Fractal dimensions of initial transients of musical instruments

Abstract

Fractal dimensions of initial transients are calculated for musical instruments. There are significant differences between a classical guitar, a violin, a clarinet, and a balinese Gender dasa. As the guitar and the clarinet have a maximum correlation-dimension of around D=4, the violin reaches up to D=5.5. The gender with its intensive inharmonic overtone structure can be up to D=6.8, and about D=2.0 within the steady state. Instruments with harmonic overtones always have D=1 during their steady state. These values seem to correspond to the number of rules governing the transient, which can be shown using zooming-in wavelet transform. In a sample of some hundred examined sounds, the guitar had just a light tendency for louder, higher, and Apoyando plucked tones to be more chaotic than for softer, lower-pitched, and Tirandu-played ones. The violin sounds differed extremely within these categories. The clarinet was also examined during pitch changes in melody. Here an information structure is proposed, which is the second derivation of time of a multifractal information-dimension and shows the stucture of information gain for these transients.