Tempo Induction and Beat Tracking for Audio Signals

1
Tempo Induction and Beat Tracking for Audio
Signals

• MUMT 611, February 2005
• Assignment 3
• Paul Kolesnik

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Contents

• Introduction and Definitions
• Overview of Works
• Summary of Common Techniques
• Conclusion

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Introduction

• Concepts
• Tempo
• rate at which a musical piece is played
• score time units per real time unit (eg. beat per
  minute)
• Beat
• unit in a sequence of impulses which define the
  tempo of a musical piece
• Has no exclusive definition, can be ambiguous and
  context-dependent (eg. 60 bpm vs. 120 bpm)
• Has period (inter-beat interval) and phase
  (estimated to beat position in score)

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Introduction

• Tempo Induction
• Process of estimating basic tempo from musical
  data
• Beat Tracking
• Definition
• The process of extracting beat information from a
  musical score (based on tempo information)
• Differentiated from score following through the
  absence of a score
• Applications
• Performance analysis, perceptual modeling, audio
  content analysis and transcription, performance
  synchronization

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Introduction

• Beat Tracking of Musical Data
• MIDI - symbolic representation, information
  needed for beat tracking is encoded directly in
  the data (eg. note onsets)
• Audio - needs preprocessing to extract symbolic
  representation of the signal

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Overview of Works

• Schloss (1985)
• One of the earliest works
• Onsets detected as peaks in the slope of
  amplitude envelope of a high-pass filtered signal
  (HFC analysis).
• Allen and Dannenberg (1991)
• Definition of a period and phase, the concept of
  beam search using multiple tempo / beat
  hypotheses
• Not clear if MIDI or Audio is used as input
• Goto and Muraoka (1995-2001)
• Extensive work on beat-tracking systems with and
  without drums, combined in 2001
• Early system (with drums) examines frequencies
  of snare and bass drums, finds onsets and matches
  them to a set of pre-stored drum patterns

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Overview of Works

• Goto and Muraoka (ctd.)
• Disadvantage limited to a specific musical
  style. Advantage highly successful for this
  style.
• Later system (without drums) using higher-level
  musical knowledge - chord changes - to determine
  low-level beat indications.
• Both systems combined into a single system that
  uses a combination of drum indications, chord
  changes and onset indications.
• Systems based on multiple agent architecture,
  with each agent predicting beat times using
  different strategies.

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Overview of Works

• Goto and Muraoka (ctd.)
• Musical-knowledge rules used by the system
• Onset-related rules
• (a-1) A frequent inter-onset interval is likely
  to be an inter-beat interval
• (a-2) Onset times tend to coincide with beat
  times (i.e. sounds are likely to occur on beats)
• Chord-related rules
• (b-1) Chords are more likely to change on beat
  times than on other positions

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Overview of Works

• Goto and Muraoka (ctd.)
• Chord-related rules (ctd)
• (b-2) Chords are more likely to change on
  half-note times than on other positions
• (b-3) Chords are more likely to change at the
  beginnings of measures than at other positions of
  half-notes
• Drum pattern-related rules (ctd)
• (c-1) The beginning of the input drum pattern
  indicates a half-note time
• (c-2) The input drum pattern has an appropriate
  inter-beat interval

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Overview of Works

• Scheirer (1998)
• Based on tuned resonators
• Signal is split in 6 frequency bands amplitude
  envolopes are extracted and passed through a set
  of 150 comb filters (each representing possible
  tempo on a discretized scale) output summed
  across frequency bands highest value determines
  the tempo and phase
• Problem filter spacing in relation of tempo
  representations

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Overview of Works

• Dixon (2001)
• Accepts audio or symbolic (MIDI) data
• Two stages of processing
• Tempo induction (examines times between pairs of
  onsets)
• Beat tracking (determines the period / alignment
  of the beats)

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Overview of Works

• Tempo Induction
• Examines times between pairs of note onsets
• Uses clustering algorithm to determine
  significant clusters of inter-onset intervals
• Each cluster represents a hypothetical tempo
• Output a list of ranked tempo hypotheses
• For audio, significant preprocessing (onset
  detection) is needed -- this is done using
  amplitude envelope techniques described in
  (Schloss 1985)

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Overview of Works

• Beat Tracking
• Tempo induction calculates the frequency/period
  of the beat
• Beat tracking calculates the phase
• This is done using the multiple hypothesis
  search, with the best output score determining
  the identified beat phase
• Each hypothesis search is conducted by a beat
  tracking agent, which predicts a beat time and
  matches it to rhythmic events, adjusts its
  hypothesis, creates a new one or deletes it if
  two identical hypotheses are reached

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Overview of Works

• Beat Tracking
• For each tempo induction-generated hypothesis,
  there is a group of agents created to track the
  piece at this tempo
• Works based on the assumption that there is at
  least one event in the initial section of music
  (5 sec) that coincides with the beat time
• Agent adjustments, creations, deletions take
  place based on the analyzed information
• Decisions are made based on how evenly spaced
  events are, how often they match the expected
  beat time values, and salience of matched events

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Overview of Works

• Musical Salience
• How significant any particular event is based on
  the higher-level knowledge of the musical context
  in which it takes place
• Examples of salience factors
• Note duration
• Simultaneous note density
• Amplitude
• Pitch

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Overview of Works

• Davies and Plumbley (2004)
• A realtime audio beat-tracking system, allowing
  tempo changes and different styles
• Performs onset detection using high frequency
  content and complex domain algorithms
• Tempo induction and beat alignment (phase)
  estimation are similar to techniques implemented
  in Scheirer (1998) and Dixon (2001)
• Uses autocorrelation function to determine the
  beat period, and comb filters for beat phase
  detection

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Summary of Common Concepts

• Audio Tempo Induction and Beat Tracking is more
  complex than MIDI due to its non-symbolic nature
• Note onset is the most popular element used for
  tempo induction
• Common tempo induction techniques are HFC
  analysis for signals with drums present, and
  complex frequency analysis as a more general tool
• Higher-level musical knowledge rules can
  facilitate the tempo induction process

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Summary of Common Concepts

• Beat tracking of the signal involves determining
  the phase (alignment) of the signal and is done
  based on onset detection data and tempo induction
  (period estimation) data
• Multiple hypotheses techniques (introduced as a
  beam search technique by Allen and Dannenberg
  1991) is commonly used and is superior to
  individual solution approach used in early
  systems, since it allows to recover from
  encountered tempo induction and beat tracking
  errors

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Conclusion

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