This book addresses the central problem of music cognition: how listeners' responses move beyond mere registration of auditory events to include the organization, interpretation, and remembrance of these events in terms of their function in a musical context of pitch and rhythm. Equally important, the work offers an analysis of the relationship between the psychological organization of music and its internal structure. Combining over a decade of original research on music cognition with an overview of the available literature, the work will be of interest to cognitive and physiological psychologists, psychobiologists, musicians, music researchers, and music educators.

Cognitive Foundations Of Musical Pitch

Human language, music and a variety of animal vocalizations constitute ways of sonic communication that exhibit remarkable structural complexity. While the complexities of language and possible parallels in animal communication have been discussed intensively, reflections on the complexity of music and animal song, and their comparisons, are underrepresented. In some ways, music and animal songs are more comparable to each other than to language as propositional semantics cannot be used as indicator of communicative success or wellformedness, and notions of grammaticality are less easily defined. This review brings together accounts of the principles of structure building in music and animal song. It relates them to corresponding models in formal language theory, the extended Chomsky hierarchy (CH), and their probabilistic counterparts. We further discuss common misunderstandings and shortcomings concerning the CH and suggest ways to move beyond. We discuss language, music and animal song in the context of their function and motivation and further integrate problems and issues that are less commonly addressed in the context of language, including continuous event spaces, features of sound and timbre, representation of temporality and interactions of multiple parallel feature streams. We discuss these aspects in the light of recent theoretical, cognitive, neuroscientific and modelling research in the domains of music, language and animal song.

https://royalsocietypublishing.org/doi/pdf/10.1098/rstb.2014.0097

Principles of structure building in music, language and animal song

This paper reveals the way in which musical pitch works as a peculiar form of cognition that reflects upon the organization of the surrounding world as perceived by majority of music users within a socio-cultural formation. The evidence from music theory, ethnography, archeology, organology, anthropology, psychoacoustics, and evolutionary biology is plotted against experimental evidence. Much of the methodology for this investigation comes from studies conducted within the territory of the former USSR. To date, this methodology has remained solely confined to Russian speaking scholars. A brief overview of pitch-set theory demonstrates the need to distinguish between vertical and horizontal harmony, laying out the framework for virtual music space that operates according to the perceptual laws of tonal gravity. Brought to life by bifurcation of music and speech, tonal gravity passed through eleven discrete stages of development until the onset of tonality in the seventeenth century. Each stage presents its own method of integration of separate musical tones into an auditory-cognitive unity. The theory of "melodic intonation" is set forth as a counterpart to harmonic theory of chords. Notions of tonality, modality, key, diatonicity, chromaticism, alteration, and modulation are defined in terms of their perception, and categorized according to the way in which they have developed historically. Tonal organization in music, and perspective organization in fine arts are explained as products of the same underlying mental process. Music seems to act as a unique medium of symbolic representation of reality through the concept of pitch. Tonal organization of pitch reflects the culture of thinking, adopted as a standard within a community of music users. Tonal organization might be a naturally formed system of optimizing individual perception of reality within a social group and its immediate environment, setting conventional standards of intellectual and emotional intelligence.

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Evolution of tonal organization in music mirrors symbolic representation of perceptual reality. Part-1: Prehistoric

General-purpose compression algorithms encode files as dictionaries of substrings with the positions of these strings’ occurrences. We hypothesized that such algorithms could be used for pattern discovery in music. We compared LZ77, LZ78, Burrows–Wheeler and COSIATEC on classifying folk song melodies. A novel method was used, combining multiple viewpoints, the k-nearest-neighbour algorithm and a novel distance metric, corpus compression distance. Using single viewpoints, COSIATEC outperformed the general-purpose compressors, with a classification success rate of 85% on this task. However, by combining 8 of the 10 best-performing viewpoints, including seven that used LZ77, the classification success rate rose to over 94%. In a second experiment, we compared LZ77 with COSIATEC on the task of discovering subject and countersubject entries in fugues by J.S. Bach. When voice information was absent in the input data, COSIATEC outperformed LZ77 with a mean score of 0.123, compared with 0.053 for LZ77. However, w...

/pdf/using-general-purpose-compression-algorithms-for-music-4lgqq63k3d.pdf

Using general-purpose compression algorithms for music analysis

Kulitta: a Framework for Automated Music Composition

Kulitta: A Framework for Automated Music Composition

This article presents a method of inductive inference whose aim is to build formal quantitative models of musical structure. The models are constructed by statistical extraction of significant patterns from a musical corpus. The minimum description length (MDL) principle is used to select the best model from among the members of a non-parametric model family characterized by an unbounded parameter set. The chosen model achieves optimal compromise between goodness-of-fit and model complexity, thereby avoiding the over-fitting normally associated with such a family of models. The MDL method is illustrated through its application to the Hidden Markov Model (HMM) framework. We derive an original mathematical expression for the MDL complexity of HMMs that employ a finite alphabet of symbols; these models are particularly suited to the symbolic modelling of musical structure. As an illustration, we use the proposed HMM complexity expression to construct a model for a common melodic formula in Greek church chant...

