Symmetry of music meter

A special element of the symmetry of rhythmic structure is the symmetry of the musical meter - the symmetry regularities which appear as the order of accented and unaccented parts of the meter (thesis and arsis). In all these cases it is reduced to a linear structure within which repetition (translation) and retrograde repetition (mirror reflection) can appear. The order of accented beats can also be studied from the aspect of antisymmetry (accented part - unaccented part) (Fig. 2.8).

The regularity of these linear structures can be broken by moving the accent (for example, as is the case with syncope).




Figure 2.8 a) Mirror symmetry of the dactyl and the anapest; b) F. Schubert: Death and the Girl, an example of the dactyl; c) Good is love, an example of the anapest (Lemacher and Schroeder, 1967).


The examples of symmetry we have examined here are an important indicator of its organizational complexity. Basically, all the mentioned symmetries can be divided into static and dynamic symmetries. The first category includes translational repetition and, in part, retrograde repetition. On the other hand, the presence of other symmetries introduces an appropriate level of dynamics into the studied structures, at the same time indicating the necessary level of conservation which is crucial for the existence of any organized structure. The delicate balance between these two parameters: symmetry and asymmetry, formal rules and artistic freedom, is the prerequisite for the creation of every work of art.