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Showing papers in "Perspectives of New Music in 1971"



Journal ArticleDOI
TL;DR: Here the authors enter the domain of "musical systems," the normal subject matter of what is traditionally thought of as "music theory," though it is still "metatheory" relative to the "foreground" layers of theoretical discourse.
Abstract: Here we enter the domain of "musical systems," the normal subject matter of what is traditionally thought of as "music theory," though it is still "metatheory" relative to the "foreground" layers of theoretical discourse. It is at this stage that a point of divergence from maximum generality is reached by our music-structural system; the necessity of such a divergence arises as a direct consequence of the implementation of certain of our systematic objectives which, as the preceding section reveals, are mutually incompatible within a single system at a single functional level in particular, the systematic incorporation of both content-determinacy and order-determinacy presents a difficulty of this nature. Further construction, moreover, awaits the explicit articulation of such syntax-building objectives as are essential for the conceptual guidance of our systematic formulations, if those formulations are to lead us to a system offering ranges and types of functions adequate to the construction of, say, "tonal" and "12-tone" syntactical models into which we could cleanly plug adequate analytic models of, respectively, the Schenker-tonal and Babbitt-"serial" types. Such syntaxbuilding objectives are perhaps better represented as extrasystematic than as systematic notions," since they may be favorably viewed as concepts whose observable implementations are practically enabled by, rather than formally generated by, or generative of, the constructions under consideration.

17 citations






Journal ArticleDOI
TL;DR: In this article, the principle of octave equivalence was applied to the pitch class (pc) of the integers 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11.
Abstract: C. pitch-class (pc)-all pitches whose frequencies are related by powers of 2 belong to one pc, and only those pitches whose frequencies are so related belong to that pc. There are twelve distinct pc's: c, ct, d, d, e, f, f#, g, g#, a, a#, b or their enharmonic equivalents. These may be represented by the integers 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11. Note that integers which belong to the same equivalence class, mod 12, represent octave-related pitches. This shows the principle of "octave equivalence." If pc's are not the same, they are distinct.

3 citations