‹‹ JSCM Home

Journal of Seventeenth-Century Music

Journal of Seventeenth-Century Music

‹‹ Table of Contents
Volume 21 (2015) No. 1

Published 2017

Toward a New Grammar of Mid-Seventeenth-Century Harmonic Language: Hearing Expressive Harmonies in Motets from the Habsburg Court of Ferdinand III (1637–57)

Andrew H. Weaver*


Harmonic analyses of seventeenth-century music are traditionally based on modal theory, an analytical approach that may be hampering our understanding of seventeenth-century harmonic practice more than helping it. This article proposes a new conception of mid-seventeenth-century harmonic space based on analyses of the entire surviving body of motets from the Habsburg court of Holy Roman Emperor Ferdinand III (r. 1637–57). Explicating a new grammar of mid-seventeenth-century harmonic language provides the means to understand and interpret moments of text expression that heretofore either have seemed incomprehensible or have been missed entirely by modern listeners. Six specific types of expressive harmonies are defined and illustrated with examples from the Habsburg motet literature.

1. Introduction: Tonality, Modality, and Harmonic Grammar

2. Theoretical Premises and Principles

3. Normative Harmonic Practice in the Habsburg Motet Repertoire

4. Expressive Harmonies within a Single System I: The Phrygian Cadence

5. Expressive Harmonies within a Single System II: Durus–Mollis Contrast

6. Expressive Harmonies within a Single System III: Hexachordal Shifts

7. Expressive Harmonies within a Single System IV: Double Finals

8. Expressive Harmonies Incorporating Multiple Systems I: New System, Same Final

9. Expressive Harmonies Incorporating Multiple Systems II: New System, New Final

10. Expressive Harmonies in Combination: Two Analyses

11. Conclusion




Audio Examples



1. Introduction: Tonality, Modality, and Harmonic Grammar

1.1 Over seventy-five years ago, Donald Tovey called his readers’ attention to the famous C-sharp in measure 7 of Beethoven’s Third Symphony: “Whatever you may enjoy or miss in the Eroica Symphony, remember this cloud.”[1] Tovey’s pleading was hardly necessary, for from Beethoven’s day until our own, listeners—regardless of their musical knowledge—have experienced that measure as a powerful “expressive harmony,” a non-normative sonority employed to catch the listener’s attention.[2] The impact of this “cloud” is made possible by the fact that for more than three centuries western audiences have been immersed in a shared harmonic “grammar” (to use Margaret Bent’s term) furnished by the system of major-minor functional tonality.[3] Even someone who has no idea what “E-flat major” means can intuitively hear that C-sharp as a “wrong note” that adds tension and propels Beethoven’s otherwise commonplace triadic melody forward.

1.2 The same cannot be said for music composed before 1700. As much as modern listeners may enjoy the harmonies in “pre-tonal” works, because we have not internalized the grammar of earlier harmonic languages, we are quite likely oblivious to many expressive harmonies that to contemporaneous listeners would have been as immediately and intuitively powerful as Beethoven’s C-sharp. The problem is especially acute for seventeenth-century music, the harmonic language of which is superficially similar enough to tonality (especially in its local chord progressions and cadential formulas) that modern ears almost automatically want to hear all the harmonic relationships in tonal terms. While this helps us hear such obvious “clouds” as the common juxtaposition of third-related chords (e.g., G major and E major, familiar to modern listeners from such works as Monteverdi’s Zefiro torna e di soavi accenti and Giovanni Gabrieli’s In ecclesiis) and rising chromatic semitones in the voice (Poppea’s seductive allure in Act I, scene 3 of L’incoronazione di Poppea), listening with “tonal ears” often leaves us with an overriding impression of many seventeenth-century chord progressions and tonal plans as (at best) unusual or (at worst) incoherent, incomprehensible, or even bland. As Eva Linfield once put it in an important article on modulatory techniques in Schütz’s music, “Although the overall plan in some of Schütz’s music … may emphasize tonic and dominant—finalis and cofinalis in seventeenth-century terminology—as major structural cadential articulations, his compositions allow for greater tonal freedom on a small-scale, modulatory level. It is on that level that the music lacks a ‘normative background of expectable musical relationships’, adhering instead to an elusive tonality” that “permits non-teleological chord progressions.”[4]

1.3 The general assumption undergirding most scholarly studies of seventeenth-century harmonic language (including Linfield’s) is that the best way to understand these chord progressions is as part of a closed “modal system” akin to our modern tonal system. With varying levels of success, scholars—myself included—have pored over theoretical treatises and analyzed musical works in a concerted effort to construct a rational system within which we can analyze and understand the harmonic choices of seventeenth-century composers.[5] Such attempts, however, may actually be impeding efforts at understanding seventeenth-century harmonic language more than helping them. For one thing, much of the work in constructing a modal system has been undertaken in the service of a larger agenda to elucidate the process by which modality morphed into tonality, as evidenced by the large number of studies bearing some version of the title “From Modality to Tonality.”[6] Such an approach often betrays a tonal bias that causes the analyst to seek out a concept of modality that is structurally similar to tonality, highlighting harmonic elements that bear similarities to tonality while minimizing those that do not.[7] Once a closed modal system has been conceptualized, moreover, the modern analyst’s primary task becomes to squeeze previously composed works into newly constructed boxes, regardless of whether the composer consciously worked within the system or not. In doing so, we lack the proper frame of reference and vocabulary to understand harmonies that do not fit into the boxes, and much of the analysis is often spent attempting to explain the exceptions away rather than profitably illuminating the composer’s harmonic choices.

1.4 Even Eric Chafe’s influential monograph Monteverdi’s Tonal Language is affected by a tonal bias.[8] Already in the very first paragraph, Chafe praises seventeenth-century musical developments for giving “one of the most enduring of such systems to the world, that of harmonic tonality, a model so all-pervading that it virtually defined the nature and limits of Western music until the twentieth century.”[9] Although he qualifies his use of the terms “dominant” and “subdominant” in the following analysis of Monteverdi’s famous madrigal Cruda Amarilli, he concludes the chapter by claiming, “Yet the increasing tonal interpretation of modal characteristics causes the transfer of the characteristics of some modes or keys to others, ultimately to render anachronistic concepts such as subdominant, relative major and minor, and the like more broadly applicable and hence to reinforce the perception of two basic key types.”[10] While the “interpretation” and “perception” he mentions ostensibly refer to the seventeenth-century composer and listener, it is Chafe himself who is interpreting and perceiving, extrapolating backward from his twentieth-century tonal grammar.[11]

1.5 A more serious objection to studies that seek to construct a modal system is the fragile ontological status of mode in the seventeenth century (and earlier). Over thirty years ago Harold Powers warned us that modality is not “a precompositional universal for sixteenth-century polyphony” but rather “a music-theoretical construct,”[12] and in 1992 he answered his own question “is mode real?” with a resounding (if qualified) no: “A 16th-century piece is not in a ‘mode’ that is part of a ‘modal system’ in a way analogous to the way an 18th-century piece is necessarily in a ‘tonality’ that is part of the ‘tonal system.’”[13] Even many scholars who believe in the “realness” of mode admit that there is no single, universal “modal system”; Frans Wiering, for example, has argued in favor of two contrasting views of mode in the sixteenth century, an “internal” (philosophical) view propounded by music theorists and a much more flexible “external” view used by practicing musicians.[14] By the seventeenth century, modal theory was a confusing welter of contradictory ideas, with not only many different interpretations of the modes but with a number of writers conflating (or confusing) the twelve (or eight) modes with the eight “church keys” derived from polyphonic psalmody.[15] That mode in the seventeenth century existed more as an abstract theoretical construct than as a practical compositional tool has been convincingly argued by Gregory Barnett, who in a series of recent papers has examined modal polemics in the seventeenth and eighteenth centuries and concluded that for composers and theorists mode was an “intangible ideal” not realizable in practice.[16] From close readings of treatises (ranging in date from 1623 to 1781) in which the authors criticized composers’ application of mode in works of various genres, Barnett has concluded that mode was a tool not for composition or analysis but for making aesthetic judgments tied to ideals both Catholic (in that the modes originated in plainchant) and humanist (in that the modes exemplified Pythagorean ratios). Referencing the dichotomy of syntax and style in language, he has distinguished “tonal coherence as a matter of musical syntax” as separate from “the constraints of style imposed by modal theory for ideological reasons,”[17] thereby making a clear distinction between harmonic practice (syntax) and modal theory (style).

1.6 What, then, is the modern analyst to do? In what follows I shall follow Barnett in divorcing harmonic practice from mode and propose a conception of seventeenth-century harmonic space that is completely independent from modal theory. In doing so I hope to elucidate a grammar of seventeenth-century harmonic language within which we can begin to “re-hear” expressive harmonies in a way that has thus far not been possible with modal analysis. I must stress that in doing so I am not dismissing the modes as illusory constructs or as unimportant aspects of seventeenth-century music theory; on the contrary, as Barnett has shown, mode was very much the subject of passionate debate throughout the period, and detailed examinations of theoretical treatises on the modes continue to contribute valuably to our understanding of seventeenth-century musical thought. Nor do I wish to argue that composers had no concept of mode. Many of the pieces that I will be discussing in this article can be easily identified as being in such-and-such a mode, and indeed, composers at times went to great lengths to write music that conformed to one of the competing theories of mode in the seventeenth century. Nevertheless, I have come to believe that harmonic practice was an entity entirely separate from mode, an innate aspect of the compositional process based not on theoretical treatises but on widespread conventions and a shared harmonic grammar acquired through constant exposure to this music from a young age. Only by recognizing and internalizing this grammar ourselves can we truly begin to hear expressive harmonies in a comprehensible way.

1.7 Developing a grammar of seventeenth-century harmonic language is a formidable task, certainly not achievable in a single article. This is where the preposition that opens my title comes into play: rather than attempting to develop a universal system applicable to all seventeenth-century music, I instead offer a case study as a first step in that much larger project. By necessity, this study is based on a circumscribed repertoire: a sizable body of works of a single genre (the motet) from the same musical center (the imperial court in Vienna) composed within a limited time span (the reign of Emperor Ferdinand III, 1637–57).[18] Studying the music of multiple composers working in the same chapel permits an investigation of the harmonic language of composers from a variety of backgrounds, while at the same time allowing for a certain common ground, as these composers who performed each other’s music day in and day out were undoubtedly influenced by each other, if only on a subconscious level. Although the 133 works examined for this article by no means account for the complete body of motets written by composers at the imperial court, it is nevertheless substantial enough to be representative (see the Appendix for a complete list of the motets).[19]

2. Theoretical Premises and Principles

2.1 In the absence of seventeenth-century theoretical writings explicating a harmonic grammar, I begin with the music itself. My analytical approach differs, however, from the typical mode- or key-centered analysis. Whereas a mode-centered analysis begins by first identifying the mode and then analyzing the harmonies according to the limitations imposed by the composer’s choice of mode, I have instead found it profitable to take a more empirical approach, observing the harmonies on their own terms as they unfold in the course of the composition. Like a listener hearing the work for the first time, I begin by literally mapping the harmonies, placing them into a conceptual theoretical framework that proceeds from three basic premises.

