Topic 5 Central symmetry

A central symmetry is a reflection of a figure about a point called the center of symmetry. To each point of the initial figure corresponds one such that the center of symmetry coincides with the midpoint of the segment that connects the two corresponding points. 

A central symmetry can also be seen as a composition of an axial symmetry with a vertical axis and an axial symmetry with a horizontal axis. 

Or, in other terms still, central symmetry is nothing more than a 180° rotation of the figure with respect to the center of symmetry .

In music, a central symmetry is identified precisely with a combination of retrograde (vertical axis symmetry) and inversion (horizontal axis symmetry). The result obtained by applying this transformation is called retrograde-inversion of the original melody. 

Let’s see an example:

We should note that these techniques do not a guarantee a pleasant musical composition, since there are too many factors that make a certain music “beautiful”. Let’s say that they are tools that the composer uses to develop the composed material and give it a certain coherence.

To end this lesson I propose an exercise. Start from the given melody and obtain its retrograde and then the inversion of the retrograde. Use the second line of the stave as the horizontal axis of symmetry, i.e. the one on which the G note of the first bar is. 

Then write the part on a writing program or play it directly on the piano