Transcript
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
Meinard Müller: Fundamentals of Music Processing© Springer International Publishing Switzerland, 2015
Chapter 6: Tempo and Beat TrackingSlide 3
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.
Meinard Müller: Fundamentals of Music Processing© Springer International Publishing Switzerland, 2015
Chapter 6: Tempo and Beat TrackingSlide 4
6 Tempo and Beat TrackingTeaser
Meinard Müller: Fundamentals of Music Processing© Springer International Publishing Switzerland, 2015
Chapter 6: Tempo and Beat TrackingSlide 5
6 Tempo and Beat TrackingFig. 6.1
Time (seconds)
Meinard Müller: Fundamentals of Music Processing© Springer International Publishing Switzerland, 2015
Chapter 6: Tempo and Beat TrackingSlide 6
6 Tempo and Beat TrackingFig. 6.1
Meinard Müller: Fundamentals of Music Processing© Springer International Publishing Switzerland, 2015
Chapter 6: Tempo and Beat TrackingSlide 7
6 Tempo and Beat TrackingFig. 6.1
Meinard Müller: Fundamentals of Music Processing© Springer International Publishing Switzerland, 2015
Chapter 6: Tempo and Beat TrackingSlide 8
6.1 Onset DetectionFig. 6.2
Meinard Müller: Fundamentals of Music Processing© Springer International Publishing Switzerland, 2015
Chapter 6: Tempo and Beat TrackingSlide 9
6.1 Onset DetectionFig. 6.3
Local energy function
Discrete derivative
Local energy functionLocal energy functionLocal energy function
Novelty function (half-wave rectification)
Novelty function (logarithmic energy)
Annotated note onsets
Meinard Müller: Fundamentals of Music Processing© Springer International Publishing Switzerland, 2015
Chapter 6: Tempo and Beat TrackingSlide 10
6.1 Onset DetectionFig. 6.3
Time (seconds)
Local energy function
Annotated note onsets
Meinard Müller: Fundamentals of Music Processing© Springer International Publishing Switzerland, 2015
Chapter 6: Tempo and Beat TrackingSlide 11
6.1 Onset DetectionFig. 6.3
Time (seconds)
Annotated note onsets
Discrete derivative
Meinard Müller: Fundamentals of Music Processing© Springer International Publishing Switzerland, 2015
Chapter 6: Tempo and Beat TrackingSlide 12
6.1 Onset DetectionFig. 6.3
Time (seconds)
Novelty function (half-wave rectification)
Annotated note onsets
Meinard Müller: Fundamentals of Music Processing© Springer International Publishing Switzerland, 2015
Chapter 6: Tempo and Beat TrackingSlide 13
6.1 Onset DetectionFig. 6.3
Time (seconds)
Novelty function (logarithmic energy)
Annotated note onsets
Meinard Müller: Fundamentals of Music Processing© Springer International Publishing Switzerland, 2015
Chapter 6: Tempo and Beat TrackingSlide 14
6.1 Onset DetectionFig. 6.4
Piano Violin Flute
Waveform and energy-based novelty function of the note C4 (261.6 Hz)
Meinard Müller: Fundamentals of Music Processing© Springer International Publishing Switzerland, 2015
Chapter 6: Tempo and Beat TrackingSlide 15
6.1 Onset DetectionFig. 6.5
Magnitude spectrogram Compressed spectrogram Gamma = 1
Compressed spectrogram Gamma = 1000
Meinard Müller: Fundamentals of Music Processing© Springer International Publishing Switzerland, 2015
Chapter 6: Tempo and Beat TrackingSlide 19
6.1 Onset DetectionFig. 6.6
Compressed spectrogram
Novelty function Δ Spectral and local average function
Annotated note onsets
Novelty function subtracting the local average
Meinard Müller: Fundamentals of Music Processing© Springer International Publishing Switzerland, 2015
Chapter 6: Tempo and Beat TrackingSlide 20
6.1 Onset DetectionFig. 6.7
Energy-based novelty function
Spectral-based novelty function
Annotated note onsets
Meinard Müller: Fundamentals of Music Processing© Springer International Publishing Switzerland, 2015
Chapter 6: Tempo and Beat TrackingSlide 21
6.1 Onset DetectionFig. 6.8
Meinard Müller: Fundamentals of Music Processing© Springer International Publishing Switzerland, 2015
Chapter 6: Tempo and Beat TrackingSlide 22
6.1 Onset DetectionFig. 6.9
Wrapped phase
