Layers from Harmonic-Percussive Source Separation (HPSS)
Harmonic-Percussive Source Separation (HPSS) is a method for decomposing the spectrum of a signal into two parts that should sum together to the original signal. One of these parts contains more of the 'percussive' material (transient-like) and the other contains more of the 'harmonic' material (tone-like). It can sometimes be useful to extend this slightly to using three parts by exercising more stringency on what counts as harmonic and what counts as percussive, and putting any residual content in to a third layer. In any case, the basic modelling assumption is that the sound in question can be represented by the simple mixing of these layers. Read more about HPSS.
Here is a basic demo. Click 'play' to listen to the layers being played back, and use the faders to adjust the balance between the layers:
HPSS was developed on the basis of being considerably computationally simpler than other approaches to source separation, whilst producing results that were good enough for use in certain contexts. If one listens to the layers in isolation, typically we will notice that the separation of tonal and percussive material isn't very crisp, and there may be spectral artefacts. However, when playing the layers together, these side-effects tend to mask each other and we can, for example, adjust the apparent balance between percussive and tonal components in quite complex sounds without noticeable effects (up to a point). By choosing between different methods for performing the separation we can explore trade-offs between how separated the layers sound, and how many artefacts they have.
We can also do more radical things by using the isolated layers independently of each other. For instance, we can process them separately, such as by reverberating the harmonic layer but not the percussive, or by applying different kinds of granulation to each. We can also use the layers as pre-processing to condition the signal for something else. For example, we might find that for some sounds, slicing is more successful if we use only the percussive layer, or that pitch tracking is more stable on the harmonic layer.