Implicit learning of recursive context-free grammars

Context-free grammars are fundamental for the description of linguistic syntax. However, most artificial grammar learning experiments have explored learning of simpler finite-state grammars, while studies exploring context-free grammars have not assessed awareness and implicitness. This paper explores the implicit learning of context-free grammars employing features of hierarchical organization, recursive embedding and long-distance dependencies. The grammars also featured the distinction between left- and right-branching structures, as well as between centre- and tail-embedding, both distinctions found in natural languages. People acquired unconscious knowledge of relations between grammatical classes even for dependencies over long distances, in ways that went beyond learning simpler relations (e.g. n-grams) between individual words. The structural distinctions drawn from linguistics also proved important as performance was greater for tail-embedding than centre-embedding structures. The results suggest the plausibility of implicit learning of complex context-free structures, which model some features of natural languages. They support the relevance of artificial grammar learning for probing mechanisms of language learning and challenge existing theories and computational models of implicit learning

Comments on "Facilitation and Coherence Between the Dynamic and Retrospective Perception of Segmentation in Computer-Generated Music," by Freya Bailes and Roger T. Dean

Although the study by Bailes & Dean (2007) addresses an underresearched area of auditory and musical perception, it raises questions concerning stimuli, methodology, and the study's relation to previous research, that are outlined in this commentary

A statistical MMN reflects the magnitude of transitional probabilities in auditory sequences

Within the framework of statistical learning, many behavioural studies investigated the processing of unpredicted events. However, surprisingly few neurophysiological studies are available on this topic, and no statistical learning experiment has investigated electroencephalographic (EEG) correlates of processing events with different transition probabilities. We carried out an EEG study with a novel variant of the established statistical learning paradigm. Timbres were presented in isochronous sequences of triplets. The first two sounds of all triplets were equiprobable, while the third sound occurred with either low (10%), intermediate (30%), or high (60%) probability. Thus, the occurrence probability of the third item of each triplet (given the first two items) was varied. Compared to high-probability triplet endings, endings with low and intermediate probability elicited an early anterior negativity that had an onset around 100 ms and was maximal at around 180 ms. This effect was larger for events with low than for events with intermediate probability. Our results reveal that, when predictions are based on statistical learning, events that do not match a prediction evoke an early anterior negativity, with the amplitude of this mismatch response being inversely related to the probability of such events. Thus, we report a statistical mismatch negativity (sMMN) that reflects statistical learning of transitional probability distributions that go beyond auditory sensory memory capabilities

Wie wissenschaftlich muss Musiktheorie sein?. Chancen und Herausforderungen musikalischer Korpusforschung

Korpusbasierte Forschung nimmt in der Sprach- und Literaturwissenschaft schon seit Langem einen wichtigen Platz ein. In der Musikforschung dagegen gewann sie erst vor Kurzem an Bedeutung. Die Gründe für diese verspätete Akzeptanz sind vielfältig und mitunter einer tiefgreifenden Skepsis gegenüber der Anwendung statistisch-quantitativer Methoden auf Musik als Kunstobjekt geschuldet. Der vorliegende Beitrag motiviert musikalische Korpusforschung, indem er grundsätzliche Probleme herkömmlicher Repertoireforschung (intuitive Statistik, methodische Intransparenz, Urteilsheuristiken) und gegenwärtiger Korpusforschung (z.B. Stichprobenerhebung, mangelnde Korpora und Annotationsstandards) aufzeigt und anhand repräsentativer Studien in den Bereichen Harmonik, Kontrapunktik, Melodiebildung und Rhythmik/Metrik exemplarisch diskutiert. Der Beitrag schließt mit einem Plädoyer für die Einbeziehung quantitativer Ansätze in der Musiktheorie im Rahmen eines übergeordneten ›Mixed Methods‹-Paradigmas. Corpus-based research has long been occupying a prominent position in literary studies and linguistics. In musicology, by contrast, it is about to gain in importance only fairly recently. The reasons for this delayed acceptance are manifold. Among other things, they are rooted in a deep skepticism toward applying statistical-quantitative methods to music as an object of art. This article supports musicological corpus research by pointing out general problems inherent to traditional repertoire research (intuitive statistics, methodological non-transparency, and heuristics in judgment) as well as current corpus research (e.g., biased sampling, paucity of corpora, and lack of annotation standards). These problems are discussed in reference to prominent studies in the domains of harmony, counterpoint, melody, and rhythm/meter. The article concludes by making a case for the integration of quantitative approaches in music theory into the overarching framework of a ›mixed methods‹ paradigm

Western listeners detect boundary hierarchy in Indian music: a segmentation study

