source file: mills2.txt Date: Tue, 4 Mar 1997 07:22:48 -0800 Subject: Re: Schenker and tuning From: Daniel Wolf Rick wrote: '' Now, to which degree does the Schenkerian I-V-I "Ursatz" analyzed out of "tonal" music afect choice of tuning? Maybe someone more familiar with this kind of lingo can speak on that. For instance, I want to know, does the V_I dominant-tonic cadence require a certain tuning for proper performance?'' Schenker himself wrote precious little that was useful about intonation and - a contemporary of Schoenberg and Hauer - was active in a Vienna that was solidly committed to equal temperament (listen to any recording by Kolisch). As the ''Ursatz'' is supposed to be a simple cadence prolonged over the course of an entire movement, the essential intonational quality would be that the tonic chord is identical at the begining and ending of the movement. So, comma slipping is presumably out of the question. All the pitches between the initial and final chord are derived by scalar infills of the tones of this chord, but such infills seems not to be essentially affected by intonation, i.e. if the fourth degree is sometime represented by the subdominant and other times by the seventh of the dominant. (Heinz Bohlen has proposed a model of scale building through an analogous infill). Schenker's methods of prologation are indeed based upon classical species counterpoint, but the rules of counterpoint, with their clear relationship to tuning, are portable to an ET environment with no loss of coherence (indeed the compounding of acoustical puns - the fourth degree is one example - tends to strengthen rules about interval restrictions). What would be very interesting would be to take one of Schenker's graphic analyses and to construct a tuning for the piece based up projecting the simplest rational interpretations at each stage of prolongation and elaboration. Schenker's treatment of the minor tonic triad - as a kind of ''clouded'' Major triad - is, in the end, a matter of taste. I recall doing a layered Schenker-style analysis of a small Schumann _Papillion_ in f minor as an undergrad, and the most convincing _Urlinie_ that I could hear was an _ascending_ phrygian line - the inversion of the expected descending Major scale - and the basic harmonic motion was inverted as well. But then again, Schenker viewed some Schumann as already past the acceptable edge of tonal practice. Received: from ns.ezh.nl [137.174.112.59] by vbv40.ezh.nl with SMTP-OpenVMS via TCP/IP; Tue, 4 Mar 1997 17:26 +0100 Received: by ns.ezh.nl; (5.65v3.2/1.3/10May95) id AA05876; Tue, 4 Mar 1997 17:26:30 +0100 Received: from ella.mills.edu by ns (smtpxd); id XA05861 Received: from by ella.mills.edu via SMTP (940816.SGI.8.6.9/930416.SGI) id IAA23567; Tue, 4 Mar 1997 08:21:30 -0800 Date: Tue, 4 Mar 1997 08:21:30 -0800 Message-Id: <331C4C79.5128@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