An introduction to Schaeffer's idea of the sound object, and a more detailed article explaining the idea of phenomenology in general and Schaeffer's development of it to sound.
Denis Smalley built on scheffer's idea to talk about the spectromorphology of sound. Here is an overview with list of additional sources.
Francis Dhomont's Acousmatic update gives his view as a composer influenced by Schaeffer and spectromorphology.
One of the important contribution of phenomenology is the observation that an object and our perception of it are not identical:
"Keeping this table steadily in view as I go round it, changing my position in space all the time, I have continually the consciousness of the bodily presence out there of this one and self-same table, which in itself remains unchanged. But the perception of the table is one that changes continuously; it is a continuum of changing perceptions. I close my eyes. My other senses are inactive in relation to the table. I have now no perception of it. I open my eyes, and the perception returns. The perception? Let us be more accurate. Under no circumstance does it return to me individually as the same. Only the table is the same, known as identical through the synthetic consciousness which connects the new perception with the recollection" (Husserl ideas 1928: 117–18)
Our mind actively constructs a unified table from momentary perception.
Schaeffer developed a similar approach focusing on sound objects. According to him an understanding of these requires a "taxonomy of sounds and a theory of listening" (Kane L’Objet Sonore Maintenant Organised Sound 12:1)
Building on Schaeffer's ideas Michel Chion talks about 3 types of listening:
Here is an extract from his excellent book Audio-Vision.
Schaeffer developed a typology of sounds based on 3 pairs of attributes. The first and most important he named mass-facture. Mass is an extension of pitch which has 4 categories: definite, complex, slightly variable, unpredictable. Facture relates to the source implied by the sound: formed, redundant, unpredictable. Duration-Variation & Balance-Originality are the other pairs (You can read more about those here and here).
This typology of sound was summarised by Schaeffer into a table TARTYP: TAbleau Récapitulatif de la TYPologie.