Revisiting Meter Tracking in Carnatic Music using Deep Learning Approaches

Master thesis on Sound and Music Computing Universitat Pompeu Fabra “Revisiting Meter Tracking in Carnatic Music using Deep Learning Approaches” Satyajeet Prabhu Supervisor: Martín Rocamora Co-Supervisor: Thomas Nuttall August 2025 Acknowledgments I would like to express my sincere gratitude to Prof. Xavier Serra for giving me the opportunity to be part of this prestigious program despite my limited experience in software development. His encouragement to explore research in Indian Art Music has been a source of inspiration for me and many aspiring music computation researchers from India. I am deeply grateful to my supervisor, Dr. Martín Rocamora, whose constant guidance over the two years of this program has been invaluable. From teaching one of the most engaging courses in the program to offering me an internship opportunity at the MTG and ultimately supervising my thesis, he has played a pivotal role in shaping me as a researcher. I am thankful to my supervisor Thomas Nuttall - Tom, as he is affectionately known - whose support began even before the program, sparked by our meeting at the ISMIR satellite workshop in India in 2022. My gratitude also extends to Genís, Adithi, Oguz, Behzad, Esteban, Jyoti, Alia and all the other PhD students and researchers at MTG, who have always been willing to offer assistance and guidance in both professional and personal matters. I also want to sincerely thank Ajay Srinivasamurthy, the author of the work on which this study is based, for being generous with his time and constantly offering his support despite his busy schedule. It has been a privilege to study alongside my incredibly talented colleagues in the SMC Masters program, who I now proudly call friends. Special thanks to Anmol Mishra, now my co-author as well, for the banter and for the constant encouragement to take on new challenges and to Robin Doerfler for some of the most philosophical and intellectually stimulating conversations I have ever had. Lastly, I am immensely thankful to my parents for their unwavering support in my musical (mis)adventures over the years, and to my close family and friends, who continually encourage me to keep exploring and growing. 3 Abstract Beat and downbeat tracking, jointly referred to as Meter Tracking, is a fundamental task in Music Information Retrieval (MIR). Deep learning models have far surpassed traditional signal processing and classical machine learning approaches in this domain, particularly for Western (Eurogenetic) genres, where large annotated datasets are widely available. These systems, however, perform less reliably on underrepresented musical traditions. Carnatic music, a rich tradition from the Indian subcontinent, is renowned for its rhythmic intricacy and unique metrical structures (t¯al .as). The most notable prior work on meter tracking in this context employed probabilistic Dynamic Bayesian Networks (DBNs). The performance of state-of-the-art (SOTA) deep learning models on Carnatic music, however, remains largely unexplored. In this study, we evaluate two models for meter tracking in Carnatic music: the Temporal Convolutional Network (TCN), a lightweight architecture that has been successfully adapted for Latin rhythms, and Beat This!, a transformer-based model designed for broad stylistic coverage without the need for post-processing. Replicating the experimental setup of the DBN baseline on the Carnatic Music Rhythm (CMRf) dataset, we systematically assess the performance of these models in a directly comparable setting. We further investigate adaptation strategies, including fine-tuning the models on Carnatic data and the use of musically informed parameters. Results show that while off-the-shelf models do not always outperform the DBN, their performance improves substantially with transfer learning, matching or surpassing the baseline. These findings indicate that SOTA deep learning models can be effectively adapted to underrepresented traditions, paving the way for more inclusive and broadly applicable meter tracking systems. 4 Contents Abstract 4 1 Introduction 7 1.1 Background .................................... 7 1.1.1 Metrical Structure in Music . . . . . . . . . . . . . . . . . . . . . . . . 7 1.1.2 Rhythm in Carnatic Music . . . . . . . . . . . . . . . . . . . . . . . . . 8 1.2 Motivation..................................... 10 1.2.1 Specific Challenges in Carnatic Music . . . . . . . . . . . . . . . . . . 10 1.3 Research Question and Objectives . . . . . . . . . . . . . . . . . . . . . . . 11 1.3.1 Research Questions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11 1.3.2 Objectives................................... 11 2 State of the Art 13 2.1 Signal Processing Approach . . . . . . . . . . . . . . . . . . . . . . . . . . 13 2.2 BayesianApproach................................ 14 2.2.1 Bar Pointer model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15 2.2.2 Inference in Bayesian Meter Tracking . . . . . . . . . . . . . . . . . . 17 2.3 Deep Learning Approach . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18 2.3.1 DNN Pipeline for Meter Tracking . . . . . . . . . . . . . . . . . . . . . 18 2.3.2 Overview of Architectures . . . . . . . . . . . . . . . . . . . . . . . . . 19 2.4 Evaluation..................................... 19 2.4.1 F-Measure................................... 20 2.4.2 Continuity-based Metrics . . . . . . . . . . . . . . . . . . . . . . . . . . 20 3 DNN Models for Meter Tracking 23 3.1 Temporal Convolutional Network . . . . . . . . . . . . . . . . . . . . . . . 23 3.1.1 Architectural Details . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23 3.1.2 Adaptation and Generalization . . . . . . . . . . . . . . . . . . . . . . 25 3.1.3 Multi-task Learning Formulation . . . . . . . . . . . . . . . . . . . . . 26 3.2 Beat This! : Tracker without Post Processing . . . . . . . . . . . . . . . . 27 3.2.1 Architectural Details . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27 3.2.2 Shift-tolerant Loss . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28 3.3 Practical Considerations: TCN vs Beat This! . . . . . . . . . . . . . . . . 29 4 Methodology 30 4.1 Dataset....................................... 30 4.2 Baseline ...................................... 31 4.2.1 BaselineSetup ................................ 31 5 4.3 ExperimentSetup ................................ 32 4.3.1 TCN...................................... 32 4.3.2 BeatThis!................................... 34 4.4 Musically Informed Strategies . . . . . . . . . . . . . . . . . . . . . . . . . 34 4.4.1 Music-Informed Training . . . . . . . . . . . . . . . . . . . . . . . . . . 34 4.4.2 Music-Informed Post-Processing . . . . . . . . . . . . . . . . . . . . . . 