2.2 The first two premises come from seventeenth-century writings about music. First, every piece has a tonal center (which I call the “final”), which not only provides a sense of “finality” (marking the end of the piece) but also possesses a degree of “tonicity” in that it functions as the most important pitch class in the work, providing the foundation (as it were) of the harmonic space.[20] Second, the basso continuo is a “grammatically fundamental voice,”[21] even the most grammatically fundamental voice. As YouYoung Kang has pointed out, seventeenth-century contrapuntal treatises invariably single out the bass as the principal voice against which all other voices must be considered (in contrast to the primacy of the tenor in sixteenth-century counterpoint), and successful modern analyses (including Kang’s own) emphasize the role of the bass—the actual bass, not the Rameauian “fundamental bass”—in defining the harmonies.[22] Seventeenth-century figured bass treatises, moreover, all agree that the bass determines the triadic harmony of a composition. In my view, an especially important function of the bass is that it defines cadences, which serve, by emphasizing specific pitches, as one of the primary tools with which harmonic space can be measured.

2.3 The third premise is based on modern theoretical work with Monteverdi’s music rather than on seventeenth-century writings: the theory that seventeenth-century composers worked within a harmonic system based not on the modes but on the hexachords. This so-called “modal-hexachordal system,” developed by Chafe (building on the work of Carl Dahlhaus), takes as its starting point the three hexachords used pedagogically as solmization devices since the Middle Ages, but with the pitches reordered not as a scale but in fifths from flattest to sharpest (that is, the hexachord C–D–E–F–G–A rearranged to F–C–G–D–A–E).[23] I label this conceptualization of the hexachord as a series of fifths a “harmonic hexachord,” to distinguish it from the more familiar scalar version, or “melodic hexachord.” When the three harmonic hexachords are placed alongside each other, they create a system of three interlocking hexachords, in which the natural harmonic hexachord is flanked by the other two, each extending a fifth beyond it (Table 1). The three-hexachord system taken as a whole delimits the boundaries of the total available harmonic space for a given composition, roughly analogous to the way a modern major scale encapsulates the harmonic language of a strictly diatonic tonal work. Notably, the entire three-hexachord system is bounded by chromatic inflections of the same pitch class, a crucial distinction between this system and a modern key. Seventeenth-century composers had more options available to them than just the system illustrated in Table 1, for they could transpose the system by moving any other harmonic hexachord to the central position, thereby resulting in a harmonic vocabulary containing more flats or sharps than those indicated in Table 1. The choice of system was a pre-compositional decision, and composers typically indicated that a work was based on the flat harmonic hexachord (or flatter) by providing a signature of one flat. Although a modern concept, the application of this modal-hexachordal system to seventeenth-century music can be justified by the widespread discussions of the hexachords (even if not conceived in this way) and the use of such terminology as cantus mollis and cantus durus in seventeenth-century theoretical treatises, as well as by the apparent function of the key signature in this repertoire (serving not as an indicator of the final but of the transpositional level of the system). Even if the concept of the harmonic hexachord was completely foreign to seventeenth-century composers, I contend that the modal-hexachordal system offers a useful model for conceptualizing the harmonic space of their compositions; the harmonic hexachords may very well just be a modern means of visualizing something that was innate for seventeenth-century musicians and listeners.

2.4 My comprehensive analysis of the motet repertoire at Ferdinand III’s court proceeding from these three premises reveals the harmonic practice of composers in mid-seventeenth-century Vienna to be as follows. Cadence points are consistently limited to the six pitches of the central harmonic hexachord of the system. The total harmonic vocabulary, however, can be drawn from the pitches of all three harmonic hexachords, with each pitch able to serve as the root of a chord (usually a triad). I use “root” here in its modern sense of fundamental bass pitch regardless of its position in the chord; although seventeenth-century composers did not have a concept of chord inversion, they nevertheless frequently used first-inversion chords, even when doing so resulted in a bass pitch that lay beyond the bounds of the system. At times, bass notes of inverted chords (which I call “non-functional” bass pitches) do help clarify the system, but this does not happen consistently enough to allow for any general conclusions as to the function of all bass pitches. One place, however, where the bass note is always functional is at cadences, for with only two exceptions discussed below (in par. 2.6 and 4.3), the bass pitches of both chords in a cadence are found in the system, even when one of the chords is inverted.[24]

2.5 In his explication of the modal-hexachordal system, Chafe introduced only two systems, cantus durus and cantus mollis, presumably because Monteverdi used only two signatures (one flat or no signature) in his music.[25] Although Habsburg composers continued to use only these two signatures, they nevertheless based their music on systems centered on a variety of harmonic hexachords. In order to label the systems precisely, it is thus necessary to introduce additional names. Accordingly, I call the system based on the natural harmonic hexachord cantus naturalis (a term that existed in the seventeenth century), reserving the term cantus durus for the system based on the hard harmonic hexachord. I continue to use cantus mollis for the system based on the soft harmonic hexachord, and I augment the names of increasingly flatter systems with the terms duplex, triplex, and so on (thus, cantus duplex mollis is the system centered on the two-flat harmonic hexachord, cantus triplex mollis is the system centered on the three-flat harmonic hexachord, etc.).[26] The labels can also be augmented in the sharp direction (cantus duplex durus, etc.), but no surviving motets from Ferdinand III’s reign use such extreme sharp systems.[27]

2.6 Given the importance of cadences in helping to clarify a work’s system, it is crucial to define the various cadences I have observed in the imperial motet repertoire (see Example 1). There are five main types of cadences, which for the sake of convenience I label with familiar modern names; in no way, however, should any causal connections be made between the cadence types and their function in the tonal system. The most common cadence is that which is also the most familiar to us today: the “authentic cadence” (AC), in which the final pitch is approached via a falling fifth or rising fourth in the bass. In contrast to the authentic cadence’s similarity to functional tonality, the next most common cadence type hearkens back to sixteenth-century contrapuntal practice: the “tenor cadence” (TC), in which the final bass pitch is approached by step, usually a falling whole step but occasionally a rising half step.[28] In full-voice counterpoint, the stepwise motion in the bass would be complemented by contrary stepwise motion to the same pitch class in another voice; in monody in the stile moderno, however, this rule is not consistently observed. The rather rare tenor cadence with a rising half step in the bass is one of the exceptions to the previously stated convention that both bass pitches at cadences are drawn from the system, for the penultimate bass pitch sometimes extends beyond the system in the sharp direction. The third type of cadence is the “plagal cadence” (PC), in which the final bass pitch is approached by a falling fourth or rising fifth,[29] and the fourth type is the “Phrygian cadence” (Phry), in which the final bass pitch is always approached by a falling half step. Occasionally the falling semitone motion (fa–mi) that defines the Phrygian cadence appears in an upper voice over a rising whole step to the same pitch in the bass, resulting in the fifth type of cadence, a variation of the tenor cadence that I call the “inverted Phrygian cadence” (IPC). A sixth but rare type of cadence is the “evaded cadence” (EC), in which the bass of a chord with a 4–3 suspension moves anywhere but down a fifth or up a fourth, often creating the effect of a tonal deceptive cadence (V–vi). There are only twelve instances of evaded cadences in the surviving Habsburg motet repertoire (in ten works by two composers), and in all cases both the expected and the actual final chords lie within the central harmonic hexachord.[30] In contrast to tonal deceptive cadences, none of these twelve cadences seems to serve any specific expressive function; rather, they function primarily to keep the musical fabric moving forward, as taught by Zarlino.[31] In identifying cadences I follow two main criteria: the bass movement as defined here (and, in the case of the inverted Phrygian cadence, the fa–mi motion in an upper voice), and whether the last chord coincides with either an obvious caesura in all voices or a syntactical break in the text in at least one voice. Even if other voices move through a cadence without pause, producing what I call a “weak cadence” (as in Example 4, m. 9; Example 13, mm. 120, 122, 124, and 130; and Example 21, mm. 84 and 86), to my ears these two criteria are sufficient for establishing the moment as a marker of harmonic space. One thing that has no bearing on the nature of the cadence is the major or minor quality of either chord; throughout the period under examination it was conventional to end cadences with a major chord, so there is little value in trying to extrapolate any larger expressive significance from the quality of the last chord in particular.[32] Composers also seem to have felt free to alter the major or minor quality of any chord without regard for the system, often for an expressive effect that is immediately apparent to modern ears.

3. Normative Harmonic Practice in the Habsburg Motet Repertoire

3.1 An important premise of Margaret Bent’s argument about the grammar of early music is that in order to truly internalize the grammar, one must establish a solid “normative” baseline from which one can then identify expressive transgressions.[33] To this end, I offer the following observations about normative harmonic practice in the Habsburg motet repertoire, along with representative examples, most of them from works based on the same final (G, by far the most frequently used final in the repertoire) but in a variety of systems.[34] Throughout this article, I identify the harmonic space of a work with a letter for the final and the descriptive term for the system (mollis, naturalis, durus, etc.) in Roman type. Upper- and lowercase letters represent the major or minor quality of the final; however, when describing chords, I use only uppercase letters.

3.2 A very important (if basic) aspect of normative harmonic practice is that the final is always given special emphasis, which helps endow it with “tonicity.” An important place this happens is at the beginning of the piece. In all but one of the works examined for this article, the final is the first bass pitch of the work,[35] and composers often employed a number of additional means to further emphasize it. One common method is duration, as can be seen in Example 2 and Example 3, in which a G-major chord is sustained for the first two and three measures of the piece, respectively, and then serves as the cadence point for the opening phrase.[36] In both examples, the composer also emphasizes the final melodically in the continuo by means of a semitone lower neighbor in the first measure. Another typical method for stressing the final is frequency. In Example 4 (Audio Example 1), for instance, a G-minor chord sounds in the first measure and then reoccurs in mm. 4, 6, and 7, followed by cadences on G in mm. 9 and 11. Even though the first complete syntactic unit of the text ends in m. 17 with an authentic cadence on a pitch other than the final, the early emphasis on G in the first eleven measures ensures that we hear it as the final. In Example 5, the frequent iteration of G-major chords in mm. 1–4 establishes G as the final, even in the absence of cadences to that pitch in the entire first section of the composition.[37] After establishing the final at the beginning of the piece, a composition typically continues to stress it by frequently returning to it, both melodically and as a cadence point. In only rare instances does a pitch other than the final receive the most cadences in a piece, and the final is the most common choice of cadence point at important structural junctions.[38]

3.3 Another aspect of normative harmonic practice in the Habsburg motet repertoire is that the most frequently heard sonorities are typically those that sit closest to the final on the central harmonic hexachord. A representative example is the first section of Georg Pichelmair’s Canite tuba in Sion (Example 2), a work in G naturalis that limits its entire harmonic vocabulary to the natural hexachord. After the final, the most frequently heard sonorities in this passage are C and D, while the harmonies that appear the least often are those on the edges of the harmonic hexachord (see Table 2). In many works, however, the most frequent harmonies are not those directly adjacent to the final. This is especially true when a work is in a mollis or durus system and/or when the final sits toward the edge of the central harmonic hexachord, in which case an emphasis on sonorities not adjacent to the final can help aurally establish the system. For instance, the most frequent harmonies in the first syntactic unit of Antonio Bertali’s Exultate et cantate (Example 4; Audio Example 1), a work in g mollis, are G and D, but the next most frequent harmony is F (first heard in m. 5), which together with the authentic cadence in m. 14 on B-flat (the flattest point on the soft harmonic hexachord) solidly establishes the system as cantus mollis (see Table 3). In contrast, the first section of Giovanni Felice Sances’s G-durus Magnificemus in cantico (Example 5) gives practically equal emphasis to D and A, with chords on E sounding more frequently than those on C (see Table 4).

