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School of Music Federal University of Rio de Janeiro Brazil

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School of Music Federal University of Rio de Janeiro Brazil
The Musical Contour Theory (Morris 1993) is constructed from abstractions of levels,
ordered from zero (lowest level) up to n-1 (where n is the number of different levels in the
structure), and assessing the relations between the levels.
The transposal of such abstraction to field of musical texture can formalize the
movements of textural complexity, allowing the measurement and the comparison
between different textural configurations. This proposal is called here as Textural
Contour.
The methodological tools and concepts provided by the Partitional Analysis (PA) by
Gentil-Nunes (2009) can handle textural organization using numeric representations
(read as integer partitions) that express the relations of concurrent musical components
in the texture. PA is a new analytical tool for the study of musical texture considering the
approximation of Wallace Berry’s (1976) proposal and the Theory of Integer Partitions,
building a partially ordered organization that relates partitions by its transformational
process in an exhaustive taxonomy that encompasses all partitions from 1 to a "predefined number using mainly the inclusion relation.
The flute theme of Debussy’s Prélude draws a linear and flowing waveform, with a
predominance of movements between adjacent melodic levels in the contour. The last
part of the theme presents a sudden sectioning caused by the biggest gap between
sequential levels (8 and 1), just after the melodic apex (level 9), followed by a sense of
relaxation.
Textural Contour of the first 10 measures of Debussy’s Prélude shows different treatment
compared to the melody. Textural motion concerns predominance of non-adjacent
movements between levels, with only one adjacent movement (from level 14 and 15).
The alternation of conjunctions and gaps between levels implies textural complexity, with
abrupt changes between the textural configurations. This is also reflected in the
recurrence of levels, where most of the levels are articulated only once.
Figure 2: Melodic contour of flute theme from Debussy’s Prélude à l'après-midi d'un
Faune.
Figure 1: Application of contour < 1 2 0 > to different musical structures.
Textural Contour is developed from the ranking of the partitions ordered from simplest to
the most complex, therefore establishing a textural progression curve. The partitions form
a partially ordered set, which implies that its ranking is not totally linear and some
partitions are incomparable. Incomparable partitions receive the same level in Textural
Contour.
The ability to compare and relate two distinct textural progression to a single contour is
an important feature provided by Textural Contour. Textural Contour, as an vectorial
abstraction, not only express textural behavior, but also allows the objective connection of
other musical parameters (such melody and rhythm) with textural progression and with
the recurrence of musical gestures (see more about Textural Contour in: Moreira 2013 &
2015; Moreira and Gentil-Nunes 2014) .
Figure 3: Textural Contour of first ten measures from Debussy’s Prélude à l'après-midi
d'un Faune.
The analyzed section presents 19 different partitions,
with 2 groups, each one with 2 incomparable partitions
(indicated by brackets), totalizing 17 different levels in
only 10 measures, leading to a more complex textural
progression.
Both melodic and Textural Contour present expansion
and relaxation curves (waveform), but while the melodic
contour performs descending curves toward the lowest
level (zero), the Textural Contour performs upward
curves toward the highest level (level 16).
The differences between the textural treatment and the melodic contour suggest an
compensatory equilibrium. The melody, with a chromatic and linear movement and a
tonal center well defined, articulated by a simple and metrical rhythm, leads to a
simplification of the melodic flow. Textural progression, on the other side, is more
complex, with many abrupt changes of textural configuration.
The investigation of the relations between the flute theme and the overall textural
progression, including other parameters are subject to future research
BERRY, W.:. Structural functions in music. Nova
Iorque: Dover Publications, 1976.
GENTIL-NUNES, P.: Análise particional: uma
mediação entre análise textural e a teoria das
partições. Thesis (Ph.D in Music). Centro de
Letras e Artes, Universidade Federal do
Estado do Rio de Janeiro. Rio de Janeiro
(2009).
MOREIRA, D.: Contornos particionais: aplicações
metodológicas na Introdução da Sagração da
Primavera de Igor Stravinsky. Anais do 12º
Colóquio de Pesquisa do Programa de PósGraduação da Escola de Música da UFRJ.
Rio de Janeiro: UFRJ (2013).
MOREIRA, D.:. Textural Contour: a Proposal for
Textural Hierarchy through the Ranking of
Partitions lexset. In: International Congress on
Music and Mathematics. Puerto Vallarta,
México (2015).
MOREIRA,
D.
and
GENTIL-NUNES, P.:
Contornos musicais e os operadores
particionais: uma ferramenta computacional
para o planejamento textural. In: Congresso
da Associação Nacional de Pesquisa e Pósgraduação em Música (ANPPOM), XXIV.
Anais… São Paulo: UNESP (2014).
MORRIS, R.:. New directions in the theory and
analysis of musical contour. Music Theory
Spectrum, vol. 15, p. 205-28 (1993).
Table 1: Levels and Partitions of first ten
measures from Debussy’s Prélude à
l'après-midi d'un Faune.
School of Music
Federal University of Rio de Janeiro
Brazil
Coordenação de
Aperfeiçoamento de
Pessoal de Nível
Superior
Research group
www.musmat.org
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