An Analysis of Using Fuzzy Annotations in
CRNN-Based Joint Beat and Downbeat Tracking
Tian Cheng and Masataka Goto
National Institute of Advanced Industrial Science and Technology (AIST), Japan{tian.cheng, m.goto}@aist.go.jp

Abstract—This paper addresses joint beat and downbeat
tracking by using a Convolutional Recurrent Neural Network(CRNN) trained on Mel-spectral and chroma features of musicalaudio signals. Since beats and downbeats occur sparsely, we
extend the original beat/downbeat annotation ranges to create
fuzzy annotations for a better-balanced training. We compare
three fuzzy annotations generated by convolving the original
annotations with triangular, Gaussian, and rectangular windows.
In comparison to the baseline model trained with the original
annotations, our model of using fuzzy annotations improves thebeat and downbeat tracking performance on pieces with tempi
slower than 80 bpm. We analyzed the activation functions fromthe CRNN outputs and found that the improvements are mainly
due to enlarged activation functions and phase error correction.
The results showed that the proposed models provide promising
results on test datasets with various music styles.
Index Terms—Convolutional Recurrent Neural Network,
Fuzzy Annotations, Joint Beat and Downbeat Tracking

I. I NTRODUCTION
Beat and downbeat are two fundamental metrical concepts
for music, defining a hierarchical beat structure in two rhythmic levels: beat-level and bar-level [1]. They appear quasiperiodically along music pieces, and hence beat and downbeat
tracking has been applied as an intermediate processing stepfor time regulation in other music analysis tasks, such asmusic transcription [2], [3], chord estimation [4]–[6], structure
analysis [7], [8], and so on. Beat and downbeat tracking is also
important for music-synchronized applications [9]–[11]. The
close relationship between beat and downbeat tracking andother musical features is evidenced by several joint estimation
systems for drums [12], [13], onsets [2], [13], chords [14], andtempo [15], [16].
Beat and downbeat tracking not only depends on local
musical features, such as onsets and harmonic changes, butalso deals with more global consistency to obtain steadytracking results. Current beat and downbeat tracking methods
employ deep learning techniques to learn beats and downbeatsfrom labeled music annotations, and feed the deep networks
with spectral features extracted from musical audio signals.
Mel-spectrograms and their temporal differences have beenused as input features in beat and downbeat tracking papers and show promising results [17]–[19]. Chroma features
show close relations to downbeat tracking and have beenused in several downbeat tracking systems [20]–[22]. Various
This work was supported in part by JST CREST Grant Number JPMJCR20D4, Japan.

ISBN: 978-1-6654-6798-8

deep models have been applied for such tasks, ranging from
Recurrent Neural Network (RNN) [17]–[20], Convolutional
Neural Network (CNN) [21], [23], Convolutional Recurrent
Neural Network (CRNN) [22], [24] to the most latest Temporal
Convolutional Network (TCN) [15], [16], [25]. In these models
the convolution layers detect the local spectral events, such as
onsets and harmonic changes, and sequence models (RNN or
TCN) estimate beats and downbeats in a larger timescale.
In this paper, we also adapt the advantages from both signal
processing and machine learning domains to tackle beat anddownbeat tracking jointly. We extended a CRNN model in ourprevious paper [24] by including both Mel-spectral and chromafeatures. Since the appearance of those labels is imbalanced,
the beat/downbeat annotation ranges are extended to create
fuzzy annotations by convolving the original annotations withthree different kinds of windows: triangular, Gaussian, andrectangular windows. The results showed that the proposedmodels outperform state-of-the-art methods on beat and downbeat tracking in two public available datasets (SMC [26] andBeatles [27]). In comparison to the baseline method trainedwith original annotations, using fuzzy annotations improves
the beat tracking performance on the SMC dataset [26] andthe downbeat tracking performance on the Songle dataset [24],[28]. We analyzed the performance improvements on individual pieces and found that using fuzzy annotations improves thebeat and downbeat tracking performance on pieces with tempi
slower than 80 bpm. Using fuzzy annotations can enlarge theactivation functions, which makes the beat/downbeat detection
easier, and suppress spurious inter-beat peaks, which helps
the phase error correction. We also found that using fuzzy
annotations is helpful when the annotations contain somedeviation because the enlarged beat range is more likely toinclude the true beat times.
Related work: Fuzzy annotations have been used recently,
including those created by convolving the original annotations
with a triangular window [15], [16], [25], Gaussian window[23], [29], and rectangular window [24]. However, only one
kind of window has been studied in individual papers. In thispaper, we compare three different kinds of windows (triangular, Gaussian, and rectangular) and analyze the performance
improvement of each individual piece. In our early study on
using the Gaussian windows with different window sizes, wefound that increasing window size did not improve the beattracking performance [29]. Therefore, we focus on windowsof small sizes in this paper.

