Lecture 6. Rhythm Analysis. (some slides are adapted from Zafar Rafii and some figures are from Meinard Mueller)
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1 Lecture 6 Rhythm Analysis (some slides are adapted from Zafar Rafii and some figures are from Meinard Mueller)
2 Definitions for Rhythm Analysis Rhythm: movement marked by the regulated succession of strong and weak elements, or of opposite or different conditions. Beat: basic unit of time in music ---- Oxford English Dictionary Tempo: speed or pace of a given piece, typically measured in beats per minute (BPM) ECE 272/472 (AME 272, TEE 272) Audio Signal Processing, Zhiyao Duan, 208 2
3 More Definitions Onset: single instant marking the beginning of transient Onsets often occur on beats. Attack: sharp increase of energy Transient: a short duration with high amplitude within which signal evolves quickly Waveform of one piano note ECE 272/472 (AME 272, TEE 272) Audio Signal Processing, Zhiyao Duan, 208 3
4 More Definitions Measure (or bar): segment of time defined by a given number of beats A 4-beat measure drum pattern. [ ECE 272/472 (AME 272, TEE 272) Audio Signal Processing, Zhiyao Duan, 208 4
5 More Definitions Meter: organization of music into regularly recurring measures of stressed and unstressed beats Hypermeter: 4-beat measure and 4-measure hypermeasure. Hyperbeats in red. [ ECE 272/472 (AME 272, TEE 272) Audio Signal Processing, Zhiyao Duan, 208 5
6 Rhythm Analysis Tasks Onset Detection Beat Tracking Tempo Estimation Higher-level Structure Analysis ECE 272/472 (AME 272, TEE 272) Audio Signal Processing, Zhiyao Duan, 208 6
7 Intellectual merit Why is it important? Important component of music understanding Music cognition research Broad applications Identify/classify/retrieve by rhythmic similarity Music segmentation/summarization Audio/video synchronization Source separation ECE 272/472 (AME 272, TEE 272) Audio Signal Processing, Zhiyao Duan, 208 7
8 Signal processing: define a detection function Energy-based Spectral-based Phase-based Machine Learning: learn patterns from labeled data Probabilistic models Neural networks Onset Detection ECE 272/472 (AME 272, TEE 272) Audio Signal Processing, Zhiyao Duan, 208 8
9 Energy-based Onset Detection Waveform Signal Envelope (energy) Envelope Derivative (half-wave rectified) Thresholding Onsets ECE 272/472 (AME 272, TEE 272) Audio Signal Processing, Zhiyao Duan, 208 9
10 Energy-based Onset Detection Pros and Cons Simple Works well for percussive sounds Soft onsets by string/wind instruments are hard to detect Tremolo/vibrato can cause false detections How to improve Use logarithmic-energy to replace linear energy Perform analysis in different frequency bands, then summarize ECE 272/472 (AME 272, TEE 272) Audio Signal Processing, Zhiyao Duan, 208 0
11 Spectral-based Onset Detection STFT to get magnitude spectrogram χ (optional) compression Spectral flux: Take derivative w.r.t. time (half-wave rectified) ECE 272/472 (AME 272, TEE 272) Audio Signal Processing, Zhiyao Duan, 208
12 Spectral-based Onset Detection Pros and Cons More complex than energy-based Can weigh different frequencies differently Works better for soft onsets (e.g., legato notes) and polyphonic music Still doesn t work very well for vibrato ECE 272/472 (AME 272, TEE 272) Audio Signal Processing, Zhiyao Duan, 208 2
13 Tempo Estimation Tempo = beats / minutes Beat tracking is sufficient but not necessary condition for tempo estimation How to estimate tempo without tracking beats? Idea: look at the regularity of onsets Assumptions Onsets mostly occur on beats Tempo is constant within a period of time ECE 272/472 (AME 272, TEE 272) Audio Signal Processing, Zhiyao Duan, 208 3
14 Tempo Estimation Onset strength curve Onsets Take the onset strength curve and analyze its periodicity Autocorrelation STFT Tempogram ECE 272/472 (AME 272, TEE 272) Audio Signal Processing, Zhiyao Duan, 208 4
15 Beat Tracking Identify the beat times, i.e., the times to which we tap our feet Detected onsets provide useful but noisy information, since not all onsets are on beats. Estimated tempo tells us the space between two beats, but not the exact locations (i.e., phase). How to identify beats? To simply the problem, we assume Onsets, especially strong ones, are mostly on beats. Tempo is constant. ECE 272/472 (AME 272, TEE 272) Audio Signal Processing, Zhiyao Duan, 208 5
