An effective, simple tempo estimation method based on self-similarity and regularity

Abstract

Tempo estimation is a fundamental problem in music information retrieval. It also forms the basis of other types of rhythmic analysis such as beat tracking and pattern detection. There is a large body of work in tempo estimation using a variety of different approaches that differ in their accuracy as well as their complexity. Fundamentally they take advantage of two properties of musical rhythm: 1) the music signal tends to be self-similar at periodicities related to the underlying rhythmic structure, 2) rhythmic events tend to be spaced regularly in time. We propose an algorithm for tempo estimation that is based on these two properties. We have tried to reduce the number of steps, parameters and modeling assumptions while retaining good performance and causality. The proposed approach outperforms a large number of existing tempo estimation methods and has similar performance to the best-performing ones. We believe that we have conducted the most comprehensive evaluation to date of tempo induction algorithms in terms of number of datasets and tracks.

Exploiting global features for tempo octave correction

“…The proposed method schr1 was compared with the best performing algorithms [24,25,26,27] 4,5 discussed in [5] and a baseline method schr0 using the same five datasets, with the aforementioned improved ground truth. 6 The baseline schr0 consists of just the pulse estimation part described above, but without the SNM82-based octave correction.…”

“…Because the time complexity of computing SNML is quadratic, we prefer smaller L. We found that the value determined for GTZAN, L = 82, represents a good tradeoff between correlation and runtime behavior. To compute the linear regression with WEKA [22], we use the combined five datasets [7,9,3,23,14] also used in [5], but a ground truth improved by Percival. The resulting regression for the rough perceived tempo estimate TO is given by:…”

“…Similar to computing a spectral sum [21] or an enhanced beat histogram [5], BE incorporates harmonics by simply adding to each bin the magnitudes of the bins corresponding to two times and to four times of its own frequency. 3 Because most popular Western music is in 4 /4-time, and most octave errors are by factor of two [2], we purposefully leave out the third harmonic.…”

“…Their classifier uses a support vector machine (SVM) trained with the same periodicity vectors that are also used to find tempo candidates. While Gkiokas et al use a rather complex periodicity detection, employing constant Qtransforms and harmonic/percussive separation, Tzanetakis and Percival [5] chose to simplify state-of-the-art tempo estimation as much as possible, relying on an onset detection function, its autocorrelation, and its cross correlation with an idealized pulse train. Octave correction is achieved with a very simple heuristic.…”

“…Besides fluctuating tempi and other issues [4], one big problem in tempo estimation is the so-called octave error, i.e., results are fractions or multiples of the perceived tempo. Current algorithms are very accurate when ignoring the octave error, but accuracy decreases significantly when requiring the correct octave [5]. Therefore choosing the right octave or metrical level has been the subject of recent research and is the main focus of this paper.…”