相关论文: On Mathematical Functions for Theoretical and Expe…
Indian classical music relies on a sophisticated microtonal system of 22 shrutis (pitch intervals), which provides expressive nuance beyond the 12-tone equal temperament system. Existing symbolic music processing tools fail to account for…
This paper presents a computational methodology for analyzing intonation and deriving tuning systems in microtonal oral traditions, utilizing pitch histograms, Dynamic Time Warping (DTW), and optimization techniques, with a case study on a…
In this paper we obtain the chord length distribution function for any regular polygon. From this function we conclude the density function and the distribution function of the distance between two uniformly and independently distributed…
This paper presents an attempt to study the aesthetics of North Indian Khayal music with reference to the flexibility exercised by artists in performing popular compositions. We study expressive timing and pitch variations of the given…
Temporal dynamics are among the cues to expres siveness in music performance in different cultures. In the case of Hindustani music, it is well known that expert vocalists often take liberties with the beat, intentionally not aligning their…
In North Indian Classical Music, raga forms the basic structure over which individual improvisations is performed by an artist based on his/her creativity. The Alap is the opening section of a typical Hindustani Music (HM) performance,…
Tabla Stroke Transcription (TST) is central to the analysis of rhythmic structure in Hindustani classical music, yet remains challenging due to complex rhythmic organization and the scarcity of strongly annotated data. Existing approaches…
Music is a string of some of the notes out of 12 notes (Sa, Komal_re, Re, Komal_ga, Ga, Ma, Kari_ma, Pa, Komal_dha, Dha, Komal_ni, Ni) and their harmonics. Each note corresponds to a particular frequency. When such strings are encoded to…
This paper aims at developing a systematic study for the weak rate of convergence of the Euler-Maruyama scheme for stochastic differential equations with very irregular drift and constant diffusion coefficients. We apply our method to…
The mathematics of musical intervals and scales has been extensively studied. Vastly simplified, our ears seem to prefer intervals whose frequency ratios have small numerator and denominator, such as 2:1 (octave), 3:2 (perfect fifth), 4:3…
Hindustani music is a performance-driven oral tradition that exhibits the rendition of rich melodic patterns. In this paper, we focus on generative modeling of singers' vocal melodies extracted from audio recordings, as the voice is…
We prove lower large deviations for geometric functionals in sparse, critical and dense regimes. Our results are tailored for functionals with nonexisting exponential moments, for which standard large deviation theory is not applicable. The…
Estimating parameters of drift and diffusion coefficients for multidimensional stochastic delay equations with small noise are considered. The delay structure is written as an integral form with respect to a delay measure. Our contrast…
This paper addresses the nonparametric estimation of the drift function over a compact domain for a time-homogeneous diffusion process, based on high-frequency discrete observations from $N$ independent trajectories. We propose a neural…
Musical chords, harmonies or melodies in Just Intonation have note frequencies which are described by a base frequency multiplied by rational numbers. For any local section, these notes can be converted to some base frequency multiplied by…
This paper is concerned with numerical analysis of two fully discrete Chorin-type projection methods for the stochastic Stokes equations with general non-solenoidal multiplicative noise. The first scheme is the standard Chorin scheme and…
We calculate all twist-two, three and four parton distribution functions involving two quark correlations using the wavefunction of the MIT bag model. The distributions are evolved up to experimental scales and combined to give the various…
The HRT (Heil-Ramanathan-Topiwala) conjecture asks whether a finite collection of time-frequency shifts of a non-zero square integrable function on $\mathbb{R}$ is linearly independent. This longstanding conjecture remains largely open even…
Accurate synchrotron transfer coefficients are essential for modeling radiation processes in astrophysics. However, their current calculation methods face significant challenges. Analytical approximations of the synchrotron emissivity,…
In this work, we are interested in building the fully discrete scheme for stochastic fractional diffusion equation driven by fractional Brownian sheet which is temporally and spatially fractional with Hurst parameters $H_{1}, H_{2}…