The Semantic Evolution of Chromatic Mediants: A Baroque Origin of M8M Progressions^*

Introduction

[0.1] In contemporary film and popular music, chromatic mediants (CMs) often signify the “magical,” the “fantastical,” and similar ideas.⁽¹⁾ Example 1 presents a scene from the 1988 film Dirty Rotten Scoundrels and Erik Heine’s (2018) transcription of Miles Goodman’s score to the scene. In this scene, the character Freddy, a con artist, “magically” regains his ability to walk after feigning paralysis. The soundtrack underscores this moment with major triads a major third apart, which constitute two CM pairs (E+ and C+, C+ and A♭+).⁽²⁾ As Heine (2018, 113–14) argues, the CM progressions (which Heine calls the “Magic” motion) heighten the dramatic impact of Freddy’s supposedly miraculous recovery, adding to this scene an aura of mockery and humor.

[0.2] The expressive and narrative use of CMs to evoke the magical and the fantastical in film and popular music has been traced back not only to (post-)Romantic chromaticism (Cohn 2004, 2012a, 2012b; Forrest 2017a; Heetderks 2015; Taruskin 2010) and Richard Wagner’s Musikdrama (Bribitzer-Stull 2012; Hunt 2007), but also to Italian operas of the early nineteenth century (Rothstein 2008, 2023). Example 2 summarizes the many narrative connotations associated with CMs that scholars have described in various repertoires. Despite the evocative power of CMs since the nineteenth century, little evidence exists on how pre-Romantic composers established the convention of using CMs for narrative purposes. This article examines the question of how CMs first gained their extra-musical connotations and became a viable musical sign by convention.

[0.3] To trace the conventional origins of the semantics of CMs, I propose a lineage through which CMs—particularly the descending major-third motion of major triads (as seen in Example 1)—gained their narrative meaning from Baroque music. My argument unfolds in five parts. First, supplementing Richard Cohn’s (2004, 2012a, 2012b) argument by homology, I explain the semantics of CMs by convention. Second, I describe how the juxtaposition of two conventional Baroque compositional devices—Phrygian half cadences (HCs) and bifocal tonality, to be formally introduced below—constitutes bifocal transitions between movements in Baroque instrumental works. The bifocal transition provides a musical context that fosters the narrative potential of CMs. Third, through examples from Baroque vocal music, I demonstrate that bifocal transitions following Phrygian HCs endow the resulting CMs with a connotation of death-to-life transcendence, representing a semantic synthesis of the two devices. As the CMs became recognizable to composers and listeners as a distinct musical symbol, their meaning expanded to encompass the broader conceptions of the magical, the dramatic, and the miraculous. Fourth, I discuss musical examples from Classical works that adopt the Baroque convention of combining HCs and bifocal tonality to portray death-to-life transcendence and related conceptions. Last, I examine how CMs in Classical works retained their semantic connotation, even as they dissociated from the formal context of the half cadence and took on other formal functions. In sum, this article expands current scholarship by showing that the semantic evolution of CMs predates nineteenth-century chromaticism and proposing that the narrative connotations of CMs arise from the combination of two initially distinct compositional devices in the Baroque.

1. The homology-vs.-convention argument

[1.1] To introduce the semantic evolution of CMs, I consider the nature of musical signs with respect to Charles Peirce’s (1960) triadic classification of signs—icon, index, and symbol.⁽³⁾ Daniel Chandler (2022, 42–59) offers a succinct account of these three types of relations between signs and their objects. In Chandler’s (2022, 42–43) words, the signifying power of an icon depends on a “perceived resemblance . . . involving some recognizably similar quality,” an index on a “direct connection (physical or causal),” and a symbol on a “fundamentally unmotivated, arbitrary, or purely conventional” association. While signs typically involve one of these three relationships, Peirce’s tripartite classification is contextual, and the categories can sometimes overlap (Chandler 2022, 43).

