Particle Filtering Applied to Musical Tempo Tracking

RIGHTS : This article is licensed under the BioMed Central licence at http://www.biomedcentral.com/about/license which is similar to the 'Creative Commons Attribution Licence'. In brief you may : copy, distribute, and display the work; make derivative works; or make commercial use of the work - under the following conditions: the original author must be given credit; for any reuse or distribution, it must be made clear to others what the license terms of this work are.This paper explores the use of particle filters for beat tracking in musical audio examples. The aim is to estimate the time-varying tempo process and to find the time locations of beats, as defined by human perception. Two alternative algorithms are presented, one which performs Rao-Blackwellisation to produce an almost deterministic formulation while the second is a formulation which models tempo as a Brownian motion process. The algorithms have been tested on a large and varied database of examples and results are comparable with the current state of the art. The deterministic algorithm gives the better performance of the two algorithms.Peer Reviewe

Reliability-Informed Beat Tracking of Musical Signals

Abstract—A new probabilistic framework for beat tracking of musical audio is presented. The method estimates the time between consecutive beat events and exploits both beat and non-beat information by explicitly modeling non-beat states. In addition to the beat times, a measure of the expected accuracy of the estimated beats is provided. The quality of the observations used for beat tracking is measured and the reliability of the beats is automatically calculated. A k-nearest neighbor regression algorithm is proposed to predict the accuracy of the beat estimates. The performance of the beat tracking system is statistically evaluated using a database of 222 musical signals of various genres. We show that modeling non-beat states leads to a significant increase in performance. In addition, a large experiment where the parameters of the model are automatically learned has been completed. Results show that simple approximations for the parameters of the model can be used. Furthermore, the performance of the system is compared with existing algorithms. Finally, a new perspective for beat tracking evaluation is presented. We show how reliability information can be successfully used to increase the mean performance of the proposed algorithm and discuss how far automatic beat tracking is from human tapping. Index Terms—Beat-tracking, beat quality, beat-tracking reliability, k-nearest neighbor (k-NN) regression, music signal processing. I

A Model of Rhythm Transcription as Path Selection Through Approximate Common Divisor Graphs

We apply the concept of approximated common divisors (ACDs) to estimate the tempo and quantize the durations of a rhythmic sequence. The ACD models the duration of the tatum within the sequence, giving its rate in beats per minute. The rhythm input, a series of timestamps, is first split into overlapping frames. Then, we compute the possible ACDs that fit this frame and build a graph with the candidate ACDs as nodes. By building this graph, we transform the quantization problem into one of path selection, where the nodes represent the ACDs and determine the note values of the transcription and the edges represent tempo transitions between frames. A path through the graph thus corresponds to a rhythm transcription. For path selection, we present both an automated method using weights for evaluating the transcription and finding the shortest path, and an interactive approach that gives users the possibility of influencing the path selection

Rhythm Transcription of Polyphonic MIDI Performances Based on a Merged-output HMM for Multiple Voices

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Note Value Recognition for Piano Transcription Using Markov Random Fields

This paper presents a statistical method for use in music transcription that can estimate score times of note onsets and offsets from polyphonic MIDI performance signals. Because performed note durations can deviate largely from score-indicated values, previous methods had the problem of not being able to accurately estimate offset score times (or note values) and thus could only output incomplete musical scores. Based on observations that the pitch context and onset score times are influential on the configuration of note values, we construct a context-tree model that provides prior distributions of note values using these features and combine it with a performance model in the framework of Markov random fields. Evaluation results show that our method reduces the average error rate by around 40 percent compared to existing/simple methods. We also confirmed that, in our model, the score model plays a more important role than the performance model, and it automatically captures the voice structure by unsupervised learning

Bayesian methods in music modelling

This thesis presents several hierarchical generative Bayesian models of musical signals designed to improve the accuracy of existing multiple pitch detection systems and other musical signal processing applications whilst remaining feasible for real-time computation. At the lowest level the signal is modelled as a set of overlapping sinusoidal basis functions. The parameters of these basis functions are built into a prior framework based on principles known from musical theory and the physics of musical instruments. The model of a musical note optionally includes phenomena such as frequency and amplitude modulations, damping, volume, timbre and inharmonicity. The occurrence of note onsets in a performance of a piece of music is controlled by an underlying tempo process and the alignment of the timings to the underlying score of the music. A variety of applications are presented for these models under differing inference constraints. Where full Bayesian inference is possible, reversible-jump Markov Chain Monte Carlo is employed to estimate the number of notes and partial frequency components in each frame of music. We also use approximate techniques such as model selection criteria and variational Bayes methods for inference in situations where computation time is limited or the amount of data to be processed is large. For the higher level score parameters, greedy search and conditional modes algorithms are found to be sufficiently accurate. We emphasize the links between the models and inference algorithms developed in this thesis with that in existing and parallel work, and demonstrate the effects of making modifications to these models both theoretically and by means of experimental results