This paper presents the automatic genre classification of Indian Tamil music and western music using timbral features and fractional Fourier transform (FrFT) based Mel frequency cepstral coefficient (MFCC) features. The classifier model for the proposed system has been built using K-nearest neighbours and support vector machine (SVM) classifiers. In this work, the performance of various features extracted from music excerpts have been analyzed, to identify the appropriate feature descriptors for the two major genres of Indian Tamil music, namely classical music (Carnatic based devotional hymn compositions) and folk music. The results have shown that the feature combination of spectral roll off, spectral flux, spectral skewness and spectral kurtosis, combined with fractional MFCC features, outperforms all other feature combinations, to yield a higher classification accuracy of 96.05 %, as compared to the accuracy of 84.21 % with conventional MFCC. It has also been observed, that the FrFT based MFCC, with timbral features and SVM, efficiently classifies the two western genres of rock and classical music, from the GTZAN dataset, with fewer features and a higher classification accuracy of 96.25 %, as compared to the classification accuracy of 80 % with conventional MFCC.