3.4 Regarding movement from sonority to sonority during a composition, a very common type of chord progression is one in which the root moves by fifth. Again, the opening section of Pichelmair’s Canite tuba in Sion (Example 2) serves as a representative example, in that the bass moves by fifths in all but two instances. Notably, both cases in which the bass does not move by fifth involve the flattest and sharpest sonorities of the section, thereby helping to delimit the harmonic space.[39] A more extensive fifth-related chord progression, one that encompasses the total harmonic space of cantus mollis, can be seen in Example 6 (Audio Example 2), a later section of Bertali’s Exultate et cantate. Starting with an A-major chord in m. 44 (approached with expressive third-related harmonic motion via a cross-relation in the bass), the harmonies first trace the entire soft harmonic hexachord from sharp to flat. Upon reaching B-flat (the flattest point in the hexachord) in m. 48, the bass returns to A via a Phrygian cadence and then moves by fifth to the sharpest sonority in cantus mollis for a statement of the name of the saint being honored by the motet (the first time the saint is named in the work). This is followed by another flatward progression of fifths, which moves through every available harmony in the system from E to E-flat. This two-fold cycling through chains of fifths, which seems deliberate and carefully planned, may seem to modern ears analogous to tonal processes, but a crucial aspect of tonality is missing from the passage: any sense of teleological progression. Although it is easy for our tonal ears to interpret the harmonies as a string of V–I cadences, the defining factor of the progression is not any tonal pull exerted by the G final (or any other pitch) but rather the harmonic space of cantus mollis. Significantly, the final does not assume a privileged position in either of the two progressions, and it is the fa–mi of the soft hexachord (present in the Phrygian cadence) that serves as the fulcrum of the passage.

3.5 In many cases, chord progressions do not seem to have been planned by the composer but rather emerge simply as a result of melodic processes, especially melodic sequencing. Johann Jacob Froberger’s Apparuerunt apostolis (Example 3) provides an excellent illustration of melodic sequences that result in chord progressions that, while predominantly fifth-related, lack the functionality of modern tonality. The first phrase of the motet (mm. 1–4) establishes melodic sequencing as an important element of the work, consisting of three statements of the same motive, each transposed up a third. In m. 5, the violins initiate a descending stepwise melodic sequence that spans an octave from g´´ to g´, a process that then repeats with different melodic motives in mm. 10–12 and 12–16. Although the resulting chord progressions mimic teleological tonal movement toward a cadence, they also contain decidedly “non-functional” progressions, especially the movement from F-major to B-minor chords in mm. 6 and 11 and from B-flat-major to E-minor chords in m. 15.[40]

3.6 The first section of Sances’s Magnificemus in cantico (Example 5) offers examples of non-tonal harmonies that result from both the sequencing of melodic motives and the transposition of entire phrases. In mm. 7–12, the entire first phrase is transposed up one step from G to A, a harmonic relationship that makes little sense in tonal terms but can be understood as a means to help establish cantus durus.[41] The third phrase (mm. 13–24) then consists primarily of interlocking descending melodic sequences; while this results in some fifth-related harmonic movement (especially two C–G–D–A progressions in mm. 14–18 and 19–23), the overall progression is non-teleological, and the movement from an A-minor to a C-major chord in mm. 18–19 is decidedly non-functional.

3.7 Occasionally composers combined melodic and harmonic processes by transposing or sequencing chord progressions, especially cadential formulas. Sances’s Domine ne memineris (Example 7) opens in a completely normative way, by sustaining a G-major chord and then moving by fifth to a C-major chord (in first inversion).[42] In m. 4, however, the singer introduces a dissonant non-chord tone, which resolves by step to a tenor cadence on F.[43] Measures 4–5 are then immediately transposed down a step, initiating a descending sequence that, by concluding with a D-major chord in m. 9, leads smoothly to the first authentic cadence on the final in m. 10. Another example of transposed chord progressions can be seen in the opening ritornello of Ferdinand III’s Jesu corona virginum (Example 8), which consists entirely of three statements of the same short phrase at different transposition levels.[44] The first statement begins on the final and moves through E-flat-major and C-minor triads to an inverted Phrygian cadence on D, thereby concisely encompassing in just four chords and six beats the entire two-flat harmonic hexachord (E-flat–B-flat–F–C–G–D) and establishing that the work is in cantus duplex mollis. The emperor then transposes the phrase up a fourth (with all parts except the fourth viola maintaining the same melody), which produces two important results: the introduction of A-flat major (the flattest chord in the system) and a cadence on the final. The third statement returns to the original transposition level, but with a re-voicing that transforms the D-major chord from a cadential resolution to the penultimate chord of an authentic cadence with 7–6–5 motion above the bass. Even with a limited melodic and harmonic vocabulary, the ritornello leaves the listener with no doubt as to the final or the system.

3.8 To aid in the visualization of harmonic space in the Habsburg motet repertoire, I have found it helpful during the analytical process to chart the harmonies in what I call an “analytical map.” As an example, Table 5 presents a complete map of Pichelmair’s Canite tuba in Sion, a work chosen on account of its normative harmonies and its relatively short length. In the map, cadence points are indicated using the abbreviations defined in par. 2.6, and the root of every other sonority is identified with an asterisk; asterisks that appear on the same row as a cadence indicate the penultimate bass note in the cadence (see Table 6 for a legend of all the symbols used in the analytical maps in this article). Major section breaks (often marked by changes in meter) are indicated with thick horizontal lines, while important syntactic breaks in the text within a section are indicated with double thin horizontal lines. The final is highlighted in green, and pink is used to indicate sections that repeat verbatim (both harmonically and melodically).

3.9 While it is possible to place each of the works analyzed for this article into a three-hexachord system, it is nevertheless sometimes impossible to determine precisely in which system a work belongs. This happens when a composition does not cadence on both outer pitches of a harmonic hexachord, does not contain chords from both extremes of any given system, and also does not cadence on the sharpest and flattest sonorities in the work. A representative example is Sances’s Iste confessor, a work with a D final and a limited harmonic vocabulary.[45] As can be seen in Example 9 and Table 7, cadences appear on only three pitches (D, A, and F), and the total harmonic vocabulary extends from B-flat to E.[46] The work thus fits comfortably into either cantus naturalis or cantus mollis, and the strong emphasis on A-major sonorities—which are heard more often than chords on the final (see Table 8)—offers a compelling reason to identify the system as cantus naturalis. Sances notates the work, however, with a signature of one flat, for which reason I have placed it into cantus mollis in Table 7 and the Appendix.[47]

3.10 For seventeenth-century composers and their listeners, the fact that the system of Iste confessor is impossible to identify definitively would not have been a problem. Even though it does not take full advantage of all the available harmonies of a system, the composition nevertheless exhibits the normative features of the modal-hexachordal system and can easily be analyzed as fitting into either cantus mollis or cantus naturalis. Ultimately, there is no need for listeners to puzzle over whether the B-flat chords belong to the central harmonic hexachord (cantus mollis) or are on the flattest edge of the system (cantus naturalis). The only time when cases such as this pose a problem is when a modern analyst wishes to classify works (as in my Appendix), and I have addressed it by consistently regarding the flattest chord as the flat extreme of the system, rather than as a component of the central harmonic hexachord (unless a key signature indicates otherwise). Although this means that I would have classified Iste confessor as cantus naturalis were it not for the signature, the approach is justified by the presence of thirteen Habsburg motets (by three composers) that lack a key signature and feature B-flat chords but no B chords or cadences on E.[48] In contrast, there is only one other work in addition to Iste confessor (Sances’s Audi Domine) that has a flat in the signature but contains no E-flat chords or B-flat cadences.

3.11 I should stress that all the practices I have been discussing thus far are merely norms and not hard and fast rules. The means by which the final is established and harmonic space unfolds can vary tremendously from piece to piece, even in works by the same composer with the same final/system combination. Nor are there any common, established patterns for either chord progressions or the order and frequency of cadences on the six pitches of the central harmonic hexachord. Linfield and others were thus justified in describing seventeenth-century chord progressions and tonal plans as non-directional and unpredictable. Nevertheless, the harmonic language of the Habsburg motet repertoire does indeed seem to be guided by a “normative background of expectable musical relationships” provided by the modal-hexachordal system,[49] which can be summarized in the following four points:

  1. The final is emphasized at the start of the composition and continues to be emphasized throughout the piece, in terms of both the number of cadences and the frequency with which it is used melodically and harmonically.
  2. The most frequently heard harmonies in the composition are those close to the final on the harmonic hexachord, but not necessarily the ones directly adjacent to it.
  3. Common chord progressions are those in which the root moves by fifth, though many other options are possible, and rarely does fifth-related motion behave in a teleological manner analogous to modern tonal procedures.
  4. Many harmonic progressions result from melodic and/or harmonic sequences or the transposition of melodic phrases, chord progressions, or cadential formulas.

It is armed with this set of basic expectations for the unfolding of harmonic space that we can now identify and begin to understand the purposeful exceptions to the norm. I have identified the expressive harmonies in the imperial motet repertoire as falling into two large categories: those found within a given system, and those coupled with a change in system during the course of the work. We begin with the first category, within which there are four distinct types.

4. Expressive Harmonies within a Single System I: The Phrygian Cadence

4.1 Perhaps the most basic type of expressive harmony—and the one most easily overlooked by our tonal ears—is the Phrygian cadence. Although a common, normative cadential type, the Phrygian cadence nevertheless possesses unique qualities that led to its frequent use by Habsburg composers for text-expressive purposes.[50] Most significantly, the descending half step in the bass juxtaposes pitches that are simultaneously close to each other melodically and yet far removed harmonically, on opposite ends of a harmonic hexachord. Although certainly not every Phrygian cadence serves a text-expressive function, there are numerous examples of pieces that use this unique cadence type to draw attention to a significant text, especially when the cadence is marked by striking stylistic features, such as changes in texture, meter, or tempo. Attesting to the widely acknowledged expressive quality of the Phrygian cadence is the fact that it lived on beyond the seventeenth century; modern listeners are most familiar with it as the expressive final cadence of interior slow movements of late-Baroque sonatas and concertos.

