The Sense of Time in Henry Purcell’s Instrumental Music

T“Sense of time in music,” despite being a common expression frequently used in musical discourse, is a complex idea resting on three entirely different pillars—sense, time, and music. A discussion of each of these elements independently presents researchers with a wide range of difficulties, to say nothing of the challenge involved in combining them into a coherent concept that can illuminate both our understanding of the musical work and of the musical experience itself.

The centrality of perception in music is reflected in the well-known philosophical question: if a tree falls in a forest and no one is there to hear it, does it make a sound? In other words: does music exist at all if it is not perceived by the sense of hearing? Even if we strip philosophers of the sting of this question and assume instead that someone is indeed standing in the forest and hears the fall, the subjective nature of perception complicates almost every element of the event, and arguably every element of the musical phenomenon as a whole. Air vibrations are perceived by the auditory system only partially and are limited by the hearing thresholds of different species in nature, and of course by the hearing limits of individual listeners. Do two people listening to the sound of the tree’s fall hear the same thing? And what about two people listening to a single trumpet note? When considering music as a human activity, perceptual subjectivity also underpins the long-standing attempt to distinguish between musical elements that are universal and those that are culturally dependent—consonance versus dissonance; long versus short; loud versus soft. One of the most fascinating introductions to this topic was offered by Leonard Bernstein in his Norton Lectures at Harvard in 1973 [1], where he sought to draw systematic cross-cultural parallels between musical syntax and Chomskyan generative grammar; scholars continue to explore such cross-cultural comparisons today [2]. Even if the inner ears of the two trumpet listeners are constructed and functioning almost identically—what if one is accustomed to hearing the trumpet while the other is not? What if one has previously been exposed to loud noises that damaged the ability to perceive a certain frequency range? And what if, for either person, the sound of a trumpet is associated with an unpleasant memory? Beyond all this, the emotions that a musical work may evoke in individual listeners range widely.

If the question “What is perception?” (in the musical context) is broad, the questions relating to the other two pillars—“What is time?” and “What is music?”—are even larger. Therefore, I shall offer only a brief survey of the complexity of the compound term “musical time,” which connects these two notions. In Western music theory of the fourteenth century, for example, the term Tempus was used in its musical sense to describe the relationship between shorter note values (semibreve) and longer ones (breve) [3]. It is possible that this sophisticated understanding of time—time as the relation between shorter and longer events—was diluted over the centuries and eventually led to the common English use of the word “time” to denote musical meter. Much of the entry “Time” in Grove Dictionary describes time as “the medium essential to music and musical performance, a non-spatial continuum of past, present and future in which music exists and is apprehended”—in other words, the way music is apprehended plays a central role in defining musical time. Indeed, the author of the entry cautions that “the limitations of musical-temporal capabilities reflect our limitations as temporally bound creatures.”[4] The most widespread definitions of musical form, which concern the balance between the introduction of new material and the repetition of familiar material, inherently concern human memory (the recognition of previously heard musical material), and thus once again bring the discussion back to the capacities of each individual subject [5].

It is no wonder, then, that the discussion of the sense of time in music has tended toward two opposite poles, which I shall refer to here as “the narrowing pole” and “the expanding pole.” The narrowing pole seeks to investigate, usually under laboratory conditions, the physiological aspects of time perception as influenced by controlled and regulated musical stimuli—often a “synthetic” musical excerpt specifically composed for the experiment. Already in the 1950s, one of the pioneers of this approach, Leonard B. Meyer, borrowed his concepts and methods from Gestalt psychology [6]. Today, most research aiming at this pole adopts its methodological protocols from the fields of cognition and neuroscience. The process of operationalization—translating the research question into an empirical experiment—is the reason the findings of studies on this pole are “narrowed” [7]. It is possible, for example, to measure a group of experimental subjects’ responses to a specific musical stimulus. But if the study aims to produce precise, measurable results—reaction time, pulse, blood pressure, or brain activity—the musical variables must be reduced as much as possible. If researchers wish to engage with “live” music reflecting the endless complexity of musical parameters, it becomes impossible to correlate musical variables with listeners’ responses. If one wishes to understand listeners’ testimonies that the Adagietto from Mahler’s Fifth Symphony seems to make time stand still, the research may fail at the operationalization stage, for the simple reason that too many unknowns cannot be eliminated from the equation: Who are the listeners? How musically educated are they? Have they heard the symphony (or any Mahler) before? Are they hearing the Adagietto in the context of the entire symphony? Where are they hearing the music? What did they do earlier that day? What is their religious background? How do they report their impressions? Do they know in advance that they will be asked to report their impressions? If we add to these the musical variables—Which orchestra? Which conductor? What tempo was chosen, and how does it change throughout the piece? What of the dynamics? The phrasing?—we see that the pathway to certain “aesthetic” questions does not pass through the narrowing pole.

