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(1985) and Kapur-Narendran's (1984) ideas
(Alonso, Briales & Riscos, 1990; Chazarain,
Riscos, Alonso & Briales, 1991) and Gröbner
Bases (GB) (Adams & Loustaunau, 1994;
Buchberger, 1965; Buchberger, 1998; Cox,
Little & O'Shea, 1992; Kreuzer & Robbiano,
2000) and is implemented in the computer
algebra language CoCoA (Capani & Niesi,
1996; Perkinson, 2000). Although, in this
chapter, the ES is based on classic Boolean
logic, our method allows, as already said,
to use p-valued (p being a prime number)
modal logics.
For the sake of space, only ES1 will be consid-
ered in this chapter, because both the construction
and behavior of ES2 and ES3 are similar.
the suBsYstem es1
historical Introduction
ES1 is intended to identify musical styles of the
period that lasts from 1600 to 1827.
In this time period three musical stiles arose and
grew—Baroque, Rococo, and Classic (Groutald &
Palisca, 2004; Marco, 2002; Zampronha, 2000).
While Baroque and Classic are styles with well-
defined characteristics, Rococo shares identifiers
of both Baroque and Classic, sometimes in a not
well-defined mixture, sometimes exaggerating
the Baroque side.
The identifiers that have respectively been
assigned in this chapter to Baroque, Rococo
and Classic style (let us insist that this list of
characters may be improved or changed) are the
following ones.
Baroque's identifiers are ornamental, solemn,
ceremonious, religious, harmonic complexity,
counter point development (composed voices),
polyphony, sound contrasts, continuous bass,
use of wood wind instruments plus trumpet and
chord (in this epoch metal wind instruments did
not exist); it is also a sumptuous, over-elaborate,
luxurious music, in which form and motif are
more relevant than phrase.
Rococo is a transition epoch between Baroque
and Classic, which developed, mainly, in France.
It is a mixture of styles, and its identifiers are:
sumptuous, refined, beautiful, devoted at its
beginnings to selected audiences as the Royal
Court, continuous bass, melodic complexity and
ornamentation. The musical instruments are those
of Baroque: wood wind instruments and trumpet,
3.
A graphic user interface (GUI). It is a front-
end that helps those users of the ES who do
not necessarily master the mathematics and
computer backgrounds on which the systems
are based. By just pressing keys that corre-
spond to potential facts (the identifiers, or
their negations in this chapter), the user gets
an output that is either the identification of a
musical style in a time period or a statement
asserting that the score under study does not
belong to the period the user guessed.
our expert sYstem
To decrease its computational complexity, we have
divided our ES is into three subsystems: ES1, ES2
and ES3, which refer respectively to:
•
Baroque, Rococo and Classic (XVII-XVIII
centuries)
•
Romanticism, Nationalism and Impres-
sionism (XIX and beginnings of XX cen-
turies)
•
Anti-Impressionism, Verism and Expres-
sionism (chosen from many others styles
of the XX century because they are among
those having a best defined structure)
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