Most of the empirical models that have been proposed to estimate the frequency variation of earthquakes were based on shallow earthquake data, so the need to examine the accuracy of these relationships and provide a new relationship for intermediate-depth earthquakes is obvious. As a new attempt, the interpretation of the difference in the behaviour of the frequency content indicators with distance and magnitude for shallow and intermediate-depth earthquakes as a function of the difference in attenuation properties is discussed. The ground motion database of this study consists of 243 horizontal components of events recorded at Vrancea, Romania and Makran, Iran. The focal depth of selected events was reported between 82 and 131 km. Two scalar parameters, the average spectral period ( T a v g ) and the mean period ( T m ), have been used as frequency content indicators. In addition to examining the accuracy of previous models, a new predictive relationship has been proposed for the two selected scalar quantities as a function of moment magnitude, hypocentral distance and site conditions. Findings provide evidence that the empirical models proposed in the past could not provide accurate estimates of the frequency content of intermediate-depth events. In contrast, the quality of assessments has significantly improved based on the new model of this study. • Interpretation of the difference in the behaviour of the frequency content indicators with distance and magnitude. • A new try is carried out to examine the accuracy of past relationships for intermediate-depth earthquakes.· • New empirical method is proposed to calculate the scalar single frequency content parameters.