Nonlinearities and Synchronization in Musical Acoustics and Music Psychology

Perceptual sound field synthesis concept for music presentation

“…The structure of instrumental sounds is presented in [2][3][4][5]. Notes often have an initial transient with a high spectral density and a large bandwidth.…”

“…The high density and bandwidth can be explained by the impulsive nature of musical instrument sound generation, like the string knocking on a bridge which then deflects a top plate or a sound board, or the lips, labia, or reeds that open only shortly every period. In fact, all sound generation of musical instruments can be traced back to impulses, referred to as impulse pattern formulation [3]. So the initial transient, or attack, is more or less impulsive.…”

“…Musical instruments emit different spectra into each direction and are more or less directive. In many instruments, the radiation characteristic of a frequency depends on the used material, fundamental frequency, excited string, or the playing technique [3,4,8,9]. Recent measurements with large-scale circular microphone arrays reveal that even small musical instruments can create rather incoherent signals at listeners' ears at all angles and distances up to at least 3 m [9][10][11][12][13].…”

“…This is also the minimum duration it takes to detect the pitch of pure tones with fair strength. It is assumed that this natural integration time of the auditory system is the reason for the fact that the initial transients of most musical instruments are shorter than 50 ms [3]. Some researchers think that the auditory system uses a time window of about 16 to 20 ms to detect pitch [17].…”

“…This dimension helps, e.g., to differentiate between metallic and wooden sounds, even when they contain a similar spectrum in the quasi-stationary part. [3] The auditory system does not process sound as a whole but rather divides the spectrum into about 25 critical bands [1,21]. Frequencies that simultaneously fall into the same critical band cannot be discriminated.…”