Objects of musical composition and their modifications
In the article, musical composition is defined in a specific way. So the objects that are carriers of the compositional quality are understood in a new way. Those objects belong to different structural scales – from sections, parts of a musical piece to historical cycles, united by a structural invariant (for example, the history of variations on a given musical subject). Composition is understood as a plan for the distribution of objects in its spaces – syntagmatic and paradigmatic, as well as the result of mapping one of these spaces to another. Syntagmatic space reflects the sequence of representation of objects in three-dimensional space, the coordinates of which are a vertical, horizontal and depth. Structural positions for elements of the same class are established in each of the indicated coordinates, what forms a certain topographic plan of the composition. Paradigmatic space is formed due to variation processes, during which families of objects of the same kind with a common invariant are formed.
The composition as a whole and its paradigmatic space in particular can be considered in the unity of architectonic and procedural properties. The architectonics of paradigmatic space is associated with the coordinates of objects in a paradigmatic family. These coordinates reflect the relations of objects’ transformants. The transformants of two similar objects are the qualities of the structure that distinguish one of them from the other.
The procedural properties of the paradigmatic space of composition are considered at three levels. The most abstract level is the modification of objects. More specific second level is associated with operations, and the third one – with transformations of objects. The operations are classified according to several criteria: compositional rank, number of sub-elements in an element, coordinates in syntagmatic space, type of geometric transformation, quantity and quality of objectification directions. In this context the transformation is considered as a single manifestation of the general principle of modification. The author specifies that the aim of the said above is to mark the topography of a musical composition.
musical composition, paradigmatic space, syntagmatic space, modification, transformation, operation.
Fuksman M. Objects of musical composition and their modifications // South-Russian Musical Anthology. 2020. No. 4. Pp. 65–73.