[Smt-talk] Smt-talk Digest, Vol 43, Issue 2

Richard Cohn richard.cohn at yale.edu
Thu Aug 2 07:02:34 PDT 2012

In response to Thomas Noll's point (copied below): in the opening pages of
Studies in the Origins of Harmonic Tonality, Dahlhaus traces a basic
duality between chord-based (Riemann) and scale-based (Fétis) theories of
tonality. This basic duality manifests as a directional duality in pitch
space. From the scalar standpoint,
a transposition up by a perfect fifth is a rising motion: F "voice leads"
to F# (in Tymoczko's generalized conception of voice leading). From the
chordal standpoint, a transposition up by perfect fifth is a falling
motion: C voice leads to B, and E voice leads to D. It is worth reflecting
on why both transpositions involve right-ward motion on the Tonnetz.

--Rick Cohn

Message: 1
Date: Wed, 1 Aug 2012 15:08:37 +0200
From: Thomas Noll <noll at cs.tu-berlin.de>
To: Nicolas Mee?s <nicolas.meeus at paris-sorbonne.fr>
Cc: smt-talk at lists.societymusictheory.org
Subject: Re: [Smt-talk] Gravity (Was: Car names)
Message-ID: <7EAEB86B-3481-4552-A715-2F0683FA009E at cs.tu-berlin.de>
Content-Type: text/plain; charset="windows-1252"

If we assume a directional markedness in the pitch height dimension (e.g.
downwards being unmarked) we might assume an analogous markedness along the
line of fifths (e.g. flatward being unmarked). Such an assumption implies
an interesting question: How do the two kinds of markedness interrelate?
Jacques Handschin argues in favor of an affinity between ascending pitch
height and sharpward oriented fifths. That same type of affinity would then
hold between descending pitch and flatward oriented fifths. This affinity
is contrapuntally supported by the ultimate progression between tenor and
bass in the cadence (as well as in the Ursatz). But for modal tone
relations Handschin's assumption might nevertheless be wrong. There are
good mathematical reasons to postulate that the combination between
ascending pitch and flatward oriented fifths is the unmarked one.
Thomas Noll
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