The root of this terminology lies in linear system analysis. There steady‐state means that a clean, often periodic or almost constant excitation pattern has been present long enough so that Fourier based analysis gives proper results. Formally, when exposed to one‐sided inputs (non‐zero only if time is positive), linear systems exhibit output which can be decomposed into two additive parts: a sum of exponentially decaying components which depends on the system and a sustained part which depends on both the excitation and the system. The former is the transient part, the latter steady‐state. Intuitively, transients are responses which arise from changes of state—from one constant input or excitation function to another. They are problematic, since they often correspond to unexpected or rare events; it is often desired that the system spend most of its time in its easiest to predict state, a steady‐state. Because transients are heavily time‐localized, they defy the usefulness of traditional Fourier based methods.
In acoustics and music, the situation is similar in that frequency oriented methods tend to fail when transients are present. Moreover, in music, transients often correspond to excitatory motions on behalf of the performer (plucking a bow, striking a piano key, tonguing the reed while playing an oboe etc.), and so involve
Significant nonlinear interactions (instruments behave exceedingly nonlinearly)
Stochastic or chaotic phenomena (often from turbulence, as when sibilant sounds are produced in the singing voice)
Unsteady vibratory patterns (the onset of almost any note)
Partials with rapidly changing amplitudes and frequencies (as a result of the above).
It is kind of funny how little attention time information has received in the classical study, although one of the classic experiments in psychoacoustics tells us what importance brief, transient behavior of sound signals has. In the experiment, we record instrumental sounds. We then cut out the beginning of the sound (the portion before the sound has stabilized into a quasi‐periodic waveform). In listening experiments, samples brutalized this way are quite difficult to recognize as being from the original instrument. Furthermore, if we splice together the end of one sample and the beginning of another, the compound sound is mostly recognized as being from the instrument of the beginning part. In a musical context, the brief transient in the beginning of almost all notes is called the attack, then. For a long time, it eluded any closer inspection and even nowadays, it is exceedingly difficult to synthesize if anything but a throrough physical model of the instrument is available.
So the steady‐state part is certainly not the best part to look at if source classification is the issue. The other part of the equation are the neural excitation patterns generated by different kinds of signals—transients tend to generate excitation in greater quantities and more unpredictably. Since unpredictability equals entropy equals information, transients tend to have a significant role in conveying useful data. This is seen in another way by observing that periodic sounds leave the timing pathway of the brain practically dead—only spectral information is carried and, as is explained in following sections, spectra are not sensed very precisely by humans. Kind of like watching photos vs. watching a movie.