A spatially inhomogeneous model problem for studying turbulent nonpremixed reacting flow with reversible reaction is proposed, which admits stationary solutions that are periodic in physical space. The thermochemical state of the fluid is characterized by two composition variables: mixture fraction xi(x, t) and reaction progress variable Y(x, t). A linear gradient in the mean mixture fraction field is imposed in the x(2) direction, so that, in a forced stationary velocity field, the mixture fraction field attains statistical stationarity. The reaction progress variable Y(x, t) is statistically homogeneous in x(1) and x(3), and is statistically periodic in x(2). The flow is called periodic reaction tones. The solutions are parametrized by the Damkohler number and the reaction zone thickness parameter. At sufficiently high Damkohler number there is stable reaction, but as the Damkohler number is decreased below a critical value, global extinction occurs. The range of parameter values is chosen such that the model problem reproduces important phenomena such as stable near-equilibrium reaction, local extinction, and global extinction. Monte Carlo simulations are performed to solve for the joint probability density function of velocity, turbulent frequency, and composition. The predictions for critical Damkohler number are compared for two different mixing models: the interaction by exchange with the mean (IEM) model, and the Euclidean Minimum Spanning Tree (EMST) model. The results obtained using the simpler conditional moment closure (CMC) model are also presented for comparison. The model problem is formulated to permit direct numerical simulations (DNS) using pseudo-spectral methods, which require periodic boundary conditions. The DNS study of this model problem, which is reported in a separate publication, provides additional insight into the phenomenon of extinction in inhomogeneous turbulent reactive flows.