Page 75 - 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

ments on a lower organizational level to the ‘construction’ of the musical spa-
ce is not explicitly outlined.
Should pitch be placed in a horizontal or vertical plane? What about dura-
tion? Moreover, is verticality and horizontality sufficient to define the musical
space if colour and loudness are ‘filling’ this space in a third dimension – ‘de-
pth’ – as postulated by Marks (1978), McDermott (1972), and Morgan (1980)?
Kokkonen (1988) argues that ‘every generation of composers, every single
composer, has been forced to address the problem of how to combine the ver-
tical and horizontal elements of music, either deliberately or unconsciously.’
11
Interestingly, he is aware that each composer gives more attention to certain
musical elements than others, but that a satisfactory balance between the ‘ho-
rizontal’ and ‘vertical’ dimensions can only be achieved if all primary musical
elements are included.
Nikolsky states that musical elements are not abstract auditory signals but Lorena Mihelač ◆ FROM THE CONCEPTUALIZATION TO THE FORMALIZATION OF MUSICAL ELEMENTS
rather spatial constructs on a three-dimensional plane (time/pitch/(sonic) tex-
ture) that imply fictitious movement whenever tones are bonded together by
tonal tension. The construction of quasi-spatial interactions between musical
components (elements) is a fundamental aspect of music, and takes its ‘cues’
from the relationships that exist between physical items. Nikolsky suggests
that musical elements are constructing a musical space which is defined by ver-
tical and horizontal axes and is virtual, as it exists only in the listener’s mind.
The latter does not mean that musical space is subjective in the sense that each
listener perceives tonal tension arbitrarily (Nikolsky 2015).
McDermott sees the musical space as a ‘conceptual tool’, a structure that
is formed and shaped by the sounds that make up a piece of music as well as by
the manner in which we organize and make sense of these sounds. The (musi-
cal) space is extraordinarily complex, and its components (pitch, colour, dyna-
mic, duration, every rest, group of tones, etc.) contribute to it in substantial or
insignificant ways, not as independent ‘building blocks’ but as intricately inter-
connected entities (McDermott, 1972, pp. 489–491).
This is consistent with the viewpoints outlined in the study by Prince et al.
(2009) and Mihelač and Povh (2020), which suggest that musical elements are
never found in isolation; rather, they continually interact (more or less) with
one another in the ‘musical space’, either in a vertical plane, when the relati-
onships between notes are presented simultaneously, or in a horizontal plane
when notes are presented sequentially.
The musical space is referred to as ‘sound space’ by Kaper and Tipei (1999),
a multidimensional vector space whose elements are functions of numerous vari-
ables. After assigning values to variables, the position and perceived qualities of
an ‘object’ (musical element) are completely determined in sound space. In the

11 Kokkonen mentions only four ‘musical elements’ (rhythm, melody, harmony, and tone),
which include concepts such as form, and polyphonic or homophonic construction.

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