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Quantitative analysis has been carried out
computing a distance measure between subjects.
To this end a symmetric matrix of distances
D
between couple of segmentations made by the
subjects has been computed for each excerpts,
according to the formula:
of a boundary between two lexical units. In other
cases, like the example shown in Figure 4 for
excerpt No. 3, different strategies can be applied
by subjects in defining the presence of a boundary
between lexical units. The fact that cluster analysis
did not highlight any particular group of subjects
suggests that subjects changed their strategies
according to the excerpt to be segmented, but no
trend can be highlighted.
These results show that melodic segmentation
is a complex task, and that the concept of lexical
unit is not well defined as it is for text where, at
least for most Western languages, the organization
of sentences in words, and the existence of clear
separators between them, allows for an easy com-
putation of indexing terms. It has to be considered
that the perceptual study has been carried out only
using melodic information, and results could be
different for other dimensions. For instance, the
segmentation of the harmony may take advantage,
at least for musicians and musicologists, by the
theory on chord progressions and cadences, while
the segmentation of rhythm may be carried out
considering that rhythmic patterns tend to repeat
almost exactly, allowing for an easier identifica-
tion and subsequent segmentation.
P
[
s
,
t
]
T
s
D
[
s
,
t
]
=
1
−
wi
with
th
P
[
s
,
t
]
=
a
⋅
a
t
2
2
P
[
s
,
s
]
+
P
[
t
,
t
]
Hence
D
[
s,t
]
=
0 means that judgments of
subjects
i
and
t
are perfectly equal and
D
[
s,t
]
=
1
means that judgments of subjects
s
and
t
do not
have any marker in common. Cluster analysis and
multidimensional scaling have been carried out
using the proposed distance function, highlighting
that the group of subjects was uniform, without
any cluster of subjects.
A feature of interest for application in the in-
formation retrieval domain is the typical length of
lexical units. The average length varied consider-
ably depending on the subject and on the excerpt.
Yet, no one of the subjects indicated a lexical unit
of unitary length. Furthermore, only two subjects
indicated lexical units of two notes length, while
for four subjects the minimum length of a lexi-
cal unit was three notes. The rest of the subjects
indicated a minimum length between four and
five notes. On the other hand, subjects did not
show the same agreement regarding the maximum
length of musical phrases. Apart from subject No.
11, who indicated a musical phrase of 38 notes in
excerpt No. 4 (clearly indicating the reasons of
this choice, which then cannot be considered an
error), the maximum length of musical phrases
is within the range of 8 and 18 notes.
an experImental comparIson
of melodIc segmentatIon
technIques
Given that music is a continuous flow of events
without explicit separators, automatic indexing
needs to rely on automatic segmentation tech-
niques, that is techniques that detect automatically
the lexical units of music documents. Different
strategies of melodic segmentation can be applied,
each one focusing on particular aspects of music
information. A study has been carried out on the
effectiveness, in terms of retrieval performances,
of different approaches to segmentation. The
study has been limited to melodic segmenta-
tion, because as already stressed melody is the
results of the perceptual study
The results of the perceptual study showed that
subjects agree on perceiving a boundary between
lexical units only when there are strong cues. In
particular, the presence of long notes surrounded
by short ones seems to give the strongest evidence
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