Is timbre a physical noumenon or a perceptual phenomenon? I have a question relating the "timbre" of a sound, namely what is exactly and exhaustively defined by this word? Most definitions that I come across seem somewhat loose as "the color of the sound". So what I want to know is:

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*Is timbre physical or perceptual in nature? (Does a tree falling in the woods make a sound that has timbre?)


*Is timbre a collection of ways in which we can excite the natural frequencies of an object? (For example: plucking, bowing, hammering, kicking and whichever other way we can make a different violin sound)


*Does an object have a single timbre or multiple timbres?


*Does an randomly evolving noise have timbre? (Is timbre applicable where there is no consistency and recognizability?)
 A: A sound typically have the main harmonic, which determines its pitch and the subharmonics and/or overtones of lower energy that determine its color, which is what is usually meant by timbre.
However, this is indeed only half of the story - since human ear has different sensitivity to different frequencies/amplitudes, the same sound does not necessarily have the same color for humans and other animals, and even for different humans. The most obvious example are the sound thresholds for low and high frequencies that can be perceived by some people but not by others, e.g., depending on their age or sex.
A: Timbre does not have a precise formal definition in physics, in sense that concepts such as force, mass, charge etc have precise definitions. The word timbre is typically used to describe qualities of musical sounds other than their pitch and volume. To take your example of the violin and the didgeridoo- both instruments could play the same note at the same volume but they would sound unalike, and the differences we would refer to as their timbres.
Timbre can be used to refer to the sensory experience or to the characteristics of a musical instrument, voice etc. You could use the word timbre to describe the qualities of other sounds if you wished.
Timbre arises because sounds are very complicated waveforms which our brains classify in three quite different ways. We think of sounds as being quiet or loud, which very broadly equates to the average magnitude of the peaks of the waveform. We think of sounds being 'high' or 'low' in pitch, which broadly equates to the frequency of the most dominant component of the waveform. That leaves lots of other characteristics of waveforms that sound different to us, and we label those the timbre of the sound.
In physics, a waveform that isn't a pure sine function can be modelled as a spectrum of lots of superimposed sine functions of different frequencies, and it is the brain's response to different spectra that give the sense of timbre. If, for example, you pluck the string of a guitar at the midpoint of the string, the spectrum of the resulting sound will be dominated by the fundamental frequency of the string. However, if you pluck it closer and closer to the bridge, you will set off more overtones in the spectrum, so the resulting sound will be more 'twangy'.
With an electric guitar, or a synthesiser, the range of sounds that can be produced is extraordinarily wide, with any number of effects achievable. In physical terms, they represent waveforms that result from the superposition of different blends of pure notes.
