Schenker and tuning

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.

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