Analysis of spectral parameters of Multiphonic sounds of string- and wind-instruments and introduction of a mathematical model to simulate the frequencies and intensities of the Harmonics and the Complex tones of Multiphonics generated with woodwind

Scientific Study from the year 2022 in the subject Physics - Acoustics, grade: NA, , language: English, abstract: So called Multiphonic sounds of string instruments (cello, violin, piano) and wind instruments (trombone, flute, oboe, clarinet, saxophone) have been analyzed and their power spectra (Fast Fourier transformation of sound files) have been compared. The power spectra of Multiphonic sounds of wind instruments exhibit a structure with a) Harmonics of the two tones (=pitches) T1 and T2 with different basic frequencies (Hz) and b) Complex tones with frequencies defined according to the formula: "e;m*T1+n*T2 (m, n are integer numbers ; m*T1 and n*T2 represent frequencies "e;f1"e; and "e;f2"e; in Hz of the respective Harmonics of T1 and T2). Power spectra of so called Multiphonic sounds of string instruments do not contain Complex tones, but Harmonics of only one basic frequency. In contrast to a regular monophonic sound, the first Harmonics of this so called Multiphonic sounds are massively damped so that the listener cannot identify the basic pitch, but will recognize several higher Harmonics sounding in parallel. This mimics a Multiphonic sound although it is a monophonic sound. It is proposed to name such sounds: "e;multiphonic sounding Harmonics"e; in contrast to real Multiphonic sounds generated by wind instruments containing Complex tones. The detailed analysis of the intensities of the Harmonics as well as the frequencies and intensities of the Complex tones of Multiphonic sounds leads to the conclusion that a pair of Complex tones with frequencies "e;f1+f2"e; and "e;f2-f1"e; is a result of an interaction between one Harmonic of each basic pitch T1 and T2 with respective frequencies f1 and f2. Based on this conclusion, a mathematical model is established which proposes the mechanism of a specific coupling of two standing waves within a wind instrument as the basic process to generate the Complex tones. A simulation of a real Multiphonic sound of a wind instrument using the mathematical model results in an acceptable correlation (R2 = 0.5) of the simulated and the real intensities of the Complex tones.