In music, timbre often refers to variations in tone quality produced with different articulations on instruments such as winds and strings. The physical characteristics of sound that determine pitch are called harmonics, and those that create variation in tone quality are called partials or overtones.
Timbre can not be measured directly. It is described in terms of characteristics. An instrument’s shape determines timbre, for example, the conical or cylindrical pipe of a wind instrument, or by the frequency range within which the instrument can produce overtones, and by the envelope of the instrument's sound. It is also known as "tone color" or "timing."
When people talk about brightness or warmth, they describe the quality of sound called timbre. This is one aspect that makes each instrument unique and different from all others. If you have no reference to the pitch, a “bright” sound is always going to seem high in pitch, while a “deep, resonant” sound is going to seem low in pitch.
The tone of voice also affects our perception of brightness or warmth because some voices naturally have more overtones than others, e.g., the difference between children’s and adults’ voices. So if someone says your voice sounds bright or warm, they mean it sounds higher pitched.
The most common way for scientists who study acoustics and psychoacoustics to describe timbre is by referring to certain characteristics which can be measured objectively on an instrument called a spectrum analyzer or sonograph.
These characteristics include the average spectral centroid, which describes whether there's more energy at higher or lower frequencies, spectral roll-off that tells how quickly intensity falls off with increasing frequency, and spectral flatness that tells whether the intensity changes smoothly with frequency, and many others.
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