Sound Source Separation refers to separating sound signals according to their sources from a given observed sound. It is efficient to code and very easy to analyze and manipulate sounds from individual sources separately than in a mixture. This thesis deals with the problem of source separation in monaural recordings of harmonic musical instruments. A good amount of literature is surveyed and presented since sound source separation has been tried by many researchers over many decades through various approaches. A prediction driven approach is first presented which is inspired by old-plus-new heuristic used by humans for Auditory Scene Analysis. In this approach, the signals from different sources are predicted using a general model and then these predictions are reconciled with observed sound to get the separated signal. This approach failed for real world sound recordings in which the spectrum of the source signals change very dynamically. Considering the dynamic nature of the spectrums, an approach which uses covariance matrix of amplitudes of harmonics is proposed. The overlapping and non-overlapping harmonics of the notes are first identified with the knowledge of pitch of the notes. The notes are matched on the basis of their covariance profiles. The second order properties of overlapping harmonics of a note are estimated with the use of co-variance matrix of a matching note. The full harmonic is then reconstructed using these second order characteristics. The technique has performed well over sound samples taken from RWC musical Instrument database.