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BY GERALD BALES The first hearing of Gerald Bale's piece, ? Waited Patiently for the Lord, exposes a conflict between the obviously tonal elements present and certain passages that seem not at all to be tonally organized. Initially, the analysis of this anthem was intended to provide not only a better understanding of the music at hand but also more general insights into the structure of music that cannot comfortably be categorized as completely tonal or atonal. However, the analysis presented below, rather than offer firm conclusions, deals with the general aspects of the investigation through the refinement of questions, with indications for further research. In the early part of this century, music in such a style that is, with obviously tonal roots - was visible as part of the so-called transition between the chromaticism of the late Romantic era and the fully atonal music of later decades. This transition has become recently the focus of theoretical research; Allen Forte, for example, contributed a very detailed article on Schoenberg's creative evolution which appeared a few years ago in The Musical Quarterly (1978). However, music in this style has not been limited to the period before the First World War. More recent examples have been termed "neo-tonal" or "neo-classical." While these labels are sometimes no more than euphemisms for "anachronistic" or "inferior," they more often indicate a presupposed analytical approach to the music: that is, to analyze the piece as far as is possible in a tonal fashion and then to dismiss the more troublesome areas with simple description. Yet, this analytical approach of assuming the validity of tonality together with the verbal handwaving of such terms as "color chord," "slight alteration," or "extended passing motion" can be pejorative even with the best intentions. For by assuming this method to be adequate, the analyst implies that any such piece is indeed an inferiorly constructed tonal piece with certain peculiarities that need to be somehow excused. Consider Example 1, the conclusion of Francis Poulenc's Christmas motet, Hodie Christus natus est. The bass motion, C-F sharp-C, sorely tempts any analyst to describe this event as a "sort-of-plagal-cadence-done-up-modern"; but cannot the analyst do better than to succumb to the poverty of borrowed terms? The only excuse for using the term, "piagai," is to be able to say that this event, within the organizational system of the piece, functions in a way analogous to a piagai cadence in tonal music; yet, to be able to use this analogy, the new organizational system must be determined! This article does not pretend to present any complete theoretical system for such music; however, it does demonstrate what structures can be revealed by the application of set theoretical analysis to Bales's piece. Passing reference to tonal relationships that occur in the piece are made below, without detailed analysis, as they are more obvious. It is first necessary to summarize the essential points of set theoretical analysis.1 The most basic notion is that music can be segmented into groups, or sets, of distinct pitches. (The most relevant sets are those of cardinality 3 through 9 - that is, with three to nine elements; octave equivalence is assumed.) Pitch class C [do] is represented by the integer 0; other pitch classes are represented by integers which reflect their distance, in semitones, from C. Given the enormous number of groups of pitches which can be found in music, there must obviously be some method of reducing the universe of sets to a small number of prototypes. That the theory considers sets as equivalent if they contain the same elements regardless of the order in which the elements appear accomplishes a substantial reduction. (That is, the set [0,1,2] is equivalent to [1,0,2], [2,0,1], and so on.) Further, and somewhat less obvious, reduction of the number of sets is accomplished through the operations of transposition and inversion. …

Neo-Tonality or Neo-Atonality?: I Waited Patiently for the Lord by Gerald Bales