Research that leans toward the expanding pole seeks to conceptualize the experience of musical time using tools borrowed from drama, literature, and philosophy. Indeed, researchers working in this approach may dare to address questions such as: “Why does listening to Mahler provoke a feeling that time stops?” or “How does Schubert create the sense of time ‘freezing’ in the hurdy-gurdy player (Der Leiermann), the final song of the Winterreise cycle?” Such scholars are likely to concede in advance that they cannot implement rigorous operationalization and that their findings are unlikely to meet the positivistic scientific standards of the natural sciences. Alongside the strengths this approach provides for those coming from the humanities, it also makes it possible to discuss two sound parameters that Western notation records only in a general and imprecise manner—intensity and timbre. A Beethoven score can precisely record melodic contour, proportional relations between formal sections, or the harmonic function of a dissonant chord, but it does not provide a precise measure of forte, of piano, or of the relation between them; nor does it provide an exact measure of acceleration or deceleration, or of the “brightness” or “darkness” of French horns or of muted viola timbres.

This article asks how the listener’s spatial orientation in pitch (Which notes am I hearing now, and how do they relate to the total pitch space of the scale or mode—or in some cases to the absence of a scale or mode?) relates to the listener’s temporal orientation (Where am I now with respect to the beginning of the piece and its end?). Operationalizing such a question—tending toward the narrowing pole—would require designing an experiment in which, for example, a group of subjects (with or without prior knowledge) would hear carefully selected (or composed) musical excerpts presenting specific subsets of the mode’s pitch content, after which the subjects would be asked to estimate how much of the complete piece they had heard. The method adopted in the present study, however, leans toward the expanding pole, since I shall neither attempt to determine universal laws regarding temporal perception nor measure the experiences of real listeners. Rather, I intend to make a conceptual “shortcut” similar to that taken by Meyer (mentioned above), and propose claims about the feelings evoked by music based on score analysis alone [8]. In light of the challenges mentioned above concerning intensity and timbre, I will restrict the discussion to musical styles in which the primary notated parameters are pitch and duration, thereby allowing (even if only temporarily) the removal of intensity and timbre from the equation.

The approach taken in this study addresses pitch. Within the learned schema of sonata form, a trained ear can readily locate itself within the musical structure based on the identification of a stable dominant area, or the recognition of an unstable region generating tension around the dominant and resolving into a tonic region (various nuances of this question have been investigated reductively). But what of the chromatic aggregate? In this article, the term “chromatic aggregate” refers to the twelve pitch-classes representing all octave duplications of the twelve pitches comprising the chromatic octave (e.g., C, C♯, D, D♯ […] B♭, B). The specific octave in which any given pitch is sounded will play a secondary role in the discussion below, and therefore I shall use the term “pitch” without specifying register, meaning that the term “the pitch C” refers to any possible octave duplication of C.

It is easy to assume that in a twelve-tone composition, every pitch is located at a specific position in the row (beginning, middle, or end), and that this location is meaningful for the composer. But what about the listener? Does the listener sense where they are in the row? Over time, the row recurs again and again (with permutations), and the “equal treatment” of all twelve tones is meant to affect the listener’s sense of musical space—yet by specifically denying a tonal center and thereby making it harder for the listener to map the appearance of a pitch to a structural location in the form. The situation resembles the scientific experiment (attributed to Isaac Newton) in which a disk painted in the seven colors of the spectrum, when spun rapidly, appears white to the observer. Can the observer enjoy the visual contrast between reddish-orange and green-blue (as, for example, in Munch’s The Scream) when these same colors appear as four of the seven sectors of the Newton disk and cancel each other out when the disk is spun? How can the listener perceive an unstable region if the entire composition is, by design, tonally unstable?

This article therefore examines the sense of time in music through a single narrow lens—the completion of the chromatic aggregate in Henry Purcell’s instrumental works (1659–1695), a contemporary of Newton. Such a study must address separately two aspects: the first concerns “time in music”—the claim that in some of Purcell’s works, the unfolding of musical form over time parallels the gradual presentation of the twelve chromatic pitches. The second concerns “perception”—how that gradual unfolding of the chromatic totality may be experienced by the listener.

The Chromatic Aggregate – An Outline

The idea of exploiting the chromatic aggregate, whether partially or fully, has occupied many composers and theorists throughout the history of music. Its importance as a central compositional element for Schoenberg and his students only intensified the search for historical precedents for the use of the chromatic aggregate. In recent decades, the work of Henry Burnett has stood out as one that seeks to identify completion of the aggregate as a consistent phenomenon in music history, and to offer a comprehensive theory of tonality explaining both diatonic and chromatic processes. Together with Nitzberg, Burnett argues for a tendency of musical works from the mid-sixteenth century onwards to complete diatonic and chromatic scalar processes; for the view that compositions are derived from an eleven-note aggregate (for which they borrow the historical term gamut); for the manner in which the twelfth pitch class—absent from the system—is derived from the aggregate; for the way the hexachordal basis of the aggregate (that is, the Renaissance foundation of modal organization) underlies harmonic organization in tonal works; and for the contrapuntal principles governing all of these patterns [9].

