Transformation (music) in the context of "Augmentation (music)"

In music, development is a process by which a musical idea is transformed and restated in the course of a composition. Certain central ideas are repeated in different contexts or in altered form so that the listener can consciously or unconsciously compare the various statements of the idea, often in surprising or ironic manners. This practice has its roots in counterpoint, where a theme or subject might create an impression of a pleasing or affective sort, but delight the mind further as its contrapuntal capabilities are gradually unveiled in a fugal development

In music, a permutation (order) of a set is any ordering of the elements of that set. A specific arrangement of a set of discrete entities, or parameters, such as pitch, dynamics, or timbre. Different permutations may be related by transformation, through the application of zero or more operations, such as transposition, inversion, retrogradation, circular permutation (also called rotation), or multiplicative operations (such as the cycle of fourths and cycle of fifths transforms). These may produce reorderings of the members of the set, or may simply map the set onto itself.

Order is particularly important in the theories of composition techniques originating in the 20th century such as the twelve-tone technique and serialism. Analytical techniques such as set theory take care to distinguish between ordered and unordered collections. In traditional theory concepts like voicing and form include ordering; for example, many musical forms, such as rondo, are defined by the order of their sections.