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mp
1x2

mp
1x2

conv
7x7

conv
7x5

conv
1x9
conv
7x5

(a) Triangle
T, 36, 7

T, 36, 32

T, 18, 32

T, 18, 32

T, 9, 32

T, 9, 32

T, 1, 64(b) Gaussian(c) Rectangle

Fig. 2: Three windows used to create fuzzy annotations.

Fig. 1: Convolution (conv) and max pooling (mp) layers in the
proposed model.
3, which corresponds to the ‘downbeat’, ‘beat’, and ‘no-beat’labels.
II. CRNN MODEL FOR JOINT BEAT AND DOWNBEAT

C. Training and Post-Processing

TRACKING

A. Signal Pre-Processing
We compute Mel-spectral and chroma features in the preprocessing. To obtain Mel-spectrograms, a monaural waveformsequence is read from each audio file at a 44100 Hz samplingrate. Then the waveform is segmented into frames of window
sizes of 1024, 2048, and 4096 samples with a hop size of
441 samples [19], resulting in 10 ms temporal resolution. For
each windowed input frame we compute a magnitude Melspectrogram of 36 Mel bins within a frequency range from
30 Hz to 17000 Hz. Then we convert the Mel-spectrograms
to the log-scale and calculate, along the time axis, theirfirst-order difference with a positive half-wave rectifier. We
concatenate the three Mel-spectrograms and their differences
into 6 channels to obtain a Mel-spectral feature with a shapeof [T , 36, 6], where T is the number of the input frames.
In addition to the Mel-spectrograms, we incorporate chromafeatures into the model input. We use three different kinds ofchromagrams: a chromagram computed from a power spectrogram, a Constant-Q chromagram, and an energy normalized
chromagram [30]. Since these chromagrams put different
emphases on the frequency range, dynamics, and timbre, we
concatenate them to obtain an informative and robust chromafeature.
The concatenated chroma feature has a dimension of 36
with 12 dimensions for each chromagram. It is stacked to theabove Mel-spectral feature as another channel, resulting in an
input feature of a shape of [T , 36, 7].
B. Network Architecture
We adapt the CRNN model from our previous work [24],which consists of a CNN block, an RNN block, and a fully
connected layer. The CNN block consists of four convolutional
layers, as shown in Figure 1. In the first three layers, we
use 32 convolutional filters for each layer with the ‘same’
padding. The filter shapes are 7x7, 7x5, and 7x5, respectively.
The fourth layer consists of 64 filters, with the shape of 1x9.
There is a maxpooling layer stacked after each of the first twolayers, with the shape of 1x2.
After the CNN layers, we reshape the output into a tensor
of [T , 64] as the input of the RNN block. The RNN block
consists of 4 bidirectional layers with 64 Gated Recurrent
Units (GRUs) per layer in each direction. At the end of RNN
layers we stack a dense layer with an output dimension of

We train the CRNN model in 8-fold cross-validation withrandom splits. We apply the RMSprop optimizer [31] with alearning rate of 10−3 to minimize the cross-entropy error. We
stop training if no improvement is found on the validation set
in 15 epochs.
We adapt the post-processing method in [19]. First a threshold of 0.05 is applied on the beat/downbeat activation functions(from the CRNN model) to delete small peaks at the beginningand end of a music piece. Then a Dynamic Bayesian Network(DBN) is used to infer the metre, tempo, and beat phases
jointly based on the observation distributions converted fromthe beat/downbeat activation functions. Readers are referred to[19], [32] for more details. In the experiment, we restrict thebar lengths to 2, 3, or 4 beats.
D. Fuzzy Annotations
In the original annotations, there are several ‘beat’ labels
and a lot of ‘no-beat’ labels between adjacent ‘downbeat’labels. For example, for a piece with a 4/4 time signature
and a tempo of 120 bpm, in every 200 frames (2 sec) there
are 1 downbeat and 3 beats, with the other 196 frames labeled
as ‘no-beat’. The annotations are even more imbalanced for aslower-tempo piece. To tackle this imbalance issue, we create
fuzzy annotations by broadening the beat and downbeat labels,i.e., by convolving the original pulse-like beat and downbeat
annotations with different windows (kernels). We compare
three different windows: triangular, Gaussian, and rectangular
windows, as shown in Figure 2.
We have studied the influence of different window sizes of
the Gaussian window on beat tracking in our previous work[29], and the results showed that the best performance wasachieved with a small window size, as shown in Figure 2(b).
Based on the results, we choose the above compact windows,
with a length of 3 or 5 frames.
III. E XPERIMENT
A. Datasets
We used 11 datasets with a variety of music genres inthe experiment. Eight were used in cross-validation, Ballroom[33], [34], GTZAN [35], [36], Hainsworth [37], RWC classic,
jazz, pop, royalty [38] and RWC genre [39]. There werealso three held-out datasets for testing only. One was theSongle dataset, with 228 songs registered on [28] and with theannotations manually checked. The other two were publically