Comprehensive though it may be, the research of Burnett and Nitzberg overlooks the relevance of Henry Purcell to the phenomenon of exploiting the chromatic aggregate. As I will show, Purcell was consistent in his treatment of the aggregate, and his output provides a clear example of the use of this technique, no less than the works of his contemporaries whose music Burnett and Nitzberg analyze (especially Lully, Stradella, and Corelli). The reason I avoid tying the phenomena discussed here too closely to the findings of Burnett and Nitzberg has to do, among other things, with the fact that the theoretical framework prevailing in England during Purcell’s lifetime—and the way it rested on its modal foundations—differed in various ways from its Italian counterpart, upon which their book is focused (and this may explain why Burnett and Nitzberg rarely mention English composers) [10]. In addition, Burnett and Nitzberg explicitly state that they ignore those “interesting crossover relationships” between their aggregate theory and meantone tuning [11]. I would therefore like to begin with some remarks concerning meantone tuning, as it is relevant to the Purcell works analyzed here.

The quasi-axiomatic perception that the Western pitch system consists of seven diatonic notes and twelve chromatic notes (repeated across octaves) conceals within it the tacit acceptance of equal temperament. The pitch systems in general use until the eighteenth century were, in essence, infinite. Meantone or Pythagorean systems can, at least in theory, be expanded indefinitely: if one “ascends” from the note C in natural or Pythagorean fifths (with a frequency ratio of 3:2), the twelfth leap, which lands on B-sharp, produces a new pitch that is sharper (by the small interval known as the Pythagorean comma) than C [12]. Twelve additional leaps will lead to double B-sharp, and so there begin to accumulate seven sharps, seven double sharps, seven triple sharps, and so on (the same holds for flats if one “descends” in fifths). It is impossible to construct an “infinite keyboard” that contains such a system, with its infinite number of pitches [13].

Indeed, until the eighteenth century there existed keyboards that “compromised” by containing “only” fourteen keys per octave. On such keyboards, each octave contained separate keys for A-flat and G-sharp, separate keys for E-flat and D-sharp, and so forth. Especially bold were the experiments of Nicola Vicentino (1511–1575), who built keyboards containing many more pitches (his archicembalo contained 36 keys per octave). Even so, the use of twelve notes—at the cost of compromise by selecting a single enharmonic alternative for each pitch class—was already common in the Renaissance, and the familiar layout of the twelve-note keyboard was already widespread compared to more extended alternatives.

The foundational work of the chromatic aggregate is, of course, Johann Sebastian Bach’s Well-Tempered Clavier (1685–1750). It is customary to say of this collection that it broke through the limitations of earlier temperaments and enabled travel around the circle of fifths—that is, the use of all twelve tones as the fundamental notes of major and minor keys. However, the work may also be seen, and the twelve tones at its foundation understood, as a “restrictive” gesture: one that seeks to maintain musical activity by eliminating pitches, by renouncing the infinite pitch continuum and confining it to just twelve tones. Keyboards with fourteen, fifteen, or sixteen keys per octave offer no advantage for the performance of the Well-Tempered Clavier as a whole (even if they may “refine” the tuning of some individual preludes and fugues). In other words, the Well-Tempered Clavier marks the moment in music history when musicians celebrated not the infinity of the system, but its finite circularity. This notion aligns with the linguistic analogy suggested by Leonard Bernstein in his Norton Lectures mentioned above. According to Bernstein, the twelve-tone system—the phonological basis for the entire spectrum of possible musical “languages”—was brought by Bach to such a powerful and precise balance that it remained firmly in place for roughly a century.

To facilitate discussion of the circularity of the system, I will adapt for my purposes the labeling system that Burnett used in an earlier study with O’Donnell. According to this adapted system (see Diagram 1), we “ascend” by fifths step by step, and each new note generated receives a number from 1 to 12. The starting point will be the pitch F-sharp (or G-flat, which are equivalent in the circular system), which will receive the label PC1. We ascend a fifth to C-sharp (or D-flat), which becomes PC2; continuing upward to A-flat (or G-sharp) (PC3), E-flat (PC4), and B-flat (PC5). The ascent continues into diatonic notes: F (PC6), C (PC7), G (PC8), D (PC9), A (PC10), E (PC11), and B (PC12). A further fifth above B returns us, of course, to F-sharp (PC1), thus completing the circle. This circle resembles the familiar clock-like diagram of the circle of fifths, with one difference—at the “top” of the circle (where the clock face reads 12) appears PC7, and at the “bottom” (where the clock reads 6) appears PC1.