[1.2] For a musical example, consider how the appoggiatura (followed by its downward resolution) represents grief, a gesture often referred to as the “sigh motif” or the Seufzer topic (Agawu 1991, 30; Mirka 2014, 40–41; Taruskin 2010, 91). In Example 3, appoggiaturas in the solo violin part (indicated by arrows) illustrate a musical gesture that “mediates continuously between the impulse towards striving and the weight of grief” (Cumming 1997, 22). This gesture of grief takes place in an aria from St. Matthew Passion, where the violin represents the listener’s persona that empathizes with “Peter’s grieved state” after his denial of Jesus (Cumming 1997, 18). The appoggiatura’s signification involves both iconic and symbolic relations. It is iconic because the downward pitch motion sonically resembles a sorrowful sigh, and symbolic because this representation has been reinforced through conventional association (Monelle 1992, 199). Since the relationship between an icon and its object relies on similarity but not identity, some degree of conventionalization is necessary to reinforce the sign’s meaning (Chandler 2022, 50–51).

[1.3] Musical signs are non-specific in that their meaning is inherently flexible. They are characterized by their “semantic range,” which could encompass multiple meanings (Swain 1997, 44–58). For instance, while appoggiaturas may represent grief, as shown in Example 3, their presence does not always carry this specific connotation. As Robert Hatten (2006, 4) suggests, in the Classical style, the appoggiatura figure does not necessarily represent the sigh motif, but may instead contribute to a formulaic cadential gesture related to “the galant gesture of ‘graciousness.’” Similarly, a flute trill can signify birdsong—functioning as an icon—when supported by contextual cues such as nature-related lyrics and the pastorale topic, as in the aria “Augelletti, che cantate” in George Frideric Handel’s Rinaldo (Monelle 2006, 235). Alternatively, as in Franz Waxman’s film score for Sunset Boulevard, the flute trill symbolizes Norma Desmond’s “delusional persona” and “madness” (Lawson and MacDonald 2018, 266). Thus, the semantic range of a flute trill encompasses multiple meanings, and it does not always represent birdsong, despite its iconic resemblance. For the iconic signification to be activated, the trill must be placed in an appropriate musical context—one that is readily available in the musical style (such as cues related to the pastorale topic). Mere resemblance between the signifier and the signified is not sufficient for establishing an iconic signification; conventional reinforcement within a recognized musical context is also necessary.

[1.4] Regarding the signifying relationship between CMs and the uncanny, Cohn (2004, 286) argues that this signification arises “not only by convention, but also in part from a homology between the properties of uncanniness . . . and those of the harmonic progression.” By “homology,” Cohn refers to an intrinsic resemblance between CMs and the quality of uncanniness (2012b), which encompasses notions such as the “paradoxical, supernatural, magical, weird, dark, [and] dead” (2004, 285). In discussing how CMs express uncanniness, Cohn identifies the hexatonic pole as the prototype for CMs, arguing that intervallic properties of the hexatonic pole evoke a paradox of contradicting harmonic and voice-leading expectations (2004, 303–6; 2012a, 17–25; 2012b, 50–52).⁽⁴⁾ Such intervallic properties are present not only in the hexatonic pole, but also in other CM progressions (Cohn 2004, 22; Murphy 2014a, 308). Example 4 illustrates Cohn’s homology argument with the CM pair of E+ and C+ triads. Although these juxtaposed triads are related by parsimonious voice-leading with semitone steps, their relation is also characterized by non-diatonic intervals. As shown in Example 4a, if these two triads are spelled diatonically, the semitone step between G♯ and G♮ of the respective triads will be an augmented unison instead of a minor second, which is the perceptual default for notes that are a semitone apart (Temperley 2001, 128). Alternative spellings could reinterpret this semitone interval as minor seconds, but this would result in dissonant spellings for the triads. The C+ triad would then include the harmonic intervals of an augmented second and a doubly diminished fifth (Example 4b), or the E+ triad a diminished fourth and an augmented second (Example 4c). Cohn argues that this paradox—where supposedly consonant triads consist of dissonant intervals—is uncanny and contributes to the iconic signifying power of CMs. Therefore, according to Cohn, the semiotic association between CMs (exemplified by the hexatonic pole) and the uncanny is not arbitrary (as a symbol would be)—but iconic, substantiated by a resemblance between intrinsic properties of the CM triads and the notion of uncanniness.⁽⁵⁾

