Developments in music theory, musical acoustics, and psychoacoustics over the last 15 to 20 years have resulted in a single structural basis that provides common ground for analysis of musical systems that include non-standard/non-octave systems, microtonal systems, and systems that use unusual tunings common in non-western music. These developments make it likely that a confluence of understanding in musical acoustics, psychoacoustics, and music synthesis is about to take place. This common structural basis will lead to generalized rules of composition, unheard of since the classic work Treatise On Harmony by Rameau (1722), based on generalizations of the well-known properties of our familiar 12- tone scales. Indeed, some of these generalizations have already been articulated. As participants in various aspects of this work for the past 14 years [1-7], we are in a unique position to collect, assess, and distill the important contributions to this, truly, multidisciplinary field. It is our purpose, in this paper, to articulate a 21st century approach to music composition using the latest results from mathematical music theory and musical acoustics. In our presentation we will produce audio and visual examples applying these techniques.