Monday, June 8, 2015

Variations of Melodic Shape of a Non Mathematical Kind

excerpt from Arnheim's Art and Visual Perception showing the results of an experiment
asking a shape to be remembered after a split second showing.
Common discussions on melodic variation often deal with modifying melody by structural means like those found in the previous post. This post is not to discourage it but to augment it. We expect in the course of this blog there might be many representatives of mathematical means. In contrast composers might  imitate a melodic contour quite freely as being enough. Even here it is worth mentioning some "psychological" modifications noticed in the visual field that could just as well be applied to a melody. Gestaltist Rudolf Arnheim in his Art and Visual Perception points out who happens when people are showed an image for a slight section and asked to reproduce it. Below is a modified picture from his book showing a general overall sharpening or levelling of details by the following processes: Symmetry Enhanced, Non-fitting detail Isolated, Over-all shape simplified, Closing of boundaries, Repetition of similar shape, Subdivision enhanced, and a change from oblique to vertical which in terms of a melody might be less a simplifying of it direction as already included, but maybe the inclusion of harmonic elements or arpeggiation which is common form of variation, if one has "harmony" which one can no longer assume. Some of these might result in the same thing such as enhancing the symmetry and simplifying the over-all shape. The above list is in no way inclusive of all that can be done, but points out those things that melody might do to a over time.  Possibly things that can be heard as a result of the process of them in folk music.