[1.5] Cohn only briefly acknowledges the role of convention in the signifying relationship between CMs and the uncanny.⁽⁶⁾ His 2004 article focuses on the association between hexatonic poles and the nineteenth-century notion of the uncanny, instead of the historical trajectory of the semantics of CM. Consequently, his homology argument and the bulk of nineteenth- and twentieth-century musical examples suffice for the purpose of that article. Cohn’s (2004, 291–94) compendium of hexatonic-pole examples includes only a few pre-nineteenth-century works—two by Carlo Gesualdo, one by Claudio Monteverdi, and one by Joseph Haydn. As Cohn (2004, 293) explains, these earlier passages are not proper examples of the musical uncanny, since they do not fit into a consolidated framework of tonal expectations, but are rather “potential model[s] . . . for later generations.” Compared with the typical musical syntax of their times, these examples are so peculiar and experimental that they do not demonstrate the existence of a convention by which pre-Romantic composers convey the meanings of CMs in the contemporaneous musical language. For CMs to function as musical signs of the uncanny—or other related labels—there should be “a cultural context that recognizes the conventional associations” of such signification (Agawu 1991, 16). Therefore, to enhance our understanding of the semantic evolution of CMs, I propose to supplement Cohn’s work by exploring the conventional aspects of such practice and examining musical examples from before the mid-nineteenth century.

[1.6] William Rothstein traces the semantic evolution of CMs to Italian operas of the early nineteenth century, particularly those by Gioachino Rossini.⁽⁷⁾ He analyzes a cabaletta in Rossini’s 1813 opera Tancredi, in which the title character’s tribute to Amenaide’s radiant eyes brings about a CM progression from C+ to A♭+ (Rothstein 2008, [16]; 2023, 197–99). Example 5 reproduces this passage from the cabaletta. The CM relation between C+ and A♭+ in mm. 101–2 enhances the dramatic impact of this passage: this “thrilling” progression heightens Tancredi’s longing for his lost lover and evokes a fantastical vision of her (Rothstein 2008, [16]). This example indicates that composers have been exploiting the semantic potential of CMs at least since the early nineteenth century, suggesting that tracing the semantic evolution of CMs could be a fruitful avenue of inquiry. In the rest of this paper, I examine how composers before Rossini have shaped the semantic connotations of CMs and how this signification is manifested within contemporaneous musical syntax.

[1.7] Among multiple possible CM relations,⁽⁸⁾ this study focuses on one specific type—a major triad going down a major third to another major triad. This triadic progression corresponds to a PL transformation of a major triad in neo-Riemannian terminology (abbreviated as PL(M) in Lehman [2018]), or an M8M progression—the uppercase M’s indicate that both triads of the CM pair are major triads, and 8 refers to the ordered pitch-class interval between the root of the triads (Forrest 2022).⁽⁹⁾ Despite the exclusion of other CM progressions, I argue that, for two reasons, the M8M progression serves as a prototype for the semantic effects of other CM relations. First, as both Matthew Bribitzer-Stull (2006, 169) and David Kopp (2002, 11) suggest, M8M is the most common type of CM relation in nineteenth-century music—including Rossini’s operas (Rothstein 2023, 194)—and also the first to be widely used. Second, different types of CMs may be considered analogous to each other in terms of their semantic effect. Rothstein observes that Rossini treats various CM relations as equally effective portrayals of “miraculous moments” in his operas (2023, 203).⁽¹⁰⁾ Similarly, Cohn argues that the hexatonic pole, on which his study focuses, is the semantic prototype for other CM relations. More specifically, the hexatonic pole represents the most expressively intense form of CM relation, and other CM relations are “milder version[s] of the same effect” (2012b, 51).⁽¹¹⁾ These findings suggest an overlap in the semantic effects of different CM relations. Therefore, as I explore the Baroque origin of the semantics of CMs, I propose that the M8M type originating from the Baroque model may have served as a prototype that later composers develop to achieve similar effects.