35 5 Results and Discussion 36 5.1 Model-wise Performance . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36 5.2 T¯al .a-wisePerformance ............................. 37 5.3 OutlierAnalysis ................................. 39 5.4 Tempo and T¯al .a Cycle Duration Effects . . . . . . . . . . . . . . . . . . . 40 6 Conclusions and Future Work 42 6.1 Summary of the Study . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42 6.2 Conclusions .................................... 43 6.3 FutureWork ................................... 43 List of Figures 45 List of Tables 45 Bibliography 47 Appendices 50 A Software and Other Resources 50 B Detailed Analysis Plots 52 Chapter 1 Introduction 1.1 Background Rhythm analysis is a central topic in Music Information Retrieval (MIR), aimed at computationally analysing or modelling the temporal structure of music. It encompasses a variety of tasks such as onset detection, tempo estimation, beat and downbeat tracking, pattern analysis, microtiming analysis and synchronization among others, which together enable a comprehensive understanding of musical timing. This work focuses on the task of automatic estimation of beats and downbeats, commonly referred to as Meter Tracking, critical for several higher-level MIR tasks such as music segmentation and structural analysis, as well as applications such as DJ mixing and automatic beat matching. 1.1.1 Metrical Structure in Music Rhythm in music is perceived as pulsations organized at multiple hierarchical levels of differing timespans, known as its meter or metrical structure [Bilmes, 1993, London, 2012]. These levels range from very fast subdivisions to larger organizational units (for example, see figure 1). The different metrical levels are described as follows: Figure 1: Perceived metrical levels in ’Twinkle, Twinkle, Little Star’ Tatum The fastest regular pulse in the music that listeners can perceive as a meaningful subdivision of rhythm. Often corresponds to a 16th note in Western 7 music, but the specific duration depends on the tempo and style. Tactus (Beat) The perceptually most salient pulse level that a listener would naturally tap their foot to. It typically corresponds to quarter notes in Western music but again depends on tempo and context. The beat level is central to most rhythm perception tasks and often serves as the reference level for tempo. Meter (Bar, Measure, Cycle) A grouping of beats into a recurring structure that establishes musical phrasing and form. Measures are typically marked by accent patterns and serve to shape listeners’ expectations of timing and emphasis. In Western music, meter is commonly represented using time signatures, such as 4/4, which indicates four beats per measure, with each beat typically being a quarter note in duration (see figure 2). Other common meters include 3/4 (e.g., waltz). Downbeat The first beat of a bar or cycle, often marked by a strong accent or structural change. It acts as a temporal anchor and plays a crucial role in conveying the start of a measure. Accurate downbeat perception is essential for understanding musical form and phrasing. Figure 2: Musical meter in Western music. Figure from Wikipedia, Metre (music). 1.1.2 Rhythm in Carnatic Music Carnatic music, one of the two principal traditions of Indian art music (IAM), is predominantly practiced and appreciated in the southern regions of the Indian subcontinent. It is distinguished by its dedicated audiences, sophisticated theoretical framework, and high level of musicianship. Traditionally, training in Carnatic music is transmitted orally through a lineage of teachers, with a strong emphasis on performance and improvisation. A typical Carnatic performance features a lead performer, a rhythmic accompaniment, a continuous background drone, and a melodic accompaniment. Unlike Western tonal music, Carnatic music does not employ harmony; instead, it is structured around the melodic framework of r¯aga and the rhythmic framework of t¯al .a[Sambamoorthy, 1998]. Consequently, Carnatic music has become an important subject in MIR research as it presents unique challenges and opportunities for computational analysis [Rao et al., 2023]. Rhythmic organization in Carnatic music is governed by the t¯al .a system, a hierarchical framework of time cycles that underlies melodic and rhythmic phrasing as well as improvisation. Within each t¯al .a cycle, sub-structures are defined to track progression through the cycle. While there are some conceptual parallels with Western metrical structures, the terminology and organization within the t¯al .a system differ significantly. Table 1 presents approximate correspondences between metrical hierarchies in Western and Carnatic frameworks. Western Carnatic Tatum aks .ara Beat (indicated by hand gestures) Measure ¯avartana Downbeat sama Table 1: Mapping of Western and Carnatic rhythmic concepts Moreover, the t¯al .a framework includes elements unique to the Carnatic tradition that lack direct equivalents in Western metrical theory, resulting in 175 theoretically possible t¯al .as. In practice, however, a core set of 35 t¯al .as is predominantly used in performance and pedagogy. Table 2 lists the four most commonly employed t¯al .as in Carnatic music, alongside their total number of beats per cycle. T¯al .a #Beats ¯ Adi 8 R¯upaka 3 Miśra ch¯apu 7 Khan .d .a ch¯apu 5 Table 2: Popular t¯al .as in Carnatic music Figure 3 illustrates some of the concepts from table 1 using the example of an ¯ Adi t¯al .a cycle (8 beats). It also demonstrates how beats are further grouped into sections called a˙ngas. The progression through the t¯al .a cycle is marked by distinctive hand gestures, which indicate both individual beats and the different types of sections within the cycle. Figure 3: Illustration of ¯ Adi t¯al .a. Figure from [Srinivasamurthy, 2016] The model also features prominently in Ajay Srinivasamurthy’s 2016 doctoral thesis [Srinivasamurthy, 2016] on automatic rhythm analysis of Indian Art Music, which remains the most comprehensive study of meter tracking in Carnatic music to date. The bar pointer model introduces a hypothetical "pointer" that moves through the metrical cycle and resets at the downbeat. Figure 5: The Bar Pointer model. Figure taken from [Srinivasamurthy, 2016]. Hidden Variables in the BP-model •Bar Position (ϕk) : Variable indicating position in the bar; ϕ=0denotes the downbeat. •Tempo ( ˙ ϕk) : Rate of progression of the pointer through the bar; modeled stochastically to allow for natural tempo fluctuation. •Rhythmic Pattern Index (rk) : Encodes discrete rhythmic templates, capturing expected accent structures across different metrical styles. Transition Model The transition model defines how the hidden state evolves over time: P(xk∣xk−1)=P(ϕk∣ϕk−1,˙ ϕk−1, rk−1)⋅P(˙ ϕk∣˙ ϕk−1)⋅P(rk∣rk−1, ϕk, ϕk−1) The first term updates the bar position ϕkbased on the previous position ϕk−1and tempo ˙ ϕk−1. The second term enforces smooth tempo changes by modelling ˙ ϕkbased on ˙ ϕk−1. The third term allows rhythmic pattern rkto change, but only at the end of a bar (i.e., when ϕk<ϕk−1). Observation Model The observation model P(yk∣xk)defines the likelihood of observing feature ykgiven the current state. It is often implemented using Gaussian Mixture Models (GMMs) trained on bar-position-aligned rhythmic patterns derived from annotated data. The model captures how likely an onset or spectral event is to occur at each position in the bar, for each pattern. 