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Music and Rhythm

Fundamentals – History – Analysis

Peter Petersen

This book sets forth the first really novel theory of rhythm since Hugo Riemann: the components theory. Its approach will be of interest to musicologists and music theoreticians alike as well as to music performers, since it will enable them to describe and understand the rhythmic shape of music better and more fully than was previously possible. Instead of conceiving rhythm simply as interplay of short and long, of accents and meters, the present analysis takes its departure from secondary rhythms that are not notated but depend on specific qualities of a given sound or sound formation. Together with the basic rhythms, these components rhythms form a total rhythmic texture, whose temporal and weight structure allows a novel way of perceiving musical meter as not being primarily prescriptive but above all as the product of an overall compositional calculation of component rhythms.


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Part One: Theory of Components


Sound 19 Rhythms and Components Definition of Terms Sounds are the stuff of which musical structures are made. Like other objects of perception, they are subject to the categories of space and time. Because they are experienced as fleeting and intangible, we easily overlook the fact that sounds are material objects. Yet one only needs to think of membranes or other vibrating bodies that condense and compress and rarefy air and leave their traces as sensations of pressure to realize the bodily and therefore spatial nature of sounds. This actually banal signification of sounds as »things« is important to our inquiry concerning rhythm and music insofar as it helps distinguishing the spatial character of the phenomenon of sound from its manifestation in the temp- oral continuum. Leibniz’s graphic saying that there was »coexistences« and »successions« in all things 4 means in our context that sounds and rhythms are subject to different modes of perception. About sounds we ask »what,« about rhythms we ask »when.« »What« questions provide access to the entire universe of the audible in music: sound and tone as simple events; harmonies, chords, tone sequences as complex formations. Every individual sound incident and every sound event can be described in terms of its specific features. Individual tones are determined by their pitch (frequency), color (sound spectrum), degree of lightness (octave position), loudness (dynamic), form (articulation), etc. Chords are distinguished according to their pitch content, interval structure, octave level, type of inversion, function, etc. Melodic figures may be determined...

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