Musical timbre is a phenomenon of auditory perception that allows the recognition of musical sounds. The recognition of musical timbre is a challenging task because the timbre of a musical instrument or sound source is a complex and multifaceted phenomenon that is influenced by a variety of factors, including the physical properties of the instrument or sound source, the way it is played or produced, and the recording and processing techniques used. In this paper, we explore an abstract space with 7 dimensions formed by the fundamental frequency and FFT-Acoustic Descriptors in 240 monophonic sounds from the Tinysol and Good-Sounds databases, corresponding to the fourth octave of the transverse flute and clarinet. This approach allows us to unequivocally define a collection of points and, therefore, a timbral space (Category Theory) that allows different sounds of any type of musical instrument with its respective dynamics to be represented as a single characteristic vector. The geometric distance would allow studying the timbral similarity between audios of different sounds and instruments or between different musical dynamics and datasets. Additionally, a Machine-Learning algorithm that evaluates timbral similarities through Euclidean distances in the abstract space of 7 dimensions was proposed. We conclude that the study of timbral similarity through geometric distances allowed us to distinguish between audio categories of different sounds and musical instruments, between the same type of sound and an instrument with different relative dynamics, and between different datasets.
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