Musical instruments are self-organizing systems. Only due to their complex and nonlinear nature they are able to produce a very simple output, the harmonic overtone spectrum we call a musical tone. Without this self-organizing feature musical instruments would sound inharmonic and we could not make music with them at all.
The different instrument families have different mechanisms. Wind instruments are governed by turbulence of their driving mechanism. The heavy turbulent damping at a first vortex produced a pressure-gradient which is the transfer from flow to acoustic energy. This gradient is a temporal impulse which travels through the instrument and is heavily distorted due to the horn at the tube end, the finger holes or a complex tube geometry. When it reappears to the driving mechanism, the reed with saxophones or clarinets, the wind with flutes, it only triggers a new impulse again produced by the turbulent vortex. This new impulse is the same as the previous one and therefore perfect synchronization happens. Only due to this very robust mechanism it is possible to produce harmonic overtone spectra out of very complex wind instruments.
With string instruments there is a string, mostly damped only slightly, and a resonance box, damped very strong like with guitars, violins or pianos. Additionally this box is three-dimensional while the string is only one-dimensional. According to theory, the system which is less damped and the system with the lower dimensionality forces the other system into its frequencies. Therefore the string always wins the game agains the wooden box and forces it to vibrate with its frequencies, again forming a self-organizing system.
This very basic principle of musical instrument allows music at all, musical tones with harmonic spectra. Still there is a struggling phase, where the system builts up, the initial transient phase. There synchronization is not perfect and the system shows inharmonic spectra, noise, scratches, popps and the like. They are crucial for identifying musical instruments.
Bader, R.: Musical Instruments as Self-Organized Systems. In: R. Bader (ed.): Springer Handbook of Systematic Muscilogy. Springer, Heidelberg, 171-196, 2018.
Bader, R..: Nonlinearities and Synchronization in Musical Acoustics and Music Psychology. Springer Series Current Research in Systematic Musicology, Vol. 2, Springer Heidelberg , 2013.
Bader, R. (ed.): Synchronization and Self-Organization as Basis of Musical Performance, Sound Production, and Perception. In: R. Bader (ed.): Sound – Perception – Performance. Springer Series ‘Current Research in Systematic Musicology, Vol. 1., 1-41, Springer Heidelberg 2013.