Point-set algorithms for pattern discovery and pattern matching in music

An algorithm that discovers the themes, motives and other perceptually significant repeated patterns in a musical work can be used, for example, in a music information retrieval system for indexing a collection of music documents so that it can be searched more rapidly. It can also be used in software tools for music analysis and composition and in a music transcription system or model of music cognition for discovering grouping structure, metrical structure and voice-leading structure. In most approaches to pattern discovery in music, the data is assumed to be in the form of strings. However, string-based methods become inefficient when one is interested in finding highly embellished occurrences of a query pattern or searching for polyphonic patterns in polyphonic music. These limitations can be avoided by representing the music as a set of points in a multidimensional Euclidean space. This point-set pattern matching approach allows the maximal repeated patterns in a passage of polyphonic music to be discovered in quadratic time and all occurrences of these patterns to be found in cubic time. More recently, Clifford et al. (2006) have shown that the best match for a query point set within a text point set of size n can be found in O(n log n) time by incorporating randomised projection, uniform hashing and FFT into the point-set pattern matching approach. Also, by using appropriate heuristics for selecting compact maximal repeated patterns with many non-overlapping occurrences, the point-set pattern discovery algorithms described here can be adapted for data compression. Moreover, the efficient encodings generated when this compression algorithm is run on music data seem to resemble the motivic-thematic analyses produced by human experts

A comparative evaluation of algorithms for discovering translational patterns in Baroque keyboard works

We consider the problem of intra-opus pattern discovery, that is, the task of discovering patterns of a specified type within a piece of music. A music analyst undertook this task for works by Domenico Scarlattti and Johann Sebastian Bach, forming a benchmark of 'target' patterns. The performance of two existing algorithms and one of our own creation, called SIACT, is evaluated by comparison with this benchmark. SIACT out-performs the existing algorithms with regard to recall and, more often than not, precision. It is demonstrated that in all but the most carefully selected excerpts of music, the two existing algorithms can be affected by what is termed the 'problem of isolated membership'. Central to the relative success of SIACT is our intention that it should address this particular problem. The paper contrasts string-based and geometric approaches to pattern discovery, with an introduction to the latter. Suggestions for future work are given

Using discovered, polyphonic patterns to filter computer-generated music

A metric for evaluating the creativity of a music-generating system is presented, the objective being to generate mazurka-style music that inherits salient patterns from an original excerpt by Frédéric Chopin. The metric acts as a filter within our overall system, causing rejection of generated passages that do not inherit salient patterns, until a generated passage survives. Over fifty iterations, the mean number of generations required until survival was 12.7, with standard deviation 13.2. In the interests of clarity and replicability, the system is described with reference to specific excerpts of music. Four concepts–Markov modelling for generation, pattern discovery, pattern quantification, and statistical testing–are presented quite distinctly, so that the reader might adopt (or ignore) each concept as they wish

The Semantic Web MIDI Tape: An Interface for Interlinking MIDI and Context Metadata

The Linked Data paradigm has been used to publish a large number of musical datasets and ontologies on the Semantic Web, such as MusicBrainz, AcousticBrainz, and the Music Ontology. Recently, the MIDI Linked Data Cloud has been added to these datasets, representing more than 300,000 pieces in MIDI format as Linked Data, opening up the possibility for linking fine-grained symbolic music representations to existing music metadata databases. Despite the dataset making MIDI resources available in Web data standard formats such as RDF and SPARQL, the important issue of finding meaningful links between these MIDI resources and relevant contextual metadata in other datasets remains. A fundamental barrier for the provision and generation of such links is the difficulty that users have at adding new MIDI performance data and metadata to the platform. In this paper, we propose the Semantic Web MIDI Tape, a set of tools and associated interface for interacting with the MIDI Linked Data Cloud by enabling users to record, enrich, and retrieve MIDI performance data and related metadata in native Web data standards. The goal of such interactions is to find meaningful links between published MIDI resources and their relevant contextual metadata. We evaluate the Semantic Web MIDI Tape in various use cases involving user-contributed content, MIDI similarity querying, and entity recognition methods, and discuss their potential for finding links between MIDI resources and metadata

Improving the running time of repeated pattern discovery in multidimensional representations of music

Methods for discovering repeated patterns in music are important tools in computational music analysis. Repeated pattern discovery can be used in applications such as song classification and music generation in computational creativity. Multiple approaches to repeated pattern discovery have been developed, but many of the approaches do not work well with polyphonic music, that is, music where multiple notes occur at the same time. Music can be represented as a multidimensional dataset, where notes are represented as multidimensional points. Moving patterns in time and transposing their pitch can be expressed as translation. Multidimensional representations of music enable the use of algorithms that can effectively find repeated patterns in polyphonic music. The research on methods for repeated pattern discovery in multidimensional representa- tions of music is largely based on the SIA and SIATEC algorithms. Multiple variants of both algorithms have been developed. Most of the variants use SIA or SIATEC directly and then use heuristic functions to identify the musically most important patterns. The variants do not thus typically provide improvements in running time. However, the running time of SIA and SIATEC can be impractical on large inputs. This thesis focuses on improving the running time of pattern discovery in multidimensional representations of music. The algorithms that are developed in this thesis are based on SIA and SIATEC. Two approaches to improving running time are investigated. The first approach involves the use of hashing, and the second approach is based on using filtering to avoid the computation of unimportant patterns altogether. Three novel algorithms are presented: SIAH, SIATECH, and SIATECHF. The SIAH and SIATECH algorithms, which use hashing, were found to provide great improvements in running time over the corresponding SIA and SIATEC algorithms. The use of filtering in SIATECHF was not found to significantly improve the running time of repeated pattern discovery

Perception based approach on pattern discovery and organisation of point-set data

The general topic of the thesis is computer aided music analysis on point-set data utilising theories outlined in Timo Laiho’s Analytic-Generative Methodology (AGM) [19]. The topic is in the field of music information retrieval, and is related to previous work on both pattern discovery and computational models of music. The thesis aims to provide analysis results that can be compared to existing studies. AGM introduces two concepts based on perception, sensation and cognitive processing: interval–time complex (IntiC) and musical vectors (muV). These provide a mathematical framework for the analysis of music. IntiC is a value associated with the velocity, or rate of change, between musical notes. Musical vectors are the vector representations of these rates of change. Laiho explains these attributes as meaningful for both music analysis and as tools for music generation. Both of these attributes can be computed from a point-set representation of music data. The concepts in AGM can be viewed as being related to geometric methods for pattern discovery algorithmsof Meredith, Lemström et al.[24] whointroduce afamily of ‘Structure Induction Algorithms’. These algorithms are used to find repeating patterns in multidimensional point-set data. Algorithmic implementations of intiC and muV were made for this thesis and examined in the use of rating and selecting patterns output by the pattern discovery algorithms. In addition software tools for using these concepts of AGM were created. The concepts of AGM and pattern discovery were further related to existing work in computer aided musicology

Discovering distorted repeating patterns in polyphonic music through longest increasing subsequences

We study the problem of identifying repetitions under transposition and time-warp invariances in polyphonic symbolic music. Using a novel onset-time-pair representation, we reduce the repeating pattern discovery problem to instances of the classical problem of finding the longest increasing subsequences. The resulting algorithm works in O(n(2) log n) time where n is the number of notes in a musical work. We also study windowed variants of the problem where onset-time differences between notes are restricted, and show that they can also be solved in O(n(2) log n) time using the algorithm.Peer reviewe