How are listeners able to follow and enjoy complex pieces of music? Several theoretical frameworks suggest links between the process of listening and the formal structure of music, involving a division of the musical surface into structural units at multiple hierarchical levels. Whether boundaries between structural units are perceivable to listeners unfamiliar with the style, and are identified congruently between naïve listeners and experts, remains unclear. Here, we focused on the case of Indian music, and asked 65 Western listeners (of mixed levels of musical training; most unfamiliar with Indian music) to intuitively segment into phrases a recording of sitar ālāp of two different rāga-modes. Each recording was also segmented by two experts, who identified boundary regions at section and phrase levels. Participant- and region-wise scores were computed on the basis of "clicks" inside or outside boundary regions (hits/false alarms), inserted earlier or later within those regions (high/low "promptness"). We found substantial agreement—expressed as hit rates and click densities—among participants, and between participants’ and experts’ segmentations. The agreement and promptness scores differed between participants, levels, and recordings. We found no effect of musical training, but detected real-time awareness of grouping completion and boundary hierarchy. The findings may potentially be explained by underlying general bottom-up processes, implicit learning of structural relationships, cross-cultural musical similarities, or universal cognitive capacitie

Towards a Unified Model of Chords in Western Harmony

Chord-based harmony is an important aspect of many types of Western music, across genres, regions, and historical eras. However, the consistent representation and comparison of harmony across a wide range of styles (e.g., classical music, Jazz, Rock, or Pop) is a challenging task. Moreover, even within a single musical style, multiple theories of harmony exist, each relying on its own (possibly implicit) assumptions and leading to harmonic analyses with a distinct focus (e.g., on the root of a chord vs. its bass note) or representation (e.g., spelled vs. enharmonic pitch classes). Cross-stylistic and cross-theory comparisons are therefore even more difficult, particularly in a large-scale computational setting that requires a common overarching representation. To address these problems, we propose a model which allows for the representation of chords at multiple levels of abstraction: from chord realizations on the score level (if available), to pitch-class collections (including a potential application of different equivalences, such as enharmonic or octave equivalence), to pitch- and chord-level functions and higher-order abstractions. Importantly, our proposed model is also well-defined for theories which do not specify information at each level of abstraction (e.g., some theories make no claims about harmonic function), representing only those harmonic properties that are explicitly included and inducing others where possible (e.g., deriving scale degrees from root and key information). Our model thus represents an important step towards a unified representation of harmony and its various applications.This research was supported by the Swiss National Science Foundation within the project “Distant Listening – The Development of Harmony over Three Centuries (1700–2000)” (Grant no. 182811). This project is being conducted at the Latour Chair in Digital and Cognitive Musicology, generously funded by Mr. Claude Latour

Modelling the Syntax of North Indian Melodies With a Generalized Graph Grammar

Hierarchical models of music allow explanation of highly complex musical structure based on the general principle of recursive elaboration and a small set of orthogonal op- erations. Recent approaches to melodic elaboration have converged to a representation based on intervals, which al- lows the elaboration of pairs of notes. However, two prob- lems remain: First, an interval-first representation obscures one-sided operations like neighbor notes. Second, while models of Western melody styles largely agree on step- wise operations such as neighbors and passing notes, larger intervals are either attributed to latent harmonic properties or left unexplained. This paper presents a grammar for melodies in North Indian raga music, showing not only that recursively applied neighbor and passing note oper- ations underlie this style as well, but that larger intervals are generated as generalized neighbors, based on the tonal hierarchy of the underlying scale structure. The notion of a generalized neighbor is not restricted to ragas but can be transferred to other musical styles, opening new perspec- tives on latent structure behind melodies and music in gen- eral. The presented grammar is based on a graph represen- tation that allows one to express elaborations on both notes and intervals, unifying and generalizing previous graph- and tree-based approaches

MuseReduce: A Generic Framework for Hierarchical Music Analysis

In comparison to computational linguistics, with its abundance of natural-language datasets, corpora of music analyses are rather fewer and generally smaller. This is partly due to difficulties inherent to the encoding of music analyses, whose multimodal representations—typically a combination of music notation, graphic notation, and natural language—are designed for communication between human musician-analysts, not for automated large-scale data analysis. Analyses based on hierarchical models of tonal structure, such as Heinrich Schenker’s, present additional notational and encoding challenges, since they establish relations between non- adjacent tones, and typically interpret successions of tones as expressions of abstract chordal sonorities, which may not be literally present in the music score. Building on a published XML format by Rizo and Marsden (2019), which stores analyses alongside symbolically encoded scores, this paper presents a generic graph model for reasoning about music analyses, as well as a graphical web application for creating and encoding music analyses in the aforementioned XML format. Several examples are given showing how various techniques of music analysis, primarily but not necessarily hierarchical, might be unambiguously represented through this model