In this work the Fan Chirp Transform (FChT), which provides an acute representation of harmonically related linear chirp signals, is applied to the analysis of pitch content in polyphonic music. The implementation introduced was devised to be computationally manageable and enables the generalization of the FChT for the analysis of non-linear chirps. The combination with the Constant Q Transform is explored to build a multi-resolution FChT. An existing method to compute pitch salience from the FChT is improved and adapted to handle polyphonic music. In this way a useful melodic content visualization tool is obtained. The results of a frame based melody detection evaluation indicate that the introduced technique is very promising as a front-end for music analysis.