Unwrapped phase
Meinard Müller: Fundamentals of Music Processing© Springer International Publishing Switzerland, 2015
Chapter 6: Tempo and Beat TrackingSlide 23
6.1 Onset DetectionFig. 6.10 Jointly consider phase and magnitude
Meinard Müller: Fundamentals of Music Processing© Springer International Publishing Switzerland, 2015
Chapter 6: Tempo and Beat TrackingSlide 24
6.1 Tempo AnalysisFig. 6.11
Tempogram with harmonics
Tempogram with sub-harmonics
Meinard Müller: Fundamentals of Music Processing© Springer International Publishing Switzerland, 2015
Chapter 6: Tempo and Beat TrackingSlide 25
6.2 Tempo AnalysisFig. 6.12
Assumptions:- beat positions occur at note onset positions- beat positions are more or less equally spaced
Meinard Müller: Fundamentals of Music Processing© Springer International Publishing Switzerland, 2015
Chapter 6: Tempo and Beat TrackingSlide 26
6.2 Tempo AnalysisFig. 6.13
Fourier Tempogram
Meinard Müller: Fundamentals of Music Processing© Springer International Publishing Switzerland, 2015
Chapter 6: Tempo and Beat TrackingSlide 30
6.2 Tempo AnalysisFig. 6.13
Autocorrelation Tempogram
Meinard Müller: Fundamentals of Music Processing© Springer International Publishing Switzerland, 2015
Chapter 6: Tempo and Beat TrackingSlide 39
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
Meinard Müller: Fundamentals of Music Processing© Springer International Publishing Switzerland, 2015
Chapter 6: Tempo and Beat TrackingSlide 40
Time (seconds)
6.3 Beat and Pulse TrackingFig. 6.18
Tem
po
(B
PM
)
Meinard Müller: Fundamentals of Music Processing© Springer International Publishing Switzerland, 2015
Chapter 6: Tempo and Beat TrackingSlide 41
Time (seconds)
6.3 Beat and Pulse TrackingFig. 6.18
Tem
po
(B
PM
)
Meinard Müller: Fundamentals of Music Processing© Springer International Publishing Switzerland, 2015
Chapter 6: Tempo and Beat TrackingSlide 42
Time (seconds)
6.3 Beat and Pulse TrackingFig. 6.18
Tem
po
(B
PM
)
Meinard Müller: Fundamentals of Music Processing© Springer International Publishing Switzerland, 2015
Chapter 6: Tempo and Beat TrackingSlide 43
Time (seconds)
6.3 Beat and Pulse TrackingFig. 6.18
Tem
po
(B
PM
)
Meinard Müller: Fundamentals of Music Processing© Springer International Publishing Switzerland, 2015
Chapter 6: Tempo and Beat TrackingSlide 44
Time (seconds)
6.3 Beat and Pulse TrackingFig. 6.18
Tem
po
(B
PM
)
Meinard Müller: Fundamentals of Music Processing© Springer International Publishing Switzerland, 2015
Chapter 6: Tempo and Beat TrackingSlide 45
6.3 Beat and Pulse TrackingFig. 6.19
Meinard Müller: Fundamentals of Music Processing© Springer International Publishing Switzerland, 2015
Chapter 6: Tempo and Beat TrackingSlide 51
6.3 Beat and Pulse TrackingFig. 6.21
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
Meinard Müller: Fundamentals of Music Processing© Springer International Publishing Switzerland, 2015
Chapter 6: Tempo and Beat TrackingSlide 52
6.3 Beat and Pulse TrackingFig. 6.22
Beat sequence
Score function
Meinard Müller: Fundamentals of Music Processing© Springer International Publishing Switzerland, 2015
Chapter 6: Tempo and Beat TrackingSlide 53
6.3 Beat and Pulse TrackingTable 6.1 Accumulated score
Meinard Müller: Fundamentals of Music Processing© Springer International Publishing Switzerland, 2015
Chapter 6: Tempo and Beat TrackingSlide 54
6.3 Beat and Pulse TrackingFig. 6.23
Meinard Müller: Fundamentals of Music Processing© Springer International Publishing Switzerland, 2015
Chapter 6: Tempo and Beat TrackingSlide 55
6.3 Beat and Pulse TrackingFig. 6.23
Time (seconds)
Meinard Müller: Fundamentals of Music Processing© Springer International Publishing Switzerland, 2015
Chapter 6: Tempo and Beat TrackingSlide 56
6.3 Beat and Pulse TrackingFig. 6.23
Time (seconds)
Meinard Müller: Fundamentals of Music Processing© Springer International Publishing Switzerland, 2015
Chapter 6: Tempo and Beat TrackingSlide 57
6.4 Further NotesFig. 6.24
top related