Minimum description length modelling of musical structure

We describe a data representation for voice leading between two sonorities in a chorale texture, and a similarity measure for these voice leadings. These tools are used in an empirical study of the relationship between voice leading and harmonic function in a corpus of Bach chorales and a corpus of Lutheran chorales from a hundred years earlier. Common voice-leading types in the corpora are subjected to a cluster analysis that is readily interpreted in terms of harmonic functional syntax. We are thus able not only to read a theory of harmony directly out of a corpus, but to do so without building in a priori notions of chord structure, rootedness, or even key. The cluster analysis also clarifies important syntactic differences between the pre-tonal (modal) corpus and the Bach (tonal) corpus.

Voice-leading prototypes and harmonic function in two chorale corpora

Hidden Markov Models (HMMs) have been successfully employed in the exploration and modeling of musical structure, with applications in Music Information Retrieval. This paper focuses on an aspect of HMM training that remains relatively unexplored in musical applications, namely the determination of HMM topology. We demonstrate that this complex problem can be effectively addressed through search over model topology space, conducted by HMM state merging and/or splitting. Once successfully identified, the HMM topology that is optimal with respect to a given data set can help identify hidden (latent) variables that are important in shaping the data set’s visible structure. These variables are identified by suitable interpretation of the HMM states for the selected topology. As an illustration, we present two case studies that successfully tackle two classic problems in music computation, namely (i) algorithmic statistical segmentation and (ii) meter induction from a sequence of durational patterns.

HMM Analysis of Musical Structure: Identification of Latent Variables Through Topology-Sensitive Model Selection

While substantial evidence suggests that key perception depends in part on the statistical distribution of pitch classes in a given piece, it has also been suggested that structural factors may play an important role. To further the understanding of what such structural factors might be, we conducted two experiments using statistically ambiguous yet structurally unambiguous stimuli that consisted of a uniform distribution of diatonic pitches drawn from the union of two neighboring keys, sequenced to clearly imply one particular key. In Experiment 1, subjects with substantial music theory training were asked to listen to melodic sequences and identify the key. The results indicate that purely structural factors can greatly influence key perception when statistical information about overall key profile is highly ambiguous. In Experiment 2, we examined the temporal psychophysics of structurally-based key induction by systematically varying the tempo of a subset of the statistically ambiguous/structurally unambiguous materials presented in Experiment 1 at rates ranging from 7 BPM to 3400 BPM. Twenty-two musically trained subjects were asked to indicate whether each sequence sounded resolved (ending on an implied tonic) or unresolved (ending on an implied dominant). The results agree strongly with those from Experiment 1 and show a preferred range of tempi in which participants provide robust key judgments (30 BPM 400 BPM). This suggests that structurally-based key-finding can be accurately computed by trained listeners in as little as 150ms per note or 1.2s for an entire sequence of eight notes.

The effect of structure and rate variation on key-finding

Background and Aims This paper presents an experimental investigation into how the tonal interpretation of a pitch affects its retention in short-term memory. The hypothesis that a clear tonal context facilitates the retention of pitches over longer time-spans as compared to tonally ambiguous or atonal contexts has been examined before in previous work (Cuddy, Cohen, & Mewhort, 1981; Cuddy, Cohen, & Miller, 1979; Dewar, Cuddy, & Mewhort, 1977; Krumhansl, 1979). We present two experiments that aim to partly replicate previous findings while controlling for additional parameters. In contrast to the conclusions drawn from previous experiments, we postulate that it is impossible to conclude that tonal context aids pitch memory because subjects are in actuality responding to the tonal fitness of a probe tone, as described by Krumhansl and Kessler (1982), and are not actually executing a pitch recall task. As in the case of Krumhansl’s (1979) studies, we use Deutsch’s (1972) experimental paradigm for our experiment. The task involves comparing a probe tone to a target that is separated by interference tones. We experimentally manipulated the degree of tonality of the interference tones and the scale degrees of the target and probe, while fixing factors such as the time interval between target and probe, and the overall pitch register. Beyond experimental design considerations, the way we analyse and interpret our data is significantly different from prior work.

Panayotis Mavromatis

Papers

Minimum description length modelling of musical structure

Voice-leading prototypes and harmonic function in two chorale corpora

HMM Analysis of Musical Structure: Identification of Latent Variables Through Topology-Sensitive Model Selection

The effect of structure and rate variation on key-finding

The effect of tonal context on short-term memory for pitch