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SMC

F1

CMLt

AMLt

Proposed(Rectangle)
Böck et al. [16] †

0.548
0.544

0.444
0.443

0.614
0.635

(a) Beat tracking results
Beatles

F1

CMLt

AMLt

Proposed(Rectangle)
Durand et al. [21] †Fuentes et al. [22] †Böck et al. [16] †

0.856
0.847
0.86
0.837

0.757
0.722

0.887
0.875

0.742

0.862

(b) Downbeat tracking results

Fig. 3: Beat and downbeat tracking F-measures (F1) of the
proposed models on the three test datasets. The baseline model
was trained with the original annotations, and ‘Rectangle(nochroma)’ denotes the model trained with the rectangular
window on Mel-spectrograms only [24].
available datasets: the Beatles dataset [27] and the SMC
dataset [26]. Note that the SMC dataset was built as a difficult
dataset and only includes beat annotations, and hence there is
no downbeat tracking result for this dataset.
B. Results
The beat and downbeat tracking results on the test datasets
are shown in Figure 3. We first compared the proposed
methods with the baseline method (trained with the original
annotations) on individual datasets. For the Beatles dataset,the baseline method obtained the F-measure (F1) of 0.928 forthe beat tracking task and obtained the F-measure of 0.86 forthe downbeat tracking task. Using the fuzzy annotations did
not bring significant differences in the performance of bothtasks. For the Songle dataset, the baseline method obtained Fmeasures of 0.913 and 0.855 for beat tracking and downbeat
tracking, respectively. Using the fuzzy annotations had no
significant influence on beat tracking results but improved
downbeat tracking results. There were improvements of 1.8,
1.7, and 1 percentage points brought by using triangular,
Gaussian, and rectangular windows, respectively. For the SMC
dataset, the beat tracking F-measure was 0.496 by using thebaseline method. The performance was improved to 0.527,
0.534, and 0.548 by using the fuzzy annotations with the threewindows, respectively. In general, using the fuzzy annotations
can provide better or at least competitive results.
We also analyzed the effect of adding chroma features bycomparing two methods trained using the rectangular window
with and without chroma features (‘Rectangle’ vs. ‘Rectangle(no chroma)’ [24] in Figure 3). We found that adding
chroma features brought a clear improvement of downbeat
tracking, with improvements of 2.3 percentage points on
the Beatles dataset and 1.4 percentage points on the Songle
dataset. However, it had different effects on beat tracking fordifferent datasets: it decreased the F-measure on the Beatles
dataset for 1.2 percentage points, had no effect on the Songle
dataset, and brought an improvement of 2.1 percentage points
on the SMC dataset. This beat tracking performance could

TABLE I: A comparison to other state-of-the-art methods.
† indicates cross-validation results reported in corresponding
papers.

be interpreted by considering music types contained in thedatasets. Music in the Beatles dataset has clear rhythmic clues,
and the key problem is to find a constant tempo in ambiguousand noisy situations. Adding chroma features would makesome situations more complicated, which would somehow
decrease the beat tracking performance. On the other hand,music in the SMC dataset tends to have blurring onsets andthere is much less information corresponding to the beats.
Adding chroma features could be helpful in such situations.
Table I shows a comparison between the proposed method(trained with the rectangular window) and other state-of-the-art
methods on two datasets. Noticeably, our testing-only results
are comparable to the best existing cross-validation results.
The testing-only evaluation is considered more difficult thantypical cross-validation evaluation and shows its robustness
on unseen music data. For the SMC dataset in Table I(a), we
compared to a model built on CNN and TCN in [16] on thebeat tracking performance. The proposed method provided aslightly better F-measure (F1). In the continuity-based metrics(CMLt and AMLt [27]), the model [16] (with an AMLt of
0.635) outperformed the proposed method (0.614) by 2.1
percentage points, showing better tolerances on errors likedouble/half tempo and off-beats. For downbeat tracking resultsof the Beatles dataset in Table I(b), the proposed method
outperformed the methods of Durand et al. [21] and Böck et
al. [16] on all three metrics. The F-measure of the proposed
method was 0.856, slightly worse than the best F-measure of
0.86 in Fuentes et al. [22].
C. Performance Improvement Analysis
To understand how the fuzzy annotations work, we analyzed
the performance improvements brought by using the fuzzy
annotations for each individual piece in the three test datasets.
In Figure 4(a), the y-axis of each point (‘+’) indicates theperformance improvement for a musical piece brought byusing the fuzzy annotations with each window; and the x-axis
indicates the tempo of the piece computed from its groundtruth beat annotations. The lines represent the moving averagesof the improvements along tempo (x-axis), with the average
taken over pieces with similar tempi (in a range of 10 bpm). In
Figure 4(b) with only the moving averages, it is clear that the226(a) Tempo histogram of pieces in all three datasets.

