Study of Tonal Progression through the prime Numbers Three, Five and Seven
by Michael Hewitt
Volume 96 of our Orpheus series, 495 pages, hard-cover, 61,00 €, ISBN 3-922626-96-3
Beginning with the consideration of the nuclear unit of European art music – the musical tone – this book initially looks at the way in which musical tones combine to form pitch structures. In addition to the four rational properties of pitch, intensity, timbre and duration, musical tone also possesses an important quintessential property: the valency. Representing the innate capacity of musical tones to bond together, an appreciation of this natural binding force underlying the continuum of tonal relationships enables many interesting phenomena to be explained.
For example, note ratios are important because they represent apreeise eneryption of the valent bonds by which the ear connects musical tones. The theory of valency explains much else besides, including the universality of certain intervals, consonan- ce and dissonance, the organic nature of tonality and the reasons why the minor triad must stand as the natural counterpart to the major triad, Implicating a multi- dimensional view of tonal space, the theory of valency further provides an explana- tion for one of the mysteries of musical theory: the place of the 7/4 relation in the web of tonal relationships. It has long been suspected that the 7/4 relation represents the spearhead of a new musical possibility. The problems surrounding the understan- ding and exploration of that possibility are considerable.
What is the true place of 7/4? What interval does it form in the musical concour- se? What new possibilities does it offer? Exploring these questions and the contribu- tions made towards their understanding by such distinguished theorists as Euler, Sor- ge, Helrnholtz, F okker and more recently Vogel, it soon becomes clear that the theo- ry of valency offers the rational means by which the latent musical possibility of the 7/4 relation may be unfolded.
The results of this exploration are startling. Despite equal temperament and the expediency offunctional intonation it becomes apparent that the 7/4 relation has been used intuitively in music for a long time, manifesting as it does through the characte- ristic interval of the augmented sixth. Exarnining musical examples of the various chromatic chords in which the augmented sixth participates brings the study to an important point.
Such usage not only transcends the bounds of the twelve-tone chromatic scale but
implicates a more complex nineteen-tone enharmonie scale that represents its natural
successor. Here lies the foundation for a new system oftonality, the seeds ofwhich
already lay latent within the music of the eighteenth and nineteenth centuries. Chal-
lenging Schoenberg’s belief in the historical inevitability of atonality, this book demonstrates that many of the important developments of twentieth century music represent the emergence of that new tonal system – a system which is as Iogical and
coherent as the major and minor system of tonality which preceded it.