Burnett and O’Donnell adjust the specific pitch values represented by each PC number according to the key of the work under examination. However, in Purcell’s works—which combine modal pitch systems with moments that threaten to unravel tonal functionality from within—such a dynamic system does not simplify analytical work. Therefore, in contrast to Burnett and O’Donnell, the association of each PC number with a specific pitch remains fixed.

It goes without saying that this circularity is, in itself, “infinite.” In fact, this idea is similar to the duality of the “small” infinity and the “large” infinity, discussed in the past by Naftali Wagner in these very pages [17]. The large infinity expands and produces new pitches without limit—toward an infinity of sharps and an infinity of flats. The small infinity is generated by endless motion within a finite number of pitch classes. The twelve-tone technique, for example, enables the creation of an equal, circular pitch foundation that undermines (or “de-”) the tendency to assign primacy to a single, “tonal” pitch—achieved through the repeated presentation of a single “row.”

Henry Purcell’s Instrumental Music

The summer of 1680 may be regarded as a watershed moment in the career of the twenty-one-year-old English composer Henry Purcell. Just before he achieved his first theatrical successes, and not long before he was formally appointed a court composer under King Charles II and began publishing music in print, Purcell devoted himself to an ambitious artistic project that was entirely futile from a commercial standpoint. He began entering into his personal music notebook a series of short fantazias for a consort of viols [18]. The dates he inscribed on each piece suggest that they were written with remarkable speed, and perhaps were composed as exercises. The models upon which Purcell drew belonged to a local tradition that had already gone out of fashion when he was a child, and which was associated with private music-making among the upper classes and the professional musicians in their employ. Ultimately, these works remained a “professional secret” and were not published until more than 230 years after the composer’s death [19].

In parallel with composing the fantasias, Purcell wrote an impressive series of sonatas for two violins and basso continuo. However, in contrast to the “private” fantasias, which were not intended for publication, the sonatas were designed to conform to contemporary tastes and were presumably planned for print. This plan came to fruition three years later, when Purcell published a dozen of the sonatas in a luxurious edition (at his own expense and without the support of a publisher), using them as a means to present himself as a young, fashionable, and successful composer. The title page describes Purcell as “composer in ordinary to His Majesty and organist of His Chapel Royal”; his portrait appears on the inner title page, and in the prefatory letter to the reader, the composer openly declares his desire that these works be “a just imitation of the most famed Italian masters.” After his death, ten additional sonatas (one of them a single-movement chaconne) were found on his desk, and they were published in 1697 as part of the memorialization and publishing enterprise undertaken by his widow, Frances Purcell, and his publisher, Henry Playford [20]. The English public’s growing taste for fashionable Italian music—intended for the then-fashionable violins—was, of course, in tension with the century-old consort tradition, already in decline for several years and written for viols, which were by then outmoded.

Yet Purcell’s works in these two contrasting genres share a number of fundamental characteristics, reflecting the compositional mindset that typified the young composer: a tendency toward sophistication, the loading of the composition with symmetrical structures, the use of bold chromatic harmonies, and an almost defiant insistence on exhausting the contrapuntal potential of every musical idea presented. These patterns, which I have already surveyed elsewhere [21], can easily be explained in terms of the musical thought of the time in which the works were composed, or framed within theoretical systems surely familiar to the composer. In addition, structural features in both the sonatas and the fantasias may be explained through the concept of the chromatic aggregate, despite the apparent anachronism of applying a term coined in the early twentieth century to late seventeenth-century repertoire.

Let us consider the bass part of the trio sonata in D major (Z 811) from the posthumous Ten Sonatas (1697) (Example 1). This sonata is in five movements, at the center of which lies a tiny seven-bar Grave. The bass part of this Grave contains no more than 22 pitches, yet among them are no fewer than 11 distinct tones of the chromatic aggregate. Is the presence of 11 aggregate tones in so short a movement merely coincidental?

On the one hand, it is impossible to rule out the possibility that this dense appearance of chromatic tones is merely coincidental, at least until unequivocal historical evidence emerges—such as a written testimony by Purcell, a draft, a list of pitches, or even similar evidence from other composers of the period indicating that they conceived of the chromatic aggregate as a compositional principle. On the other hand, there are several recurring patterns in Purcell’s work that may be interpreted as circumstantial evidence that the composer attributed significance to various aspects of the “exploitation” of all tones of the aggregate, or at least all tones available for use. Purcell, who was constrained by the tuning systems commonly used in England in his day, made a notable effort to “complete” all possible keys already within the published volume of sonatas. Composing a sonata in every major and minor key on each pitch-class (as in a “well-tempered keyboard”) was not feasible for him, but in the twelve sonatas of 1683 he encompassed most of the keys available to him: sonatas in C, D, F, G, and A (each with a major and a minor example), B♭ major and E minor—keys that Purcell later “completed” with the first two posthumous sonatas, in B minor and E♭ major. Even within these fourteen keys, Purcell stretched the boundaries of the system available to him, requiring from his keyboard players either subtle retuning or other forms of adjustment.

