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Contents

Music in the Late Twentieth Century

FULL REALIZATION

Chapter:
CHAPTER 3 The Apex
Source:
MUSIC IN THE LATE TWENTIETH CENTURY
Author(s):
Richard Taruskin
Full Realization

ex. 3-24 Milton Babbitt, Composition for Four Instruments, superimposed rhythmic series

As its very title promises, Babbitt's next composition, Composition for Twelve Instruments (1948, revised 1954), is an attempt to extend the controlling techniques even further, integrating durations even more systematically into the serial texture by creating a complete durational analogue to a full chromatic tone row. This is done by assigning to every member of a row two numbers, the first denoting its order within the set, the second its pitch measured in semitones from an arbitrary “zero” If the first pitch in the row is taken as the “zero” pitch, then that pitch will be defined by the numerical pair (0, 0) and the rest will be computed from it. Once assigned to the pitches of P0, the pitch numbers are treated as constants or absolutes throughout the composition. Applied to the row in the Composition for Twelve Instruments (given together with its combinatorially related inversion at the perfect fifth), the assignment of dual designations is shown in Ex. 3-25.

Citation (MLA):
Richard Taruskin. "Chapter 3 The Apex." The Oxford History of Western Music. Oxford University Press. New York, USA. n.d. Web. 23 Oct. 2017. <http://www.oxfordwesternmusic.com/view/Volume5/actrade-9780195384857-div1-003008.xml>.
Citation (APA):
Taruskin, R. (n.d.). Chapter 3 The Apex. In Oxford University Press, Music in the Late Twentieth Century. New York, USA. Retrieved 23 Oct. 2017, from http://www.oxfordwesternmusic.com/view/Volume5/actrade-9780195384857-div1-003008.xml
Citation (Chicago):
Richard Taruskin. "Chapter 3 The Apex." In Music in the Late Twentieth Century, Oxford University Press. (New York, USA, n.d.). Retrieved 23 Oct. 2017, from http://www.oxfordwesternmusic.com/view/Volume5/actrade-9780195384857-div1-003008.xml
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