2.2.2 Inference in Bayesian Meter Tracking Once a Bayesian model (like the bar pointer model) is defined, the core computational task is inference. Given the observations y1∶K, the goal is to estimate the hidden state sequence x1∶K— tempo, bar position, and rhythmic pattern — that best explain the observed audio features. Goal: arg max x1∶K P(x1∶K∣y1∶K) Depending on how the hidden state space is modeled — discretely or continuously — different inference techniques are used. The two dominant approaches are: Viterbi Decoding The Viterbi algorithm is a dynamic programming method that finds the single most likely i.e. Maximum A Posteriori (MAP) sequence of hidden states. It assumes a discrete state space - the bar position ϕ, tempo ˙ ϕ, and rhythmic pattern rare discretized into a fixed grid. This approach provides exact inference under the discrete model and is efficient when the state space is moderately sized. However, it becomes computationally expensive with fine discretization, for example in cases with long bars, and it is inflexible in real-time or online settings. To tackle these scalability challenges, Krebs et al. proposed an Efficient State Space Model [Krebs et al., 2015] that restructures the original bar pointer model resulting in better accuracy and drastically reduced computational complexity. Particle Filtering When the hidden state space is modeled as continuous (or very high-dimensional), exact inference becomes intractable. Particle filtering provides an approximate solution by using a set of weighted samples, called particles, each representing a possible state trajectory. In other words, each particle represents a hypothesis for the hidden state at time k:x(i) k=[ϕ(i) k,˙ ϕ(i) k, r(i) k]. Particle filtering naturally incorporates uncertainty and multimodality, such as multiple possible tempo hypotheses, making it better suited for online or real-time applications. However, it is computationally intensive, requires tuning the number of particles, and since it is an approximate method, the results may vary between runs. 2.3 Deep Learning Approach Currently, data-driven deep learning approaches dominate the landscape for the meter tracking task as they offer several advantages. Deep Neural Networks (DNN) are capable of learning complex representations from raw input data, processing large-scale datasets more efficiently, generalising better across data and multi-task learning. The availability of GPUs and specialized deep learning frameworks (e.g., TensorFlow, PyTorch) has made training and deploying DNNs more practical. 2.3.1 DNN Pipeline for Meter Tracking Figure 6: DNN based meter tracking pipeline. Figure adapted from Tempo, Beat and Downbeat ISMIR Tutorial 2021 [Davies et al., 2021]. A typical pipeline for a DNN-based meter tracking system (see Figure 6) consists of two stages - feature learning and temporal decoding. DNNs first learn features from the input audio or its time-frequency representation and output an activation or salience function containing the possible beat and downbeat candidates. This is similar to the novelty function, but while the novelty function is derived from hand-crafted features, the activation function is produced by the network’s complex internal representation. The output activations of DNNs are often noisy and cannot be directly used for predictions. DBNs are proven in their ability to impose temporal consistency and metrical structure and are commonly used as a post-processing step to infer beats and downbeats from DNN activations. However, DBNs can also introduce several limitations due to their inherent properties. They do not work for music with time signature changes, tempo changes outside the prescribed range, and metric structures not represented in the state space. To overcome bias introduced by DBNs and generalise across music genres, recent efforts have attempted to remove this post-processing stage. 2.3.2 Overview of Architectures Since beat and downbeat estimation is a sequence modelling problem, the most successful architectures applied to this task include Recurrent Neural Networks (RNNs), Temporal Convolutional Networks (TCNs) and transformer-based models, all of which are well-suited for capturing temporal dependencies in musical signals. Böck et al. [Böck et al., 2016] utilise RNN, specifically Bidirectional Long ShortTerm Memory (BLSTM) architecture, for a supervised classification task to simultaneously detect beats and downbeats. This significant work outperformed standalone DBN-based meter tracking, especially on the downbeat detection task for most Western music datasets. Convolutional Neural Networks (CNN) are known to excel at extracting local features, such as transients, while having a relatively low model complexity. However, they suffer from a lack of long-term context, which makes it difficult to identify global rhythmic structures. Hybrid approaches that incorporate both spatial and temporal understanding are, therefore, utilised for meter tracking. BeatNet [Heydari et al., 2021] uses CRNN (Convolutional Recurrent Neural Network), which combines CNNs for feature extraction and recurrent layers for sequential modelling. Temporal Convolutional Network has emerged as another powerful architecture for beat and downbeat tracking. TCNs utilise convolutional layers with dilations to achieve a large receptive field, allowing them to model long temporal contexts efficiently. More recently, the transformer architecture - originally successful in natural language processing - has been applied to meter tracking. Transformers utilise a self-attention mechanism that allows the model to weigh the importance of different parts of the input sequence when making predictions. This enables them to capture both local and global dependencies effectively while covering the entire input sequence. Hung et al. [Hung et al., 2022] employ a spectral-temporal transformer (SpecTNT) architecture for this task. Beat This!, a transformer-based system that removes the post-processing stage, achieves state-of-the-art beat and downbeat tracking performance on a number of Western music datasets. 