1. Structure in Post-Tonal Music

2. Definition Musical form and structure represent very different aspects of music, though invoking these names often produces similar interpretations. For this book, musical form refers to aspects of the musical surface that state, contrast, and develop themes and motives. For example, terms such as A and B (representing contrasting areas of material) often catalog the formal aspects of a musical work. Musical structure, on the other hand, refers to the process of hierarchical differentiation of more significant elements from less significant elements.

3. Tension and Release Really what Schenker’s structural analysis is all about Applicable easily in P-T music Need definitions of tension and release Context is everything

4. Tension

5. Examples

6. Rhythm and Meter

7. In Music

8. Nomenclature One might argue that traditional analyses indicates different functions for identical chords, particularly when such chords appear in different keys. For example, a C–E–G tonic chord in C major in one location in a work does not have the same function as a C–E–G subdominant chord in G major elsewhere in the same work. One could further argue that pivot chords in modulation provide even more complicated double meanings. However, these tonal examples clearly represent special cases. To offer the kind of differentiations referred to in the previous paragraphs requires that an analysis process delineate differences between C–E–G chords in exactly the same register within the same key. Therefore, the previously discussed processes might actually designate a C–E–G chord in C major in one location in a work and a C–E–G in G major elsewhere in the same work as equivalent in function. In each of these last two cases, the context determines the analysis, not the opposite.

9. SPEAC For many years I have usefully employed a contextual analysis process called SPEAC (pronounced “speak”). SPEAC stands for S (statement) for stable, P (preparation) for weakly unstable, E (extension) for fairly stable, A (antecedent) for very un- stable, and C (consequent) for strongly stable. SPEAC identifiers thus follow the order of stability of A–P–E–S–C, with the most unstable identifier on the left and the most stable identifier on the right. Basing analysis on a combination of root, musical tension, and context most clearly parallels my musical sensibilities and represents the core of the analysis component of my algorithmic composing programs (see Cope 1991 and 1996). SPEAC antecedents and consequents have more tension than statements, preparations, or extensions. Likewise, statements have more tension than either preparations or extensions. Following the work of Heinrich Schenker (1979), SPEAC provides useful insights into musical function, even in the analysis of post-tonal music.

10. Further To assign SPEAC identifiers generally requires the setting of the highest tensions of a group to antecedents (A) and the lowest tensions to consequents (C), with statements (S) closest to consequents (C), preparations (P) closest to antecedents (A), and extensions (E) falling equidistant between Cs and As. Other factors must also play a role. For example, the first-heard chord or grouping will most likely receive a P or an S, depending on its tension level. These assignments result from a lack of context within which to judge the music.

11. Yet further No two groupings labeled A in SPEAC, however, have precisely the same amount of “A-ness.” Therefore, not only can SPEAC differentiate between two identical groupings, but it can also further differentiate between two groupings, both of which have the same SPEAC analysis. Suffixed subscripts allow SPEAC to represent such differentiations. Thus, a C 1 and a C2 both represent consequences, but they have different degrees of consequence. The hierarchy of these subscripts flows from high value to low value in inverse proportion to the size of the number. There- fore, a C 1has more C-ness than a C2. For example, in the passage P1S1A2C2A1C1 the final C 1has deeper consequence than the earlier occurring C2.

12. Examples

13. Other Techniques The large-scale progression of the piece, then, is A 0–A2–A7–A0. Obviously Schoenberg has in mind some kind of analogy to the tonal motion I–II–V–I. But there is more than an analogy at work here. Look again at the first three notes of the series—they form set class 3-9 (0,2,7). The set of areas A 0–A2–A7thus reflects the initial set of pitch classes. The large-scale progression of the piece composes out its initial melodic idea. (2005, 259)