Content-Based Indexing of Symbolic Music Documents - Intelligent Music Information Systems: Tools and Methodologies - page 11

Table 1. Number of different indexes when quan-
tization is applied to ascending and descending
intervals within an octave (including unison)

generic information needs the user had to provide
more complete information, in particular using
long melodic excerpts to create his query.
A similar approach to quantization can be car-
ried out on rhythmic information. In this case it
has to be noted that the same score representation
is a quantized version of possible performances,
because it is not expected that onset times and du-
ration are played using the exact values computed
from the beats per minute (when that happens
the performance sounds mechanic). In the case
of scores that are transcriptions of pre-existing
performances, the transcriber chooses which is
the level of quantization as a compromise between
the readability of the score and the precision
of the reported times. Rhythmic quantization
for index conflation can be carried out with an
approach similar to melodic quantization, from
milliseconds to very coarse levels (such as the
levels long and short ). A number of approaches
to melodic indexing do not take into account note
durations, but are based only on pitch informa-
tion, and they can be considered as a limit case
where there is only one level of quantization for
note onsets and durations.

Quantization Level #symbols

Cents 2401

Semitones: 0, +1, +2, … 25

Music intervals: unison, second, third, … 15

Perceptual intervals: unison, small, medium,
large

9

Direction: up, down, same 3

As for stemming, quantization may improve
recall because more documents may contain a
quantized lexical unit. The increase in recall usu-
ally correspond to a lowering in precision, because
a quantized lexical unit is usually more generic
and it describes less precisely a user information
need. From a computational point of view, quan-
tization may also speed up retrieval, because the
decrease of the number of different symbols used
as building blocks of the index correspond to a
decrease in the computational cost to perform the
matching. This characteristic has been exploited
in system for melodic retrieval (Ghias et al., 1995)
where only three levels have been used. Authors
reported that, in order to overcome the problem of

Figure 2. Graphical representation of the information loss when increasing levels of quantization of
pitch and duration are applied (from top: original score, removal of rhythm, pitch quantization, removal
of pitch)