Is there a non-verbal equivalent to the text in instrumental music? I believe there is. Every instrument, except those in the category of electronica, has a distinctive timbre and specific acoustical properties distributed unevenly throughout its range.
No matter how hard the music establishment has tried to brainwash us into thinking the contrary, this is the case also for the piano. The various registers of the instrument are distinct and affect the total sound differently. Then let us not forget the mechanical/acoustical difference between white-key and black-key resonance.
Contemporary commerce-driven culture is eager to sell the public on the notion that it doesn't matter how pitch is produced since all pitches are interchangeable--correction, since musicians are trained to believe that producing interchangeable pitches is a good idea. A gifted young singer recently told me that even singers are being trained to perform to this standard.
All you have to do is go hear some really fine early-music players to be reminded of the extent to which lyricism is inherent in instruments as it is in the human voice. After all, most instruments were modeled after the voice.