Tools for Music Information Retrieval and Playing - Intelligent Music Information Systems: Tools and Methodologies - page 128

where H 0 = ∅, and the alpha coefficients are posi-
tive coefficients which depend upon the weights
assigned to the different trail lengths in the power
graphs H i and phi varies among all the possible
isometries of the vertex sets.
In the next section we introduce the MX en-
vironment that allows for handling of symbolic
music and audio as well.

Figure 15. (a) Music information layers and (b)
relations among them

mx: an xml multIlaYer
envIronment for musIc

In MX music information is represented according
to a multi-layered structure and to the concept of
space-time construct. In fact, music information
can be structured by a layer subdivision model,
as shown in Figure 15.
Each layer is specific to a different degree
of abstraction in music information: General,
Structural, Music Logic, Notational, Performance,
and Audio. Longari (2005) gives an exhaustive
description of this format and the issue of the
integration between MX and other formats is
covered in Longari (2003).
The main advantage of MX is the richness of
its descriptive features, which are based on other
commonly accepted encodings aimed at more
specific descriptions.
The multilayered music information structure
is kept together by the concept of spine . Spine is
a structure that relates time and spatial informa-
tion (see Figure 16), where measurement units
are expressed in relative format. Through such
a mapping, it is possible to fix a point in a layer
instance (e.g., Notational) and investigate the
corresponding point in another one (e.g., Perfor-
mance or Audio).
The Structural layer contains explicit descrip-
tions of music objects together with their causal
relationships, from both the compositional and
musicological point of view, that is how music
objects can be described as transformation of
previously described music objects.

An example of a particular structural object
is Theme which represent exactly the concept of
musical theme of the musical piece (or part of it)
under consideration.
Theme objects may be whether the output
of an automatic segmentation process (Haus,
Longari, & Emanuele, 2004) or the result of a
musicological analysis.
A content-based information retrieval method
must take advantage of the presence of new meta-
data specifically oriented to retrieval in order to
improve processes and algorithms.
Within IEEE WG on musical application of
XML it is under development an XML language,
named MX, specifically designed to support inter-
change between musical notation, performance,
analysis, and retrieval applications.
The goal is the integration of audio and sym-
bolic contents into the same framework through
a search engine for music files that can handle
standard XML music metadata (such as author,
title, album, etc.) as well as new metadata provided
by MX such as structural information, analysis,
harmony, theme, melody, rhythm, and so forth,
and structural audio features extracted from audio
formats like PCM, MP3, and AAC.

mx layers

XML organizes information in a hierarchic struc-
ture, so MX represents each layer as a secondary