The perceived 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 better understand the differences in the perceived quality of reeds by making use of acoustical measurements. A perceptual study, involving a panel of 10 musicians, was first conducted on a set of 20 reeds of the same strength. Each musician assessed each of the 20 reeds according to three descriptors: Brightness, Softness, and Global quality. Second, signal recordings during saxophone playing (saxophone playing by a musician in the laboratory, called in vivo measurements) were made of the pressures in a player's mouth, in the mouthpiece, and at the bell of the instrument. These measurements enable us to deduce specific acoustical variables, such as the threshold pressure or the spectral centroid of the notes. After an analysis of the perceptual and acoustical data (assessment of the agreement among the assessors and the main consensual differences between the reeds), correlations between the perceptual and acoustical data were performed. A modeling of the descriptors Brightness and Softness according to the acoustical variables is proposed using multiple linear regression. Results show that the pressure in the mouth at the beginning of the permanent regime is an important variable to predict the softness of the reed. The performance of the models in the prediction of the perceptual dimensions provides important clues for a more objective assessment of perceived reed qualities.