4.2 A very common function of the Phrygian cadence in the Habsburg motet repertoire is to articulate sections of a piece. A total of forty-two motets use the Phrygian cadence in this way, usually at the beginning of sections to draw attention to an important new idea in the text. In Bertali’s Exultate et cantate (Example 10; Audio Example 3), for instance, a pair of Phrygian cadences in mm. 112–15 articulates an important shift in focus in the text. Up to this point, the text has offered general praise of the saint, but this last section contains the main point of the motet: a request for the saint to intercede on our behalf and protect us from enemies. Significantly, the Phrygian cadences highlight the action verbs the singers are about to undertake: “Hunc precemur, hunc rogemus” (Now let us pray, now let us request). The succeeding Phrygian cadence in m. 120 then helps to articulate the close of that syntactic unit of the text, just before the singers address the saint by name and make their request. In Sances’s O dulcis Virgo virginum (Example 11), a d-mollis work setting a Marian prayer, three Phrygian cadences, all concluding the same distinctive musical phrase on the text “be patron to my miserable self,” are used not only to articulate a new syntactic unit in the text but also to highlight the most important request in a work filled with requests. Elsewhere the text beseeches the Virgin to intercede with Christ for the remission of sin, which many might consider to be the most important request in the text. Nevertheless, the request highlighted in mm. 48–70—asking the Virgin to become the singer’s patron—relates directly to the political event for which the motet was written, when Ferdinand III declared the Blessed Virgin of the Immaculate Conception the patron of his realm in thanks for her protection of Vienna during a siege by the Swedish army.[51] When articulating new sections, Phrygian cadences are often marked by shifts in meter and/or texture; a good example of the latter can be seen in Sances’s O Jesu mi dulcissime (Example 12), in which the composer highlights the beginning of a new section containing a request to Jesus (mm. 94–95) with both a Phrygian cadence and a shift from contrapuntal to homophonic texture.[52]

4.3 Because a Phrygian cadence highlights the outer pitches of a harmonic hexachord, it can be tempting to interpret every Phrygian cadence as a marker of harmonic space; Susan Shimp, for instance, has argued that the Phrygian cadence serves as a “hexachordal signifier.”[53] To claim that seventeenth-century composers deliberately used Phrygian cadences to demarcate hexachords, however, presupposes that they had a conscious conception of the harmonic hexachord, whereas there is no evidence from the seventeenth century that hexachords were ever conceived as anything but a scalar collection of solmization syllables. While very often Phrygian cadences do seem to define the central harmonic hexachord of a composition, this is by no means a strict rule. In fact, the modal-hexachordal system’s existence as a set of norms rather than as a closed, rule-based theoretical system is precisely what allowed the Phrygian cadence to serve an expressive function, for Habsburg composers seem to have felt free to introduce Phrygian cadences on a wide variety of pitches regardless of the controlling harmonic hexachord. As a result, the Phrygian cadence is the second exception to the above-mentioned norm that both bass pitches in a cadence are always found in the system. Whereas the other exception, the tenor cadence with a rising semitone in the bass, serves no expressive function, a Phrygian cadence that extends beyond the system always serves a specific expressive purpose. Sances’s O dulcis Virgo virginum provides an excellent case in point, as two of the three Phrygian cadences in Example 11 seemingly “break the rules”: the second one (mm. 54–55) ends on a pitch outside the central harmonic hexachord, and the third (mm. 63–64) uses a pitch (A-flat) that lies outside the system entirely. Rather than interpret these cadences as shifts between the soft, natural, and two-flat harmonic hexachords (which is not borne out by the other harmonies in the passage, all of which sit comfortably in cantus mollis), it is more reasonable to view them as expressive moments that catch the ear and draw attention to the important request. It is only when the Phrygian cadence sets an important text that I have encountered this cadential exception in the Habsburg motet repertoire, and it happens in enough pieces (sixteen works by three different composers) that it must be a conscious transgression of the norm rather than an inconsistency in the harmonic grammar.[54]

4.4 Even when not used in an articulative way, Phrygian cadences often emphasize important ideas in the text. For instance, the first two Phrygian cadences in Bertali’s Exultate et cantate (mm. 48 and 102; the first one is included in Example 6; Audio Example 2) both immediately precede mentions of the saint’s name. In Froberger’s Apparuerunt apostolis, the only Phrygian cadence in the work occurs on the first mention of the words “Spiritus sanctus” (mm. 46–48), an especially important idea in a motet for Pentecost. An excellent example of a marked Phrygian cadence highlighting a text that might not otherwise seem significant is in Sances’s Miserere servorum tuorum, a prayer beseeching Mary for liberation from sin (Example 13). Within a contrapuntally imitative section marked “presto” and “allegro,” the words “in fine” (in the end) are unexpectedly highlighted in mm. 125–26 and 137–39 by a tempo change and shift to a homophonic texture, all over a Phrygian cadence. There seems little reason for emphasizing these words, which refer to the end of life or the apocalypse. I have argued elsewhere, however, that the motet can be interpreted as requesting liberation from enemies during the Thirty Years’ War, in which case this otherwise inexplicable emphasis on “in fine” could be a request for help in ending the disastrous conflict.[55]

5. Expressive Harmonies within a Single System II: Durus–Mollis Contrast

5.1 Much of the expressive power of the Phrygian cadence comes from its juxtaposition of harmonically distant pitches. Following this same principle, Habsburg composers created expressive harmonic passages by contrasting sonorities on the extremes of a system, either in close proximity or over the span of a complete passage; the fact that every system is bounded by chromatic alterations of the same pitch class thus takes on expressive potential, for these pitches can be exploited in meaningful ways. The result is often chord progressions that seem nonsensical according to functional tonality but that make sense and take on expressive qualities when viewed within the context of the modal-hexachordal system.

5.2 Many instances of durus–mollis contrast are connected to Phrygian cadences; in fact, we have already encountered two examples. In Bertali’s Exultate et cantate (Example 6, mm. 44–50; Audio Example 2), because the Phrygian cadence introducing the first mention of the saint’s name comes at the end of a long flatward progression of fifths, the sudden appearance of an E-major triad after the cadence is strikingly incongruous and cannot help but grab the listener’s attention for the statement of the saint’s name, especially coming so soon after a B-flat in the bass. The three-fold repetition of the phrase “Esto patrona misero” in Sances’s O dulcis Virgo virginum is another excellent example (Example 11), for the appearance of Phrygian cadences on three different pitches produces functional bass notes ranging from E to A-flat in the space of just seventeen measures.

5.3 The use of durus–mollis contrast often seems to draw upon the extra-musical connotations of “hardness” and “softness” implied by the Latin terms. For example, shifts in the sharp direction frequently emphasize such harsh ideas as cruelty, sin, and suffering, and they also sometimes connote vigor and action. In Sances’s Gaude Virgo (Example 14), a work in g duplex mollis, a mention of Christ’s crucifixion concludes in m. 49 with an incongruous Phrygian cadence on A, the sharpest pitch in the system; notably, the cadence appears precisely on the word “pati” (etymologically related to “passionem”). In Sances’s Plagae tuae, Domine (Example 15), the request “Miserere rogo mihi peccatori” (have mercy on me, a sinner) is set to an unexpected authentic cadence on E (the sharpest pitch of the natural harmonic hexachord), which comes only five measures after a cadence on the final in this C-naturalis work.[56] Ferdinand III gives similar treatment to the concept of sins in his hymn for Epiphany, Crudelis Herodes (Example 16). In this d-naturalis work, a reference to Jesus’ cleansing us of sins he did not commit sets the beginning of the phrase (mm. 71–75) to extreme sharp harmonies (an E-major triad approached via chromatic third from G major and then a “quasi-tenor cadence” from F-sharp to E) followed immediately in mm. 76–77 by a Phrygian cadence on E on “detulit,” thereby juxtaposing F-sharp and F-natural in the bass in the space of just four measures.[57] Flat harmonies, in contrast, are often used to highlight such gentle, uplifting ideas as love, grace, mercy, and divine goodness, and they also sometimes emphasize the act of pleading. Sances’s Dulcis amor Jesu provides a striking example (Example 17).[58] In this G-naturalis work, the introduction of the phrase “quia langueo pro te” (because I languish for you), an expression of longing for mystical divine love, places the extreme pitches of the system, B-flat (m. 50) and B-natural (m. 54), in close proximity in the bass, while also introducing an incongruous F-minor chord on the word “quia” (m. 50).

5.4 Durus and mollis extremes also sometimes appear on a large-scale structural level to highlight contrasting ideas over the course of a passage or between sections. Large-scale durus–mollis contrast within a single passage is experienced in Ferdinand III’s Popule meus, in which mollis harmonies emphasize God’s benevolence and durus harmonies Christ’s suffering due to human cruelty. The text is drawn from the Improperia, a chant sung on Good Friday in which Christ reproaches the Jewish people from the cross; in a recurring refrain, Jesus asks his people what he did to upset them, and then in four solo verses he contrasts a miraculous thing that God did for the Jewish people with one of the indignities he suffered during the Passion. Each of the solo sections of this c-duplex-mollis work begins by emphasizing E-flat, the flattest pitch on the two-flat harmonic hexachord (often cadencing on that pitch), and all four of them conclude with an authentic cadence to D, the sharpest pitch on the hexachord. Example 18 provides the first solo section; the conclusion on D is especially striking in that it results from the unexpected upward transposition of a phrase that had concluded on the final (mm. 66–75). This tonal plan from E-flat to D makes no sense in the context of either modern tonality or modal theory, but it is comprehensible—and meaningful—when understood as taking advantage of the extremes of the two-flat harmonic hexachord for expressive purposes.[59]

5.5 Large-scale durus–mollis contrast across sections of a work can be experienced in two solo Marian motets by Sances that use durus harmonies to emphasize mortal yearning and mollis harmonies to symbolize the Blessed Virgin. The first work, Ardet cor meum, follows a typical structure for mid-seventeenth-century solo motets in that sections in duple-meter recitative alternate with passages in triple-meter aria style.[60] Throughout this d-naturalis work, the recitative sections implore Mary for aid, while the aria sections praise her, and Sances emphasizes the textual contrast not only stylistically but also harmonically (the first two sections are provided in Example 19). After solidly establishing the final through three full measures of a sustained D-minor chord, the first section immediately emphasizes the sharp side of the system through authentic cadences on E (m. 5) and A (m. 8), with striking chromatic motion in the voice further stressing the durus harmonic (and melodic) palette. Although the first triple-meter section opens with an authentic cadence on A (m. 27), this is immediately followed in the next measure by a B-flat in both voice and continuo, which introduces the soft melodic hexachord and leads to an authentic cadence on F (m. 30) followed by a Phrygian cadence on A (m. 34), thereby placing the motet firmly in a mollis harmonic region. Significantly, this section sets a text from the Song of Songs that in the seventeenth century was widely understood as a reference to the Immaculate Conception of the Blessed Virgin Mary, an especially important aspect of Ferdinand III’s devotional life; Steven Saunders and I have argued that imperial composers consistently used mollis harmonies as an expressive symbol of the Immaculata.[61]

5.6 The second motet, O Maria Dei genitrix, exhibits a large-scale structure similar to that in Ardet cor meum, but in this work the laudatory triple-meter section opens the work and then recurs throughout as a refrain, separating imploring sections of duple-meter recitative (Example 20).[62] This work is also in d naturalis, but the system is not immediately recognizable, for the first thing we hear after the establishment of the final in mm. 1–2 is a Phrygian cadence to A (mm. 3–4). The prominent B-flat in the bass and the outlining of the flat harmonic hexachord seem to establish cantus mollis, but the immediately following phrase ends with an authentic cadence on A (mm. 8–9), thereby opening up the harmonic space in the sharp direction. All the same, the harmonies in this section fit comfortably in cantus mollis, especially considering the authentic cadence to F in mm. 17–18 and the frequent appearance of B-flat-major triads, which appear more frequently than chords on E (see Table 9 for an analytical map of this example). Only in the next section can we be sure that the work is in cantus naturalis, thanks to a large-scale use of durus–mollis contrast that emphasizes the sharp side of the system. After the opening D-major sonority (with F-sharps in the voice), the second measure introduces a B-natural in the bass (thus introducing the hard melodic hexachord), which moves to A via G-sharp (m. 28) and then to an authentic cadence on E (mm. 29–30), which introduces the sharpest sonority in cantus naturalis. Sances then transposes the phrase up a step, which further emphasizes the durus palette by introducing G-sharps in the voice. When the refrain recurs in m. 40, it is abbreviated by omitting the phrase that ends with an authentic cadence on A, thereby heightening the durus–mollis contrast between this and the preceding section.

