Tool for the Analysis of Fugues
Description
A fundamental problem of creating a content-based index of musical
pieces is the automatic extraction of musical key words. Since
research in this field is still in its beginnings, one should restrict
oneself to a well-structured class of musical pieces. In the world of
the so-called classical music, fugues seem to be a good starting
point because of their highly structured form. This page shortly describes
an experimental tool which tries to recognize musical phrases
of a fugue.
Functionality
The program reads a fugue given as a MIDI file in which each voice is
stored in an own track. The following screen shot shows in different
colours the individual voices of J.S.Bach's fugue in C major of the
first book of the Well Tempered Clavier. The task is to recognize
musical phrases within each voice, esp. subject, counter-subject and
interludes.
A first try
Typically, a fugue begins with the subject, played by a single
voice. The subject will be repeated during the further course of the
piece, where it will be transposed and modified and contrasted
simultaneously by counter-subjects. The passages of strict
counterpuntal work are joined by interludes, introducing new themes.
That means, important phrases recur several times. Thus, an obvious
way for extracting phrases is to recognize repeating interval
sequences which may be slightly varied.
Using an appropriate quantization of intervals and difference
quotients of note durations, one can detect modified repetitions with
exact pattern matching: The voices are quantized and stored in a
Suffix-Tree. By using the length, frequency of occurance and time of
first occurance of a substring, a phrase list is generated.
The following screen shot shows the result of the analysis of the
above-mentioned fugue.
Conclusion
Tests showed that above heuristics are too simple. One has to consider
musicological and musicpsychological insights more explicitely in
order to obtain satisfactory results in most cases. Especially, the
phrase boundaries have to be determined on a musicpsychological base.
Furthermore, slight rhythmic variations should be recognized, e.g. by
using a music-orientated correlation method.
Uni-Bonn
Computer Science
Projects
MiDiLiB, Part 2
