Tracking metrical structure changes with sparse-NMF

Abstract

The estimation of rhythmic properties such as tempo, beat positions or metrical structure are central aspects of Music Information Retrieval (MIR) research. Meter inference algorithms are typically designed to track metrical structure in presence of mild deviations of the feature estimates over time in order to account for performance imprecisions, expressive timing or musical effects such as accelerando. Abrupt changes of metrical structure over time are comparatively rarely addressed. In this paper, we present an unsupervised approach to detect metrical structure changes. Formulating the problem as a metrical structure based segmentation retrieval task, we present a variant of sparse NMF and compare it to existing methods. For evaluation, we introduce a new dataset of music recordings containing metric modulations with the corresponding annotations.

Dynamic Time Signature Recognition, Tempo Inference, and Beat Tracking Through the Metrogram Transform

“…In order to evaluate the performance of our approach on extracts with both beat and time-signature variations, a metrically diverse custom dataset is presented. Although several other datasets have been presented with either irregular or time-varying time signatures [6], [8], [10], [13], [14], [16], [32], none are available for extracts that exhibit both simultaneously with rubato, as is the case in improvisatory genres such as jazz. This custom dataset was recorded by the first author and features 43 extracts (primarily jazz piano) with primary time signature divisions of 2, 3, 4, 5, and 7 (35 extracts), as well as several metrically ambiguous extracts with dynamic (time-varying) time signature divisions and tempo (rubato).…”

“…As a consequence of their construction, R CW T has harmonics associated with the rhythmic components, whilst R AC has sub-harmonics. Harmonic and tempo ambiguity in Tempograms have been encountered previously in the literature, with certain methods proposed, such as exploiting the combined properties of the Autocorrelation (R AC and Fourier Tempograms (R DF T ) through multiplication [16], [27], [28] and performing octave removal [26]. However, as a consequence of the methods employed (such as DFT as opposed to CWT) to generate R AC and R CW T in [16], [27], [28], and the limitations of purely targeting octave removal in [26], fundamental "rhythmic" frequencies remain largely inseparable from their harmonics.…”

“…Harmonic and tempo ambiguity in Tempograms have been encountered previously in the literature, with certain methods proposed, such as exploiting the combined properties of the Autocorrelation (R AC and Fourier Tempograms (R DF T ) through multiplication [16], [27], [28] and performing octave removal [26]. However, as a consequence of the methods employed (such as DFT as opposed to CWT) to generate R AC and R CW T in [16], [27], [28], and the limitations of purely targeting octave removal in [26], fundamental "rhythmic" frequencies remain largely inseparable from their harmonics. This paper by contrast proposes combining the properties of the presented CWT and Autocorrelation Tempograms, employing the same receptive fields σ ω bpm in each case, via computing the geometric mean of the two arrays such that harmonics and sub-harmonics are attenuated and the resulting Tempogram normalised.…”

“…HMM bar pointer models have also been successfully applied to irregular ("odd") time signature beat tracking tasks [6], [8], [13], [14], however, the approaches assume a constant metric division (often a priori). Likewise, for methods that tackle time-varying time signatures using HMMs [10], [16] or RNNS [24], [39], the models employ cascade formats, such that joint beat and bar tracking is performed sequentially resulting in beat lengths independent of metric properties. The subjectivity of perceived pulse (beat) positions and lengths is addressed in literature through the employment of agents [5], [31], yet the process has not been generalised to joint time signature and beat tracking tasks.…”