6. Expressive Harmonies within a Single System III: Hexachordal Shifts

6.1 Thus far we have seen expressive harmonies that primarily employ only the available sonorities within a system. For even more striking effects, composers temporarily shifted to harmonic hexachords other than the central one; while this sometimes only went so far as one of the other two hexachords constituting the system, composers occasionally moved to hexachords even further afield. Such shifts constitute either momentary introductions of foreign sonorities within a single phrase or larger-scale shifts for an entire section.

6.2 The most obvious hexachordal shifts are those that introduce harmonies foreign to the system. In these instances the composer uses the same freedom to present off-system sonorities discussed in par. 4.3 with the expressive Phrygian cadence, but the shift often makes use of cadential, harmonic, or melodic figures other than the Phrygian cadence. For example, Sances’s Veni sponsa Christi (Example 21), a work in C naturalis, introduces an unexpected authentic cadence on B (the sharpest pitch in the system) in mm. 83–84, thereby emphasizing the word “iniquitatem” (sin) with extreme durus sonorities. The use of the F-sharp-major triad, made possible by the melodic C-sharps in the canto coupled with a bass line that in mm. 81–83 mimics a normative progression leading to a tenor cadence on G, shifts the harmonies to the hard harmonic hexachord for just this one phrase. Another example is Ferdinand III’s Crudelis Herodes, a d-naturalis work that features many instances of durus–mollis contrast throughout, using durus harmonies to emphasize human sins, as in Example 16 (discussed in par. 5.3). The final “amen” concludes the work in a decidedly mollis (and thus divine) harmonic realm by means of the simple process of transposition (Example 22). After a cadential phrase on the final that appears successively in the voices and strings (mm. 175–79 and 180–84), the entire phrase is unexpectedly transposed down one step, thereby moving to the two-flat harmonic hexachord with the introduction of C-minor, F-minor, and A-flat-major chords. After an echo by the strings, the work returns to the original harmonic palette by simply restating mm. 175–84 back at the original transposition level.

6.3 Hexachordal shifts are occasionally used in a structural manner by shifting the harmonic fabric to a new hexachord for an entire section, rather than just an individual phrase. Often the shift extends only as far as to another harmonic hexachord within the system, which often makes it a judgment call as to whether it is a true hexachordal shift or merely the structural use of durus–mollis contrast (as in Sances’s Ardet cor meum and O Maria Dei genitrix, discussed in par. 5.5 and 5.6). In these instances, I deem that a hexachordal shift has occurred if the harmonies of the section stay within the new hexachord, if the shift is clearly marked by striking stylistic features, and if the shift back to the original hexachord follows a logical and seemingly deliberately planned strategy. Sances’s three-voice O crux benedicta offers an excellent example (Example 23).[63] The recurring opening section of this G-naturalis work extols the redemptive power of the cross, while the central section focuses on the human singers, who declare their intention to praise Jesus and then implore him for mercy. The opening section extends no sharper than E (on the edge of the natural harmonic hexachord), but the central section, which shifts from triple to duple meter as well from tutti to solo texture, is articulated by a Phrygian cadence to B (m. 37) that enacts a shift to the hard harmonic hexachord. The harmonies remain entirely within the new hexachord until the crucial phrase “miserere nobis” (mm. 54–56), which signals a shift back to the natural melodic hexachord through an expressive F-natural in the voice on the downbeat of m. 55 (the first F-natural, in either melody or sonority, in this section); flat harmonies appear at the same moment, as indicated by the B-flat in the figured bass. Three successive transpositions of this phrase down a fifth follow, eventually reintroducing the natural harmonic hexachord with an F in the bass (m. 59), followed shortly by a functional B-flat (m. 61). The hexachordal shift not only marks a change in focus in the text but also makes the ensuing flat harmonies, which emphasize the plea to Christ, more expressive than they would be otherwise.

7. Expressive Harmonies within a Single System IV: Double Finals

7.1 Among the most perplexing phenomena I encountered while mapping harmonies in the Habsburg motet repertoire were pieces for which I could not easily pinpoint a single tonal center. In every case, two pitches seemed to function as the final, and it happened in enough works that I could not dismiss it as a mistake or meaningless irregularity. I call this phenomenon the “double final”: two pitches consistently share the function of tonicity (that is, neither one dominates the other as the most important pitch class in the work) within the context of a single system. The idea that a composition could possess multiple finals was not foreign to seventeenth-century composers and theorists; famously, in his 1607 explanation of Monteverdi’s preface to the Fifth Book of Madrigals, Giulio Cesare Monteverdi cited Zarlino’s concept of “mixed modes” to defend his brother’s “multimodal” madrigal O Mirtillo against Artusi’s attack.[64] The concept of the double final that I propose here, however, differs in one very significant aspect from mixed modes: because each mode is essentially its own system, a work featuring modal mixture contains multiple systems, whereas the works I have identified as containing double finals are easily analyzed as staying in one system throughout. For modern listeners and analysts, double finals can perhaps best be conceptualized by comparison to the concept of “tonal pairing” in nineteenth-century music.[65] In tonal pairing, each tonic maintains its independent function within its own key; there are thus two systems in play over the course of the work, so one chord could have two different functions depending on which pitch is acting as tonic at a given moment. By contrast, because seventeenth-century double finals appear within a single system, all the other sonorities function exactly as they would were there a single tonal center, without creating the sense of conflict often present in tonal pairs. Even without this conflict, however, double finals in seventeenth-century music can serve expressive functions.

7.2 I have identified double finals in five motets, all by Ferdinand III. Because the emperor is the only imperial composer who is known to have explored double finals, one could argue that this was not in fact a standard practice, and that Ferdinand was simply taking advantage of his amateur status to experiment freely. Nevertheless, an examination of the emperor’s double-final works offers valuable insights into the expressive potential of the modal-hexachordal system and the harmonic grammar at his court. These five motets present just two possible pairs of finals, though two of the works also contain system changes during the course of the work that produce new finals (discussed in par. 9.3).

7.3 One of the sets of double finals is seemingly analogous to the tonal system. The finals of the hymn settings Veni creator Spiritus and Jesu redemptor omnium are C and a in cantus naturalis, thereby producing what modern listeners would interpret as relative major and minor keys. To interpret them in this way, however, misses their expressive potential, for their significance lies not in their contrasting major and minor qualities but in the fact that the two finals lie toward the flat and sharp ends of the natural harmonic hexachord.

7.4 In the Pentecost hymn Veni creator Spiritus, the two finals consistently distinguish the divine Holy Spirit (C) from the mortals calling out for its arrival (a). This is apparent already in the first verse (Example 24). The first phrase (mm. 1–9) clearly establishes C as the final, with a C-major chord sustained for three full measures, followed by an authentic cadence on C (m. 6) that is immediately echoed by all the voices (m. 9). Immediately, however, the emperor harmonically transposes the same phrase down a third (mm. 10–16; the melody is slightly altered), thereby establishing A as the final in the same way. By setting the same text to both finals, the music emphasizes equally both the Holy Spirit being addressed and the mortal singers calling out to it. After a phrase that cadences between the two finals on G (m. 20), the fourth phrase (mm. 21–27), which mentions the Spirit’s “superna gratia” (heavenly grace), cadences on C, and the last phrase (mm. 28–36), setting the words “Quae tu creasti pectora” (the hearts you created), cadences back on A. Table 10 provides a line-by-line text and translation of the entire work, specifying on which pitch each line cadences and other important harmonies. Probably more shocking to most modern listeners than the presence of two finals in this work is that fact that the final cadence is on neither of them; rather, the work ends on E. To students of modal theory, this is not so alarming, as many seventeenth-century theorists and composers conflated the modes on E with those on A.[66] In this work, Ferdinand III seems to have let contemporaneous modal theory influence his choice of final cadence; perhaps he felt that because the two finals are emphasized fairly equally throughout the work, ending on a pitch other than one of them was a convenient way to avoid having to decide which one should be given the last word. In contrast to Veni creator, in which almost every verse includes cadences to both finals, in Jesu redemptor omnium each verse usually emphasizes only one of the finals, again using C to symbolize divinity and a to symbolize humanity.[67] The predominant harmonies of each verse are indicated in Table 11; in this work the emperor again takes advantage of the A/E modal conflation in that the hymn opens by emphasizing E as the final rather than A.

7.5 The other set of double finals, which appears in three of Ferdinand III’s motets (two in cantus naturalis and one in cantus mollis), is more difficult for modern listeners to explain, and indeed, I can offer no justification for it aside from my observation that it exists. These works combine the finals G and a. In this section we shall examine just the two cantus naturalis works (Deus misereatur nostri and Humanae salutis sator); the cantus mollis work (Miserere) will be discussed beginning in par.10.6.[68]

7.6 Deus misereatur nostri is a curious piece. On one hand, it is brimming with a wide range of expressive stylistic and harmonic devices in almost every measure.[69] On the other hand, the work comes across as a rather pedestrian compositional effort; it is almost as though it were a student work in which the emperor was trying his hand at as many expressive compositional techniques he could imagine. One aspect of the piece that contributes to this impression is the fact that the stylistic and harmonic devices often do not seem related to the text, on account of which the following discussion will not include consideration of the words. Harmonically, the work treats the double finals in a manner similar to Veni creator Spiritus, using both of them as cadence points within sections. In fact, the treatment of the first syntactic unit is very similar to the other work (Example 25): after the full vocal ensemble declaims the first word to a plagal cadence on E, the rest of the syntactic unit is sung to two statements of the same two-measure cadential phrase, first by the upper three voices on A (mm. 2–3) and then by the lower three voices transposed down a step on G (mm. 4–5). Transposition continues to be the main technique through which the harmonic progressions are created. The second syntactic unit (mm. 6–17), for instance, features eleven statements of the same five-beat motive transposed to end on all points of the natural harmonic hexachord except E, ultimately concluding the first section with an authentic cadence on G (m. 17). The next section (mm. 18–26) opens by sequencing a new phrase three times to reach an authentic cadence on A (m. 26). Having reached A, the words “misereatur nostri” recur in mm. 27–30 to a varied repetition of mm. 2–5, cadencing again on A and G. In the work as a whole, G appears as both a sonority and a cadence point more frequently than A, due primarily to an extended fanfare-like section (mm. 37–59) that sits extensively on G. But because the motet both begins and ends on A, it is impossible to assert that one of them is the sole final.