2. Phrygian HC, bifocal transition, and M8M CMs in Baroque instrumental works

[2.1] Two conventional Baroque compositional devices form the foundation of the semantic evolution of M8M CMs.⁽¹²⁾ The first is the use of Phrygian inflections, which relate to the long-standing association between the Phrygian mode and the musical portrayal of death (Kimmel 1980; McDowell 1991). A characteristic feature of the Phrygian mode is the Phrygian tetrachord (Example 6a), often referred to as the “lament bass,” consisting of a whole-whole-half stepwise descent leading to the Phrygian final. In a tonal context, the Phrygian tetrachord corresponds to scale degrees $\hat{1}$–$\hat{7}$–$\hat{6}$–$\hat{5}$ of a (natural) minor scale. In a modal framework where the Phrygian final serves as the first degree of the scale, the tetrachord maps onto scale degrees $\hat{4}$-$\hat{3}$–$\hat{2}$–$\hat{1}$.⁽¹³⁾ When articulated in the context of a minor key (often embellished with chromatic passing tones), this descending tetrachord evokes the Phrygian mode, symbolizing death and lamentation (Rosand 1979; Williams 1997). Nonetheless, it is not necessary to introduce the entire Phrygian tetrachord to invoke death; the final semitone descent alone functions as a Phrygian inflection that carries the same connotation (Example 6b) (Biamonte 2012, 59; Kimmel 1980, 55–57; Schachter 1995, 152). Since the Phrygian final is interpreted as mi in solmization (Hynes-Tawa 2020; Judd 1992; Powers [1998] 2014), William Kimmel (1980, 47) calls this semitone descent the “fa-mi inflection.” The descending diatonic or chromatic tetrachord—or simply its final semitone descent—in the bass line can articulate an HC in a minor key,⁽¹⁴⁾ with the Phrygian final functioning as scale degree $\hat{5}$ and supporting the dominant harmony (Example 6c). As I will show in section 3, the death association of Phrygian HCs in Baroque vocal music plays a crucial role in the semantic evolution of M8M CMs.

[2.2] Another Baroque device that contributes to the semantic evolution of CMs is bifocal tonality, a term coined by Jan LaRue ([1957] 2001). LaRue observes that Baroque composers often treated relative key pairs (e.g., C major and A minor) as a unified harmonic area. This principle implies that a V chord in a minor key could also function as a dominant to the tonic in its relative major.⁽¹⁵⁾ The bifocal transition—referring to the progression from V/vi to I in the relative major or from V to III in the relative minor (Example 7)—offers an alternative to the fifth-related dominant-tonic root motion, which becomes a general expectation as tonal musical thinking crystallizes in the late sixteenth century (Long 2020). This concept of bifocal transition is historically exemplified in Francesco Gasparini’s 1708 treatise on keyboard harmony (Example 8), where he illustrates bifocal transitions that follow a Phrygian-tetrachord bass line in three different keys. Gasparini describes these progressions as “a kind of cadence, coming to rest on a note with its major third [the dominant (V)], and then makes a new start, moving to the third below [the relative major tonic (III)]” (translated in Stillings 1963, 39).⁽¹⁶⁾ In other words, as shown in Example 7, a Phrygian HC in a minor key does not necessarily move to its tonic, but may instead lead to the tonic of its relative major.

[2.3] Regarding my discussion of the bifocal transition as a distinct musical unit, one might argue that the Phrygian HC signals a sense of closure, thus disconnecting the triads that form the CM relation. Nonetheless, in Poundie Burstein’s (2014) words, the status of HCs as an ending formal unit is often “slippery” and “paradoxical.” Due to the dominant-tonic tension that has emerged since the late-sixteenth century (Long 2020), HCs create a “harmonic volatility” that undermines the sense of closure (Burstein 2015, 85). Additionally, Liam Hynes-Tawa’s (2020, 230–31) historical study shows that, even in pre-tonal music set in the Phrygian mode, the Phrygian cadence exhibits a “general, trans-historical lack of finality” and “always . . . keep[s] something expressly unresolved.” Along with the arguments for the lack of finality of the Phrygian cadence, the musical examples I present in sections 3–5 demonstrate how the textual and narrative ties that straddle the bifocal transition and the proximate temporal connection of the triads lead one to perceive the CMs as a continuous event.

