Some dabblings into musical theory (a paper introduction that I'm fairly proud of)...
Music has a surface. The notes on the page create a stratum, a topography, a terrain on and through which the different pitches act. In more precise terms, a musical surface is the sum total of the aurally noticeable parts of the music, the activity that stands out. This can be demonstrated either by clear chord progressions, discernable melodic material, rhythmic drive, counterpoint, or any other point of continuity. Music with a greater amount of surface is either busier (as in a Bach fugue), more complex (Schoenberg or Bruckner), more transparent (Mozart or Rimsky-Korsakov), or simply has more perceptible, meaningful activity. The composers mentioned are all stylistically very different, but share the common element of writing music that has understandable shape and progression with discernable causality connecting two musical points. Stravinsky may jump between radically different musical ideas, but they are all located within the same topological space (the ending of the Rite of Spring, though entirely different from the opening, is still part of the same musical universe). Surface doesn’t necessarily preclude emotional impact, but it generally exhibits only a certain range of emotions and deals with them in a limited number of ways. You can’t say that Mozart’s Requiem isn’t deeply touching, but you can say that it has a large amount of surface to it; the types of emotions to be explored in each section are spelled out rather quickly, leaving few surprises.
Music with less surface, on the other hand, is full of surprises and unexpected twists and turns. Since there is not as clear a sense of geography to the music, you often find yourself in unfamiliar surroundings, unsure of how you got there. Points without surface are referential to nothing, seem to come from nowhere, and exist as self-contained moments that give some kind of deep meaning that their more defined neighbors can only allude to. It’s as if you were skiing down a mountain and see this beautiful vista on a neighboring mountain, and half way down the run you suddenly find yourself teleported there. No piece of music from before the 20th century can be completely devoid of surface, otherwise there would be no logic to the piece whatsoever, no skeleton or connective tissue. Some of the characteristics listed above will be found in sections of music with no surface, but there will be more pressing needs to be addressed that overrule them. Consequently, there can be ambiguity about whether or not music has surface; Wagner is either all surface or none; Mahler is simultaneously all and none, as is later Beethoven, with the Grosse Fuga and possibly the ninth symphony as textbook examples; Debussy has it on the days he doesn’t get eaten by the whole-tone scale; and Webern transcends the concept of surface entirely (though the serialism that followed him is nothing but surface). Musical surface is not, however, an evaluative concept. The amount of surface a piece does or does not have does not determine its overall value, since musical perception is an inherently subjective thing. Surface is related more to the Benjaminian “aura” than anything else: surface is the type of thing that can be readily reproduced (which is why Bach can be arranged for any instrumental combination while Brahms cannot), while a surface-free moment exhibits “[a] presence in time and space, [a] unique existence at the place where it happens to be.” (Walter Benjamin in The Work of Art in the Age of Mechanical Reproduction) When surfaces entirely disappear, when music sublimates into a vapor, are amongst the most transcendent moments in all of music. [I then go on to talk about Schubert for a very long time]
Stepping off my classical music high horse, it can be argued that the vast majority of music is surface heavy. The only musicians/groups I can think of that break down surfaces in the way I'm thinking are US Maple, some Sun Ra, some Coltrane, some points in Radiohead, and some Johnny Cash (especially on the American records). I know I'm leaving things out and that I'll probably expand this list as time goes on and I have a chance to let my brain go. Until then, this will have to do for an explanation.