ***

-- Ray Tomes -- rtomes@kcbbs.gen.nz -- Harmonics Theory --
http://www.kcbbs.gen.nz/users/rtomes/rt-home.htm

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