Music and the inversion principle
The inversion principle can be used for transforming one thing into another, for both large- and small-scale form. It produces a certain skeletal consistency but is not the rigid system one might suppose, as it allows the artist imaginative choices and flexibility, enabling personality to be imposed as part of the process. Logic is nothing to be afraid of when applied to art; it is simply part of human thought, spatial relations, balance and the law of nature. It is the human imprint on the method of inversion that is of real significance.
The relation between the inversion principle and music is one of similarity rather than exactitude. The twelve-note method, as devised by Arnold Schoenberg, is in essence a simple device for ensuring complete structural unity in the spheres of melody and harmony. It affirms the unity of musical space and the relationship of all ideas in a work.