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Pointset algorithms for pattern discovery and pattern matching in music
 In ContentBased Retrieval, Dagstuhl Seminar Proceedings
, 2006
"... Abstract. 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 ..."
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Abstract. 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 voiceleading structure. In most approaches to pattern discovery in music, the data is assumed to be in the form of strings. However, stringbased 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 pointset 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. [1] 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 pointset pattern matching approach. Also, by using appropriate heuristics for selecting compact maximal repeated patterns with many nonoverlapping occurrences, the pointset 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 motivicthematic analyses produced by human experts. Keywords. Contentbased music information retrieval, pointset pattern matching 1
COSIATEC and SIATECCompress: Pattern discovery by geometric compression
 in Music Information Retrieval Evaluation Exchange (Competition on “Discovery of Repeated Themes & Sections”) (MIREX
, 2013
"... Three versions of each of two greedy compression algorithms, COSIATEC and SIATECCOMPRESS, were run on the JKU Patterns Development Database. Each algorithm takes a pointset representation of a piece of music as input and computes a compressed encoding of the piece in the form of a union of translat ..."
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Three versions of each of two greedy compression algorithms, COSIATEC and SIATECCOMPRESS, were run on the JKU Patterns Development Database. Each algorithm takes a pointset representation of a piece of music as input and computes a compressed encoding of the piece in the form of a union of translational equivalence classes of maximal translatable patterns. COSIATEC iteratively uses the SIATEC algorithm to strictly partition the input set into the covered sets of a set of MTP TECs. On each iteration, COSIATEC finds the “best ” TEC and then removes its covered set from the input dataset. SIATECCOMPRESS runs SIATEC just once to get a list of MTP TECs and then selects a subset of the “best ” TECs that is sufficient to cover the input dataset. Both algorithms select TECs primarily on the basis of compression ratio and compactness. 1.
Pitch spelling: Investigating reductions of the search space
"... Abstract — Pitch spelling addresses the question of how to derive traditional score notation from pitch classes or MIDI numbers. In this paper, we motivate that the diatonic notes in a piece of music are easier to spell correctly than the nondiatonic notes. Then we investigate 1) whether the genera ..."
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Abstract — Pitch spelling addresses the question of how to derive traditional score notation from pitch classes or MIDI numbers. In this paper, we motivate that the diatonic notes in a piece of music are easier to spell correctly than the nondiatonic notes. Then we investigate 1) whether the generally used method of calculating the proportion of correctly spelled notes to evaluate pitch spelling models can be replaced by a method that concentrates only on the nondiatonic pitches, and 2) if an extra evaluation measure to distinguish the incorrectly spelled diatonic notes from the incorrectly spelled nondiatonic notes would be useful. To this end, we calculate the typical percentage of pitch classes that correspond to diatonic notes and check whether those pitch classes do indeed refer to diatonic notes in a piece of music. We explore extensions of the diatonic set. Finally, a good performing pitch spelling algorithm is investigated to see what percentage of its incorrectly spelled notes are diatonic notes. It turns out that a substantial part of the incorrectly spelled notes consist of diatonic notes, which means that the standard evaluation measure of pitch spelling algorithms cannot be replaced by a measure that only concentrates on nondiatonic notes without losing important information. We propose instead that two evaluation measures could be added to the standard correctness rate to be able to give a more complete view of a pitch spelling model. I.
Compactness in the Eulerlattice: A parsimonious pitch spelling model
, 2009
"... Compactness and convexity have been shown to represent important principles in music, reflecting a notion of consonance in scales and chords, and have been successfully applied to wellknown problems from music research. In this paper, the notion of compactness is applied to the problem of pitch spe ..."
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Compactness and convexity have been shown to represent important principles in music, reflecting a notion of consonance in scales and chords, and have been successfully applied to wellknown problems from music research. In this paper, the notion of compactness is applied to the problem of pitch spelling. Pitch spelling addresses the question of how to derive traditional score notation from 12tone pitch classes or MIDI. This paper proposes a pitch spelling algorithm that is based on only one principle: compactness in the Eulerlattice. Generally, the goodness of a pitch spelling model is measured in terms of its spelling accuracy. In this paper, we concentrate on the parsimony, cognitive plausibility and generalizability of the model as well. The spelling accuracy of the algorithm was evaluated on the first book of Bach’s Welltempered Clavier and had a success rate of 99.21%. A qualitative discussion of the model’s cognitive plausibility, its parsimony and its generalizability is given.
USING POINTSET COMPRESSION TO CLASSIFY FOLK SONGS
"... Thirteen different compression algorithms were used to calculate the normalized compression distances (NCDs) between pairs of tunes in the Annotated Corpus of 360 Dutch folk songs from the collection Onder de groene linde. These NCDs were then used in conjunction with the 1nearestneighbour algorit ..."
