83 research outputs found

    Electronic Locator of Vertical Interval Successions (ELVIS): The first large data-driven research project on musical style

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    The ELVIS project had three locally based teams (in Canada, at McGill, in Scotland, at Aberdeen, and in New England, USA, divided between MIT, the lead, and Yale), each of which focused on a different aspect of the overall research program: using computers to understand musical style. The central unifying concept of the ELVIS project was to study counterpoint: the way combinations of voices in polyphonic music (e.g. the soprano and bass voices in a hymn, or the viola and cello in a string quartet, as well as combinations of more than two voices) interact: i.e. what are the permissible vertical intervals (notes from two voices sounding at the same time) for a particular period, genre, or style. These vertical intervals, connected by melodic motions in individual voices, constitute Vertical Interval Successions. In more modern terms, this could be described as harmonic progressions of chords, but what made ELVIS particularly flexible was its ability to bridge the gap to earlier, contrapuntally-conceived music by using the diad (a two-note combination) rather than the triad (a combination of three notes in particular arrangements) as a basis (since triads and beyond may be expressed as sums of diads)

    The hardness of perfect phylogeny, feasible register assignment and other problems on thin colored graphs

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    AbstractIn this paper, we consider the complexity of a number of combinatorial problems; namely, Intervalizing Colored Graphs (DNA physical mapping), Triangulating Colored Graphs (perfect phylogeny), (Directed) (Modified) Colored Cutwidth, Feasible Register Assignment and Module Allocation for graphs of bounded pathwidth. Each of these problems has as a characteristic a uniform upper bound on the tree or path width of the graphs in “yes”-instances. For all of these problems with the exceptions of Feasible Register Assignment and Module Allocation, a vertex or edge coloring is given as part of the input. Our main results are that the parameterized variant of each of the considered problems is hard for the complexity classes W[t] for all t∈N. We also show that Intervalizing Colored Graphs, Triangulating Colored Graphs, and Colored Cutwidth are NP-Complete

    The Yale-Classical Archives Corpus

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    The Yale-Classical Archives Corpus (YCAC) contains harmonic and rhythmic information for a dataset of Western European Classical art music. This corpus is based on data from classicalarchives.com, a repository of thousands of user-generated MIDI representations of pieces from several periods of Western European music history. The YCAC makes available metadata for each MIDI file, as well as a list of pitch simultaneities ( salami slices ) in the MIDI file. Metadata include the piece\u27s composer, the composer\u27s country of origin, date of composition, genre (e.g., symphony, piano sonata, nocturne, etc.), instrumentation, meter, and key. The processing step groups the file\u27s pitches into vertical slices each time a pitch is added or subtracted from the texture, recording the slice\u27s offset (measured in the number of quarter notes separating the event from the file\u27s beginning), highest pitch, lowest pitch, prime form, scale-degrees in relation to the global key (as determined by experts), and local key information (as determined by a windowed key-profile analysis). The corpus contains 13,769 MIDI files by 571 composers yielding over 14,051,144 vertical slices. This paper outlines several properties of this corpus, along with a representative study using this dataset

    Big Data, Big Questions: A Closer Look at the Yale–Classical Archives Corpus (c. 2015)

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    This paper responds to the article by Christopher White and Ian Quinn, in which these authors introduce the Yale-Classical Archives Corpus (YCAC). I begin by making some general observations about the corpus, especially with regard to ramifications of the keyboard-performance origins of many pieces in the original MIDI collection. I then assess the accuracy of the scale-degree and local-key fields in the database, which were generated by the Bellman-Budge key-finding algorithm. I point out that some of the inaccuracies from the key-finding algorithm's output may influence the results we obtain from statistical studies of this corpus. I also offer an alternative analysis to the authors' finding that the ratio of V7 to V chords increases over time in common-practice music. Specifically, I conjecture that this finding may be the result of (or related to) increasing instrumental resources over time. I close with some recommendations for future versions of the corpus, such as enabling end users to help repair transcription errors as well as offer ground truths for harmonic analyses and key area information

