Excerpt
The last quotation concerning the conclusions of there being only one key comes from Paul Hindemith written in 1937 as taken from the Barnes and Noble Outline Series On Musical Theory. "Hindemith believed that any theory of tonal music should start with the twelve possible pitches of the tempered scale, rather than with seven or some smaller number. These twelve pitches, freely written in harmonic notation are then organized around one tonal Center. The tonal center is emphasized by several factors: duration, accent, the first and last notes, the tone most often returned to, and so on-but principally by the relative strength of the root movement surrounding it."
In the spirit of the above assertions concerning a single tonality, the purpose of this book is to present a type of logic which is similar in intent to the views expressed in the quotations provided above but opens the "tonal playing field" in an entirely new way.
In the past, an important feature of tonality has been to emphasize harmonic constructions which are formed upward from a fundamental bass tone. In other words, the chord root has been the principal reference point from which to establish individual chords, scales, and the resulting possible melodic activity.
In contrast, according to transtonal theory, harmonic origination begins at the top of a chord, commences downward to the bottom note, and is completed by the addition of appropriate inner chord tones.