7.7 The Ascension hymn Humanae salutis sator combines aspects of both Veni creator Spiritus and Jesu redemptor omnium: the first section emphasizes both finals equally, but subsequent sections tend to focus on just one final (see Table 12 for a line-by-line harmonic explication).[70] The opening measures (Example 26) establish G as the final through both duration and frequency, but following the procedure observed in Veni creator Spiritus and Deus misereatur nostri, Ferdinand III immediately transposes the phrase in mm. 5–9 up a step (mm. 10–14), thereby also setting the second line on A. As in Veni creator, this line—“Jesu voluptas cordium” (Jesus, delight of hearts)—references both the divine and the mortal, which sets up the same mollis–durus symbolism seen in many other imperial motets. The emperor treats the fourth line, which again mentions both Jesus and man (“Et casta lux credentium” [and holy light of the faithful]), in a similar manner, stating it a total of three times: first on G (mm. 18–24), transposed to A (mm. 25–31), and then back at its original transposition level (mm. 32–38). The following sonata and the next two verses (mm. 42–131) enact a system change to flatter regions (discussed in par. 9.3), but the sonata following the third verse (mm. 132–43) brings us squarely back to A, reestablishing the final through both duration and frequency; both that sonata and the fourth verse (mm. 144–52), in which the singer implores Jesus to bestow his grace, consist almost exclusively of A-major triads and authentic cadences on that pitch. The last verse, which continues the request, is also centered squarely on A; however, the phrase setting the last line—“Sis dulce vitae praemium” (be the sweet reward of life)—is transposed down a step to end the work on G (mm. 186–93), with the flatter final reinforced by a repeated cadential figure on G for “amen” (mm. 194–99). With this last shift from the durus A to the more mollis G, the harmonies seem to send a message of confidence that Jesus will in fact grant the request and bestow his goodness on the listeners. Only by recognizing the expressive significance of the double finals can we glean this important message.

8. Expressive Harmonies Incorporating Multiple Systems I: New System, Same Final

8.1 One large category of expressive harmonies remains to be examined: those that exhibit a full-scale shift from one system to another. With these works we enter the murky realm of seventeenth-century “modulation.” Changes in “system,” “tone,” or “mode” were not foreign concepts to theorists of the time; Athanasius Kircher, for instance, distinguished between two types of harmonic shifts, mutatio modi and mutatio toni.[71] Kircher’s definitions of these terms and his illustration of them with music examples have been interrogated at length by modern scholars, but many questions remain, especially the precise distinction between them.[72] My task is not to ponder such questions, however, but rather to inquire how changes in system might be perceivable within the grammar of seventeenth-century harmonic language outlined here. Although only eight of the 133 works examined for this study feature shifts in system, the harmonic processes among them are consistent enough to draw conclusions. Overall, I have observed two types of system changes: those that maintain the same final, and those that move to an entirely new final (unmistakably recognizable as a modulation).

8.2 It might seem that the most obvious way for a work to mark a change in system is through a signature change; this only happens, however, in three works from Ferdinand III’s court. Of the eight examples featuring a system change, these three are the only ones that bear any resemblance to tonal practice, for the immediate impression is of a switch between a major key and its parallel minor; the expressive effect, however, is not always what we might expect. Two of the works shall be examined in Chapter 10; for now, we focus on Ferdinand III’s setting of the Marian hymn Ave maris stella (Example 27; Audio Example 4).

8.3 Most of Ave maris stella is centered solidly in G durus. The opening ritornello (a later statement of which can be seen in the example) begins with a transpositional scheme similar to that in Sances’s Magnificemus in caelo (Example 5). A phrase emphasizing G and D is transposed up one step, thereby stressing A and E and grounding the harmonies in the center of the hard harmonic hexachord; by the end of the ritornello, the bass has traversed all pitches of the hard hexachord. At the start of the fifth verse (m. 166), however, the emperor heightens a stylistic change from triple to duple meter with a striking plunge down three systems to g duplex mollis. Even listeners who are not following a score and therefore cannot see the introduction of the flat in the signature are immediately alerted to the system change by the G-minor chord on the downbeat and the melodic B-flats in both voice and continuo in the first measure, which introduce a hexachord not available in cantus durus. An immediate transposition down a fifth introduces the two-flat melodic hexachord, and cantus duplex mollis is confirmed in m. 169 by the prominent A-flat (the flattest pitch in the system) in the bass.

8.4 Modern listeners, trained to hear shifts from major to minor as indicating a move from positive to negative emotional states, would likely interpret this system change as emphasizing a sorrowful or uncertain affect as the singer beseeches the Blessed Virgin for a life free from sin; this interpretation is seemingly confirmed by the fact that the joyful final line of the sixth stanza (“Semper collaetemur” [may we rejoice together forever]) returns to triple-meter cantus durus. Such a reading becomes strained, however, when one realizes that similar requests appear in earlier verses, where they are sung in the same lilting triple meter accompanied by durus harmonies found in the ritornello.[73] An important clue to the expressive significance of the system change is the fact that the shift back to triple meter and cantus durus in m. 182 occurs not just in the midst of the sixth verse but also in the middle of a poetic line, precisely on the word “Jesum.” The music thus sharply differentiates the Blessed Virgin from her son, and due to the use in the fifth verse of such adjectives as “singularis” (unique) and “castos” (spotless), this seems to be another piece that, like Sances’s Ardet cor meum discussed in par. 5.5 (Example 19), uses mollis harmonies to signify the Immaculate Conception, the feast of which occurred less than three weeks after the emperor composed the hymn.[74]

8.5 The other two examples of system changes over the same final occur in Sances’s Ardet cor meum and Audi Domine, both of which have finals of d. The system changes in these works are more difficult for modern listeners to discern than the one in Ferdinand III’s Ave maris stella, since in neither case does the final change its minor quality. Indeed, some might argue that these works do not change system at all, but in both cases the harmonic shift is accompanied by other stylistic changes that confirm its expressive function and argue in favor of a full-scale change in system. We shall here examine only Audi Domine, in which a system change from cantus mollis to cantus naturalis signifies a shift from imploring uncertainty to confidence in divine protection, thereby using mollis harmonies to emphasize pleading and durus harmonies to highlight the Lord’s action.[75]

8.6 Audi Domine opens with a recurring refrain sung in a homophonic style by the upper three (of four) voices (see Example 28 and Audio Example 5), who beseech the Lord to hear the prayer offered “today” by his servant. After establishing the final through alternations of D and A in mm. 1–2, the B-flat in the continuo on the downbeat of m. 3 introduces the soft melodic hexachord and pushes the harmonies into cantus mollis, which is confirmed by cadences on F (mm. 4–5) and C (mm. 7–8) and by the fact that there are no additional D or A chords until the final authentic cadence (mm. 10–11). The next section, sung by a solo bass in an affective recitative style, offers the prayer, stating that if the people repent and pray, the Lord will hear them and will deliver them from enemies. Although starting firmly in mollis territory, with a Phrygian cadence on A and an emphasis on F, B-flat, and C sonorities in mm. 15–17, the section gradually moves in a sharp direction. The first indication of this sharpward move is the tenor cadence on G approached from A (mm. 18–19), followed shortly by the first E-major chord in the work (m. 21), from which the bass rises in scalar fashion to a tenor cadence in which G is approached from an F-sharp in the bass (mm. 22). The scalar ascent continues in mm. 23–24, but the sharpward move is soon quashed by an unexpected B-flat in m. 24, which reintroduces the soft melodic hexachord as the section comes to a close and ushers in the return of the refrain.[76]

8.7 Another section for solo bass follows the second statement of the refrain, which sets a different text but nevertheless contains the same message and opens with the same melodic and harmonic figure as the previous solo section (Example 29; Audio Example 6). This section has an even stronger inclination for durus harmonies than the previous one, with frequent D-major, G-major, and A-major harmonies, as well as a tenor cadence on A approached from a B-natural in the bass (m. 54). This section ends with the same text as the previous bass section, and Sances set the words “tu exaudies de caelo Domine” (you shall hear them from Heaven, Lord) to the same phrase as before (mm. 58–59). Instead of ending with the E-major triad, however, this time the E chord resolves via a falling fifth to A, the first authentic cadence to this pitch in the work. This unexpected cadence is marked by an equally unexpected stylistic change, for the upper voices now enter with the same text, and all four voices join together for the first tutti texture in the motet. From here to the end of the work, the voices interact in a busy contrapuntal texture, a style that stands in strong contrast to the plodding, homophonic refrain and is completely unlike anything heard thus far in the work. The alteration of previously heard music, in combination with the introduction of a new style, signals a full-scale change of system from cantus mollis to cantus naturalis, a shift that is further confirmed by a small but telling melodic detail. In its first presentation, the melodic motive setting the words “tu exaudies de caelo” has a semitone between the second and third pitches, so it would be sung to the solmization syllables sol–fa–mi–re–ut in the natural melodic hexachord. When the motive is first sung by one of the upper voices (the canto) in mm. 59–60, however, the semitone moves to the third and fourth pitches, which means that the melody is now sung to la–sol–fa–mi–re in the hard melodic hexachord. This introduction of the hard melodic hexachord helps establish that the harmonies have indeed switched to cantus naturalis.

8.8 Although we occasionally still hear B-flats (both melodically and harmonically) after m. 60, the shift to cantus naturalis is confirmed by the predominance of G-major rather than G-minor triads, as well as by the evaded cadence in m. 72, which we expect to resolve to G but instead moves to E, thereby introducing a cadence point that is available in the natural but not the soft harmonic hexachord. In fact, all the B-flats that appear in this section can be explained by melodic procedures. For instance, after the reorientation of the “tu exaudies” motive to begin on la, the new solmization is used for each remaining appearance of the motive. Thus, the transposition of the motive to begin on D in mm. 63–64 necessitates a melodic B-flat to maintain the fa–mi between the third and fourth pitches; although some might argue that the introduction of the soft melodic hexachord negates the system change, it must be remembered that cantus naturalis contains the soft harmonic hexachord, thereby permitting the use of B-flats. After m. 66, the only other B-flat is in m. 81, where it appears as part of a descending melodic line in the bass that resolves to A, setting up the final cadence; whereas in m. 24 (at the end of the first solo bass section) the appearance of B-flat disrupted an ascending line and shattered a potential shift to a sharper system, here the B-flat fits comfortably into the firmly established cantus naturalis and supports rather than disturbs the movement to the cadence. With this system change from cantus mollis to cantus naturalis, Sances managed to change completely the meaning of a repeated text. Whereas on its first occurrence it is a conditional statement, declaring that God’s intervention and protection will come only if the people repent their sins, the change in system at the end of the work injects a ray of optimism, turning the conditional future statement into a positive vision of the future.[77]

9. Expressive Harmonies Incorporating Multiple Systems II: New System, New Final

9.1 The second type of system change is both easier for modern listeners to hear and yet at the same time harder to comprehend, for there often seems to be little reason as to why the music should move to that particular final. In all three of our examples, however, the relationship between the original and new finals is easily explained by the modal-hexachordal system and the harmonic grammar outlined in this article. In the three motets that feature shifts of both system and final (all by Ferdinand III), the new final occupies the same position on the new central harmonic hexachord that the previous final did on the original central hexachord. Thus, the result seems to be not so much a modulation from one mode to another as the wholesale transposition of a single system.

