Model selection criterion

Problem: What is a non stationary partial?
Possible answer: Physical interpretation!

Impulse driven systems:

• Linear systems respond with modes that can be identified as partials with variable amplitude.

Continually driven systems:

• Can be described in terms of attractors.

• There exist only four attractor classes: steady state, periodic, quasi periodic, chaotic.

• Musical instruments are generally non chaotic.

• Quasi periodic attractors are related to non harmonic line spectra $\Rightarrow$ Stationary partials.

• Attractor depends on excitation and system parameters.

• Attractors and partials of non stationary structurable stable systems change smoothly with excitation and system parameters
  $\Rightarrow$ Non stationary partials.

Non stationary partials have to be physically reasonable!