An Expert System Devoted to Automated Music Identification and Recognition - Intelligent Music Information Systems: Tools and Methodologies - page 100

1+z[1]
1+z[2]
0
1+z[4]

conclusIon

We have presented a prototype of an ES for musical
styles identification, based on classical two-val-
ued logic and computer algebra techniques. As a
matter of interest, this study is representative of
the wide range of topics that can be studied using
Gröbner Bases.
Obviously the goal is not to substitute the spe-
cialist. There are two possible uses: first, helping in
the process of detecting a style by nonspecialists,
that must later consult specialists and, second, to
allow specialists to compare their own opinions
with those suggested by the system. We believe
that the system is especially useful for learning
and teaching history of music.
The KB of the system could be improved,
detailed or updated without modifying either
the inference engine or the method of knowledge
management described in the chapter.

As “0” is the output of:

NF(NEG(z[3]),I+J+K3);

it means that the composition is Classic. Actually,
the piece of music considered is the Concert for
trump No. 4 by Mozart.

fourth example

The user presses 23 keys of the GUI as shown
in Figure 6. The ideal K4 is then introduced to
CoCoA and the corresponding normal forms are
asked for:

K4:=Ideal(NEG(F1),NEG(F2),NEG(F3),NEG(F4),NEG(F5)
,NEG(F6N),NEG(F7N),NEG(F8N),NEG(F9),NEG(F10
),NEG(F11N),NEG(F12),NEG(F13),NEG(F14N),NEG
(F15N),NEG(F16N),NEG(F17),NEG(F18),NEG(F19)
,NEG(F20),NEG(F21),NEG(F22N),NEG(F23N));

acknoWledgment

This work was partially supported by the re-
search project MTM2004-03175 (Ministerio de
Educación y Ciencia, Spain) and the grant of the
research group ACEIA (Universidad Complutense
de Madrid - Comunidad de Madrid).
We would like to thank the editors of the topic
and the anonymous referees of this chapter for
their most valuable comments.

NF(NEG(z[1]),I+J+K4);
NF(NEG(z[2]),I+J+K4);
NF(NEG(z[3]),I+J+K4);
NF(NEG(z[4]),I+J+K4);

in this case, the outputs are:

1+z[1]
1+z[2]
1+z[3]
0

references

Adams, W. W., & Loustaunau, P. (1994). An
introduction to Gröbner Bases . Providende, RI:
Graduate Studies in Mathematics, American
Mathematical Society.

As “0” is the output of:

NF(NEG(z[4]),I+J+K4);

it means that this is not a score of this period.

Alonso, J. A., Briales, E., & Riscos, A. (1990).
Preuve Automatique dans le Calcul Propositionnel
et des Logiques Trivalentes. In Proceedings of