[2.4] The following musical examples demonstrate the juxtaposition of Phrygian HC and bifocal transition. More importantly, they show how M8M CMs arise from this conventional pairing of the two compositional devices. The combination of these two devices pervades multi-movement instrumental works of the Baroque. One notable example—also mentioned in LaRue ([1957] 2001, 284)—is from Johann Sebastian Bach’s Brandenburg Concerto no. 3 (Example 9), where the one-measure inner movement comprises only a Phrygian HC in E minor and precedes a finale in G major, the relative major of the inner movement and the home key of the concerto.⁽¹⁷⁾ The juxtaposition of the V of vi (B+) and the major tonic (G+) forms a bifocal transition that creates an M8M CM progression.

[2.5] LaRue ([1957] 2001, 286) identifies sonatas and concertos by Arcangelo Corelli as a major source of this model of inter-movement transitions linking the inner slow movement and the finale.⁽¹⁸⁾ Example 10 shows one such case, in which an inner movement (the Corrente) ends with an HC over a Phrygian tetrachord and leads into the Allemanda in the relative major, forming an M8M progression from E+ to C+. Bifocal transitions like this are present in works by many seventeenth- and early eighteenth-century composers, in addition to J. S. Bach and Corelli. LaRue ([1957] 2001, 286, 289–92) offers an extensive list of Baroque instrumental works that feature bifocal transitions, written by composers such as Antonio Vivaldi, Alessandro Scarlatti, Georg Philipp Telemann, and Dieterich Buxtehude. As LaRue ([1957] 2001, 291) suggests, the model of bifocal transition was so conventional that “our descending third progression must have seemed entirely usual to Baroque ears.”

[2.6] This Baroque model of inter-movement transition has influenced sonata form, where formal junctures typically associated with dominant harmony may also involve M8M relations. James Hepokoski and Warren Darcy (2006, 26) refer to the i:HC medial caesura that leads into a secondary theme in the relative major as “the second-level default” for expositions of minor-key sonatas. Burstein (2020, 75–80) discusses the bifocal exposition in Galant sonatas and Heinrich Christoph Koch’s interpretations of such transitions. In addition to sonata expositions, development sections could also stand on V/vi or III♯ (instead of V of the home key) before the recapitulation of the major tonic of the home key.⁽¹⁹⁾ While one could study the syntactic parallels between bifocal transitions in Baroque works and their counterparts in sonata theory, I now focus on the Baroque origin of the semantic evolution of CMs. Although these two approaches—syntactic and semantic—pursue different objectives, they are compatible and can synergize in future studies to offer a more holistic understanding of the development of bifocal transitions and M8M progressions.

3. Semantic synthesis of M8M CMs in Baroque vocal works

[3.1] In the previous section, I established the conventional combination of Phrygian cadence and bifocal transition, from which M8M progressions arise in Baroque instrumental works. Still, the semantic implications of these CMs warrant further examination. Resulting from bifocal transitions, the modal change from minor to major can depict dramatic transitions in music. Major and minor modes often connote contrasting affective qualities—with major connoting positive emotional valence and minor negative—and this contrast is evinced by extensive cross-cultural research in music cognition and psychology (Bowling 2013; Fritz et al. 2009; Korsakova-Kreyn and Dowling 2014; Virtala and Tervaniemi 2017). These contrasting affective associations were present as early as the emergence of Western tonal harmony in the sixteenth and seventeenth centuries and have been reinforced by convention in tonal compositions (Horn and Huron 2015; Parncutt 2014; Steblin 2002). This affective dichotomy has led nineteenth-century composers to exploit the modal opposition between parallel keys as musical metaphors for dramatic contrasts in poetry (Terrigno 2021). I will demonstrate that Baroque composers have also employed the technique similarly—but with relative keys—and in a way that would shed light on the semantic evolution of CMs.

