To quote from Computer Music by Dodge and Jerse (an excellent reference), "Helmholtz concluded that the spectral description of a sound had the most straitforw

To quote from Computer Music by Dodge and Jerse (an excellent reference), "Helmholtz concluded that the spectral description of a sound had the most straitforward correlation with its timbre.... For instance the qualitative description of 'brilliant' or 'bright' characterizes spectra that have a great deal of energy at high frequencies [e.g. brass instruments] ... A spectrum with little energy in the even-numbered harmonics characterizes the particular timbre that is produced by the clarinet in its low register...." (2nd Ed. Section 2.6) Understanding that each instrument produces a spectrum of harmonics peculiar to it ... and that those harmonics have relatively different pitches and amplitudes and evolutions ... that vary with how the instrument is played ... is key to quantifying its timbre. (At first, not an easy thing to grasp let alone quantify. But Partch made a lot of progress!)