Purcell’s attempt to use all tones of the aggregate and to present each key once within a single book of sonatas strongly reinforces the claim that he was aware of the concept of “completing” an aggregate (even if only partially). Yet it is difficult to relate such a large-scale principle across an entire book of sonatas to the listener’s temporal experience: must the listener hear all fourteen sonatas in sequence in order to perceive a process of “completion”? Upon reaching the final sonata, how likely is it that listeners still “remember” the tonal content of the first? Processes like the one we observed in Sonata Z811 may be far more perceptible to attentive and focused listeners. Indeed, in eight of the nine multi-movement sonatas in the examined volume there is a short slow movement whose bass line contains a significant number of tones from the aggregate: in four sonatas Purcell presents nine tones, in one he presents ten, in two he presents eleven, and in one movement he presents all twelve tones of the aggregate. In each of these movements, tones of the aggregate constitute a substantial proportion of the total notes, but even more striking is that the completion of the set is typically spread across a significant portion of the movement. In other words, the arrival of the ninth, tenth, eleventh, or twelfth tone occurs near the end of the movement.

If we accept the conventional view of musical composition as a process of tension and release, we may posit that the compression of a large number of tones into a short span of time was undertaken consciously by the composer as a challenge (i.e., a source of tension), and that the arrival of the final tone constitutes a kind of “solution” to the compositional challenge of compressing the aggregate (i.e., release). The biblical author of Lamentations “solves” the acrostic challenge of each chapter upon reaching the verses beginning with the letter Tav. Similarly, if the composer wished to present eleven of the twelve tones within a short movement, the appearance of the eleventh tone would have enabled him to conclude the movement. If we examine the position of each pitch-class within the fourteen 4/4 bars constituting the Grave from the D major sonata under discussion, we see that the first pitch (PC12) appears immediately at the beginning—after 0% of the movement; the second (PC10) after 14%; the third (PC8) after 18%; and so on, until the tenth tone (PC7) appears after 67%, and the eleventh tone—the tonic pitch (PC9), which is also the final note of the movement—appears after 98%. The retention of the tonic chord in root position for the last sonority of the movement represents not only a significant harmonic resolution (the movement began on the sixth degree, which is not tonic), but aligns perfectly with the compositional resolution of compressing the aggregate.

The bass line of the trio sonata in G minor (Z809) presents an even more extreme example [Example 2]. This sonata consists of five movements arranged symmetrically: two homophonic outer movements, two fugues as the second and fourth movements, and at the center of the symmetry axis a brief seven-bar Grave (see Example 3). The bass line of this Grave contains no more than twenty-one notes, of which twelve make up the complete chromatic aggregate. This “run” through all chromatic tones appears too perfect to be accidental. The new pitches seem to be “revealed” at a measured pace; the appearance of the chromatic tones (PC1–PC5) is distributed across the movement; and the completion of the chromatic aggregate occurs after roughly four-fifths of the movement [22].

The question raised by the two analyses above is that it is difficult to determine whether the composer expected listeners to follow the gradual presentation of eleven and then twelve pitch classes (respectively). Did he expect them to perceive a sense of release once the twelfth pitch appeared? And if he indeed intended to convey this sense of release to his listeners, then does the interruption of the process at the eleventh pitch (i.e., without reaching the twelfth, as in the first analysis, in Sonata Z811) amount to leaving the tension unresolved? No less significant is the fact that in both analyses only the bass line was examined, while there is no reason to assume that the sense of “freshness” of a pitch appearing for the first time should depend on the voice in which it is heard.

The Fantazia upon One Note is among the best-known of Purcell’s consort works, both in its original version [23] and in Peter Maxwell Davies’s highly imaginative arrangement. The compositional device on which the work is based is a cantus firmus “reduced ad absurdum to a single middle C” [24].  This work may shed light on the issues raised by the first two analyses. First, here one can examine the appearance of pitches not only in the bass but in all voices. In addition, this is a work that pushes to an extreme the tension between compositional craftsmanship (writing over a single-note cantus firmus) and communication with the listener, who may well notice (even without professional training) the continuous recurring note and the (literally) monotony it produces.

For the purposes of the present discussion, we shall set aside Purcell’s most remarkable artistic achievement—the ability to weave a rich “horizontal,” i.e., contrapuntal, texture over such a restrictive cantus firmus. Instead, we shall focus on the “vertical,” that is, harmonic, aspect of the work. How can the piece be supported by a coherent harmonic structure that departs from a “home” key, moves into other keys (thus creating formal-harmonic tension), and eventually returns “home” (thereby resolving the formal-harmonic tension)?

A simple solution to the challenge Purcell set for himself—composing a Fantazia over a single pitch—could have been the construction of a convincing harmonic progression in which every chord contains C (three major triads, three minor triads, four dominant sevenths). Purcell chose to compose the Fantazia in F major. This is an “appropriate choice”: in this key the note C (which sounds continuously) can function both in a tonic and in a dominant context. C major would also have been suitable, since the note C could function both tonically and subdominantly.