2.4 Evaluation The evaluation of meter tracking systems typically involves comparing predicted beat and downbeat times against annotated ground truth. In order to account for the inherent imprecision in annotations and musical events, most evaluation metrics allow a tolerance window around the annotated times. 2.4.1 F-Measure The F-measure, also known as the F1-score, evaluates the accuracy of predicted beat times by comparing them to ground truth annotations within a fixed temporal tolerance window (commonly ±70 ms). This metric intends to provide a measure of how many beats are correctly predicted without over or underpredicting. Downbeats are evaluated similarly, but due to their lower frequency, errors are more impactful. It is defined in terms of: True Positives (NTP): Number of predicted beats that fall within the tolerance window of a ground-truth beat. False Positives (NFP): Number of predicted beats that do not match any groundtruth beat within the tolerance window. False Negatives (NFN): Number of ground-truth beats for which no predicted beat lies within the tolerance window. Figure 7: Tolerance window for F-measure. Figure from Tempo, Beat and Downbeat ISMIR Tutorial 2021 [Davies et al., 2021]. Precision and Recall are defined as: Precision =NTP NTP +NFP ,Recall =NTP NTP +NFN Then, the F-measure is the harmonic mean of precision and recall: F1=2⋅Precision ⋅Recall Precision +Recall While the F-measure is a widely used and intuitive metric, it is prone to systematic issues that can give a misleading impression of tracking quality. For instance, changing the size of the tolerance window can dramatically change the value of the measure. As a result of using a fixed tolerance window, beats inside the window are considered accurate regardless of their position inside the window. So, predictions consistently offset from the annotation would result a high F1 score. 2.4.2 Continuity-based Metrics Continuity-based metrics were introduced to address some of these gaps by evaluating not just alignment accuracy, but also the consistency of metrical phase and tempo over extended regions. That is, evaluating not just whether beats are detected, but whether they are detected consistently across time and at the correct metrical level. This is especially important for applications such as real-time tracking, where maintaining stable and accurate beat information over time is crucial for synchronization and responsiveness. Continuity Criteria A predicted beat at time ˆ biis considered accurate only if it satisfies two conditions: 1. The predicted beat ˆ bimust lie within a predefined tolerance window around the corresponding ground-truth beat bi. This window is not absolute but relative to the inter-beat interval (IBI), typically set to ±17.5% of the local IBI. 2. The preceding beat ˆ bi−1must also fall within its own tolerance window. Furthermore, the IBI between ˆ bi−1and ˆ bimust be consistent with the IBI between bi−1and bi. These conditions together define what is referred to as a continuous segment: a sequence of at least three consecutive beats that are temporally aligned, metrically consistent, and phase-correct. Only such segments contribute to the continuitybased metrics. Metrical Ambiguity Continuity metrics are designed to be sensitive to a range of metrical errors which may all have similar F-measure values but vastly different perceptual implications. To achieve this, continuity-based metrics introduce metrical variants of the reference annotation grid and evaluate predictions against each variant. The highest resulting score is selected. Commonly used metrical variants include: •Same metrical level, in-phase (i.e., beats align exactly with annotations) •Same metrical level, off-phase (i.e., beats occur halfway between annotations) •Double tempo (Twice the annotated metrical level) •Half tempo (even-phase) (every other annotation starting from the first) •Half tempo (odd-phase) (every other annotation starting from the second) Definitions of Continuity Metrics Let Nseg correct be the number of beats in the longest continuous correct segment, and Nall correct be the total number of correct beats (even across multiple segments). Four metrics are derived from this principle, distinguishing between strict (annotated) and lenient (allowed) metrical levels: •CMLc(Correct Metrical Level - continuous): CMLc=Nseg correct Npred •CMLt(Correct Metrical Level - total): CMLt=Nall correct Npred •AMLc(Allowed Metrical Levels - continuous): Same as CMLc, but allows metrical ambiguities. •AMLt(Allowed Metrical Levels - total): Same as CMLt, but allows metrical ambiguities. Low continuity scores - especially when paired with a high F-measure - suggest that predictions are fragmented or metrically inconsistent, even if individual beats are frequently close to annotations. Comparing CML and AML variants can also reveal whether a system is making metrical-level errors (e.g., consistently tracking at half or double tempo) that still result in perceptually acceptable output. Overall, continuity metrics offer a more structurally aware evaluation than frame-level accuracy alone. Chapter 3 DNN Models for Meter Tracking This work focuses on two main architectures: Temporal Convolutional Network and Beat This!. The following sections take a closer look at each system, explaining their key components and how they approach the task of meter tracking. 3.1 Temporal Convolutional Network TCNs have been shown to outperform traditional RNN-based models such as BLSTMs in meter tracking tasks. The TCN architecture uses dilated convolutions to model temporal dependencies, allowing the model to process audio sequences in parallel. Unlike BLSTMs, which are inherently sequential and thus difficult to parallelize, TCNs enable parallel training across time steps, significantly reducing training times and computational costs. Through dilated convolutions, TCNs are capable of modelling long-range temporal dependencies (spanning entire bars or phrases) with significantly fewer parameters. These characteristics make TCNs not only more scalable but also better suited for real-time or low-latency applications. Figure 8 shows an overview of beat tracking pipelines for the two architectures. 