Music analysis and, in particular music criticism, two fundamental tools of historical research and musicology in the broadest sense have become extremely difficult and problematical disciplines in the last few decades. The actual practice of analysis and criticism has by no means come to a halt, but the amount of 'truth' which was once thought obtainable from them or, at least, which was believed to have been won in the actual moment of undertaking them has diminished. We have begun to question the validity of certain elementary notions current in musicological parlance, for instance those connected with the concept of phraseology;' the harmonic concepts which have been the pillars of our musical thinking are now being discussed and reexamined from different points of view,2 and even the very idea of 'talking about music' must be revised with regard to its epistemological foundations.3 From all this it is clear that no scholar today can write about music with the same confidence and equanimity as his predecessors. His responsibilities are greater, and the fields he has chosen to research require kinds of knowledge that had previously been thought neither necessary nor relevant. These difficulties arise from at least two factors. First, there is the obvious problem that the analysis (or description) of a musical text always presupposes, sometimes implicitly or even quite unconsciously, some underlying theoretical basis: even in the most elementary analytical discussions for example when numbers of bars are counted, or corresponding phrases are distinguished reference is inevitably made to a set of theoretical ideas4 sometimes even without the writer being directly acquainted with it. What is more, the latent ideas which support an analytical or descriptive statement are

The concept of musical grammar

The thesis investigates the perception of musical metre and phrasing, which together form a hierarchical rhythmic structure, represented in tree-diagram form. Rather than study human perceptual processes, a mechanistic approach is adopted. It is shown that the most likely rhythmic structure of a passage can be generated largely from the pitch and durational information in scores, through the perception of certain features, termed structural characteristics, supported by some general perceptual preferences. Each characteristic is itself a perceptual preference, capable of selecting certain groupings of notes or chords as phrase groupings or highlighting particular temporally disjunct notes or chords as structural accents, each of which is a potential metrical accent. Mental connections between relatively long notes, a preference for regular metre, and the grouping of relatively close attacks establish a basic (if sometimes ambiguous) rhythmic structure, which may be modified or developed by repetition, a longer-note accompaniment, harmonic rhythm, dissonance and resolution, pitch patterning, and notated dynamics and articulation. Phrase structure influences the perception of tonality, in conjunction with the Harmonic Series, for whose contribution a tonal map is put forward. The characteristics may be temporally congruent or incongruent (cross rhythmic) and are of unequal strength, thus giving rise, in their many different configurations, to further perceptual preferences, which are illustrated by several hundred musical examples. The differences in relative strength permit metre and phrase grouping to be read qualitatively, as a product of the characteristics which generate it.

Rhythmic structure in music : a study of the perception of metrical and phrase structure, from a mechanistic viewpoint

As an essential subset of Chinese music, traditional Chinese folk songs frequently apply the anhemitonic pentatonic scale. In music education and demonstration, the Chinese anhemitonic pentatonic mode is usually introduced theoretically, supplemented by music appreciation, and a non-Chinese-speaking audience often lacks a perceptual understanding. We discovered that traditional Chinese anhemitonic pentatonic folk songs could be identified intuitively according to their distinctive bell-shaped pitch distribution in different types of pitch histograms, reflecting the Chinese characteristics of Zhongyong (the doctrine of the mean). Applying pitch distribution to the demonstration of the Chinese anhemitonic pentatonic folk songs, exemplified by a considerable number of instances, allows the audience to understand the culture behind the music from a new perspective by creating an auditory and visual association. We have also made preliminary attempts to feature and model the observations and implemented pilot classifiers to provide references for machine learning in music information retrieval (MIR). To the best of our knowledge, this article is the first MIR study to use various pitch histograms on traditional Chinese anhemitonic pentatonic folk songs, demonstrating that, based on cultural understanding, lightweight statistical approaches can progress cultural diversity in music education, computational musicology, and MIR.

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Bell Shape Embodying Zhongyong: The Pitch Histogram of Traditional Chinese Anhemitonic Pentatonic Folk Songs

This paper details a corpus study examining Renaissance voice-leading practices. Palestrina’s masses are searched for progressions matching contrapuntal ‘rules’ taken from Vicentino (1555).  Vicent...

Vicentino versus Palestrina: A computational investigation of voice leading across changing vocal densities

We describe a method for automatically extracting symbolic compositional rules from music corpora. Resulting rules are expressed by a combination of logic and numeric relations, and they can therefore be studied by humans. These rules can also be used for algorithmic composition, where they can be combined with each other and with manually programmed rules. We chose genetic programming (GP) as our machine learning technique, because it is capable of learning formulas consisting of both logic and numeric relations. GP was never used for this purpose to our knowledge. We therefore investigate a well understood case in this study: dissonance treatment in Palestrina’s music. We label dissonances with a custom algorithm, automatically cluster melodic fragments with labelled dissonances into different dissonance categories (passing tone, suspension etc.) with the DBSCAN algorithm, and then learn rules describing the dissonance treatment of each category with GP. Learning is based on the requirement that rules must be broad enough to cover positive examples, but narrow enough to exclude negative examples. Dissonances from a given category are used as positive examples, while dissonances from other categories, melodic fragments without dissonances, purely random melodic fragments, and slight random transformations of positive examples, are used as negative examples.

Machine learning of symbolic compositional rules with genetic programming: dissonance treatment in Palestrina

Dissonance and consonance are basic attributes of any music whether it be modal, tonal, atonal, or twelve-tone, etc. The decision processes required of the listener for recognizing a particular sound event as a dissonance (and distinguishing its components) will be different for the various musical styles (presumably, those processes will not be too different between some modal and tonal music). This study represents an effort to formalize, in a computer program, a sequence of possible processes for the recognition of component elements of selected dissonant structures in the modal music of the Renaissance composer, Josquin Desprez.' Voice-Leading in Dissonances. Assuming the intervals of a 2nd, 7th, 4th (with lowest sounding voice), and their octave equivalents to be dissonant, we addressed ourselves initially to the following problem: Given two pitches, e.g., G and A (Ex. 1), that form a dissonance, which is the dissonant pitch?

Karen Strickler

Papers

A computer-assisted study of dissonance in the masses of Josquin Desprez