Quantifying sound colour of musical instruments – precise harmonic timbre coordinates of like instruments

Abstract

Timbre – sound “colour” – is an abstract, delicate property of sound, especially in a high-value context such as musical instruments. It is a perceptual construct so intangible that it cannot be considered a quantity. Since sound nevertheless reaches our ears as a complete physical reality, we hypothesize that this inherent abstraction of its timbre is primarily due to the lack of a meaningful, musically relevant, and robust quantification that would do justice to the subtlety of human auditory perception. It is therefore not surprising that not a single aspect of timbre is to be found in the specifications of musical instruments. We introduce harmonic timbre coordinates, concrete and robust numbers that quantify a partial aspect of timbre of an instrument’s sound – its harmonic structure – with a precision that allows relevance in the musical context. These numbers could, for example, help a buyer find an instrument whose sound is closer to his or her preferences. Or they could enable precise tracking of harmonic changes in sound, and more.

Keywords

• musical instruments
• harmonic timbre coordinates
• robust and precise measure of harmonic timbre
• linear harmonic timbre vector space