So let us begin with a more in depth discussion of the Primary Chromatic Array. During the course of any major musical work, chromaticism may be presented on any number of ordered levels. But, as previously stated, on its deepest, most fundamental level, the notes of the PCA are created by a chromatic filling in of the ascending tonic octave.
Please note the following characteristic features of the PCA:
- In its most fundamental form, this underlying chromatic edifice unfolds in a precise order, by rising half steps, throughout a single-movement composition or a single movement of a larger composition.
- The PCA forms the slowest moving level of ordered chromatic aggregates, and is initiated by the tonic and its upper chromatic neighbor. The PCA then ascends half step by half step until the entire octave is achieved.
- This unfolding process invariably comes out of the long-range harmonic unfolding of the piece.
- The PCA may unfold once or more than once depending upon the form of the composition. The pitch classes 0 – 11 are used to denote both PCA pitches and secondary chromatic arrays:
C – C#/D flat – D – D#/E flat – E – E#/F – F#/G flat – G – G#/A flat – A – A#/B flat – B/C flat – C
pc0 pc1 pc2 pc3 pc4 pc5 pc6 pc7 pc8 pc 9 pc10 pc11 pc0
The Primary Chromatic Array of a C (‘0’) System
Implications that are Apparent with the Discovery of the Existence of the PCA:
- Chromaticism is not present simply to add color or sophistication, although it certainly accomplishes this and much more. It is a necessary component whose fundamental structure has distinct similarities from one composition to another. Such a proposition is strategically not all that different from a Schenkerian stating that all Mozart symphonies have similar background structures or a jazz theorist suggesting that most songs of the Mississippi Delta follow standard blues progressions. In this case, all the music we will discuss and analyze on this website has a PCA that will have sufficient similarities between compositions to make broad generalizations about its presentation from one symphony to the next or even from one composer to the next.
- The entry of chromatic notes motivates the appearance of others and often in predictable ways. Many compositions contain serialized segments that descend or ascend. Some do both: Haydn’s Symphony no. 103 is an example of a work that has an ascending PCA and a concurrent descending one operating on a lesser fundamental level. Many compositions’ first chromatic departures are ordered by fifths, a probable by-product of serial ordering, such as the first movement of the Brahms Sonata for Violin and Piano in G major, op. 78. All such works order their chromatics in such a way as to create a succession of rising half steps over large portions of a movement. The ordering by half steps is of particular interest here, since that ordering ultimately leads to the establishment of a PCA.
- The third implication of the discovery of the PCA is that there is an interaction of chromatic and non-chromatic elements, each dependent upon the other for its own lifeblood. This feature may be effectively labeled as a dyad conflict. When Burnett more closely began to examine the chromatic sphere in this manner, it became evident that chromatic notes, by necessity, had to be closely associated with their diatonic counterparts, creating dyadic conflicts. Conflicts that turned out to be the most compelling were those that were present throughout an entire composition, spanning several movements. And sometimes, a single entity of a dyadic pair might be either consonant or dissonant depending upon the tonic of the movement, giving the composer considerably more cannon fodder for his developmental process to evolve. Successive dyadic pairings may ultimately become responsible for the generation of large-scale chromatic issues and the eventual generation of entire twelve-note cycles over large spans of a composition.
- The tendency toward aggregate completion will cause chromaticism to become a significant compositional element. This fourth consideration involving the significance of chromaticism is one that other writers have noted as well, such as James Baker in his “Chromaticism in Classical Music”. In fact, Baker speculates here that Mozart and other Classical composers may have been sensitive to the need for aggregate completion. Therefore, twelve-note cycles were not exceptions to the rule or “special cases” within larger diatonic frameworks, but, in sizable compositions, the entire procedure was intricately linked to these large-scale chromatic unfoldings and their various segmentations. However, Burnett was the first to realize a consistent framework behind these all-12-note presentations that led him to advance and explicate a theory of the Primary Chromatic Array. That is, the theoretical difficulty was not just to recognize the inclination for total aggregate completion in sophisticated works, but to uncover the fundamental basis for that chromaticism and the ultimate logic through which it became a structural element of the developmental process.
QUESTIONS? Confusion regarding the PCA and how it operates? Please send us your questions and comments. We would love to discuss them further with you.
Now that you have a basic understanding as to how the PCA functions, let us move on to a discussion of the second main element in Eleven Pitch Class Analysis:
The Missing Pitch.