Short answers, pulled from the story.
Timbre is the attribute that allows a listener to judge that two nonidentical sounds are dissimilar despite sharing pitch and loudness. It depends primarily upon the frequency spectrum, sound pressure, and temporal characteristics.
Robert Erickson identified five major acoustic parameters that determine what he called the elusive attributes of timbre. These parameters include the range between tonal and noiselike character, the spectral envelope, and time envelopes described by the acronym ADSR for attack, decay, sustain, and release.
Hector Berlioz and Richard Wagner made significant contributions to orchestral development during the nineteenth century. Wagner's Sleep motif from Act 3 of his opera Die Walküre passes through a gamut of orchestral timbres including flute, oboe, massed strings, and brass instruments like French horns.
The tristimulus model measures the mixture of harmonics in a given sound grouped into three sections. The first tristimulus measures the relative weight of the first harmonic while the second measures the combined weight of the second third and fourth harmonics and the third measures the relative weight of all remaining harmonics.
Psychoacoustic experiments from the 1960s onwards tried to elucidate the nature of timbre using multidimensional scaling algorithms. The most consistent outcomes show brightness or spectral energy distribution as important factors along with bite rate and synchronicity rise time of the attack.