3.1.1 Architectural Details There are two main components at the heart of a TCN-based meter tracker: Convolutional Block The convolutional block acts as the frontend feature extractor in the TCN-based meter tracking pipeline. Its role is to transform the input spectrogram into a more compact and informative set of learned features that emphasize the spectral-temporal patterns relevant to rhythm perception. Importantly, all convolution operations are performed without temporal downsampling. The convolutional block is designed to reduce spectral dimensionality while preserving the temporal resolution that is critical for tracking beat-related events. As seen in figure 9, a typical convolutional block includes: 23 Figure 8: Comparison of BLSTM and TCN architectures for beat tracking. Figure taken from [Davies and Böck, 2019]. •Multiple 2D convolutional layers, each with a small kernel size (e.g., 3×3) to capture local time-frequency patterns. •Pooling along the frequency axis, which compresses the spectral dimension while maintaining the original temporal resolution. •Nonlinear activation functions, such as ELU, applied after each convolution to introduce nonlinearity. Figure 9: Convolutional block in a TCN-based meter tracker. Figure taken from [Böck and Davies, 2020]. TCN Block The input to the TCN is a highly sub-sampled feature vector derived from the magnitude spectrogram by the convolutional block, but which retains the same temporal resolution. The TCN block is the core temporal modelling component of the architecture. Its primary function is to model the sequential dependencies and periodic structures required for beat and downbeat prediction. It does so by learning filters via dilated convolution. Dilation is equivalent to skipping samples in the input sequence. In a standard 1D convolution, each filter “slides” across the time axis of the input feature map, processing a local window (e.g., 3 frames) at each step. This is analogous to scanning for repeating rhythmic motifs. However, to model longer contexts, TCNs introduce dilated convolutions. A dilation defines the spacing between the elements in the filter’s receptive field. For example, referring to figure 10 : A dilation of 1 corresponds to adjacent time steps(t−1, t, t +1). A dilation of 2 looks at every second time step (t−2, t, t +2). A dilation of 4 expands further (t−4, t, t +4). By stacking layers with exponentially increasing dilations (e.g., 1, 2, 4, 8...), the network can effectively model patterns over a large time span without a proportional increase in the number of parameters. Figure 10: Temporal Convolutional Network. Figure taken from ISMIR 2021 tutorial on Tempo, Beat, and Downbeat Estimation.[Davies et al., 2021]. Advantages for Meter Tracking: •Temporal resolution is preserved: Unlike RNNs, TCNs can maintain the full temporal granularity of the input. •Efficient long-term modelling: Due to dilation, a TCN with 10 layers and kernel size 3 can access 210 =1024 time steps—several seconds of music— without loss of resolution. •Parallel training: All time steps can be processed simultaneously, making the model highly suitable for GPU acceleration. 3.1.2 Adaptation and Generalization In the context of meter tracking, Davies and Böck [Davies and Böck, 2019] first successfully repurposed the TCN design inspired by WaveNet [Van Den Oord et al., 5. Preservation of T¯al .a Distribution: The experimental setup preserves t¯al .a distribution in each fold. Specifically, the distribution of t¯al .as in the training and test folds mirrors the distribution of t¯al .as in the full dataset. 4.3 Experiment Setup For both models under evaluation, we first replicate the data splits and training setup as described in the previous section. Additionally, we establish common procedural guidelines to ensure a fair and consistent comparison between the models: •The dataset, comprising 176 samples, is divided into two predetermined folds of 88 examples each, identical to those used in the baseline experiment’s twofold cross-validation scheme. In each iteration, one fold is used for training while the other serves as the test set, with the folds alternating roles between iterations. •The train fold is further subdivided into training (80%) and validation (20%) subsets. Consequently, each fold contains 70 training examples and 18 validation examples. •We perform three training runs per fold. To ensure reproducibility of validation splits and network initializations, we set predetermined random seeds [42, 52, 62] for each respective run. As a result, six distinct models are generated for every training strategy, and the results are reported as the mean performance across these six models. •Validation loss is employed as the primary metric for monitoring training progress and for early stopping. Training is terminated when no improvement in validation loss is observed. •The models are evaluated using the F-measure as well as the continuity metrics CMLtand AMLtfor both beat and downbeat. The evaluation process is carried out using the Python package mir_eval [Raffel et al., 2014]. 4.3.1 TCN Model The experimental setup for the TCN employed in this study is based on the opensource implementation of Deconstruct, Analyse, Reconstruct [Böck and Davies, 2020] made available by the authors as part of the ISMIR 2021 tutorial on Tempo, Beat and Downbeat Estimation. This implementation was subsequently repurposed in Adapting Meter Tracking Models to Latin American Music [Maia et al., 2022], and an updated, user-friendly version is provided in the Tutorial for LAMIR 2024 Hackathon [Morais et al., 2024]. The present study utilises these prior works and their respective experimental setups as the basis for the TCN implementation. Trainable Parameters : 72.3K Training Strategies For the TCN model, we evaluate three strategies inspired by [Maia et al., 2022]. •Baseline (TCN-BL) First, we train a model on the popular Western datasets for meter trackingGTZAN, Ballroom, Beatles and RWC datasets following [Maia et al., 2022]. This model is assumed to be a good starting point for a baseline evaluation of the TCN on Carnatic data as well as for subsequent transfer learning experiments. Following protocol, we perform three training runs and report mean performance on the CMRfdataset. •Fine-tuning (TCN-FT) Under this strategy, the model with the lowest validation loss from TCN-BL is used as a starting point for fine-tuning the network on Carnatic data. The assumption is that, although the model was pre-trained on Western datasets, it has learned a representation that can be adapted for a different musical tradition, as demonstrated in [Maia et al., 2022]. •Training from Scratch (TCN-FS) This strategy involves training a randomly initialized network (using one of the predefined seed values) from scratch on each fold. Loss Function We employ a simple loss function defined as the sum of the binary cross-entropy (BCE) for beat and downbeat predictions: L=BCEbeat +BCEdownbeat Table 6 provides a summary of the training configuration settings employed across the different TCN strategies. Acronym Strategy Models Trained Epochs Early Stoppage Learning Rate LR Reduction (Factor) TCN-BL TCN Baseline 3 100 20 0.005 0.2 TCN-FS Train from Scratch 6 100 20 0.005 0.2 TCN-FT Finetune from Baseline 6 50 10 0.001 0.2 Table 6: Training configurations for the TCN strategies Post Processing For post-processing network activations, a DBN-based post-processor is used. The Python library madmom [Böck et al., 2016] offers an open-source joint beat and downbeat DBN post-processor approximated by a Hidden Markov Model (HMM), based on [Böck et al., 2016, Krebs et al., 2015]. In this work, we use its offline mode utilising the Viterbi algorithm for inference. 