alternations of tensions and relaxations;that is,interaction of the cogni-
tive organization of pitch and duration groupings on the one hand,and
of phrases of stability and instability on the other,of which the succes-
sion and ordering are of both cognitive and affective nature.In fact,two
essential notions define reductions of temporal webs in the GTTM:struc-
tural beginning and structural conclusion (or cadence) articulate the
structure of groupings at the phrase level.Lerdahl and Jackendoff indi-
cated that the movement of a phrase can be defined as a path between
these two structural points,which themselves are stable events.Con-
cerning these prolongational reductions,the experience of stability con-
sists of a succession of tension and relaxation events that give the listener
the feeling of a conclusion;that is,of a psychic release,a resolution of
the tension that preceded it.Interaction between the two levels of orga-
nization in tonal music is thus psychologically clear,and structural
stability coincides with dynamic and emotional stability.
A final condition,prior to the other two,is that auditory events that
are perceptively salient are also stable.In the GTTM,rules concerning
salience indicate that an event is salient not only when it is in a strong
metric or tonal position (the preceding conditions),but also when it is
in an extreme register,when it has a remarkable timbre or a color,or
when it acquires a particular formal significance (e.g.,a thematic one).
We thus define here a correspondence between perceptual and structural
stability that constitutes the fundamental hypothesis of the GTTM as a
model of musical competence.Reductions are both a pertinent structural
description of the underlying schema at any tonal musical surface and a
model of the listener’s mental operations for capturing the organic unity
of the surface structure and storing its information in memory.The tonal
system is thus based on a triple correspondence among music’s emo-
tional dynamics,its internal structure (grammar),and the mental opera-
tions that allow encoding and decoding of the perceptual surface in
memory and the subject’s perception through an interplay between
complex intuitions and anticipations.
In atonal music,this triple correspondence does not exist,and the
notion of functional hierarchy is in question,since the musical space is
“flat”(functionally equivalent pitches,syntactically equivalent conso-
nances and dissonances).From an analysis of Schoenberg’s pieces,
Lerdahl (1989) formulated a new proposal:in atonal music,prolongation
structures are structures of the hierarchical organization of salience.On
the surface,they are those of auditory events that immediately capture
the listener’s attention;on a more abstract level,they are those of motivic
relations and of parallelisms in structure.In other words,to the extent
that we cannot define stability conditions,conditions of contextual or rel-
ative salience are those that organize webs and prolongational structures456 Michel Imberty