Chapter 6: Tempo and Beat Tracking

Tempo and beat are further fundamental properties of music. In Chapter 6 of [Müller, FMP, Springer 2015], 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.

6.1 Onset Detection
6.2 Tempo Analysis
6.3 Beat and Pulse Tracking
6.4 Further Notes

Notebooks

Topic	Relation to [Müller, FMP, Springer 2015] & Description	HTML	IPYNB
Onset Detection	[Section 6.1] Transient; attack; onset; novelty function; peak picking; sonification; Queen example (Another One Bites the Dust); C4-note example; Borodin example (String Quartet No. 2, 3rd movement)	[html]	[ipynb]
Energy-Based Novelty	[Section 6.1.1] Local energy; half-wave rectification; novelty function; Queen example (Another One Bites the Dust); C4-note example	[html]	[ipynb]
Spectral-Based Novelty	[Section 6.1.2] Spectral flux; logarithmic compression; half-wave rectification; Queen example (Another One Bites the Dust)	[html]	[ipynb]
Phase-Based Novelty	[Section 6.1.3] Principle value; phase wrapping; phase unwrapping; principle argument function; Queen example (Another One Bites the Dust)	[html]	[ipynb]
Complex-Domain Novelty	[Section 6.1.4] Phase; magnitude; Queen example (Another One Bites the Dust)	[html]	[ipynb]
Novelty: Comparison of Approaches	[Section 6.1] Queen example; C4-note example; Shostakovich example (Waltz No. 2)	[html]	[ipynb]
Peak Picking	[Section 6.1] Peak; local maximum; smoothing; adaptive thresholding; minimal peak distance; implementations (MSAF, scipy, LibROSA, Boeck, Roeder); Shostakovich example (Waltz No. 2)	[html]	[ipynb]
Tempo and Beat	[Section 6.2.1] Tempogram; pulse level; tempo octave; tempo harmonic; tempo subharmonic; global tempo; Queen example; Happy Birthday example; further examples	[html]	[ipynb]
Fourier Tempogram	[Section 6.2.2] Fourier analysis; windowed sinusoid; tempo resolution; click-track example; Shostakovich example (Waltz No. 2)	[html]	[ipynb]
Autocorrelation Tempogram	[Section 6.2.3] Short-time autocorrelation, time–lag representation; tempo harmonic; tempo subharmonic; Shostakovich example (Waltz No. 2); click-track example	[html]	[ipynb]
Cyclic Tempogram	[Section 6.2.4] Scaling parameter; tempo octave; tempo harmonic; tempo subharmonic; tempo feature; click-track example; Brahms example (Hungarian Dance No. 5); Zager and Evans example (In the Year 2525)	[html]	[ipynb]
Predominant Local Pulse	[Section 6.3.1] Fourier tempogram; windowed sinusoid; overlap–add; local pulse; tempo range; pulse levels; Shostakovich example (Waltz No. 2); Brahms example (Hungarian Dance No. 5); Burgmüller example (Op. 100 No. 2)	[html]	[ipynb]
Beat Tracking by Dynamic Programming	[Section 6.3.2, Exercise 6.12] Penalty function; beat sequence; dynamic programming; Shostakovich example (Waltz No. 2); Brahms example (Hungarian Dance No. 5)	[html]	[ipynb]
Adaptive Windowing	[Section 6.3.3] Beat-synchronous feature; transient removal; chromatic scale example	[html]	[ipynb]