Patterns as objects. Collections of pitches, durations, dynamics, etc. could be construed as objects that can be identified as such. Usually they are created during the pre-composition stage. In traditional music, cells, motives, themes are such objects, building blocks to be used liberally during the work. Stricter examples are the isorhythms of the Ars Nova period or tone-rows: in both cases, and entire composition is build through their exclusive use. In Wagner operas, leitmotifs are mappings between a character, an object, an action, etc. and a short musical statement. Mappings are correspondences between two sets, the domain and the co-domain or image. http://en.wikipedia.org/wiki/Map_(mathematics) and, for some images: http://en.wikipedia.org/wiki/Bijection,_injection_and_surjection Wagner utilizes such correspondences in various ways: from being redundant or a counterpoint to the action on stage, to following the mental processes of a person (as in Parsifal, act II, the kiss). Musical set theory considers collections of pitches while ignoring the difference between their sequential use (in any order) or as simultaneous aggregates and treats them as unitary “objects”. Integral serialist composers such as Boulez and Stockhausen have used the tone-row not as a theme (as did Schoenberg) but as a series of proportions thus making it applicable to other parameters besides pitch. It is a more abstract view of the “object”. They go a step further by creating “formants”, identifiable conglomerates of sounds in various textures; Gruppen für drei Orchester by Stockhausen is a good example and the concept is defined in his article “...how time passes...”. http://en.wikipedia.org/wiki/Gruppen_(Stockhausen) In some movements of Le marteau sans maître, Boulez uses a very personal Domains technique. A tone-row is divided into segments that are treated as chords; each of them is then “multiplied” with all the others. The “multiplication” translates into transposing one chord on every pitch of the other. A matrix can thus be created from five segments (a, b, c, d, e) of the tone row: aa ab ac ad ae ba bb bc bd be ca cb cc cd ce da db dc dd de ea eb ec ed ee Each column and each line contains a common element forming what Boulez calls “partial isomorphisms” with ba = ab, cd = dc, etc. while unique elements (aa, bb, cc, dd, ee) are located on the diagonal. Then, a group (eg. db) is treated as a “reservoir of pitches” used in a consistent way. Lev Koblyakov has detailed all this in his book Pierre Boulez: A World of Harmony. A final example, James Tenney's use of klangs – cohesive groupings of sounds (see his book Meta + Hodos) not very different from the more recent idea of windows or from Boulez's multiplied aggregates.