A reduced model is introduced to represent an oscillation of a jet by edge tones. The edge tone is one of the indispensable elements in air-reed musical instruments, such as a recorder, a flute, a flue organ pipe, etc. The main approach is to obtain a representation by a one-dimensional partial differential equation (PDE) which is intended to shorten a computational time. Several parameter values are determined through a comparison between model functions and results by two-dimensional fluid mechanics calculations. Through a numerical integration of our model PDE and time measurements, it is shown that this model is applicable to real-time simulations to describe dynamics of air-reed instruments.