4.3.2 Beat This! Model For Beat This!, we use the stock implementation for baseline evaluation. For finetuning, however, we build upon a modified implementation that facilitates finetuning of the stock model. Despite these modifications, we retain the default training configurations, including data augmentation schemes, and utilise the pre-trained models provided by the original authors. Trainable Parameters : 20.3M Training Strategies We adopt only two strategies: Baseline and Fine-tuning. Given that Beat This! is a transformer-based architecture, it is highly data-intensive, which makes training from scratch on a single dataset impractical. •Baseline (BeatThis-BL) We utilise the three pre-trained checkpoints provided with the stock model, namely final0,final1 and final2, all of which have been trained on a large corpus comprising 18 different datasets (excluding GTZAN). We evaluate these models on the CMRfdataset and report the mean performance across all three models as the baseline performance for Beat This!. •Fine-tuning (BeatThis-FT) The fine-tuning process begins with the default (final0) checkpoint as the pretrained baseline, which is then further fine-tuned over the course of 50 epochs. Lastly, we use the built-in Shift-tolerant weighted BCE loss and skip post-processing. 4.4 Musically Informed Strategies Incorporating musicological insights into meter tracking systems can enhance their performance. This section explores strategies used during training and postprocessing to help our DNN meter tracking systems adapt better to Carnatic Music. 4.4.1 Music-Informed Training These strategies applied at the training stage aim to ensure that the model is exposed to rhythmic diversity consistently during the training process: Stratified T¯al .a-based Train/Validation Split To ensure consistent performance across t¯al .as, we implement a stratified train/validation split based on t¯al .as. This balances representation of all t¯al .as in training and validation, enabling per-t¯al .a error analysis and targeted improvements for underperforming t¯al .as. Interleaved Train Data Loader An issue with the CMRfdataset is imbalanced class distribution - some t¯al .as appear more frequently than others. We use an interleaved data loader that proportionally spaces rarer t¯al .as like khan .d .a ch¯apu in training, ensuring a more balanced learning process. 4.4.2 Music-Informed Post-Processing One impactful strategy for enhancing the performance of meter tracking systems is post-processing. The DBNDownBeatTrackingProcessor from the madmom library allows us to tune parameters to reflect musical characteristics of the data being processed. We set the following parameters based on musicological knowledge as well as insights from the dataset: •beats_per_bar = [3, 5, 7, 8] based on the four t¯al .as in our dataset instead of the default [3, 4] •min_tempo = 55 and max_tempo = 230, reflecting the tempo range observed in the dataset (see Figure 12). This range, chosen based on preliminary experiments, covers 99% of all tempos and provides a constrained search space for the post-processor, with results showing slight performance improvement compared to a max tempo of 300 BPM (99.9% of all tempos). Figure 12: Distribution of tempos in the CMRfdataset. For reproducibility, all relevant code repositories, software resources, and dataset references utilised in the experiments are catalogued in Appendix A. Chapter 5 Results and Discussion This chapter presents and examines the performance of models trained with the various strategies described in the previous chapter. Each approach is evaluated using quantitative metrics, including F-measure and continuity scores, to provide a robust comparison. In addition, a detailed breakdown by t¯al .a is conducted to highlight how each model responds to the unique rhythmic structures of Carnatic music, allowing their respective strengths and weaknesses to emerge more clearly. 5.1 Model-wise Performance Table 7 below shows the overall performance of the two models and their strategies against the Bar Pointer model baseline with the highest performing metrics highlighted in bold. Model Beat Downbeat F-measure CMLtAMLtF-measure CMLtAMLt BP-HMM 71.8 — 72.2 44.0 — — BP-AMPF 82.5 — 90.6 57.4 — — TCN-BL 77.1 51.6 77.9 28.9 21.6 33.8 TCN-FT 80.7 50.2 91.9 52.9 35.3 57.8 TCN-FS 84.6 62.9 88.0 63.9 52.1 67.0 BeatThis-BL 71.3 39.2 56.8 27.6 2.0 8.7 BeatThis-FT 90.3 78.0 80.0 66.8 38.2 53.7 Table 7: Model-wise Performance Comparison Both the TCN-BL and BeatThis-BL models, which were trained on Western music datasets, fail to achieve baseline performance levels in meter tracking for Carnatic music. Although the beat tracking accuracy of these models approximates baseline performance, their downbeat tracking performance remains substantially below baseline, despite being trained on extensive datasets. 36 This disparity reveals the fundamental differences in rhythmic structures between Western and Carnatic music and illustrates the challenges faced by neural networks in directly transferring learned knowledge across distinct musical traditions. In contrast, the TCN-FT model nearly attains baseline performance, notably achieving the highest beat AMLtscore among all evaluated models. Interestingly, preliminary experiments demonstrated comparable results when fine-tuning a model initially trained only on the GTZAN dataset. These findings further highlight the necessity for the network to re-optimize its hyperparameters when adapting from Western to Carnatic music, indicating that the quantity of data used during pretraining may be less significant compared to the subsequent fine-tuning on Carnatic music. In fact, the performance of the TCNFT model may be hindered by being undertrained. Additional fine-tuning could enhance the results, effectively equating to training the model from scratch. Both TCN-FS and BeatThis-FT significantly outperform the DBN baseline in beat and downbeat tracking, with BeatThis-FT establishing itself as the most effective approach for achieving raw accuracy in meter tracking of Carnatic music. Meanwhile, TCN-FS excels in maintaining temporal continuity, particularly in the downbeat tracking task. The difference in performance between the two models is as expected, given their respective architectures (see Chapter 3) and the application of post-processing in the TCN model. The Beat This! architecture emphasizes the accuracy of local predictions, while the TCN model paired with the postprocessor promotes globally coherent predictions. Additionally, the powerful transformer architecture used by Beat This! is able to extract more meaningful features from the Carnatic data compared to the relatively lightweight TCN model, although this advantage comes with increased computational demands. 