This paper analyzes intermittent self-excited thermoacoustic oscillations in which the pressure (P′) and heat release rate (q̇′) fluctuations are harmonically coupled. That is to say, P′ and q̇′ do not oscillate at the same frequencies, but rather at frequencies in integer ratios. Thus, this system represents a case dominated by nonlinear cross-mode coupling. The measurements were obtained in an optically-accessible combustor equipped with an industrial gas turbine fuel injector operating with liquid fuel under partially-premixed conditions at elevated pressure. High-speed chemiluminescence (CL) imaging of OH* was used as an indicator of the heat release rate. The data was processed using spectral proper orthogonal decomposition (SPOD) to isolate the dominant heat release and pressure modes. Synchronization theory was used to determine when the modes are coupled and how their interaction manifests in the measurements, particularly how it relates to the observed intermittency. The results show three distinct intervals of synchronized oscillation shared by all the mode pairs analyzed. The first interval exhibits the same characteristics as a pair of noisy, phase-locked self-oscillators, with phase-slipping and frequency-pulling. While the behaviour of the second interval differs among mode pairs, strong frequency-pulling is observed during the third interval for all pairs.