16 A 2-step approach Beat Tracking Step : Tempo estimation Step 2: Identify beats from onsets using the tempo Create an impulse train (i.e., comb ) with the tempo Cross-correlate the comb with the onset strength curve. The lag that gives us the highest cross-correlation value tells us the beat phase. ECE 272/472 (AME 272, TEE 272) Audio Signal Processing, Zhiyao Duan, 208 6
17 Beat Tracking A 2-step approach, illustration Onset strength curve Combs with the same tempo but different phases Problem: too rigid about beat spacing ECE 272/472 (AME 272, TEE 272) Audio Signal Processing, Zhiyao Duan, 208 7
18 Beat Tracking by Dynamic Programming Beat tracking: finding a sequence of beat locations such that they Score function ) are well aligned with strong onsets 2) mostly regularly spaced [Ellis, 2007] Rough estimate of beat spacing Beat sequence Onset strength Regularity penalty function Find B = (b, b 2,, b L ) that maximizes S(B) ECE 272/472 (AME 272, TEE 272) Audio Signal Processing, Zhiyao Duan, 208 8
19 Beat Tracking by Dynamic Programming Suppose beat locations are precise to audio frames, and suppose there are N frames, then how many possible sequences? 2 N (although many are bad ones!) Can t enumerate all! Key idea: reuse calculations by recursion! ECE 272/472 (AME 272, TEE 272) Audio Signal Processing, Zhiyao Duan, 208 9
20 Beat Tracking by Dynamic Programming Consider a beat sequence B n = b, b 2,, b L where b L = n. Let D(n) be the maximal score over all such sequences ending at n. Then if L > if L = recursion ECE 272/472 (AME 272, TEE 272) Audio Signal Processing, Zhiyao Duan,
21 Beat Tracking by Dynamic Programming Considering the two cases, we have We can calculate D(n) from D =. Record the preceding beat Best score Trace back from to get the best sequence ECE 272/472 (AME 272, TEE 272) Audio Signal Processing, Zhiyao Duan, 208 2
22 Rhythmic Structure Tatom Tactus Measure time (s) Beginning of Another one bites the dust by Queen. One approach: detect onsets; analyze tempo and beats at different levels. Another approach: analyze repetition of spectral content Beat spectrum ECE 272/472 (AME 272, TEE 272) Audio Signal Processing, Zhiyao Duan,
23 Definition Beat Spectrum Using the autocorrelation function, we can derive the beat spectrum [Foote et al., 200] Beginning of Another one bites the dust by Queen time (s) lag (s) Beat Spectrum. ECE 272/472 (AME 272, TEE 272) Audio Signal Processing, Zhiyao Duan,
24 Use Beat Spectrum The beat spectrum reveals the hierarchically periodically repeating structure of the audio Periodicity at the measure level Sub-periodicity at the kick level 0 - Beginning of Another one bites the dust by Queen time (s) Sub-periodicity at the beat level lag (s) Beat Spectrum. ECE 272/472 (AME 272, TEE 272) Audio Signal Processing, Zhiyao Duan,
25 Calculation 0 - Beat Spectrum Compute the power spectrogram from the audio using the STFT (square of magnitude spectrogram) Audio time (s) frequency (khz) x 0 4 Power spectrogram time (s) ECE 272/472 (AME 272, TEE 272) Audio Signal Processing, Zhiyao Duan,
26 Calculation Beat Spectrum Compute the autocorrelation of the rows of the spectrogram x 0 4 Power spectrogram x 0 4 Autocorrelation plots 2 2 frequency (khz) frequency (khz) time (s) Spectrogram at 0 khz lag (s) Autocorrelation at 0 khz time (s) lag (s) ECE 272/472 (AME 272, TEE 272) Audio Signal Processing, Zhiyao Duan,
27 Calculation Beat Spectrum Compute the mean of the autocorrelations (of the rows) x 0 4 Power spectrogram x 0 4 Autocorrelation plots 2 2 frequency (khz) frequency (khz) time (s) lag (s) Beat spectrum lag (s) ECE 272/472 (AME 272, TEE 272) Audio Signal Processing, Zhiyao Duan,
28 Notes Beat Spectrum The first highest peak in the beat spectrum does not always correspond to the repeating period! The beat spectrum does not indicate where the beats are or when a measure starts! This is how you find the period lag (s) This is not Beat Spectrum. the period ECE 272/472 (AME 272, TEE 272) Audio Signal Processing, Zhiyao Duan,
29 Resources Some interesting links Dannenberg s articles on beat tracking: Goto s work on beat tracking: Ellis Matlab codes for tempo estimation and beat tracking: MIREX s annual evaluation campaign for Music Information Retrieval (MIR) algorithms, including tasks such as onset detection, tempo extraction, and beat tracking: ECE 272/472 (AME 272, TEE 272) Audio Signal Processing, Zhiyao Duan,
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