5.2 T¯al .a-wise Performance With TCN-FS and BeatThis-FT identified as the two leading strategies for tracking Carnatic meter, we proceed to analyze their performance on each t¯al .a to gain a thorough understanding of their capabilities. Tables 8 and 9 provide breakdowns of the performance of TCN-FS and BeatThis-FT, respectively, across the four t¯al .as. In terms of beat tracking, BeatThis-FT demonstrates relatively consistent performance across t¯alas compared to TCN-FS. This consistency is also evident in the continuity scores. TCN-FS struggles particularly with ¯adi (8) and r¯upaka (3) t¯alas, especially the latter. Although the beat F-measures are reasonable, the low CMLt scores indicate that while many beats are detected correctly, the system often loses correct tempo continuity throughout the sequence. The higher AMLtscores suggest that the system frequently predicts tempos that are rhythmically related, implying metrical ambiguity, likely due to the post-processing stage, which is absent in Beat This!. T¯al .a Beat Downbeat F-measure CMLtAMLtF-measure CMLtAMLt ¯ Adi (8) 77.8 52.7 84.8 62.7 42.5 84.3 R¯upaka (3) 75.8 32.8 85.0 40.7 19.5 23.8 M¯ıśra ch¯apu (7) 95.6 92.3 93.9 86.7 88.8 94.5 Khan .d .a ch¯apu (5) 93.5 84.5 88.7 68.5 64.6 65.9 Overall 84.6 62.9 88.0 63.9 52.1 67.0 Table 8: TCN-FS : T¯al .a-wise Performance Comparison T¯al .a Beat Downbeat F-measure CMLtAMLtF-measure CMLtAMLt ¯ Adi (8) 86.6 74.3 77.5 49.3 2.2 55.8 R¯upaka (3) 89.5 74.7 77.5 81.6 68.3 68.3 M¯ıśra ch¯apu (7) 94.2 86.0 86.1 72.8 49.7 50.6 Khan .d .a ch¯apu (5) 91.4 76.6 78.5 61.1 28.8 29.3 Overall 90.3 78.0 80.0 66.8 38.2 53.7 Table 9: Beat This-FT : T¯al .a-wise Performance Comparison Interestingly, even in Beat This!, the t¯alas ¯adi (8) and r¯upaka (3) score lower in beat tracking accuracy than m¯ıśra ch¯apu (7) and khan .d .a ch¯apu (5). This may seem counter-intuitive, as one might expect systems to struggle more with rarer and more complex meters. However, the difference is due to the variety of patterns within a given t¯ala. In Carnatic music, performers often improvise and vary grouping structures within a cycle, while maintaining the core framework and overall length. As explained by [Srinivasamurthy, 2016], multiple rhythmic patterns that depart from the traditional t¯ala structure can be played. For example, a musician might perform a pattern grouped as 7, 7, 4, 6, and 8 aks .aras, totaling 32 aks .aras within an ¯adi t¯al .a cycle. Popular t¯alas like ¯adi and r¯upaka tend to have more such variations, making them more difficult for beat tracking systems to generalize. This complexity is visible in the plots in figure 13, which shows the average cycle length spectral flux patterns for ¯adi and m¯ıśra ch¯apu t¯al .as in the CMRfdataset. The patterns indicate varying accent strengths at different metrical positions, reflecting the rhythmic variation within each t¯ala. Also, both models achieve high performance on m¯ıśra ch¯apu for both beat and downbeat detection. This consistency implies that m¯ıśra ch¯apu’s rhythmic pattern is relatively easier to model accurately for both architectures. When examining the downbeat detection task, the results are more nuanced. While Beat This-FT slightly outperforms TCN-FS in overall F-measure (66.8 vs 63.9), both exhibit mixed results with wide variation across t¯al .as. For example, Beat This-FT excels dramatically on r¯upaka, whereas it struggles on ¯adi downbeats. This suggests that each model may be more adept at handling certain rhythmic structures but less consistent across all t¯al .a types. For further granularity, Appendix B includes com- Figure 13: Spectral flux pattern comparison of t¯alas. Figure taken from [Srinivasamurthy, 2016]. prehensive violin plots illustrating per-track performance for both training strategies on each t¯al .a. 5.3 Outlier Analysis Due to the relatively poor performance of TCN-FS on ¯adi and r¯upaka t¯al .as, we perform a preliminary outlier analysis. Tables 10 lists the tracks with the lowest beat and downbeat F-measure scores for these t¯al .as. track id t¯al .a Beat F-measure CMLtAMLt 10047 adi 0.192975 0.100241 0.458864 11024 rupakam 0.605962 0.000145 0.903054 track id t¯al .a Downbeat F-measure CMLtAMLt 10048 adi 0.000000 0.0 1.000000 11040 rupakam 0.032501 0.0 0.000000 Table 10: TCN-FS : Worst Performing Tracks by Beat and Downbeat F-Measure Figure 14 visualizes the ground truth annotations alongside the model predictions over the spectrogram for sections of the two ¯adi t¯al .a outliers with the lowest beat (track id: 10047) and downbeat F-measure (track id: 10048) scores, respectively. In the first case, it is clear that the beat predictions are consistently shifted by half a beat, resulting in a low beat F-measure score. This is a common occurrence in Carnatic music, where creative phase offsets (ed .upu) are often employed - percussive onsets are shifted from the actual beats of the t¯al .a (i.e., played on the off-beat) - making it challenging for the network to detect the true beats. Here, the AMLt score provides a more realistic measure of beat tracking performance. For the downbeat fail case, the detected downbeats are displaced by exactly half a cycle. Though it scores zero in accuracy, it achieves a perfect AMLtscore. This issue can be attributed to the post-processor, which enforces global prediction constraints and may produce scores unrepresentative of the model’s actual performance. Figure 14: TCN-FS : Worst performing tracks for ¯adi t¯al .a visualised The r¯upaka outliers were analyzed by listening, as it is more difficult to visually identify the reasons for their poor performance. In the beat tracking outlier, the percussion switches creatively between triple and quadruple meter through metric modulation, challenging the post-processor’s ability to handle these rapid shifts. The downbeat outlier is particularly challenging because the percussion is performed at double tempo compared to the ground truth annotations, while also employing polymeter. The subpar performance of TCN-FS on r¯upaka is likely due to these factors and the difficulties they pose for the post-processing stage. 