“Pacing
Transformations and Metrical Change in Brahmsís Violin Sonatas”
This
paper explores some of the ways in which the ěpace,î the rate at which events
occur, fluctuates during changes of meter in passages from Brahmsís violin sonatas,
Opp. 78 and 100. An account of pacing builds on descriptions of meter as composite
layers of pulse by describing how metrical units at given metrical levels flow
through time, both speeding up and slowing down. Changes of meter, often described
in terms of ěmetrical dissonance,î can also be described as transformations operating
through time. A change of meter involves a change of pace, either an acceleration
or a deceleration, at one or more metrical levels. Hemiolas, for instance, can
open up multiple paths that a stream of beats may take. While acknowledging that
several paths may be possible, this paper contends that the pacing of harmonic
and melodic units helps channel a stream of metrical units toward a particular
path. When the pace of harmonic and melodic events accelerates or decelerates
at a particular level, the associated metrical level is likely to follow a similar
course.
“The
Hemiolic Cycle and Metric Dissonance in Brahms's Cello Sonata in F, op. 99”
Both
Schoenberg and Berg have argued that a direct consequence of rapid motivic development
in the pitch domain is a highly dissonant metric environment. In this view, global
patterns of metric consonance and dissonance depend on the intricacies of tonal
developing variation. While this interpretation sheds light on the relations between
pitch and metric structures in many tonal works, I contend that in another mode
of composition metric dissonances develop independently from tonal processes.
Instead, large-scale metric progressions grow out of a basic metric idea, or,
in Schoenbergian terms, a metric Grundgestalt.
A case for study is the first movement of Brahms's Cello Sonata in F major, Op.
99. In this movement, successions of metric states follow a cyclical procedure
referred to as the hemiolic cycle. The cycle is first defined as the sequence
of beat positions (in the notated meter) of accents that project the hemiola (i.e.,
<1-3-2-1>), and subsequently expanded, using transformational tools, to
provide the blueprint of metric progressions within subphrases, phrases, and formal
sections. Further, the cycle communicates closely with important tonal events,
as revealed by a Schenkerian analysis of the tonal structure. The penetration
of the cycle into different formal levels betrays its role as a sort of basic
temporal shape of the metrically complex movement.
“Fluidities
of Phrase and Form in the “Intermezzo” from Brahms’s First Symphony”
Of the four unique movements that fulfill the function of the Scherzo and Trio
in Brahms’s symphonies, that of the First Symphony, its third movement, resembles
a lyric Intermezzo in its apparently ternary form. Taxonomy aside, Brahms has
infused this more traditionally segmented form with the fluidity and developmental
impetus associated with sonata movements, to the extent that the entire movement
seems almost to fall within a single breath.
Schenker’s
enigmatic analysis of the opening five-bar unit reveals a subtle contrapuntal
displacement and fluid phrase expansion that will be seen to inform the entire
movement. This expansion is implicated in its highly original form. The opening
melody recurs as an ever-expanding antecedent but is not tonally closed until
the end of the movement and flows without break in an F-minor theme, which is
also left open and never repeated. This unique theme will be seen to result from
a motive enlargement of the opening bass line. The A section of the Intermezzo
remains suspended on a dominant half cadence; the contrasting Trio is in the key
of flat III but sounds more as a flat VI enclosed within a prolonged E-flat, which
resumes its role as dominant in an even more emphatic half cadence in the transition
after the Trio. The Trio itself has special metric conflicts, also noted by Schenker,
that will be further discussed as enhancing its feeling of tonal contingency.
The sum total is an overall effect of a single fluidly expanding antecedent that
subsumes any contrasting episodes and awaits the close of the movement for resolution.
"Re-Considering
the Affinity Between Metric and Tonal Structure in Brahms's op. 76 no. 8"
The
relation between metric and tonal structures is a controversial discussion in
music theory. Brahms's music is well-known for both its metric and harmonic ambiguities.
According to David Lewin and Richard Cohn, Brahms's Capriccio, op. 76 no. 8, is
characterized by a deep affinity between metric and tonal processes. Both theorists
analyzed the first section of the piece and found different metrical states in
6/4, 3/2, and 12/8 that correspond to harmonic regions associated with tank, subdominant,
and dominant. Starting from this coincidence, they develop mathematical arguments
supporting a deep affinity between harmony and meter. We re-consider the study
of this relation from a different perspective using independent mathematical models,
namely Metric Analysis and the Spiral Array, that describe the metric and tonal
domains. Inner Metric Analysis investigates the metric structure expressed by
the notes independently of the notated bar lines, based on the active pulses of
the piece. When applied to the Capriccio the model detects the different metrical
states of 6/4, 3/2, and 12/8. The Spiral Array Model is a three-dimensional realization
of the tonnetz which embeds higher-;level tonal structures such as triads
and keys in its interior. When applied to the Capriccio, the model segments the
piece into tonally stable sections that correspond to Lewin's and Cohn's observation.
The comparison of the results of these models provides further evidence of what
Lewin and Cohn have proposed about a close relation between harmony and meter
in Brahms's op. 76 no. 8.