Tabla is the most widely used percussion instrument in Indian music, both as an accompanying and solo instrument. It is used extensively in classical, folk, film, popular, and devotional music, and its distinctive timbre forms one of the ubiquitous signifying elements of the music of North India. Unlike Western classical music, Indian classical music makes extensive use of percussion.
Its two component drums are played with the fingers and hands and produce a wide variety of timbres, each of which has been named. A sophisticated repertoire of compositions and theme-based improvisations has developed over hundreds of years. Tabla is a natural candidate for Markov modeling because it consists, at a basic level, of a sequence of discrete states that are temporally structured. Tabla is particularly interesting because of the complex patterns and dependencies that are present in typical compositions. Although tabla is primarily learned as part of an oral tradition, it is also notated using a system that indicates strokes and their durations.
The repertoire of tabla can be divided into two basic categories, structured improvisations, and through-composed material. In the former category are qaidas, a theme and variation form, and peshkar another type of thematic improvisation, and relas. Relas are very dense, fast drum-roll-type textures, that are played in a smooth, flowing manner. In the latter category are gats, tukdas, and chakradhars, various types of fixed compositions.
For a couple of years now, Music Intelligence Group, which I have been a member of since August 2009, has been working on expressive tabla modeling, filed under the NSF CreativeIT Grant #0855758. Parag Chordia, Avinash Sastry and I have written a paper named “Predictive Tabla Modeling Using Variable-length Markov and Hidden Markov Models”, which is accepted and currently under review in Journal of New Music Research.
In the paper, we model the tabla sequences in a predictive framework with variable-length Markov models (VLMMs). Using a database containing nearly 30,000 strokes in 35 compositions, we show that VLMMs have high predictive accuracy. This basic framework is extended by the introduction of several new smoothing techniques that determine how to integrate predictions from the different order models. The model is then extended to include parallel representations of the sequence, a technique known as Multiple Viewpoint modeling.
The work is then extended to the problem of recognizing strokes from audio. In this hidden context, the identity of the previous stroke is not revealed at each time step. A variable-length Hidden Markov model (VLHMM) is used to determine the next-symbol distribution that is used in computing the perplexity. We detail how the forward probabilities can be efficiently computed for the VLHMM using by traversing a prediction suffix tree (PST) that is used to represent sequences. To the best of our knowledge, this is the first use of variable-length Hidden Markov models for music modeling or prediction.
I was responsible of preprocessing, automatic segmentation, feature extraction, class conditional probability calculation and classification by naive multivariate Gaussian distributions of tabla strokes from compositions in audio format. The compositions were synthesized using Tabla Gyan, an articial tabla improviser, which is one of the integral elements in our expressive tabla modeling. The analysis was made in MATLAB and classification was done using Weka. The testing and training feature vectors for each composition, along with the parameters of the multivariate Gaussian (MVG) for each stroke type, were used in VLHMM.
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