However, Purcell also employs the chromatic aggregate and its gradual expansion—except for PC1—as an additional layer of tension and release. Let us consider the summarized unfolding of the aggregate (Example 3). In the first section (bars 1–11) Purcell presents nine pitch classes in a measured and precisely timed manner: bars 1–4 are entirely diatonic; bar 5 introduces the ♭7 (E♭) of the key; and bar 10 introduces the ♭3 (A♭), which adds a minor coloration and leads to the cadence concluding the first section of the piece. The second section (bars 12–25) retreats from the chromatic richness and adds to the diatonic pitches only the ♭7 of the key. In fact, this section introduces no new pitch classes at all. Of the six possible chromatic pitches Purcell might have used (PC1–PC5 and PC12), two are the most difficult to integrate with the continuous pedal point—PC12 and PC2—each lying a semitone away from the pedal and therefore clashing with the stubborn cantus firmus. Purcell succeeds in avoiding the chromatic G♭/F♯ (PC1) and instead attempts, through harmonic manipulation, to create a context that allows for the introduction of B♮ and D♭. Thus, in the third section (bars 26–30) (Example 3c), Purcell reintroduces the ♭3 (this time at the cost of omitting the diatonic ♮3), and again, immediately before the cadence, adds another chromatic pitch, this time D♭. The fourth section (bars 31–49) begins with a “retreat” of two steps (it appears as though Purcell withdraws PC3 and PC2) only to introduce PC12 for the first time (accompanied by the sudden reappearance of A♭, the fondly remembered PC3) in the final five bars. 

Although it does not complete the full chromatic collection (as it omits the introduction of G♭/F♯), the Fantazia upon One Note demonstrates a clear alignment between the addition of new pitch classes and structural events within the formal design—namely, the close proximity of the appearance of A♭, D♭, and B♮ to the cadences that conclude the first, third, and fourth sections respectively. It is true that in tonal music the appearance of chromatic scale degrees almost inevitably signals excursions into different tonal regions: the raised fourth degree (♯4) may foreshadow the dominant region, while ♭3 and ♭6 may imply the parallel minor. Yet given Purcell’s unusual choice of cantus firmus—one that in practical terms hinders modulation to secondary tonal areas—it becomes evident that the correlation between the exploration of the chromatic collection and the structural segmentation of the composition is not grounded in a formal design independent of harmony. Furthermore, the chromatic notes appear in close proximity to the tonic: A♭ (♭3) provides a minor shading of the tonic, followed by a minor plagal cadence on the dominant. The ♯4 appears within the context of a descending chromatic line, also within a tonic framework. The D♭ (♭6) appears in the context of the parallel minor only after the composer “misses the opportunity” to introduce it in an equally expected setting—within A♭ major.

In addition, the analysis highlights two basic principles governing Purcell’s handling of the chromatic collection: first, that pitch-class collections play a structural role in the development of the movement (particularly the oscillation between A♭ and A♮); second, that the long-term tendency in the treatment of the collection is expansive—the gradual introduction of more and more pitch classes.

These preliminary observations regarding the Fantazia upon One Note do not fully align with the strict use of analytical tools sensitive to the historical period of the repertoire in question. Concepts such as the “circle of fifths,” even if composers like Thomas Tomkins and John Jenkins explored similar ideas in their music, had not yet matured into a comprehensive theoretical paradigm in Purcell’s lifetime [25]. Instead, hexachords still played a central role in the musical system as described in the most influential theoretical writings of Purcell’s time (or slightly earlier): Christopher Simpson’s A Compendium of Practical Music in Five Parts (1665) and John Playford’s An Introduction to the Skill of Musick, to the twelfth edition of which (1694) Purcell himself contributed a short treatise on counterpoint. Therefore, even basic analytical operations such as respelling a pitch by its enharmonic equivalent (a necessary act when dealing with the chromatic collection) must be undertaken with care when applied to seventeenth-century English repertoire, alongside additional historically sensitive considerations such as temperament, form, and sources.

Within the scope of this discussion, in which Purcell functions merely as a case study, it is beyond our limits to offer a detailed analytical account of every instance of traversal of the chromatic collection in his works. However, it is worth noting that in some compositions more than one movement or section presents a complete chromatic aggregate. The Fantazia in D minor Z437 consists of only two fugal sections (57 and 42 bars respectively), each featuring a complete traversal of the chromatic collection in the bass—each “run” concluding after covering roughly 80% of its section. In this work, as in the Fantazia upon One Note, there is a perceptible connection between the traversal of the aggregate on the one hand and the density of the counterpoint on the other [26].

