[Fwd: C# and Db:I said KEYS, not PITCHES]

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I posted this to the list on Monday, but never received my copy from the
Tuning list server, so I'll assume no-one else received it. Apologies if
you've seen it before, or if you think it was hardly worth posting in
the first place.
--
Jonathan Walker
Queen's University Belfast
mailto:kollos@cavehill.dnet.co.uk
http://www.music.qub.ac.uk/~walker/

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From: kollos@cavehill.dnet.co.uk (Jonathan Walker)
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Subject: Re: C# and Db:I said KEYS, not PITCHES
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Just to avoid any further possible misunderstandings on this matter,
I'll repeat what I said in an earlier message: within the tuning
environments of well-temperament and 12TET, while there is of course no
acoustic distinction between the pitches C# and Db, this does not
prevent us from making functional distinctions in our notational system.
But this has nothing to do with the matter under discussion. Functional
distinctions only exist within a relational system. Now if Beethoven had
been speaking of pitches within a piece, or even of keys arrived at by
means of modulation within a piece, then such a system would have
provided the context for talk of functional distinctions. But Beethoven
was talking about Db major and C# major in vacuo, as the tonics of a
piece, and therefore outside such relational systems, and so not
amenable to functional distinctions. What else is left if we cannot
distinguish the keys on grounds of acoustic difference (as is the case
in WT or 12TET), nor on the grounds of notational-functional
distinctions? Again, I offered the other possibility in previous
messages -- arbitrary associations of keys with various pieces,
instruments etc (I'll put synaesthesia in this category too: while
individuals, such as Messiaen, feel their associations to be necessary,
each synaesthesiac differs). Beethoven's statement would seem to fall
firmly into this last category.

So if not acoustic differences, nor notational-functional differences,
nor arbitrary associations, then what?

Obfuscation, nothing else.

By the way, if anyone can locate the Beethoven quotation, I'd be
grateful.
--
Jonathan Walker
Queen's University Belfast
mailto:kollos@cavehill.dnet.co.uk
http://www.music.qub.ac.uk/~walker/


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From: PAULE

>Following up Paul Erlich's suggestion, I have computed
>the LST SQR positive tunings with 7/6 and 5/3 in addition
>to 3/2, 5/4, and 7/4.

I would also include 7/5. Also, while you are taking intervals as far
removed as 15 steps on the circle of fifths, I restricted myself to a
diatonic scale in obtaining my results.

-Paul Erlich


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