Signal processing methods for the automatic transcription of music are developed in this thesis. Music transcription is here understood as the process of analyzing a music signal so as to write down the parameters of the sounds that occur in it. The applied notation can be the traditional musical notation or any symbolic representation which gives sufficient information for performing the piece using the available musical instruments. Recovering the musical notation automatically for a given acoustic signal allows musicians to reproduce and modify the original performance. Another principal application is structured audio coding: a MIDI-like representation is extremely compact yet retains the identifiability and characteristics of a piece of music to an important degree. The scope of this thesis is in the automatic transcription of the harmonic and melodic parts of real-world music signals. Detecting or labeling the sounds of percussive instruments (drums) is not attempted, although the presence of these is allowed in the target signals. Algorithms are proposed that address two distinct subproblems of music transcription. The main part of the thesis is dedicated to multiple fundamental frequency (F0) estimation, that is, estimation of the F0s of several concurrent musical sounds. The other subproblem addressed is musical meter estimation. This has to do with rhythmic aspects of music and refers to the estimation of the regular pattern of strong and weak beats in a piece of music. For multiple-F0 estimation, two different algorithms are proposed. Both methods are based on an iterative approach, where the F0 of the most prominent sound is estimated, the sound is cancelled from the mixture, and the process is repeated for the residual. The first method is derived in a prag...

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Beat tracking is what people do when they tap their feet in time to music. We present a software system which performs this task, processing music in a standard digital audio format and estimating the locations of musical beats. A time-domain algorithm detects salient acoustic events, and then a clustering algorithm groups the time intervals between events to obtain hypotheses about the current tempo. Multiple competing agents track these hypotheses throughout the music, with further agents being created at decision points. The output for each agent is a sequence of beat locations, which is evaluated for its closeness of t to the data. This approach to beat tracking assumes no previous knowledge of the music such as the style, time signature or approximate tempo; all required information is derived from the audio data. The system has been tested with various styles of music (popular, jazz, and classical) and performs robustly, rarely making errors in popular music, a...

. When a person taps a foot in time with a piece of music, they are performing beat tracking. Beat tracking is fundamental to the understanding of musical structure, and therefore an essential ability for any system which purports to exhibit musical intelligence or understanding. We present an off-line multiple agent beat tracking system which estimates the locations of musical beats in MIDI performance data. This approach to beat tracking requires no prior information about the input data, such as the tempo or time signature; all required information is derived from the performance data. For constant tempo performances, previous beat tracking systems have proved successful; however, these systems fail when there are large variations in tempo. We examine the role of musical knowledge in guiding the beat tracking process, and show that a system equipped with knowledge of musical salience is able to track the beat of music even in the presence of large tempo variations. Results are prese...

One of the difficulties with assessing tempo or beat tracking systems is that there is no standard corpus of data on which they can be tested. This situation is partly because the choice of data set often depends on the goals of the system, which might be, for example, automatic transcription, computer accompaniment of a human performer, or the analysis of expressive timing in musical performance. Without standard test data, there is the risk of overfitting a system to the data on which it is tested, and developing a system which is not suitable for use outside a very limited musical domain. In this paper, we use a large, publicly available set of performances of two Beatles songs recorded on a Yamaha Disklavier in order to compare two models of tempo tracking: a probabilistic model which uses a Kalman filter to estimate tempo and beat times, and a tempo tracker based on a multiagent search strategy. Both models perform extremely well on the test data, with the multiagent search achieving marginally better results. We propose two simple measures of tempo tracking difficulty, and argue that a broader set of test data is required for comprehensive testing of tempo tracking systems.

This thesis describes an approach to representing musical rhythm in computational terms. The purpose of such an approach is to provide better models of musical time for machine accompaniment of human musicians and in that attempt, to better understand the processes behind human perception and performance. The intersections between musicology and artificial intelligence (AI) are reviewed, describing the rewards from the interdisciplinary study of music with AI techniques, and the converse benefits to AI research. The arguments for formalisation of musicological theories using AI and cognitive science concepts are presented. These bear upon the approach of research, considering ethnographic and process models of music versus traditionally descriptive methods of music study. This enquiry investigates the degree to which the human task of music can be studied and modelled computationally. It simultaneously performs the AI task of problem domain identification and constraint. The psycholo...

Abstract. A network of relaxation oscillators is used to find downbeats in rhythmical patterns. In this study, a novel model is described in detail. Its behavior is tested by exposing it to patterns having various levels of rhythmic complexity. We analyze the performance of the model and relate its success to previous work dealing with fast synchrony in coupled oscillators. 1 Downbeat Induction The term beats refers to sounds that are perceived as being equally spaced in time. Downbeats are particularly salient beats that usually occur at a comfortable tapping rate. When you tap your feet to the radio you are finding downbeats, a skill called beat induction. Downbeats act as a unifying force, lending music the feeling of movement by allowing the listener to predict the onset of important musical events. The process of beat induction is influenced by many aspects of music including harmony, melody and rhythm [2, 9]. Because interactions are not always simple, it can be difficult to predict the locations of downbeats. For example, in rock and roll music, even though chord changes (harmonic components) usually occur on the first note of a musical bar, downbeats are usually aligned with the second note due to syncopated drumming style. Furthermore, although

This paper is concerned with the handling of rhythm in music content processing applications. Keeping this framework in mind, we briefly report on terminology issues and the interdisciplinary nature of rhythm investigations, we then review approaches to computational modeling of rhythm and rhythm representation schemes. We comment the bottomup and top-down oriented approaches to computational modeling and the parallel that some authors make with physiological and cognitive views on rhythm perception. We argue that investigations should be listener-oriented, signal-oriented and application-oriented. 1

We have developed a representation for musical rhythm and rhythmic structure based on concepts derived from African and African-American musics. Included in the representation are a model for expressive timing against an isochronous pulse, and a cellular approach to musical organization. In our implementation, the representation and its data structures are controlled and modified in real time using MAX. The richness of control over many meaningful musical quantities distinguishes our representation from those in more common usage, such as music notation programs, sequencers, and drum machines. 1 Introduction Many authors [2][4][7][8] have attempted to address the universal issue of rhythm perception and cognition. While these efforts feature rigorous approaches to data analysis and modeling, such work often contains musical assumptions specific to Western European classical music, even if the music under study lies outside of that tradition. It is clear that one cannot transcend one'...

The Normalized Positive (NPOS) model is a novel matching model that predicts downbeat location and pattern complexity in rhythmical patterns. Though similar models report success, the NPOS model is particularly effective at making these predictions while at the same time being theoretically and mathematically simple. In this paper, the details of the model are explored and a comparison is made to existing models. Several datasets are used to examine the complexity predictions of the model. Special attention is paid to the model's ability to account for the effects of musical experience on rhythm perception (McAuley & Semple, 1999; Drake, 1993).