The subjective quality of cane reeds used on saxophones or clarinets may be very different from one reed to another even though the reeds have the same shape and strength. The aim of this work is to understand the differences in the subjective quality of reeds and to explain them with objective measurements. A subjective study, involving a panel of 10 musicians, was first conducted on a set of 20 reeds of the same strength. Second, signal recordings during saxophone playing (in vivo measurements) were made of the pressures in the player's mouth, in the mouthpiece and at the bell of the instrument. These measurements enable us to deduce specific parameters, such as the threshold pressure or the spectral centroid of the notes. After an analysis of the subjective and objective data (assessment of the agreement between the assessors and the main consensual differences between the reeds), correlations between the subjective and objective data were performed. To propose a model of the subjective quality, a machine learning approach was proposed using partial least-squares (PLS) regression and PLS discriminant analysis. Results show interesting performance of the model in cross validation and open the potential for an objectification of the perceived quality.