“A
Symmetrical Property of Rotational Arrays in Stravinskyís Late Music”
“Rhythm
and Timing in the Two Versions of Berio's Sequenza I for Flute Solo: Psychological
and Musical Differences in Performance” “Sectional
Tonality in Pop-Rock Music” "Dementia
and Voice Leading in 'The Sentry,' from Peter Maxwell Davies' Eight Songs for
a Mad King
This presentation examines symmetry based on
the occurrences of pitch classes in hexachordal rotational arrays. The symmetry
directly corresponds to the interval vector of the generating hexachord. Rotational
arrays are examined using algebraic equations and a representation of concentric
circles. Stravinsky projects this symmetry in the following two excerpts: Requiem
Canticles, Exaudi (mm. 76‚80) and A Sermon, A Narrative, and A Prayer (mm. 75‚85).
In these excerpts, the symmetry is emphasized by duration or orchestration.
This paper is an investigation of rhythm/timing issues posed by the two different
editions (1958 and 1992) of Luciano Berio's Sequenza I for flute solo. The first
edition was notated proportionally (with hash marks to indicate timing), while
the later one translates the hash marks into precise rhythmic notation. Our initial
hypothesis was that the new notation results in significant differences in performances.
To test this, we used computer programs to analyze precise timings from ten professional
recordings of the piece. We discovered that there are important differences in
timing between those flutists who used the old edition and those who used the
new one. There were also differences in "musical" factors, such as phrasing,
motivic grouping, articulation, and accentuation.
The presentation consists of three parts: (1) a comparison of the rhythm/pitch
differences between the notation of the editions and discussion of the psychological
differences in playing (and teaching) from the two different scores; this discussion
is supported by interviews with professional flutists who have performed and/or
taught the piece; (2) graphic presentation of the performance data, with some
specific examples of similar and different interpretations; and (3) summary of
the rhythmic and "musical" differences between performances of the early
and late versions.
The aim of our study is not
so much to prepare a performance through analysis as it is to analyze actual performances.
However, the conclusions provide insights into the performance tradition of Sequenza
I and de-mystify the real musical differences between Berio's "free"
and "controlled" notational systems.
Pop-rock
songs that avoid tonal closure typically use one of three procedures. The first
category involves what Everett (1997) and Ricci (2000) call the “pump-up,”
a modulation by half- or whole-step at the end of a song. A second category involves
postponing tonal resolution until the opening harmony of the following song, e.g.
“Because” by the Beatles (Everett 1999, 259). A third category, which
I call sectional tonality, has received less attention from pop-rock scholars.
Everett (2000, 311-312) describes sectional tonality as follows: “Some songs
alternate between unrelated key areas, each expanded in entire sections, creating
a nontonal whole. . . . Sections revolve around separate tonics and closure is
not provided by any overall directed voice leading . . . Schenkerian analysis
would be useful in defining events within sections of such songs, but cannot suggest
organic wholes.” Everett is silent about an important issue: Without insisting
on any sort of closure, what types of closure might sectionally tonal songs employ
in lieu of tonal closure?
In this paper I demonstrate
ways in which non-pitch factors such as ritardandi, hypermeter, and clock-time
duration imbue sectionally tonal songs with a firm, though different, sense of
closure. In addition, I show that tonal, harmonic, and rhythmic motives impart
sectionally tonal songs with a degree of coherence strong enough to offset the
absence of tonal closure; this echoes Anson-Cartwright's (2001) distinction between
closure and coherence. Finally, I revisit analyses of the Beatles song “Lucy
in the Sky with Diamonds” by Everett (1999, 104-105) and Moore (1997, 32-33),
which Everett and Moore interpret as monotonal but I interpret as sectionally
tonal.
Previous representative analyses
of Eight Songs for a Mad King in general concentrate on the ìmadî nature
of the music and, in so doing, justify musical structure almost exclusively in
terms of dramatic needs. Departing from intuitive aspects of the musical grammaródensity,
cadential gestures, motivic/intervallic identityóand extending analytical strategies
of Jonathan Harvey, David Roberts, and Peter Owens, I examine harmonic progressions
in the first song of the cycle that suggest a systematic approach to post-tonal
voice leading. In these instances, register and harmonic rhythm are the only features
of the musical surface that recall traditional phrase structure; individual sets
seem sufficiently different from one another to discourage any kind of consistent
voice-leading, but, on the other hand, their juxtaposition suggests a gradation
of change, a certain order within a relatively structuredócontrolledótransformation.
Following this intuition, and since the larger sets share subsets such as [0,1,2,5]
and [0,1,2], the harmonic occurrences are hence rethought as the expression of
simultaneities arising from the combination of smaller subsets. The resulting
tricords and dyads, interlocked in a kind of contrapuntal design, generate their
own independent transformational and quasi-transformational paths. Building large
sets by combining smaller ones is an integrative way to generate pitch material;
an approach complementary of the reductive process called ìsieving.î By breaking
larger sets into contrapuntal subsets my analysis unveils a purely musical coherence,
one that is surprisingly independent from any dramatic consideration.