(a) F-measure improvements on individual pieces. Left: beat tracking;Right: downbeat tracking.
(b) Tempo histograms of individual datasets.

Fig. 5: Tempo statistics for the three test datasets.

(b) Moving averages of F-measure improvements. Left: beat tracking;Right: downbeat tracking.

Fig. 4: F-measure improvements by the three windows fordifferent tempi in the three test datasets.

fuzzy annotations worked for pieces with tempi slower than
80 bpm and brought subtle differences in the performance forpieces with tempi ranging from 80 to 150 bpm. For pieces
with tempi faster than 150 bpm, the trend is not clear. Thisis because there are fewer pieces in this range, as shown in
Figure 5(a); the average improvement was easily influenced
by certain pieces.
Figure 5(b) showed the tempo histograms of the threetest datasets. We found that the proportion of pieces withtempi slower than 80 bpm is related to the performance
improvements in Figure 3. Since the proportion of slow tempi
in the SMC dataset is much larger than those in the otherdatasets, there were larger improvements on beat tracking performance. The proportion of slow tempi in the Songle dataset
is larger than that in the Beatles dataset, and hence there were
improvements for the Songle dataset but no improvements for
the Beatles dataset.
We further investigated the activation functions and foundthat using fuzzy annotations can enlarge activation functions
and help correct phase errors. Firstly, the output (activation
functions) of the model trained with fuzzy annotations is larger
than that of the baseline model. We applied a threshold of 0.05
on the activation functions. If the activation functions are too
small, then no beat is detected. With the fuzzy annotations,the activation functions become larger, and beats are detected.
Secondly, we observed that even when we normalize theactivation functions (which can help to solve the above threshold problem), there are some noticeable peaks between beatsin the activation functions of the baseline model, as shownin Fig 6. With the fuzzy annotations, these peaks between

Fig. 6: Outputs of Piece SMC 236 (28s-34s).

beats are suppressed, making the phase errors easier to be
recovered with the context information (in the post-processing
with the DBN). We observed that the adjacent frames in the
spectrogram are similar to each other due to the overlap. It
is reasonable to put similar labels on adjacent frames aroundbeats, so that the model can focus more on learning the latentpattern of beats and no-beats, rather than distinguishing beatand no-beat on similar inputs.
We looked at the cross-validation results and found that thelargest improvement was on the Hainsworth dataset. In theexperiment, we used the old annotations which are drifted fromthe beat times (the updated annotations can be found in [19]).
When we enlarge the beat range, it is more likely to include thetrue beat times, which helps improve the results. This effect isalso important because it is common that manual annotations
are imprecise. This result suggests that it is worth trying large
windows when the temporal accuracy of beat annotations is
not high enough. This supplements our previous finding that
small windows generally work better in [33].
D. Recommended choices
Since using the fuzzy annotations and adding the chromafeatures work differently on different music styles, the best
choice depends on the target music data. For the fuzzy annotations, a rectangular window is recommended if the data tend227

to include slow-tempo pieces; otherwise, a triangular window
is recommended. The Gaussian window could be used for thedata with no prior information. Adding the chroma features isusually recommended unless the dataset has a lot of fast-tempo
pieces or downbeat tracking is not necessary.
IV. C ONCLUSIONSIn this paper we evaluated the idea of using fuzzy annotations in CRNN-based joint beat and downbeat tracking. In
comparison to the baseline model with the original annotation,using the fuzzy annotations provides better performance on
the test datasets: it improves results on relatively difficult
datasets and brings no significant differences on relatively
simple datasets. Our main contributions can be summarized
as follows. (1) We evaluated the fuzzy annotations broadenedby the three different kinds of windows, and provided stateof-the-art performance on beat and downbeat tracking. (2) We
analyzed the performance improvement of each piece, andfound that the main improvements are on pieces with tempi
slower than 80 bpm. (3) We found that the improvements aremainly due to enlarged activation functions and phase error
correction by investigating the activation functions from the
CRNN outputs.
Future work will include tempo estimation with beat anddownbeat tracking in a multi-task learning framework.
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