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Thirteen different compression algorithms were used to calculate the normalized compression distances (NCDs) between pairs of tunes in the Annotated Corpus of 360 Dutch folk songs from the collection Onder de groene linde. These NCDs were then used in conjunction with the 1nearestneighbour algorithm and leaveoneout crossvalidation to classify the 360 melodies into tune families. The classifications produced by the algorithms were compared with a groundtruth classification prepared by expert musicologists. Twelve of the thirteen compressors used in the experiment were based on the discovery of translational equivalence classes (TECs) of maximal translatable patterns (MTPs) in pointset representations of the melodies. The twelve algorithms consisted of four variants of each of three basic algorithms, COSIATEC, SIATECCOMPRESS and Forth’s algorithm. The main difference between these algorithms is that COSIATEC strictly partitions the input point set into TEC covered sets, whereas the TEC covered sets in the output of SIATECCOMPRESS and Forth’s algorithm may share points. The generalpurpose compressor, bzip2, was used as a baseline against which the pointset compression algorithms were compared. The highest classification success rate of 77–84 % was achieved by COSIATEC, followed by 60–64 % for Forth’s algorithm and then 52–58 % for SIATECCOMPRESS. When the NCDs were calculated using bzip2, the success rate was only 12.5%. The results demonstrate that the effectiveness of NCD for measuring similarity between folksongs for classification purposes is highly dependent upon the actual compressor chosen. Furthermore, it seems that compressors based on finding maximal repeated patterns in pointset representations of music show more promise for NCDbased music classification than generalpurpose compressors designed for compressing text strings. 1.
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"... ISBN 8873951554 © 2006 ICMPC Pitch spelling using compactness Pitch spelling addresses the question of how to derive traditional score notation from 12tone pitch numbers or MIDI format. This paper proposes a pitch spelling algorithm that is based on only one principle: compactness in the Eulerl ..."
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ISBN 8873951554 © 2006 ICMPC Pitch spelling using compactness Pitch spelling addresses the question of how to derive traditional score notation from 12tone pitch numbers or MIDI format. This paper proposes a pitch spelling algorithm that is based on only one principle: compactness in the Eulerlattice. The algorithm was evaluated on the first book of Bach’s Welltempered Clavier and had a success rate of 98.98 %. The algorithm is compared with other models and further improvements are discussed.
ANALYSIS BY COMPRESSION: AUTOMATIC GENERATION OF COMPACT GEOMETRIC ENCODINGS OF MUSICAL OBJECTS
"... MEL is a geometric music encoding language designed to allow for musical objects to be encoded parsimoniously as sets of points in pitchtime space, generated by performing geometric transformations on component patterns. MEL has been implemented in Java and coupled with the SIATEC pattern discovery ..."
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MEL is a geometric music encoding language designed to allow for musical objects to be encoded parsimoniously as sets of points in pitchtime space, generated by performing geometric transformations on component patterns. MEL has been implemented in Java and coupled with the SIATEC pattern discovery algorithm to allow for compact encodings to be generated automatically from in extenso note lists. The MELSIATEC system is founded on the belief that music analysis and music perception can be modelled as the compression of in extenso descriptions of musical objects. 1.
Maximal Translational Equivalence Classes of Musical Patterns in PointSet Representations
"... Abstract. Representing musical notes as points in pitchtime space causes repeated motives and themes to appear as translationally related patterns that often correspond to maximal translatable patterns (MTPs) [1]. However, an MTP is also often the union of a salient pattern with one or two temporal ..."
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Abstract. Representing musical notes as points in pitchtime space causes repeated motives and themes to appear as translationally related patterns that often correspond to maximal translatable patterns (MTPs) [1]. However, an MTP is also often the union of a salient pattern with one or two temporally isolated notes. This has been called the problem of isolated membership [2]. Examining the MTPs in musical works suggests that salient patterns may correspond more often to the intersections of MTPs than to the MTPs themselves. This paper makes a theoretical contribution, by exploring properties of patterns that are maximal with respect to their translational equivalence classes (MTEC). We prove that a pattern is MTEC if and only if it can be expressed as the intersection of MTPs. We also prove a relationship between MTECs and socalled conjugate patterns.
Author: David Meredith Title: A CompressionBased Model of Musical Learning Preference for talk or poster: NO PREFERENCE
"... A long tradition of psychological research considers perception to be governed by the simplicity principle [1,2]. Both music perception and music analysis involve searching for the simplest explanations for musical objects, where a musical object could be any quantity of music from a motive to a who ..."
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A long tradition of psychological research considers perception to be governed by the simplicity principle [1,2]. Both music perception and music analysis involve searching for the simplest explanations for musical objects, where a musical object could be any quantity of music from a motive to a whole corpus. Musical objects are usually interpreted within the context of larger objects that contain them. For example, a work might be interpreted in the context of a corpus containing all the works by the same composer. Drawing on Kolmogorov complexity theory [3], I propose that an interpretation or reading of a musical object can be modeled as a program that computes an in extenso representation of the object. On this view, when interpreting a musical work for the first time, both the analyst and the listener’s brain are seen to be attempting to find the shortest programs that compute corpora containing the new work. In the case of the listener, the new work is interpreted largely nonconsciously and in realtime in the context of a corpus which is a subset of all the music that the listener has previously heard. The analyst, on the other hand, is free to deliberately select a corpus that allows for the most satisfying (usually the most economical) interpretation of the new work. This is modelled as the modification of a preexisting program, P, that computes some corpus (i.e., a compact encoding of the corpus), so that it can additionally