9.2 An excellent case in point is the emperor’s setting of the Corpus Christi hymn Pange lingua, in which a sharpward shift from cantus triplex mollis to cantus mollis in the final (doxology) verse emphasizes a shift from humble reverence to joyful praise. The first verse (Example 30; Audio Example 7) sets up c triplex mollis by solidly encompassing the three-flat harmonic hexachord; Ferdinand III achieves this with E-flat and A-flat triads in the second measure, with authentic cadences to E-flat (m. 3) and C (mm. 6, 8, and 10), and especially with a Phrygian cadence to G (m. 7). This establishes the harmonic palette for the next five verses, all of which feature cadences only on C, E-flat, and G, the latter always approached via either a Phrygian cadence from A-flat or an inverted Phrygian cadence from F. The final verse (mm. 49–82; see Example 31 and Audio Example 8) begins along the same lines, with a Phrygian cadence to G (m. 50), but this is immediately followed by a shift to triple meter and a D-minor triad (the sharpest pitch in the system), which initiates a descending tetrachord in the bass. The tetrachord concludes in m. 54 with a Phrygian cadence on A that outlines the one-flat harmonic hexachord, which lies beyond the harmonic limits of cantus triplex mollis. While the arrival on A seems to indicate that the harmonies have shifted, it is not yet clear that the final has changed, and because the following phrase (which immediately repeats, mm. 55–58 and 59–62) transposes the previous descending tetrachord down one step, the listener might think that the final is still C. Significantly, however, the previous la–sol–fa–mi hexachord now shifts to fa–mi–re–ut, thereby introducing the hard (!) melodic hexachord and solidly confirming the sharpward harmonic move. B-naturals disappear after m. 62; the harmonies of the entire verse lie comfortably within the soft harmonic hexachord, establishing that the work is in cantus mollis, and because the following phrase (mm. 63–66) begins and ends on D (with the bass presenting another descending tetrachord, this time with another D inserted before the A), that pitch begins to emerge as the final, which is confirmed by frequent authentic cadences on that pitch for the rest of the verse.[78] Whereas the previous final had occupied the fifth position in the three-flat harmonic hexachord, the new final in the last verse holds that same spot in the one-flat harmonic hexachord. The piece remains in cantus mollis for the first statement of “amen” in mm. 83–87, but then, following the same procedure discussed in par. 6.2 for the hexachordal shift in Ferdinand III’s Crudelis Herodes (Example 22), the phrase transposes down one step to bring us back to the original system. This reintroduces C-minor and A-flat-major triads, concluding the work back where it began. The C-minor triads in particular contrast sharply with the C-major chords heard earlier in the verse and thus help confirm a large-scale return to cantus triplex mollis.

9.3 Whereas the system change in Pange lingua is achieved through transposition and a clever interplay between C and D, in the remaining two examples the composer establishes the new finals primarily through frequency. In both works—the two double-final works discussed in par. 7.4 and 7.7 (Jesu redemptor omnium and Humanae salutis sator)—the system transposes one level from cantus naturalis to cantus mollis. In the above discussions, I proposed that the two finals symbolize the human (durus) and divine (mollis) and noted that in each work the system change coincides with text that emphasizes God’s greatest wonders (see Table 11 and Table 12). In Humanae salutis, the sonata following the first verse (mm. 42–61; see Example 32) establishes the new finals by presenting three transpositions of the same phrase, the first and last cadencing on C and the middle one on D, both of these being the new finals. The following two verses (mm. 62–84 and 101–31), which celebrate the Resurrection and Ascension, then center solidly on D, as does the sonata separating them (mm. 85–100). The shift is not marked by any dramatic stylistic features; in fact, the first indication that the harmonies have moved into mollis regions is the G-minor sonority in m. 48, and only the B-flat in the continuo in m. 70 solidly confirms the soft harmonic hexachord, followed shortly by a Phrygian cadence to A (mm. 74–76).[79] Ferdinand III establishes the new finals in Jesu redemptor omnium (F and d), which first appear in the sonata following the third verse (mm. 118–36; see Example 33), in a similar fashion as in Humanae salutis, with a phrase that appears four times at two different transposition levels.[80] In this case, however, the shift is more noticeable on account of the prominent B-flats in the bass and upper voices, which are especially surprising considering the emphasis on the sharpest side of the system early in the piece.[81]

10. Expressive Harmonies in Combination: Two Analyses

10.1 Up to this point I have considered the various types of expressive harmonies only in isolation, even for works (such as Ferdinand III’s Humanae salutis sator and Jesu redemptor omnium) that feature expressive harmonies of more than one type. To tie together the individual discussions of the different types of expressive harmonies, I conclude by offering analyses of two works that feature a number of expressive harmonies in combination.

10.2 Although not a motet, Bertali’s Lamento della regina d’Inghilterra, a setting of an Italian poem by Ferdinand III’s brother Archduke Leopold Wilhelm lamenting the 1649 execution of King Charles I of England (spoken in the voice of Charles’s widowed queen), presents superb examples of the means by which various types of expressive harmonies work in combination.[82] Set in g duplex mollis, this work uses a flat system to connote mourning, but the harmonies vary widely to depict the queen’s emotional instability and almost violent outbursts, shifting to such extreme sharp areas as to require the occasional signature change.

10.3 A notable aspect of the expressive harmonies in this work is the way in which instances of durus–mollis contrast, hexachordal shifts, and system changes all work in concert to facilitate powerful expressions of the queen’s emotions. This is apparent already in the second section (the singer’s entrance following an opening instrumental sonata, mm. 26–69), which presents the queen’s opening words (Example 34). The passage begins solidly in cantus duplex mollis, with phrases that cadence on G (the final, mm. 26–30), E-flat (the flattest pitch in the two-flat harmonic hexachord, mm. 31–34), and F (mm. 35–40) before returning to the final in m. 44. The return to G is achieved through the transposition of a short motive on the words “è morto,” which Bertali first transposes down a fifth (thus emphasizing flat harmonies) and then down one step to cadence on G. The following two measures transpose the motive one last time, this time up a fifth, which moves sharpward to an authentic cadence on D (the sharpest pitch in the two-flat harmonic hexachord). The arrival on D seems to signal a shift in the sharp direction, and indeed, the B-natural in the bass in m. 47 initiates a hexachordal shift to the natural harmonic hexachord (which is not available in cantus duplex durus) as the queen begins to think of “the deed of a disloyal people” (Il fatto … Di gente infidele). An authentic cadence to A (using E, the sharpest pitch on the natural harmonic hexachord) confirms the hexachordal shift at the end of the poetic line (mm. 51–52), while the next poetic line (mm. 53–56) concludes with another cadence on D.[83] Both lines are then sung a second time to the same melody, now transposed up a fifth, with a change in the bass pitch in the fourth measure that introduces a Phrygian cadence to E in mm. 60–61. This Phrygian cadence does more than just outline the natural hexachord, for it also heralds a full-scale system change to cantus naturalis, indicated in the score with a signature change in m. 61, precisely on the arrival of the E cadence. The D–C-sharp motion in the voice in m. 62 (which mimics exactly the intervallic treatment of the first statement of this melody in m. 53) emphasizes the system change, as does an altered treatment of the final two measures, which produces an F-sharp in the voice and an authentic cadence to D in the bass. The last poetic line then repeats one last time, sung to the same melody transposed down one step. This transposition produces harmonies that sit squarely in the center of the natural harmonic hexachord (C, G, and D), but notably, the solmization changes. The melody now begins on la instead of sol, which introduces expressive B-flats and E-flats in the melody and creates G-minor and C-minor triads that ensure the listener retains a memory of the original mollis harmonies.

10.4 The following section for the bass narrator (mm. 70–81) begins with harmonies that could still be interpreted as cantus naturalis, including a Phrygian cadence on A (mm. 72–73) and A-major and D-major triads; only the G-minor chord that opens the section provides any indication that the music has moved back to a mollis system. To firmly restore cantus duplex mollis, Bertali introduces an instance of durus–mollis contrast in mm. 76–79. Within the space of just four measures we hear both an A-major triad (in the authentic cadence to D in m. 76) and an A-flat-major triad (m. 79); this use of the outermost pitches of cantus duplex mollis in close proximity leaves no doubt that the music has returned to its original system. In these two sections, then, both a hexachordal shift and durus–mollis contrast help enact a change in system; the hexachordal shift prepares the change, while the durus–mollis contrast confirms the return to the original system.

10.5 Every section of this piece is worthy of close examination, but I shall look at just one other example of a hexachordal shift used to prepare a system change in the sharp direction; this example is notable for its brief move to an extreme sharp system—cantus duplex durus—found nowhere in the surviving Habsburg motet repertoire (see Example 35 and Table 13). In m. 102, the queen calls out to Jove, accusing him of cruelty for not changing her into another living being, despite the fact that he has done so for so many others. This passage coincides with a hexachordal shift to the hard hexachord, introduced abruptly by a D-major triad after the F-major cadence in m. 101, thereby contrasting mollis harmonies depicting the queen’s “sorrow” (dolore) with durus harmonies for Jove’s cruelty. Measures 102–11 contain all the harmonies of the new hexachord, highlighted further through cadences on A (m. 107) and E (m. 109), both approached from B-natural. An instance of extreme durus–mollis contrast—a sudden plunge to very flat harmonies marked by the introduction of a B-flat-minor triad in m. 111—then powerfully expresses the queen’s change of heart as she stops berating Jove and instead pleads with him to change her into another form, the mollis harmonies carrying their conventional association with pleading. However, as she (like Monteverdi’s Ariadne) snaps back to her senses in m. 115, the music returns to more durus territory, with an A-major triad that resolves via authentic cadence to D (m. 116). The queen now begins to steel herself to take her own life; appropriately, it is at this moment that we hear the most durus harmonies in the work. A signature change over an authentic cadence to E (mm. 118–19) marks the appearance of a new system, and a tenor cadence to B approached via C-sharp in the bass (mm. 121–22) confirms that the music has moved as far as the cantus duplex durus. The harmonies do not stay there long, however, for the very next chord, a G-minor triad, returns to a flatter realm (accompanied by the return of the flat signature), and the following sonata (mm. 130–42) reestablishes cantus duplex mollis via an instance of durus–mollis contrast that places A-flat and A-natural in the bass in the space of four measures (mm. 131–34).  Even with the sharpward move interrupted by an instance of durus–mollis contrast, the hexachordal shift still helps prepare the way for a system change, and once again it is another instance of durus–mollis contrast that confirms the return to the original system.

10.6 I conclude this study with a piece that not only features the most adventurous harmonies of all Ferdinand III’s motets but that was also by far the emperor’s most well-known work in his lifetime and beyond: his Miserere, a setting of the penitential Psalm 50 for twelve solo voices and ripieno choir.[84] As mentioned in par. 7.5, this is a double-final work, based on the finals g and a in cantus mollis, but it combines the double finals with various other expressive harmonies, including durus–mollis contrast, hexachordal shifts, and system changes; the piece even ends in a different system from where it begins. The use of cantus mollis creates an effect very different from that in the two G/a-naturalis works discussed in Chapter 7; whereas in cantus naturalis the two finals both appear roughly in the middle of the central harmonic hexachord, this system contrasts one final in the middle of the soft harmonic hexachord (g) with one on the very sharp edge of it (a). This allows for an expressive use of the two finals that is also very different from the other works: throughout the setting, mollis harmonies are used to express not divinity but the somber, mournful, imploring mood of the penitent sinner. The flatter final is thus used to symbolize mankind’s sinful nature, and the sharper (or better, more natural) final the state of grace for which sinners yearn. This harmonic symbolism is apparent already in the first section of the work (Example 36). Although the piece begins with an A in the bass, g is quickly established as the final through duration, frequency, and an authentic cadence in m. 7; the harmonic space is revealed as cantus mollis by an emphasis on harmonies flatter than G, including C minor, B-flat major, and E-flat major. The last phrase (mm. 8–10), however, uses a downward stepwise transposition to end on an authentic cadence on A for the words “misericordiam tuam” (your mercy), thereby emphasizing through the sharpest pitches in the system that which sets the sinner free (see Table 14 for a line-by-line explication of the harmonies; passages that contain hexachordal shifts or system changes have been placed in bold).

