Fundamentals of Music Processing

Fundamentals of Music Processing

Chapter 6: Tempo and Beat Tracking

Meinard MüllerInternational Audio Laboratories Erlangen

www.music-processing.de

Meinard Müller: Fundamentals of Music Processing© Springer International Publishing Switzerland, 2015

Chapter 6: Tempo and Beat TrackingSlide 2

Book: Fundamentals of Music Processing

Meinard MüllerFundamentals of Music ProcessingAudio, Analysis, Algorithms, Applications483 p., 249 illus., 30 illus. in color, hardcoverISBN: 978-3-319-21944-8Springer, 2015

Accompanying website: www.music-processing.de



Chapter 6: Tempo and Beat Tracking

6.1 Onset Detection6.2 Tempo Analysis6.3 Beat and Pulse Tracking6.4 Further Notes

Tempo and beat are further fundamental properties of music. In Chapter 6, we introduce the basic ideas on how to extract tempo-related information from audio recordings. In this scenario, a first challenge is to locate note onset information—a task that requires methods for detecting changes in energy and spectral content. To derive tempo and beat information, note onset candidates are then analyzed with regard to quasiperiodic patterns. This leads us to the study of general methods for local periodicity analysis of time series.



6 Tempo and Beat TrackingTeaser



6 Tempo and Beat TrackingFig. 6.1

Time (seconds)









6.1 Onset DetectionFig. 6.2




Local energy function

Discrete derivative

Local energy functionLocal energy functionLocal energy function

Novelty function (half-wave rectification)

Novelty function (logarithmic energy)

Annotated note onsets




Time (seconds)

Local energy function





Time (seconds)


Discrete derivative




Time (seconds)

Novelty function (half-wave rectification)





Time (seconds)

Novelty function (logarithmic energy)





Piano Violin Flute

Waveform and energy-based novelty function of the note C4 (261.6 Hz)




Magnitude spectrogram Compressed spectrogram Gamma = 1

Compressed spectrogram Gamma = 1000




Compressed spectrogram

Novelty function Δ Spectral and local average function


Novelty function subtracting the local average




Energy-based novelty function

Spectral-based novelty function








Wrapped phase

Unwrapped phase



6.1 Onset DetectionFig. 6.10 Jointly consider phase and magnitude



6.1 Tempo AnalysisFig. 6.11

Tempogram with harmonics

Tempogram with sub-harmonics




Assumptions:- beat positions occur at note onset positions- beat positions are more or less equally spaced




Fourier Tempogram




Autocorrelation Tempogram



6.3 Beat and Pulse TrackingFig. 6.18

Predominant Local Pulse (PLP)

Novelty function

Tempogram (with frame-wise tempo maxima)

Optimal windowed sinusoidscorresponding to the maxima

Accumulation of all sinusoids (with overlap-add)

PLP function obtainedafter half-wave rectification



Time (seconds)


Tem

po

(B

PM

)



Time (seconds)


Tem

po

(B

PM

)



Time (seconds)


Tem

po

(B

PM

)



Time (seconds)


Tem

po

(B

PM

)



Time (seconds)


Tem

po

(B

PM

)







Penalty function measuring the deviation of agiven beat period from the ideal beat period

Since tempo deviations are relative in nature (doubling the tempo should be penalized to the same degree as halving the tempo), the penalty function is defined to be symmetric on a logarithmic axis




Beat sequence

Score function



6.3 Beat and Pulse TrackingTable 6.1 Accumulated score







Time (seconds)




Time (seconds)



6.4 Further NotesFig. 6.24

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Fundamentals of Music Processing