The Trio Sonata in F minor Z800 comprises four movements, and only the last includes a complete run through the chromatic aggregate. The very manipulation of pitch-class collections can, in itself, regulate the rate of musical acceleration [27]. Yet Purcell’s decision to leave PC5 for the final movement appears particularly significant, given that this is precisely the kind of pitch that could have challenged the meantone temperament still prevalent into Purcell’s era. (Symbolically, this brings us full circle to the tuning challenges discussed extensively at the start of the article.) Purcell not only withheld this pitch from the listener until the final movement but also chose to use it in both of its enharmonic forms. In doing so, he forced the keyboard player to decide which of the two spellings would sound correctly tuned—and which would not [28].

Conclusion

The foregoing discussion indicates that Purcell attributed structural significance to his treatment of the chromatic collection, and that the use of the chromatic aggregate—mostly or entirely—constituted for him an expansion of the familiar paradigm of tension and release. Tension and release, primarily understood as “audible” forces in Classical and Romantic music, function here on a compositional plane that is not necessarily audible; thus, they relate to the listener’s perception of time in a manner distinct from later music. The composer, or the performer or fellow composer reading the score, can detect structural progress without necessarily being able to perceive it fully as a listener.

In fact, even later composers sometimes treat “the perception of time” in music independently of real-time listening. Schumann, in the opening of his famous review of Chopin’s Op. 1, describes a situation that depends on the musician’s visual impression—recognizing the composer’s identity merely from seeing the notation [29]. Schoenberg, at the beginning of his Harmonielehre, refers to the composer’s inner ear—arguing that contemplating a written motif may clarify for the perceptive composer the optimal length of the work using that motif [30].

In other words, the “sense of time” in Baroque music is not necessarily identical to the sense of time experienced by the passive listener, but is first and foremost the sense of time as experienced by the composer—or by others aware of the “technical” (i.e., compositional) construction of the piece. This understanding of the compositional act, fundamentally different from that of later music, has sometimes been dismissed under the label “eye music.” For those who understand music primarily as a process measured above all by its impact on the passive listener, such music may indeed appear “formalistic,” lacking some of the central qualities associated with nineteenth-century German masterworks.

However, as we accelerate toward the middle of the twenty-first century, we must reassess the authority we grant to early nineteenth-century aesthetic values—not because they have ceased to be relevant (on the contrary!) but because distancing ourselves from Romantic aesthetics makes it easier to recognize that even earlier conceptions never lost their validity and may coexist productively alongside later ones. Our constant encounter with early music—much of which did not interest nineteenth-century aestheticians at all—forces us to attempt to understand each work according to our best reconstruction of the sense of time that prevailed in its cultural environment.

This is not an attempt to champion some “second-rate” composer overlooked by listeners whose musical taste derives from the Romantic style. After all, Purcell’s works continued to be performed throughout the eighteenth and nineteenth centuries, were appreciated in the age of the major Romantics, have been increasingly performed and studied since the early twentieth century, and especially since the 1980s. This is likely because the compositional sense of time discussed in this article coexists with other, more immediate layers of tension and release.

The composer’s ability to stack multiple layers of “temporal experience” one upon another resembles the modern listener’s ability to perceive, simultaneously, different aesthetics and different “temporalities”—from different periods and different cultures. These abilities of today’s listeners may well be the highest expression of counterpoint in culture, in art, and in human expression more broadly.

Footnotes

1. Leonard Bernstein, The Unanswered Question: Six Talks at Harvard (Cambridge: Harvard University Press, c1976).

2. Samuel A. Mehr et al., ‘Universality and Diversity in Human Song’, Science 366/6468 (Nov 2019).

3. See, for example, the theoretical treatise Ars novae musicae by Jean de Muris, in Oliver Strunk (ed.), Source Readings in Music History: Antiquity and the Middle Ages (New York: Norton, 1965), 172–179.

4.  Justin London, "Time." Grove Music Online. 2001; Accessed 15 Nov. 2023.

5. Heinrich Schenker, for example, defines repetition as the organizing principle of both motive and musical form. Heinrich Schenker, Harmonielehre (Stuttgart: Cotta, 1906), 4–19.

6. Leonard B. Meyer, Emotion and Meaning in Music (Chicago: Chicago University Press, 1956).

7. Elizabeth Hellmuth Margulis, The Psychology of Music: A Very Short Introduction (Oxford and New York: Oxford University Press, 2019), 3–10.

8. Meyer, Emotion and Meaning, 32.

9. Henry Burnett and Roy Nitzberg, Composition, Chromaticism and the Developmental Process: A New Theory of Tonality (Aldershot: Ashgate, 2007), 10–12.

10. On the English theoretical system, see Herissone’s book, especially the chapters dealing with pitch structure, harmony, and tonality: Rebecca Herissone, Music Theory in Seventeenth-Century England (Oxford: Oxford University Press, 2000), 74–141; 174–193.