[3.2] Music scholars have interpreted the semantic implication of bifocal transitions in instrumental music based on the modal change from minor to major. Referring to the passage in Example 9, Kimmel (1980, 66) describes the second movement of Brandenburg Concerto no. 3, which consists entirely of a Phrygian HC progression, as “meditations of death between two life-affirming allegros.” Hepokoski and Darcy (2006, 27) similarly characterize the general case where a i:HC medial caesura leads to a secondary theme in the relative major as “a sudden pull out of the ominous tonic minor into the brighter, more ‘hopeful’ mediant major.” Kimmel’s and Hepokoski and Darcy’s imagination of bifocal transitions as the transcendence from death to life and from ominousness to brightness is by no means unprecedented; as I will show in the following paragraphs, Baroque composers have employed this transition model in vocal works, where the narrative implications of the bifocal transition are illuminated by the text.⁽²⁰⁾ This compositional practice marks a crucial step in the semantic evolution of CMs, as it synthesizes the respective semantic imports of the Phrygian cadence and bifocal tonality and establishes M8M progressions as a unified musical signifier of death-to-life transcendence.

[3.3] Example 11 presents the chorus “Since by man came death” from Handel’s Messiah, with biblical text drawn from 1 Corinthians 15:21. This chorus opens with an unaccompanied Grave section, which introduces the Christian concept of original sin brought by Adam (the first “man” in the text). This opening is followed by an Allegro section, where the second half of the verse proclaims the news of salvation as Jesus (the second “man”) saves humanity from eternal death. The stark semantic contrast between the Grave and the Allegro is conveyed musically not only through changes in tempo, rhythmic density, orchestration, and texture, but also through a bifocal transition that introduces an M8M progression. In mm. 3–7, the bass voice outlines a Phrygian tetrachord (descending from A3 to E3), which is chromaticized by an applied diminished seventh over G3, a passing F♯3 in the bass, and an augmented sixth over F♮3. Kimmel (1980, 66) describes the augmented-sixth form of the Phrygian HC as “the most common, almost inevitable harmonic death gesture” in eighteenth- and nineteenth-century music. The Grave section thus culminates with an intensified Phrygian HC, where the final dominant coincides with the word “death.” After this cadence, instead of returning to the A minor tonic from its dominant, the music resumes in the relative C major. The narrative implication of this harmonic progression is apparent: the Grave section in A minor and the Phrygian HC symbolize sin and death, whereas in the subsequent Allegro, the modal change towards the relative major completes the idea of the text and suggests the transcendence from death to life through Christian salvation.

[3.4] In Example 11, the M8M progression (E+ → C+) is a necessary product of the bifocal transition, and it conveys a dramatic contrast relating to the idea of death-to-life transcendence depicted in the text. The fact that the M8M progression sounds striking in this context does not contradict my earlier claim that its use in Baroque works is conventional. Compositional devices can be conventional and familiar while still being able to invoke surprise or unexpectedness; the deceptive cadence is a characteristic example of how familiarity and unexpectedness are compatible.⁽²¹⁾ Through musical settings like Example 11, the M8M progression becomes linked to the notion of death-to-life transcendence. Over time, this semantic connection would appear recognizable to composers and listeners as a distinct musical symbol.

[3.5] Drawn from Domenico Scarlatti’s setting of Stabat Mater, Example 12 presents another instance where bifocal transitions carry the connotation of death-to-life transcendence. Set at the transition between stanzas 8 and 9 of the poem, this example occupies a pivotal position in the work, concluding the narrative on the scene of the Crucifixion and initiating a contemplative second half, which is a prayer to Mary. In the final measures of the narrative section, the text declaring Jesus’s last breath is set to an expanded Phrygian HC in B minor (mm. 178–84). Above the Phrygian bass-line motion from G3 to F♯3, the soprano inverts the typical whole-step ascent of the top voice at a Phrygian HC, spelling out a descending Phrygian scale from E5 to F♯4. The presence of both the Phrygian HC and the complete descending Phrygian scale gives this passage a distinctly Phrygian character, which reinforces the depiction of death in the text. Following this decisively Phrygian closure on an F♯+ triad, the prayer begins not in B minor, but in the relative D major, thus introducing an M8M progression. Scarlatti’s use of the bifocal transition and the ensuing M8M progression underscores the theological significance of this juncture in the text: Jesus’s death culminates in humankind’s salvation through Mary’s grace. As in Example 11, this example elucidates the association between death-to-life transcendence and bifocal transitions, along with the resulting M8M progression.