5.4 Tempo and T¯al .a Cycle Duration Effects Lastly, we delve deeper to identify the possible effects of track tempo and t¯al .a-cycle duration on model performance. Figure 15 presents a box plot of the median track tempos in the CMRfdataset, grouped by t¯al .a. For each track, inter-beat intervals (IBI) are converted to BPM values, and the median BPM is plotted. Notably, the majority of tracks in the ¯adi (8) and r¯upaka (3) t¯al .as fall within a narrow tempo range of approximately 50 to 100 bpm. In contrast, the two best-performing t¯al .as, m¯ıśra ch¯apu (7) and khan .d .a ch¯apu (5), cluster around 160 bpm but exhibit a wider tempo distribution. This stark difference raises an important question: do the ground truth annotations reflect the actual tempo, or are the ¯adi (8) and r¯upaka (3) tracks annotated at half tempo, potentially contributing to their underperformance? Next, we measure the cycle duration for each track as the interval between consecutive downbeats. Table 11 summarizes the cycle durations by t¯al .a. The ¯adi t¯al .a distinctly features longer and slower cycles compared to the others, with a median cycle duration of 5.4 seconds, more than double that of r¯upaka (2.1s) and khan .d .a ch¯apu (1.8s). This has important implications for downbeat tracking: longer cycle Figure 15: Distribution of median track tempo by t¯al .a lengths demand a larger context window for accurate detection, which can increase the complexity of the model’s task. Additionally, longer cycles mean fewer downbeat annotations per track, potentially limiting the amount of training data available to the network for learning. Another insight is that the variability in cycle duration is also greatest in ¯adi t¯al .a, with a range from 2.9 to 7.1 seconds. T¯ala Min. cycle Max. cycle Median cycle duration (s) duration (s) duration (s) ¯ Adi (8) 2.9 7.1 5.4 R¯upaka (3) 1.2 3.1 2.1 Miśra Ch¯apu (7) 1.6 3.6 2.6 Khan .d .a Ch¯apu (5) 0.9 2.9 1.8 Table 11: T¯ala-wise summary of cycle durations (in seconds). To investigate the potential effects of tempo and cycle duration on model performance, we plotted track tempo and cycle duration against beat and downbeat accuracy for both TCN-FS and BeatThis-FT. These plots, provided in Appendix B, also reflect variability in tempo and cycle duration through the point sizes. Overall, no conclusive evidence emerged linking model performance directly with tempo or cycle duration variations. Nonetheless, TCN-FS, which relies on post-processing, can benefit from informed tempo constraints that narrow the search space and reduce ambiguities like tempo octave errors. Currently, the post-processor operates in a broad range of tempos to accommodate the four t¯al .as. However, narrowing this range based on tempo analysis of the training data, especially in t¯al .a-informed meter tracking, is likely to enhance performance. This highlights the importance of tempo profiling as a preparatory step for post-processor dependent tracking systems. Mojtaba Heydari, Frank Cwitkowitz, and Zhiyao Duan. BeatNet: CRNN and Particle Filtering for Online Joint Beat Downbeat and Meter Tracking. 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Wavenet: A generative model for raw audio. arXiv preprint arXiv:1609.03499, 12, 2016. URL https://arxiv.org/pdf/1609.03499. Nick Whiteley, Ali Taylan Cemgil, and Simon J Godsill. Bayesian Modelling of Temporal Structure in Musical Audio. In ISMIR, pages 29–34, 2006. Appendix A Software and Other Resources This appendix provides a comprehensive list of key software resources, datasets, and code repositories utilised in this study. These materials enable reproducibility of the experiments and analyses presented. Additionally, relevant reference works and helpful study resources are included for further exploration. Datasets The Carnatic Music Rhythm (CMRf) dataset [Srinivasamurthy and Serra, 2014] is available for download upon request from the CompMusic Project website: https://compmusic.upf.edu/carnatic-rhythm-dataset Links to important Western music datasets commonly used for meter tracking, some of which were utilised for pretraining models in this study, can be accessed at: https://ismir.net/resources/datasets/ Reproducible Code The codebase for training the Temporal Convolutional Network (TCN) on the CMRf dataset is available at: https://github.com/satyajeetprabhu/tcn-carnatic-tracker The repository for fine-tuning the Beat This! model on the CMRfdataset can be found at: https://github.com/satyajeetprabhu/beat-this-carnatic Both repositories include the trained models from this study, evaluation results, and notebooks for reproducing the analyses and plots. Reference Implementations The TCN implementation employed, developed in PyTorch Lightning, is based on the LAMIR 2024 Hackathon Tutorial [Morais et al., 2024] on adapting deep learning 50 models for Latin American music tasks with limited data: https://lamir-workshop.github.io/lamir_hackathon/intro.html The original Beat This! [Foscarin et al., 2024] implementation is available at: https://github.com/CPJKU/beat_this The fine-tuning code for Beat This! was adapted from work by SMC Master students Milo Beuzeval and Navid Hallajian: https://github.com/smilo7/more-beats-for-this Key Software Libraries The madmom Python audio and music signal processing library [Böck et al., 2016] used for audio preprocessing tasks: https://github.com/CPJKU/madmom The madmom Dynamic Bayesian Network (DBN) post-processor [Böck et al., 2016, Krebs et al., 2015] employed alongside the TCN: https://madmom.readthedocs.io/en/v0.16/modules/features/downbeats.html The mirdata Python library [Bittner et al., 2019] used for dataset loading, validation, and parsing: https://github.com/mir-dataset-loaders/mirdata Documentation: https://mirdata.readthedocs.io/en/stable/ The mir_eval Python library [Raffel et al., 2014] used for evaluation: https://github.com/mir-evaluation/mir_eval Documentation: https://mir-eval.readthedocs.io/latest/ Additional Study Resources The ISMIR 2021 tutorial on tempo, beat, and downbeat estimation [Davies et al., 2021] provides a comprehensive overview of deep learning models for beat and downbeat tracking. It also includes an open-source, TensorFlow-based implementation of the TCN model described in Deconstruct, Analyse, Reconstruct [Böck and Davies, 2020], which is the basis for the TCN model employed in this study: https://tempobeatdownbeat.github.io/tutorial/intro.html The Python notebooks accompanying the textbook Fundamentals of Music Processing (FMP) [Müller, 2021] provide foundational material on computational music analysis using signal processing techniques. Chapter 6 (Tempo and Beat Tracking) is of special relevance to this study: https://www.audiolabs-erlangen.de/resources/MIR/FMP/C6/C6.html Appendix B Detailed Analysis Plots 52