source file: mills2.txt Date: Mon, 3 Mar 1997 04:02:31 -0800 Subject: Re: Beethoven C# and Db From: kollos@cavehill.dnet.co.uk (Jonathan Walker) Will Grant wrote: > > I don't know the reference here, but I know from personal > experience that C# and Db can be quite different. WHAT! > It would > be, of course, impossible to tune them both on the same piano > at the same time, but that doesn't make them equivalent, > except within the artificialities of ET. HUH? Either: 1. C# and Db are distinct pitches, as on a split-keyed instrument intended for meantone tunings, or else 2. the distinction is purely notational, as on any 12-per octave keyboard, whether tuned to 12TET or to a well-tempered scheme. In this case, the distinction can either be 2a. functional (e.g. a C#, and not a Db, as the leading note to D major or minor) 2b. or arbitrary (e.g. Bach's choice of Eb minor for the eighth Prelude and Fugue of Book I, but D# minor for the eighth Prelude and Fugue of Book II). Such arbitrary choices can be made on the basis of various equally arbitrary associations, such as sharps brilliance and flats mellowness etc., but they have no physical basis whatsoever (do I really need to say this?) and such associations will in any case vary from listener to listener. > 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. No! As I said above, the distinction only makes sense on instruments which allow for more than 12 pitch-classes per octave. Well-temperaments were given their name to distinguish them from other temperaments -- namely the meantone family -- which did not allow the playing of all keys, or limitless modulation on a 12-per-octave keyboard. On a well-tempered instrument, there is no acoustical difference between the keys of Db and C# (whatever different associations the different notation might evoke for Will Grant); on a meantone instrument, the issue is more complicated: taking the lower rank of keys to be C, D, E, F, G, A, B, then if there is only one upper rank key between C and D, it is of course not arbitrary whether that key is C# or Db, but a matter of intervallic relations between this key and those of the lower rank (it was always in practice C#, simply because this was needed much more often, as a ficta leading-note). However, to have two acoustically distinct scales of C# and Db on a meantone keyboard would require no less than 19 keys per octave (and still more if you wanted to play any pieces in these keys). Anyone who holds that C# major and Db major can be distinguished, on grounds that are neither acoustic, nor associational has fallen prey to terminal mystificatory impulses. If Will Grant is happy to accept the associational explanation, I have no argument. Otherwise ... (there's no arguing over mystical beliefs.) -- Jonathan Walker Queen's University Belfast mailto:kollos@cavehill.dnet.co.uk http://www.music.qub.ac.uk/~walker/ Received: from ns.ezh.nl [137.174.112.59] by vbv40.ezh.nl with SMTP-OpenVMS via TCP/IP; Mon, 3 Mar 1997 13:04 +0100 Received: by ns.ezh.nl; (5.65v3.2/1.3/10May95) id AA02796; Mon, 3 Mar 1997 13:04:36 +0100 Received: from ella.mills.edu by ns (smtpxd); id XA02804 Received: from by ella.mills.edu via SMTP (940816.SGI.8.6.9/930416.SGI) id EAA19368; Mon, 3 Mar 1997 04:02:51 -0800 Date: Mon, 3 Mar 1997 04:02:51 -0800 Message-Id: <331ABE94.602B@cavehill.dnet.co.uk> Errors-To: madole@mills.edu Reply-To: tuning@ella.mills.edu Originator: tuning@eartha.mills.edu Sender: tuning@ella.mills.edu