Neural Correlates of Processing Syntax in Music and ... - PubMan

Music Perception 11
keys related by the cycle of fifths and parallel or relative major/minor relationships; see
Figure 2-1). 3
Figure 2-1 Representation of key maps (according to Krumhansl, 1990), either unfolded (left) or on the
surface of a torus (right). The matching of the opposite edges of the unfolded map will result
in the toroidal representation. Circle of fifths for major (red) and minor keys (blue), each
wrapping the torus three times. Every major key is flanked by its relative (e.g., C major – a
minor) and its parallel minor (e.g., C major – c minor).
Specific chord types (e.g., major, minor, and diminished) appear at certain positions
within a musical scale, indicating the keys in which they appear. The degree of association
(i.e., which chord function they have in a particular key) reflects their different
functional roles in the hierarchy and supports the simultaneous interpretation of chords
in their various harmonic roles. Krumhansl and Kessler (1982) suggested that listeners
process the multiple harmonic functions of the chords and integrate this information
which gives rise to a sense of key.
Deutsch and Feroe (1981) proposed a hierarchical network involved in the representation
of pitch sequences. They assumed that elements are organized as structural units in
accordance with Gestalt laws (such as proximity and good continuation) at each level of
the hierarchy. 4 The hierarchical representation can be described formally using alphabets
(such as “chromatic scale”, “diatonic scale”, and “triad”), elementary operators
(“same”, “next”, “predecessor”, etc.), and sequence operators (e.g., “prime” [creating a
compound of two sequences], “retrograde”, and “inversion”). Alphabets rely on a small
number of highly overlearned structures that act on each other in a hierarchical fashion
(e.g., the tonic is contained in the triad which is based on notes from the diatonic scale
which is part of the chromatic scale). This allows for the production of melodic segments
of enormous variety with a very small set of basic structures. The elementary and
3
4
There are also other geometrical approximations of musical pitch structure, e.g., a conical representation
(with the tonic at the apex and the less related tones at different positions in the frustrum) proposed by
Krumhansl (1979) or a helical representation (with one dimension representing the position on the cycle
of fifths and another dimension for the tone height) proposed by Shepard (1982).
This theory is related to Schenker’s (1956) notion of a mapping from the ornamented musical surface to a
hierarchically organized set of reductions.