Dirk-Jan Povel’s research while affiliated with Radboud University and other places

This article describes the development of an application for generating tonal melodies. The goal of the project is to ascertain our current understanding of tonal music by means of algorithmic music generation. The method followed consists of four stages: 1) selection of music-theoretical insights, 2) translation of these insights into a set of principles, 3) conversion of the principles into a computational model having the form of an algorithm for music generation, 4) testing the “music ” generated by the algorithm to evaluate the adequacy of the model. As an example, the method is implemented in Melody Generator, an algorithm for generating tonal melodies. The program has a structure suited for generating, displaying, playing and storing melodies, functions which are all accessible via a dedicated interface. The actual generation of melodies, is based in part on constraints imposed by the tonal context, i.e. by meter and key, the settings of which are controlled by means of parameters on the interface. For another part, it is based upon a set of construction principles including the notion of a hierarchical organization, and the idea that melodies consist of a skeleton that may be elaborated in various ways. After these aspects were implemented as specific sub-algorithms, the device produces simple but well-structured tonal melodies.

A model is proposed for the On-Line Harmonic Processing (OLHP) of tonal melodic sequences in which each incoming tone is described in terms of its features Fittingness, compliance with the previous harmony, Uncertainty, ambiguity of a new harmony and, Chord Change, goodness of the connection between previous and new harmony. To test this model in Experiment 1 listeners rated the musical logic of 10-tone sequences presented with an induced segmentation in groups of 3-3-3-1, and following an harmonic progression of I-target-V-I, respectively, with the harmonic functions I, II, III, IV, V, or VI inserted as target fragment. The results support the Chord Change feature of the model. In Experiment 2 these sequences were rated as tone-by-tone increasing fragments, starting from the initial 3 tones up to the complete sequence. The ratings of the incremental sequences supported the findings of the first experiment. The three features in the model explained 46.4 % of the variance in the target ratings, although Uncertainty seemed to have no effect. In a comparison with two other models OLHP model performed best. Finally, an a-posteriori model consisting of Chord Change and a variable quantifying pitch proximity between consecutive tones accounted for a major part of the variance. It is concluded that listeners employ OLHP's features in their representation of the sequences and that both harmony and pitch height are indispensable factors in a model of melody perception.

By common assumption, the first step in processing a tonal melody consists in setting up the appropriate metrical and harmonic frames required for the mental representation of the sequence of tones. Focusing on the generation of a harmonic frame, this study aims (a) to discover the factors that facilitate or interfere with the development of a harmonic interpretation, and (b) to test the hypothesis that goodness ratings of tone sequences largely depend on whether the listener succeeds in creating a suitable harmonic interpretation. In two experiments, listeners rated the melodic goodness of selected sequences of 10 and 13 tones and indicated which individual tones seemed not to fit. Results indicate that goodness ratings (a) are higher the more common the induced harmonic progression, (b) are strongly affected by the occurrence and position of nonchord tones: sequences without nonchord tones were rated highest, sequences with anchoring nonchord tones intermediately, and nonanchoring nonchord tones lowest. The explanation offered is compared with predictions derived from other theories, which leads to the conclusion that when a tone sequence is perceived as a melody, it is represented in terms of its underlying harmony, in which exact pitch-height characteristics play a minor role.

This paper presents a concise description of OPTM, a computational model for the On-line Processing of Tonal Melodies. It describes the processes a listener executes when transforming a tone sequence into a tonal melody. The model is based on the assumption that a tone sequence is represented in terms of a chord progression underlying the sequence. Chord tones are directly coded in the harmonic frame, while non-chord tones can sometimes be linked to a subsequent chord tone. The model implements three primary mechanisms: key finding, chord recognition, and anchoring. The operation of the model and its associated output are displayed while the tone sequence is entered incrementally. The output consists of the evolving harmonic framework, the assimilation of non-chord tones, the arising expectations, the tones that do not fit, and an overall indication of the 'goodness' of the melodic percept.

this paper has been a means to materialize and concretize, to clarify and formalize, the intuitions that I developed over the last decade by studying the pertinent literature and by performing experiments investigating the role of various hypothetical perceptual mechanisms in the processing of tonal music. The inestimable advantage of developing a computational model is that one is forced to describe the process in the most minute detail as a result of which one readily discovers which aspects were underspecified in the initial verbalizations of the intuitions. Moreover, an operational model, even if it is only half finished, can be fed actual tone sequences and the output of the model can be compared with reactions of the human listener, thus yielding immediate feedback that shows where the model seems to be failing and providing hints as how to adapt and improve the model. A basic assumption of the model is that the listener will attempt to describe the input, a sequence of tones (see next section for definition of the domain), in a mental framework consisting of a metrical and a harmonic schema. This conception implies that the process has a bottom-up aspect in which the incoming tones are processed, and a top-down aspect in which the listener activates a pertinent metrical and harmonic framework in which the input is somehow encoded. In other words, it is assumed that a listener attempts to make a structural description in which all tones in the sequence are accounted for. If this succeeds, the listener will feel that (s)he understands the sequence, that it forms a melody (in the tonal style). As the main goal is to develop an explanation of how listeners process tone sequences, the OPTM model is designed as a series of processes unfolding in time. I.e. it describes...

We consider several perceptual issues in the context of machine recognition of music patterns. It is argued that a successful implementation of a music recognition system must incorporate perceptual information and error criteria. We discuss several measures of rhythm complexity which are used for determining relative weights of pitch and rhythm errors. Then, a new method for determining a localized tonal context is proposed. This method is based on empirically derived key distances. The generated key assignments are then used to construct the perceptual pitch error criterion which is based on note relatedness ratings obtained from experiments with human listeners.

In this study, three measures of temporal pattern complexity were compared as regards their perceptual validity. The first measure, based on the work of Tanguiane (1993), uses the idea that a temporal pattern can be described in terms of (elaborations of) more simple patterns, simultaneously at different levels. The second measure is based on the complexity measure for finite sequences proposed by Lempel and Ziv (1976), which is related to the number of steps in a self-delimiting production process by which such a sequence is presumed to be generated. The third measure, newly developed here, is rooted in the theoretical framework of rhythm perception of Povel and Essens (1985). It takes into account the ease of coding a temporal pattern and the complexity of the segments resulting from this coding. The perceptual validity of the three measures was evaluated in an experiment in which subjects judged the complexity of 35 temporal patterns. Correlations between the three measures and the ...

Three measures of rhythm complexity are considered. It is suggested that these measures be used in a system for machine recognition of music patterns as determinants of relative weights assigned to pitch and rhythm errors. The three measures are characterized and a procedure for determining parameters of one of the measures is described

In two experiments, the perceptual similarity between a strong tonal melody and various transpositions was investigated using a paradigm in which listeners compared the perceptual similarity of a melody and its transposition with that of the same melody and another transposition. The paradigm has the advantage that it provides a direct judgment regarding the similarity of transposed melodies. The experimental results indicate that the perceptual similarity of a strong tonal melody and its transposition is mainly determined by two factors: (1) the distance on the height dimension between the original melody and its transposition (pitch distance), and (2) the distance between keys as inferred from the circle of fifths (key distance). The major part of the variance is explained by the factor pitch distance, whereas key distance explains only a small part.