1. David Sears MUMT 621 12 November 2009
Audio Beat Tracking
David Sears
MUMT 621
12 November 2009

2. Outline Introduction BeatRoot Context-Dependent Beat Tracking
MIREX 2009 Beat Tracking Contest
Analytical Applications

3. Introduction
Beat tracking in audio is the task of identifying and synchronizing with the basic pulse of a piece of music (Dixon 2007).

4. Goals
Davies et al (2007) suggest 4 main desirable properties for a beat tracker:
Both audio and symbolic musical signals can be processed.
No a priori knowledge of the input is required.
Perceptually accurate beat locations can be identified efficiently and in real-time.
Changes in tempo can be followed, thereby indicating the rate of change of tempo.

5. BeatRoot
BeatRoot preprocesses the input audio file with an onset detection function. Initial iterations of BeatRoot used the “surfboard” method, which involves smoothing the signal to produce an amplitude envelope before finding peaks in its slope using linear regression (Dixon 2003). However, because this method is necessarily lossy (it fails to detect onsets in which simultaneously sounding notes mask one another), the current iteration of BeatRoot employs a spectral flux onset detection function, which sums the change in magnitude in each frequency bin where the energy is increasing.
Dixon 2007

6. However, because this method is necessarily lossy (it fails to detect onsets in which simultaneously sounding notes mask one another), the current iteration of BeatRoot employs a spectral flux onset detection function, which sums the change in magnitude in each frequency bin where the energy is increasing. Peak picking is then performed using a set of empirically determined constraints.
Spectral flux was chosen over the complex domain detection function and the weighted phase deviation based on its simplicity for programming, speed of execution and accuracy of correct onsets.
Dixon 2003

7. The tempo induction algorithm computes clusters of inter-onset intervals and then combines them by recognizing the approximate integer relationships between clusters (Dixon 2007).
Each of the clusters is then weighted based on their integer relationships, and a ranked list of tempo hypotheses is produced and passed to the beat tracking subsystem.
Dixon 2007

8. Beat tracking is performed using a tempo hypothesis derived from the tempo induction stage and the first onset of a given window is used to then predict further beats. Subsequent onsets that fall within the prediction window are treated as beats by BeatRoot, while those falling outside the window are taken to be possible beats, or disregarded altogether.
Dixon 2007

11. MIREX 2006

12. Context Dependent Beat Tracking
Complex spectral difference onset detection function
Stage 1: General State
Switches metrical levels
Switches between the on and off-beat
Stage 2: Context-dependent state
Unable to react to tempo changes
Two-State Model
Note onsets are emphasized either as a result of significant change in energy in the magnitude spectrum, and/or deviation from the expected phase values in the phase spectrum (ie change in pitch).
The role of the general state is to infer the time between successive beats, the beat period (IOI), and the offset between the start of the frame and the locations of the beats, the beat alignment.

13. Davies et al 2007

15. MIREX 2009 Two Test Sets for Evaluation
McKinney Collection: A collection of 160 musical excerpts, annotated by 40 different listeners.
Sapp’s Mazurka Collection: 322 files

16. Results—McKinney Collection
TeamID
F-Measure
Cemgil
Goto
P-Score
CMLC
CMLT
AMLC
AMLT D Dg
units ->
(%)
(bits)
DRP1
24.6
17.5
0.4
37.4
3.8
9.6
7.8
19.2
0.625
0.008
DRP2
35.4
26.1
3.1
46.5
7.5
16.9
13.8
31.7
1.073
0.062
DRP3
47.0
35.6
16.2
52.8
19.4
27.6
45.3
61.3
1.671
0.245
DRP4
48.0
36.3
19.5
53.9
22.2
29.1
50.8
64.0
1.739
0.255
GP1
54.8
41.0
59.0
26.0
35.5
49.1
66.6
1.680
0.294
GP2
53.7
40.1
20.9
57.9
25.1
33.7
47.6
63.8
1.649
0.281
GP3
54.6
40.9
22.0
48.8
66.3
1.695
0.287
GP4
54.5
40.8
21.6
59.2
26.4
48.2
64.7
1.685
0.289
OGM1
39.7
6.5
47.8
11.9
19.9
29.5
47.4
1.283
0.100
OGM2
41.5
30.4
5.7
49.2
11.7
28.2
46.4
1.340
0.092 TL
50.0
37.0
14.1
53.6
17.9
24.3
35.9
1.480
0.150

17. Results—Sapp Collection
TeamID
F-Measure
Cemgil
Goto
P-Score
CMLC
CMLT
AMLC
AMLT D Dg
units ->
(%)
(bits)
DRP1
27.9
19.9
0.0
37.3
1.5
10.3
2.3
13.8
0.126
0.008
DRP2
48.4
32.5
55.5
2.6
26.0
3.1
28.1
0.683
0.183
DRP3
67.8
61.5
2.5
65.3
7.8
42.1
9.2
45.6
1.424
0.993
DRP4
45.3
37.6
0.6
50.1
3.9
24.9
5.3
28.5
0.393
0.198
GP1
54.2
42.5
59.5
4.4
33.2
5.6
36.6
0.447
0.252
GP2
54.7
43.1
59.9
4.5
33.7
5.7
37.0
0.467
0.269
GP3
44.7
34.8
51.2
3.2
24.7
4.0
0.262
0.111
GP4
45.4
35.6
51.9
3.3
25.2
28.4
0.284
0.124
OGM1
30.7
21.9
38.6
1.7
11.0
2.8
15.4
0.134
0.014
OGM2
32.1
23.1
39.7
11.5
2.7
15.6
0.016 TL
44.9
35.7
0.3
51.0
20.5
4.7
22.5
0.440
0.095

18. Analytical Applications
Automatic extraction of expressive timing information can therefore provide a means for studying individual differences in performance nuance, as well as provide keen insights into note-level performance rules that can be observed using machine learning techniques.

19. References
Davies, M. A. Robertson, and M. Plumbley MIREX 2009 Audio beat tracking evaluation: Davies, Robertson and Plumbley. In Proceedings of the International Society for Music Information Retrieval.
Davies, M. E. P., and M. D. Plumbley Context-dependent beat tracking of musical audio. IEEE Transactions on Audio, Speech and Language Processing, 15(3):
Dixon, S On the analysis of musical expression in audio signals. Draft for SPIE/IS&T Conference on Storage and Retrieval for Media Databases. Online
Dixon, S Evaluation of the Audio Beat Tracking System BeatRoot. Preprint for Journal of New Music Research, 36. Online
Lee, T Audio beat tracking. In Proceedings of the International Society of Music Information Retrieval.
Peeters, G MIREX-09 “Audio beat tracking” task: IRCAMBEAT submission. In Proceedings of the International Society for Music Information Retrieval.
Tzanetakis, G Marsyas submissions to MIREX In Proceedings of the International Society for Music Information Retrieval.
Widmer, G., S. Dixon, W. Goebl, E. Pampalk, and A. Tobudic In Search of the Horowitz Factor. AI Magazine, 24(3):