1) The Concept of the Functional Cycle

From the mid-seventeenth to the end of the nineteenth century—and often well beyond—harmonic analysis reveals a remarkable fact: musical discourse is based predominantly, and sometimes almost exclusively, on the reiteration of a very small number of harmonic structures, structures that are nonetheless capable of innumerable variations.

Following the musicologist Itzahk Sadaï, though in a somewhat different sense, I shall refer to these structures as functional cycles. These structures are, in fact, what underlie the perception of the music as belonging to a given key. Non-modulating musical phrases are therefore ordinarily formed by a succession of functional cycles that all refer to the same key.

2) Classification

Functional cycles commonly comprise between one and five chords, though they may occasionally include more—up to ten or so. They may be classified according to the harmonic functions of the chords that constitute them. As a result, they fall into a very limited number of types. My paper will give a detailed account of the most frequent ones, such as:

• perfect cycles of the form T–D–T
• complete cycles of the form T–P–D–T
• plagal cycles of the form T–Pl–T.

Note: T, D, P, and Pl denote, respectively, tonic, dominant, predominant, and plagal functions.
Note: The elision of the initial and/or final tonic in a cycle is common practice.

Moreover, the study of the functional mechanisms involved in generating tonal orientation within cycles will only be briefly touched upon. This is a complex issue that lies at the very boundaries of the pedagogical field.

3) Identification in the scores

The identification of functional cycles may be straightforward or, on the contrary, quite difficult. Several factors may obscure their recognition, including:

• the use of substitute degrees in place of those that are functionally characteristic (e.g., degree VI assuming a tonic function)
• the simultaneous unfolding of several cycles at different hierarchical levels
• the use of harmonically complex chordal morphologies in modern music
• the presence of chords not integrated into cycles, such as ornamental chords, harmonic sequences, parallel chords...

4) Notation

My personal notation retains scale-degree notation, but clarifies it so as to indicate, depending on the context, whether or not a given chord holds a harmonic function. Functional letters are used exclusively for substitute chords.

Furthermore, in order to make the unfolding of cycles clearly legible, it is essential to employ hierarchical figured notation, distributed over at least two superimposed lines.

Conclusion

The concept of the functional cycle presents certain difficulties for students, notably because it presupposes a hierarchical approach to harmonic analysis and the notion of substitute chords. Nevertheless, the analytical effectiveness of this concept is such that, in my view, it makes its teaching indispensable.

My proposal will be illustrated with musical examples drawn from a variety of styles.

Bibliography:

Khannanov, Ildar. (2025). Function, Functional Cycle, and the Constitution of Tonality. New York: Nova Science Publishers.

Sadai, Yitzhak. (1980). Harmony in its Systemic and Phenomenological Aspects. Jerusalem: Janetz.