"Paths of Harmony" in the First Movement of Brahms's Cello Sonata in E minor, Op. 38

Bernstein, David W.

"The paths of harmony are tortuous," wrote Arnold Schoenberg in his
manuscript on the musical idea. They lead in all directions, approaching a starting point and leaving it again and again, leading astray, as they lend to a different point a momentary meaning that they soon take back again, producing climaxes that they know how to exceed, calling forth gigantic waves that ebb without coming to a standstill. Nevertheless, this seemingly
random progress is based on a profound meaning that can be
easily verified in music governed by tonality". (1995:309-11)
These words aptly describe Schoenberg's dynamic model of tonality. Harmony
creates states of rest and unrest-conditions which Schoenberg described
as "centrifugal" and "centripetal" tendencies. He defined these
relationships in terms of "distances" from the tonic, which he classified
and graphically represented by the "chart of the regions" in Structural Functions
of Harmony (1954:20,30,68-69). Schoenberg conceived of musical space in terms of two or more dimensions in which "musical ideas are presented as a unit." Tonal function
is multi-dimensional: pitches (i.e., scale-degrees), as well as chords and
regions have either centripetal or centrifugal tendencies. They create states
of rest or unrest, by either establishing the tonic region or undermining it.
Schoenberg did not consider motivic processes as separate from harmony
and large-scale tonal form, since a given motive implies certain tonal relationships.



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Columbia University
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November 5, 2014