[3.6] Examples 13 and 14 provide further evidence of Baroque composers using the combination of Phrygian cadence and bifocal transition to convey the idea of death-to-life transcendence. Example 13 is drawn from the juncture between two sections of Handel’s Funeral Anthem for Queen Caroline, where an M8M progression highlights the semantic contrast between the two parts of the eulogy. First, the text declaring the Queen’s death is set over two statements of the Phrygian tetrachord in the bass, first in C minor (mm. 1–7), then in G minor (mm. 12–14). After a Phrygian HC (also chromaticized with an augmented sixth), a bifocal transition introduces an M8M progression while the text shifts to celebrate how the queen has afforded her people comfort and relief. Similarly, Example 14 features a passage from Antonio Caldara’s oratorio Morte e sepoltura di Cristo, where a complete Phrygian tetrachord and a Phrygian HC is followed by a bifocal transition (mm. 17–21). The text leading up to the bifocal transition comprises a plea by Mary, the mother of James, who grieves before Jesus’s grave. Notably, the final dominant of the Phrygian cadence (m. 21) coincides with the word “funestra”—which translates to gloomy, fatal, or “sepulchral” (Pritchard 2015, 36)—thus underscoring the Phrygian connotation of death. After the bifocal transition, with the word “bramo (I long for),” Mary’s lament shifts to an optimistic longing for pity and compassion in the relative G major. These two examples again illustrate how Baroque composers employ the juxtaposition of Phrygian HC and bifocal transition and its associated M8M progressions to express the theme of death-to-life transcendence.

[3.7] While Examples 11–14 all feature Phrygian cadences and bifocal tonality with clear textual associations of death-to-life transcendence, other instances from Baroque vocal works show a more flexible interpretation of this connotation, setting M8M progressions to texts with a broader range of meanings. This flexibility contributes to the semantic evolution of CMs by expanding their semantic range. For instance, the M8M progression in Example 15, drawn from Jan Dismas Zelenka’s Officium defunctorum, conveys death-to-life transcendence with a twist. Before the bifocal transition, the biblical text from Job 7:21 features Job’s plea for forgiveness and an end to his suffering (mm. 48–49). Afterwards, the text reveals Job’s desired resolution: relief through death. Here, the idea of death-to-life transcendence is reversed in the literal sense, with the narrative before the transition reflecting Job’s suffering in life and the subsequent section representing death’s relief. Nonetheless, the M8M progression highlights a semantic contrast similar to previous examples. In this case, death-to-life transcendence is reinterpreted as the passage from sin and suffering to forgiveness and rest. Likewise, Example 16, taken from J. S. Bach’s cantata Ich hatte viel Bekümmernis, also presents an abstracted portrayal of death-to-life transcendence with M8M progressions. The M8M progression in mm. 27–28 divides the text from Psalm 42:11 into halves: the first half expresses the psalmist’s cry to God in “heartbreak and anguish“ after “the taunting of enemies” (Waldman 1974, 548–49), while the second conveys their hope for divine solace and salvation. Like Example 15, this example reframes death-to-life transcendence as the contrast between distress and hope. These examples demonstrate how composers extend the conventional use of M8M progressions and expand their semantic range by interpreting the notion of death-to-life transcendence more flexibly and broadly.⁽²²⁾

[3.8] Example 17 presents the only instance—out of five settings in total—in J. S. Bach’s St. Matthew Passion where the Passion chorale is set in the Phrygian mode; it is also the version with the most intense chromaticism.⁽²³⁾ While the ending of this chorale setting might be interpreted as an “ineffable close on the dominant” in A minor (Lerdahl and Jackendoff 1983, 145), it could also be read as “a proper Phrygian resolution” (Hill 1996, 539).⁽²⁴⁾ The chorale marks an important juncture in the Passion narrative where Jesus has just died, with the chorale’s Phrygian modality symbolizing death. After the chorale, the bifocal transition to C major leads into a recitative that depicts the events that follow Jesus’s death, such as the tearing of the temple veil, the earthquakes, and the resurrection of saints from their graves.