11. Burnett and Nitzberg, Composition, Chromaticism and the Developmental Process, 7.

12. Dalia Cohen, Acoustics and Music (Jerusalem: Akademon, 1983), 296–309.

13. It is possible that digital instruments may make possible an approximation of such an “infinite keyboard” by representing keys on a touchscreen, or by sensing movement in the air. Similar to the theremin, which is in principle capable of dividing the octave infinitely, it would in principle also be possible to reach an infinite number of octave displacements.

14. In this context it should be emphasized that this work, usually known as “The Well-Tempered Clavier,” was not intended for the piano, and certainly not for a piano tuned in equal temperament. Nonetheless, it was intended for performance on a keyboard instrument tuned in a way that allowed playing in all 24 major and minor keys, thereby realizing the chromatic totality.

15. Bernstein, The Unanswered Question, 37–9.

16. Henry Burnett and Shaugn O’Donnel, ‘Linear Ordering of the Chromatic Aggregate in Classical Symphonic Music’, Music Theory Spectrum 18.1 (1996): 22–49.

17. Naftali Wagner, “Musical Investigations in the Small Infinite and the Large Infinite: Beethoven’s Op. 111 According to Milan Kundera,” Peimot 1.

18. The manuscript is housed in the British Library under the call number GB-Lbl Add. MS 30,930. The manuscript is available for viewing online.

19. Peter Warlock and André Mangeot, Henry Purcell: Three Four and five part fantasias for strings (London: J. Curwen, 1927)

20.  Alon Schab, “From Composer to Myth: The Transformation of Henry Purcell into the British Orpheus, 1696–1706.” Historia 45 (2020), 27–54.

21.  Alon Schab, The Sonatas of Henry Purcell: Rhetoric and Reversal (Rochester NY: University of Rochester Press, 2018).

22. The appearance of PC2 in the second bar of the movement is unique to the composer’s autograph as found in manuscript 30,930 (p. 33v INV), whereas in the printed edition of the sonatas published after the composer’s death, the accidental is omitted and the note becomes D♮ (i.e., another appearance of PC7, which already appeared in the first bar of the movement). As explained above, we have no conclusive evidence that the realization of the complete aggregate constituted a compositional goal, and even if it did, it may have been a “professional secret,” unknown even to the editors of the 1697 edition. In such a case, it is easy for scholars to prefer the manuscript reading and argue that the omission in the printed edition was an error, and not a later revision by the composer.

23. MS 30,930 (f. 50r–49v INV).

24. Peter Holman, Henry Purcell (Oxford and New York: Oxford University Press, 1994), 85.

25. The works of Jenkins and Tomkins are likewise not discussed by Burnett and Nitzberg. For discussion of the cyclic aspect of pitch organization in their works, see Christopher D.S. Field, ‘Jenkins and the Cosmography of Harmony’ in John Jenkins and his Time: Studies in English Consort Music, Andrew Ashbee and Peter Holman (eds.), (Oxford: Clarendon, 1996), 1–74.

26. In the first section, for example, once the first five notes are presented, the fugal subject receives “spaced” imitation without stretto. The presentation of the next four notes brings stretto imitation. The final note of the aggregate appears at the moment when the density reaches full simultaneity—the prime form of the subject appears together with its inversion. At this moment Purcell adds the note D♭. Interestingly, this note, when respelled enharmonically as C♯, is the note that completes the aggregate in the second section of the piece.

27. The bass part of the opening movement presents only ten pitches. Movements two and three use the same set with the addition of the eleventh pitch (B♮); and the fourth movement completes the set with F♯ or G♭, which, as noted, is the note Purcell avoided in the one-note fantasia, also in a key whose tonic is F.

28. The more common direction for the basic pitch would have been F♯, which served most common pitch-levels of Purcell’s time; in such a case one could observe an interesting process in the final movement. Already in the first fifth of the movement, the bass plays all ten pitches that appeared in movements two and three. Only somewhat later (after 42% of the movement) does Purcell present pitch 5 for the first time, after it had been missing from the bass since the beginning of the work, now presented in correct tuning as F♯. However, perhaps in order to emphasize completion, Purcell returns this pitch, this time as untuned G♭, at the most characteristic point in the opening of the movement (after 73% of the movement), reaffirming the completion of the “run.” Martin Adams, in his analysis of the movement, emphasized the importance of the single G♭ in the bass not from the perspective of temperament but from the ways in which Purcell uses repetition, expectation, and tonal shaping. Thus, the point at which the “run” in the work is completed is not only the result of a process unfolding over several movements, but is also subtly highlighted through the aspects discussed by Adams as well as by Purcell’s sensitivity to the limitations of quarter-comma meantone temperament.

29. Robert Schumann, Gesammelte Schriften über Musik und Musiker: Eine Auswahl. (Leipzig: Reclam, 1974), 11.

30. Arnold Schoenberg, Harmonielehre, 3rd edn (Vienna, Universal, 1922), 1–2.