Page 74 - Glasbenopedagoški zbornik Akademije za glasbo, letnik 20, zvezek 40 ◆ The Journal of Music Education of the Academy of Music in Ljubljana, volume 20, issue 40

VERTICALITY AND HORIZONTALITY: MUSICAL ELEMENTS
glasbenopedagoški zbornik ◆ letnik/volume 20 ◆ številka/number 40
IN THE MUSICAL SPACE

Philosophical speculation on the nature of space in general has a long and il-
lustrious history in Western thought, and ideas about musical space have a deep
and abiding place within that tradition. Whether we are aware of it or not, the
concept of space is ever-present in the world of music, understood either in
the manner of Plato as a ‘container for objects located within it’ (Casey, 1996,
pp. 13–52), Stockhausen’s understanding of space as the direction from which
sounds originate (Stockhausen, 1996), or as an abstract concept of emptiness
that can be represented by a two- or three-dimensional space.
Discussions about the ‘placement’ of musical elements in a two-dimensi-
onal space and their interaction is not novel. The idea that physical space cor-
relates with musical structure (musical space) is found in Helmholtz (1865).
Wagner embedded instances of horizontal-vertical into his Tristan Prelude
(Forte, 1988); Schoenberg, in his lecture ‘Composition with Twelve Tones’,
presented his ‘law’ of a unified musical space in which the horizontal and verti-
cal presentation of ideas are equivalent; Scriabin considered melody to be har-
mony in horizontal form and harmony to be melody in vertical form (Bowers,
1969).
Reybrouck proposes two levels which can be distinguished in a musical
space: the level of pitch and the level of time, both defined as continua, ‘the pi-
tch continuum and the time continuum’ (Reybrouck, 1998, p. 63). Both verti-
cality and horizontality are regarded as fundamental musical characteristics in
Chomiński’s (1968) and Rosch’s research (1975, 1978).
Chomiński (1968) equates verticality and horizontality with harmony
and melody, respectively. However, in relation to the analysis of auditory sequ-
ences, he states that verticality/horizontality is a cognitive term rather than a
structural one. Therefore, in order to comprehend the functions of verticality
and horizontality in music, we must first investigate these characteristics as co-
gnitive phenomena. After recognizing them as auditory objects, we can perce-
ive their structural properties.
Rosch describes verticality and horizontality as a fundamental (music)
‘category’, i.e. the collection of objects that are regarded as equivalent (Rosch,
1978, p. 4). Horizontality refers to the dispersion of distinct examples within
the same unit, such that the category remains recognizable regardless of the de-
gree of deviation from the model. Verticality identifies the relationships betwe-
en categories, which leads to the notion of a hierarchy.
Interestingly, only melody and harmony, as musical elements on a higher
organizational level, are ‘placed’ in the musical space: harmony in the vertical
and melody in the horizontal plane, whereas the contribution of musical ele-

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