Dr. Vinoo Alluri wrote a book chapter on Neural Correlates of Timbre Processing  in Timbre: Acoustics, Perception, and Cognition published by Springer. The other author of this book chapter is Sudarsana Reddy Kadiri (currently doing postdoc in Helsinki,  P.hD from IIITH)

The brain is the most complex biological system that exists. Timbre, in its very nature, is a multidimensional concept with several levels of abstraction thus rendering the investigation of its processing in the brain extremely challenging. Timbre processing can be discussed in relation to levels of abstraction. Low- to mid-level representations can be associated with the neural representation of acoustic structure while high-level abstractions correspond to the neural representation of sound source properties. Furthermore, neural correlates of timbre can be broadly classified based on three stimulus categories, that is, those pertaining to music, speech, and environmental sounds. This chapter summarizes studies that have attempted to uncover neural correlates of varying levels of timbre abstractions. Finally, developments in methodological approaches are described, including the shift from univariate to multivariate statistical models, the employment of more naturalistic stimuli, and brain measurement paradigms from hitherto controlled auditory paradigms.