Modulation Theory and Lie Brackets of Vector Fields

Summary

In a recent book [16], we have opened the discussion of a hypergestural restatement of mathematical counterpoint theory. The present chapter aims at a discussion in the same vein of the classical mathematical modulation theory [682, 670]. The present approach to modulation theory is based on the idea that degrees in the start tonality are interpreted as gestures that move to degrees (qua gestures) of the target tonality by means of hypergestures. This means that the symmetries relating tonalities in the classical setup are replaced by hypergestures that connect gesturally interpreted degrees. The present hypergestural model solves the problem, but it opens more questions than it answers in the sense that the construction of hypergestures that replace the classical inversion symmetries is by no means unique.