10.7 The first notable expressive harmony occurs in the fifth section (mm. 43–57), during which the singers begin to confess their sins (see Example 37). The section starts with a G-minor triad, but the crucial word “peccavi” (I have sinned) is set to a sequence of four Phrygian cadences (mm. 43–46); the first is on D (using E-flat, the flattest pitch in the system), and each succeeding cadence moves a fifth sharper, ending on a B-major triad, a harmony that lies outside the system. This sequential repetition of an expressive Phrygian cadence has enacted a hexachordal shift to the hard harmonic hexachord; indeed, by m. 52, we have heard harmonies on all pitches of this hexachord, thanks to a melodic and harmonic sequence in mm. 49–51.[85] This sharpward move expresses the importance of confession as a means to grace; surely it is no accident that the very next section (mm. 58–67) features the first signature change, shifting the system temporarily to cantus naturalis.

10.8 Another significant combination of expressive harmonies appears in the ninth and tenth sections (mm. 88–124), in which the singers anticipate the great joy that will come from the absolving of sins (see Example 38 and Table 15). The ninth section (mm. 88–118) uses the two finals as a means of achieving large-scale durusmollis contrast across the section; the first syntactic unit  (“Auditui meo dabis gaudium et laetitiam” [you shall give joy and delight to my hearing], mm. 88–104) emphasizes the flat harmonies in the system and the g final, while the second syntactic unit (“et exultabunt ossa humiliata” [and my humbled bones shall rejoice], mm. 105–18) emphasizes the sharp side, using primarily D, A, and E harmonies and cadencing repeatedly on A. This large-scale durusmollis contrast helps prepare us for the tenth section (mm. 119–24), in which small-scale durusmollis contrast leads to a dramatic, unexpected hexachordal shift in the sharp direction. The verse opens on an A-minor triad and leads to a Phrygian cadence on E for the words “Averte faciem tuam” (turn your face). When the singers utter what they want the Lord to turn his face from—“a peccatis meis” (from my sins)—the harmonies are transposed down a step to begin on G and end with a Phrygian cadence to D; these four measures include harmonies spanning the entire cantus mollis, but more importantly, they clearly contrast the Lord (A) with human sins (G). As the singers go on to ask God to erase their iniquities (“et omnes iniquitates meas dele,” mm. 22–4), an E-natural in the bass (the third of a C-major chord) initiates another shift to the hard hexachord, which is confirmed by the authentic cadence to E that concludes the section.

10.9 After this moment, the harmonies continue to alternate between flatter areas centered on G and sharper areas centered on A and D; in the eighteenth section (mm. 236–44), however, the harmonies return squarely to G as the singers begin to discuss the afflicted spirit as a sacrifice to God. This pitch continues to serve as the final as the doxology commences in m. 273, but this is far from the end of the story. As the full eight-part choir enters with the second syntactic unit of the doxology in m. 291 (Example 39 and Table 16), an authentic cadence to G (m. 292) is immediately followed by an authentic cadence to the second final of A (mm. 293–94), presaging a shift in the sharp direction for the end of the piece. Indeed, the syntactic unit ends on a Phrygian cadence to B (mm. 296–97), landing the harmonies squarely in cantus naturalis (even in the absence of a signature change), where the music remains for the rest of the piece. The final four-fold statement of “amen” (mm. 297–300) traverses much of the new system from B to F before ultimately landing on an authentic cadence to A, magnificently concluding the work in the full glory of God’s benevolence to contrite sinners. For modern listeners who approach this work with tonal—or even modal—expectations, this ending seems inexplicably in the “wrong key,” both because it is not on the G tonic and also because the B harmony in m. 297 contradicts the key signature and is foreign to the work’s predominant harmonic vocabulary. When considered according to the norms of the harmonic grammar explicated in this article, however, it becomes comprehensible as a combination of double finals with a system change for powerful expressive effect.

11. Conclusion

11.1 Much work remains to be done. What holds for the harmonic language of the motets from Ferdinand III’s court may very well not be true for all mid-seventeenth-century music, so it is important to now test these findings by applying my premises and analytical approach to other repertoires by other composers from other geographical locales. In doing so, it might prove possible to further refine the “normative background of expectable musical relationships,” or we might discover that what I identified as expressive transgressions in the Habsburg motet repertoire exist as normative practice elsewhere. In addition, it may yet prove possible to bring mode back into the picture; by combining the analytical approach offered here with contemporaneous modal theory we may yet be able to illuminate how composers conceptualized mode as harmonic practice, thereby providing even more insights into both compositional practice and musical meaning in the seventeenth century. Considering the almost exclusive focus on harmonies in this article, I must stress that harmonic analysis alone does not a complete analysis make; expressive harmonies often make complete sense only when considered in tandem with melodic, textural, contrapuntal, and other stylistic features. Indeed, I demonstrated this in many of the examples, such as those that employ melodic sequencing or transposition, as well as those that support harmonic shifts with the use of melodic hexachords. All the same, harmony is an undeniably important conveyor of musical expression, and it is hoped that this article has offered a valuable first step in elucidating a long-lost harmonic grammar through which we can better understand otherwise incomprehensible harmonies and catch nuances of text expression that our tonal ears miss.


Work on various aspects of this article was supported by Grants-in-Aid from The Catholic University of America. I am deeply grateful to Steven Saunders and the Journal’s anonymous reviewers for challenging and pushing me to rethink and refine my ideas over the course of several rounds of revisions, and to Bruce Gustafson and Kelley Harness for their patience and support during the article’s extremely long gestation.


Appendix. Surviving motets from the Habsburg court of Ferdinand III


Example 1. Example 1. Cadence types in the Habsburg motet repertoire

Example 2. Georg Pichelmair, Canite tuba in Sion, mm. 1–18

Example 3. Johann Jakob Froberger, Apparuerunt apostolis, mm. 1–16

Example 4. Antonio Bertali, Exultate et cantate, mm. 1–17 (Audio Example 1)

Example 5. Giovanni Felice Sances, Magnificemus in cantico, mm. 1–24

Example 6. Antonio Bertali, Exultate et cantate, mm. 43–56 (Audio Example 2)

Example 7. Giovanni Felice Sances, Domine ne memineris, mm. 1–10

Example 8. Ferdinand III, Jesu corona virginum, mm. 1–6

Example 9. Giovanni Felice Sances, Iste confessor, mm. 1–15

Example 10. Antonio Bertali, Exultate et cantate, mm. 112–24 (Audio Example 3)

Example 11. Giovanni Felice Sances, O dulcis virgo virginum, mm. 48–70

Example 12. Giovanni Felice Sances, O Jesu mi dulcissime, mm. 89–97

Example 13. Giovanni Felice Sances, Miserere servorum tuorum, mm. 117–30

Example 14. Giovanni Felice Sances, Gaude Virgo, mm. 41–49

Example 15. Giovanni Felice Sances, Plagae tuae, Domine, mm. 57–66

Example 16. Ferdinand III, Crudelis Herodes, mm. 71–82

Example 17. Giovanni Felice Sances, Dulcis amor Jesu, mm. 45–54

Example 18. Ferdinand III, Popule meus, mm. 53–75

Example 19. Giovanni Felice Sances, Ardet cor meum, mm. 1–48

Example 20. Giovanni Felice Sances, O Maria Dei genitrix, mm. 1–48

Example 21. Giovanni Felice Sances, Veni sponsa Christi, mm. 76–89

Example 22. Ferdinand III, Crudelis Herodes, mm. 175–89

Example 23. Giovanni Felice Sances, O crux benedicta (1642), mm. 36–64

Example 24. Ferdinand III, Veni creator spiritus, mm. 1–36

Example 25. Ferdinand III, Deus misereatur nostri, mm. 1–30

Example 26. Ferdinand III, Humanae salutis sator, mm. 1–41

Example 27. Ferdinand III, Ave maris stella, mm. 150–93 (Audio Example 4)

Example 28. Giovanni Felice Sances, Audi Domine, mm. 1–28 (Audio Example 5)

Example 29. Giovanni Felice Sances, Audi Domine, mm. 49–85 (Audio Example 6)

Example 30. Ferdinand III, Pange lingua, mm. 1–10 (Audio Example 7)

Example 31. Ferdinand III, Pange lingua, mm. 49–97, voices and continuo only (Audio Example 8)

Example 32. Ferdinand III, Humanae salutis sator, mm. 42–84

Example 33. Ferdinand III, Jesu redemptor omnium, mm. 118–36

Example 34. Antonio Bertali, Lamento della regina d’Inghilterra, mm. 26–81

Example 35. Antonio Bertali, Lamento della regina d’Inghilterra, mm. 100–135

Example 36. Ferdinand III, Miserere, mm. 1–10

Example 37. Ferdinand III, Miserere, mm. 43–57

Example 38. Ferdinand III, Miserere, mm. 88–124

Example 39. Ferdinand III, Miserere, mm. 291–300

Audio Examples

Audio Example 1. Antonio Bertali, Exultate et cantate, mm. 1–17.

Audio Example 2. Antonio Bertali, Exultate et cantate, mm. 43–56.

Audio Example 3. Antonio Bertali, Exultate et cantate, mm. 112–24.

Antonio Bertali, Exultate et cantate, complete.

Audio Example 4. Ferdinand III, Ave maris stella, mm. 150–93.

Ferdinand III, Ave maris stella, complete.

Audio Example 5. Giovanni Felice Sances, Audi Domine, mm. 1–28.

Audio Example 6. Giovanni Felice Sances, Audi Domine, mm. 49–85.

Giovanni Felice Sances, Audi Domine, complete.

Audio Example 7. Ferdinand III, Pange lingua, mm. 1–10.

Audio Example 8. Ferdinand III, Pange lingua, mm. 49–97.

Ferdinand III, Pange lingua, complete.


Table 1. Table 1. The arrangement of hexachords in the modal-hexachordal system

Table 2. Length of time each sonority is heard in Pichelmair, Canite tuba in Sion, mm. 1–18

Table 3. Length of time each sonority is heard in Bertali, Exultate et cantate, mm. 1–17

Table 4. Length of time each sonority is heard in Sances, Magnificemus in cantico, mm. 1–24

Table 5. Analytical map of Pichelmair, Canite tuba in Sion (complete)

Table 6. Table 6. Legend of symbols used in analytical maps

Table 7. Analytical map of Sances, Iste confessor, mm. 1–15

Table 8. Length of time each sonority is heard in Sances, Iste confessor, mm. 1–15

Table 9. Analytical map of Sances, O Maria Dei genitrix, mm. 1–48

Table 10. Line-by-line explication of the main harmonies in Ferdinand III, Veni creator Spiritus

Table 11. Verse-by-verse explication of the main harmonies in Ferdinand III, Jesu redemptor omnium

Table 12. Line-by-line explication of the main harmonies in Ferdinand III, Humanae salutis sator

Table 13. Analytical map of Bertali, Lamento della regina d’Inghilterra, mm. 100–135

Table 14. Line-by-line explication of the main harmonies in Ferdinand III, Miserere

Table 15. Analytical map of Ferdinand III, Miserere, mm. 88–124

Table 16. Analytical map of Ferdinand III, Miserere, mm. 291–300

Copyright © 1995-2018 Society for Seventeenth-Century Music. All Rights Reserved.