“Från treklang till nonackord” – revisited

by Anders Flodin

Throughout the twentieth century, numerous publications examined functional harmony from a variety of theoretical perspectives and according to different systems of classification. Despite these contributions, no universally accepted definition of functional harmony has emerged. To clarify how the term will be used in this presentation, I therefore propose the following working definition:

Functional harmony concerns the relationships that arise between chords once their individual identities, harmonic rhythm, and metric organization have been established.

Functional harmony should not be understood as synonymous with individual chords. Rather, it denotes the structural relationships through which these parameters interact, shaping the listener’s perception of harmonic progression over time.

Among the many textbooks on the subject, Sune Smedeby’s Från treklang till nonackord is exemplary in its ability to present complex theoretical concepts with clarity and economy. During the 1960s and 1970s, Smedeby studied the system of functional analysis used by Elisabeth v. d. Osten, Ernst Tittel and Wilhelm Maler. He recognized several advantages of the notational approach, particularly its use of uppercase letters to denote major functions and lowercase letters to denote minor functions, which influenced his own notational practice.

Particularly elegant is his system of functional notation, in which uppercase and lowercase letters immediately distinguish between major and minor functions. Thus, a C-major chord functioning as the tonic in C major is designated T, whereas a C-minor chord functioning as the tonic in C minor is designated t. In compound functions—for example, the secondary dominant  (DD)—the final letter determines whether the function is major or minor. The principal advantage of this notation is its consistency: the final letter always indicates the quality of the resulting chord. Thus, Tp denotes the minor parallel of the major tonic, whereas tP denotes the major parallel of the minor tonic. The notation therefore communicates both harmonic function and chord quality at a glance.

Beyond simplifying the representation of harmonic function, Smedeby also proposed an elegant notation for distinguishing between simultaneous and successive intervals. In my view, this innovation deserves renewed attention and remains a valuable contribution to music-theoretical practice.

As Smedeby explains:

“In certain situations it is useful to indicate whether an interval is simultaneous or successive (and, in the latter case, also its direction of motion). We may therefore use symbols that directly imitate the appearance of musical notation. Simultaneous intervals are indicated by a colon (:), while successive intervals are indicated by dots arranged in an ascending (.·) or descending (·.) direction. The notation for successive intervals may be simplified by omitting the first dot. (Ascending and descending intervals may also be indicated by plus and minus signs respectively, although this risks confusion with the signs for augmented and diminished intervals.) […] These symbols are always placed before the interval number.” (Smedeby, p. 137)

Smedeby, Sune. (1978), Från treklang till nonackord. Eriks förlag. Stockholm