    Parametrised enumeration

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    In this thesis, we develop a framework of parametrised enumeration complexity. At first, we provide the reader with preliminary notions such as machine models and complexity classes besides proving them to be well-chosen. Then, we study the interplay and the landscape of these classes and present connections to classical enumeration classes. Afterwards, we translate the fundamental methods of kernelisation and self-reducibility into equivalent techniques in the setting of parametrised enumeration. Subsequently, we illustrate the introduced classes by investigating the parametrised enumeration complexity of Max-Ones-SAT and strong backdoor sets as well as sharpen the first result by presenting a dichotomy theorem for Max-Ones-SAT. After this, we extend the definitions of parametrised enumeration algorithms by allowing orders on the solution space. In this context, we study the relations ``order by size'' and ``lexicographic order'' for graph modification problems and observe a trade-off between enumeration delay and space requirements of enumeration algorithms. These results then yield an enumeration technique for generalised modification problems that is illustrated by applying this method to the problems closest string, weak and strong backdoor sets, and weighted satisfiability. Eventually, we consider the enumeration of satisfying teams of formulas of poor man's propositional dependence logic. There, we present an enumeration algorithm with FPT delay and exponential space which is one of the first enumeration complexity results of a problem in a team logic. Finally, we show how this algorithm can be modified such that only polynomial space is required, however, by increasing the delay to incremental FPT time.In diesem Werk begründen wir die Theorie der parametrisierten Enumeration, präsentieren die grundlegenden Definitionen und prüfen ihre Sinnhaftigkeit. Im nächsten Schritt, untersuchen wir das Zusammenspiel der eingeführten Komplexitätsklassen und zeigen Verbindungen zur klassischen Enumerationskomplexität auf. Anschließend übertragen wir die zwei fundamentalen Techniken der Kernelisierung und Selbstreduzierbarkeit in Entsprechungen in dem Gebiet der parametrisierten Enumeration. Schließlich untersuchen wir das Problem Max-Ones-SAT und das Problem der Aufzählung starker Backdoor-Mengen als typische Probleme in diesen Klassen. Die vorherigen Resultate zu Max-Ones-SAT werden anschließend in einem Dichotomie-Satz vervollständigt. Im nächsten Abschnitt erweitern wir die neuen Definitionen auf Ordnungen (auf dem Lösungsraum) und erforschen insbesondere die zwei Relationen \glqq Größenordnung\grqq\ und \glqq lexikographische Reihenfolge\grqq\ im Kontext von Graphen-Modifikationsproblemen. Hierbei scheint es, als müsste man zwischen Delay und Speicheranforderungen von Aufzählungsalgorithmen abwägen, wobei dies jedoch nicht abschließend gelöst werden kann. Aus den vorherigen Überlegungen wird schließlich ein generisches Enumerationsverfahren für allgemeine Modifikationsprobleme entwickelt und anhand der Probleme Closest String, schwacher und starker Backdoor-Mengen sowie gewichteter Erfüllbarkeit veranschaulicht. Im letzten Abschnitt betrachten wir die parametrisierte Enumerationskomplexität von Erfüllbarkeitsproblemen im Bereich der Poor Man's Propositional Dependence Logic und stellen einen Aufzählungsalgorithmus mit FPT Delay vor, der mit exponentiellem Platz arbeitet. Dies ist einer der ersten Aufzählungsalgorithmen im Bereich der Teamlogiken. Abschließend zeigen wir, wie dieser Algorithmus so modifiziert werden kann, dass nur polynomieller Speicherplatz benötigt wird, bezahlen jedoch diese Einsparung mit einem Anstieg des Delays auf inkrementelle FPT Zeit (IncFPT)

    A taxonomy of sublinear multiple keyword pattern matching algorithms

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    AbstractThis article presents a taxonomy of sublinear keyword pattern matching algorithms related to the Boyer-Moore algorithm [3] and the Commentz-Walter algorithm [5, 6]. The taxonomy includes, amongst others, the multiple keyword generalization of the single keyword Boyer-Moore algorithm and an algorithm by Fan and Su [9, 10]. The corresponding precomputation algorithms are presented as well. The taxonomy is based on the idea of ordering algorithms according to their essential problem and algorithm details, and deriving all algorithms from a common starting point by successively adding these details in a correctness preserving way. This way of presentation not only provides a complete correctness argument of each algorithm, but also makes very clear what algorithms have in common (the details of their nearest common ancestor) and where they differ (the details added after their nearest common ancestor). Introduction of the notion of safe shift distances proves to be essential in the derivation and classification of the algorithms. Moreover, the article provides a common derivation for and a uniform presentation of the precomputation algorithms, not yet found in the literature

    A clustering-based approach to automatic harmonic analysis: an exploratory study of harmony and form in Mozart’s piano sonatas

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    We implement a novel approach to automatic harmonic analysis using a clustering method on pitch-class vectors (chroma vectors). The advantage of this method is its lack of top-down assumptions, allowing us to objectively validate the basic music theory premise of a chord lexicon consisting of triads and seventh chords, which is presumed by most research in automatic harmonic analysis. We use the discrete Fourier transform and hierarchical clustering to analyse features of the clustering solutions and illustrate associations between the features and the distribution of clusters over sections of the sonata forms. We also analyse the transition matrix, recovering elements of harmonic function theory.Published versio

    LIPIcs, Volume 274, ESA 2023, Complete Volume

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    LIPIcs, Volume 274, ESA 2023, Complete Volum
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