Music is one of the major activities that alters the emotional experience of a person. Musical processing in the brain is a complex process involving coordination between various areas of the brain. There are less number of studies that focus on analyzing brain responses due to music using modern signal processing techniques. This research aims to apply a nonlinear signal processing technique i.e. the Recurrence Quantification Analysis (RQA) technique to analyze the brain correlates of happy and sad music conditions while listening to happy and sad ragas of North Indian Classical Music (NICM). EEG signals from 20 different subjects are acquired while listening to excerpts of raga elaboration phases of NICM. Along with behavioural ratings, the signals were analyzed using the Recurrence Quantification Analysis technique. The results showed significant differences in the recurrence plot and recurrence parameters extracted from the frontal and frontotemporal regions in the right and left hemispheres of the brain. Therefore, from the results, it can be concluded that RQA parameters can detect emotional changes due to happy and sad music conditions.