A paradigmatic approach for the melodic analysis

To analyse a musical piece is to some extent a small research project on its own right. Computer aided methods can be very helpful for gathering analytical information about particular description levels of music like melody, harmony, counterpoint, rhythm / meter, form, etc. Whenever mathematical models are proposed for a family of music-theoretical structures or processes, it is interesting, on the one hand, for the theorist to test these models in computer aided experiments. On the other hand, the analyst compares the automatically generated information by such models with her / his concrete observations about the piece in question. The paradigmatic model proposed in this thesis for the identification of prominent melodic segments aims at contributing to the discourse between the theory and the analysis from a melodic point of view in a practical way. In the so-called similarity neighbourhood model, melodic segments have been defined as consisting of consecutive notes only. A translation invariant representation mechanism based on the interval differences between the consecutive notes have been adapted. To account for contour similarities only, rhythmic features of the melodic segments have been ignored. The similarity neighbourhood model detects the repetition of the melodic segments by following the similarity by proximity principle. The correlation coefficient has been incorporated for calculating the proximity between equal length melodic segments only. The correlation coefficient as a proximity measure accounts for the translations, inversions, small interval changes of the melodies as well as the rhythmic variations without being able to distinguish them, because the rhythmic features of the melodies are ignored. Repetitions of the same melodic segment influences the melodic structure of the given piece in a significant way. The similarity neighbourhood model evaluates the significance of a melodic segment depending on the number of paradigmatic repetitions of the melodic segment normalised by the length. This principle identifies longer melodic segments more significant than the short ones. Considering the consecutive notes only and calculating the proximity relations between equal length melodies reduced the melodic domain to be searched, and enabled the melodic analysis of a complete musical piece. Furthermore, the proximity relations between equal length melodies have been used within the model to reconstruct the similarities as well as the suband super-segment relations between different length melodies. The collection of the sub-segments constitute the whole content of a melodic segment. Similarly, a sub-segment is present in different super-segments. These two perspectives to the suband super-segment relations indicate the contribution of a melodic material into the melodic development of the given piece. In the similarity neighbourhood model, the melodic structure of a given piece has been considered to be the collection of the proximity relations between equal length melodies supported by the suband super-segment relationships. These relationships have been compiled in a so-called prominence profile for the given piece, indicating the distribution of the significant melodies in different lengths throughout the given piece. This approach was tested mainly on the Two-Voice Inventions of J. S. Bach. However, in order to evaluate the generalisibility of the model, a modern piece called Keren of Iannis Xenakis was also analysed. The tests on the Two Part Inventions revealed the consistency of the results obtained by this approach with the results of the traditional music theory. The results of Keren indicate a legitimate segmentation of the piece in music-theoretical terms. The aim of this research has not been to develop a topological model to explain the melodic features of a given piece. However, the terminology used within the model is inspired by topology. A theoretical investigation of the analysis results of the similarity neighbourhood