[3.9] In this example, the M8M progression between the chorale and the recitative opens up two interpretative possibilities. First, the concept of life is implied by the events described in the recitative. In the Passion, these events affirm the divine identity of Jesus, through whose death humankind can receive eternal life. For example, theologians understand the tearing of the temple veil—the first event described in the recitative—as the beginning of humankind’s access to salvation: it symbolizes the destruction of “the barrier which separated God from humanity” (Ulansey 1991, 124), “the release of the divine presence into the world” (Dowd and Malbon 2006, 296), and “that from now on Jesus is to be their access to God” (Clarke 2003, 238). Thus, the tearing of the veil and the ensuing events can be seen as symbolic of humankind’s transcendence from spiritual death to eternal life. These interpretations trace back to Martin Luther’s theological ideas (Pelikan and Handen 1968, 203), which have had a significant influence on Bach’s sacred vocal music, including the Passions (Chafe 1991; 2014; Lloyd 2007; Schellhous 1985). In other words, the bifocal transition from the chorale to the recitative musically portrays the theological significance of this particular moment in the Passion. The theme of death-to-life transcendence is reinforced through the CM progression, which results from the juxtaposition of Phrygian cadence (in its modal form, rather than the tonal HC with a semitone bass line descent) and bifocal transition.

[3.10] Alternatively, the M8M progression in Example 17 can be understood more broadly as a musical metaphor for the dramatic and miraculous nature of this moment in the Passion. Accordingly, this reading demonstrates how the semantic range of M8M CMs expands beyond the specific description of death-to-life transcendence to encompass more abstract themes of the magical, the dramatic, and the miraculous. This semantic expansion mirrors the process of word formation in languages, where distinct root words combine to form a new word that synthesizes the original meanings, after which the semantic range of this new word expands from the concrete to the abstract.⁽²⁵⁾ For instance, the word “metaphor” originates from the Greek roots “meta (μετά)” and “phero (φέρω),” meaning “across” and “carry,” respectively. Initially, they combined to form the word “metaphora (μεταφορά),” which has the concrete meaning of “transport” or “transfer” (i.e., the literal connotation of “carry across”).⁽²⁶⁾ But over time, the word has evolved to its current abstract sense: the transfer of meaning between domains (Deutscher 2005, 116–7). As with words like “metaphor,” the semantic evolution of M8M CMs follows a path from the concrete to the abstract. These CMs derive their narrative potential from the meanings of the two distinct Baroque devices: Phrygian inflections connoting death and the modal change from minor to major implying life. The individual semantic components then lose their distinctiveness, and only the abstract meaning of the new composite progression remains recognizable. When understood in this abstract way, Example 17 demonstrates how the semantic effect of the M8M progression can be interpreted more flexibly and expanded based on the idea of death-to-life transcendence.

[3.11] As shown in Examples 11–17, M8M progressions arise from the semantic synthesis of Phrygian cadence and bifocal transition in Baroque vocal music, particularly at dramatic junctures in the texts. As the respective meanings of these two devices merge, this usage establishes a convention where composers employ this type of CM progression to musically depict the notion of death-to-life transcendence. This musical signifier of death-to-life transcendence could then be interpreted more flexibly and abstracted to represent broader concepts, such as the magical, the dramatic, and the miraculous.

4. Continuation of the Baroque convention into the Classical era

[4.1] While Baroque composers established the convention of combining the Phrygian HC and bifocal transition to create M8M CM progressions that signify death-to-life transcendence, the practice extended well into the Classical era. Examples 18 and 19 are taken from sacred vocal works by Antonio Salieri and feature M8M progressions presented in the Baroque model—with a Phrygian HC followed by a bifocal transition.⁽²⁷⁾ The text in Example 18 explicitly conveys death-to-life transcendence: the Phrygian cadential progression in B minor (mm. 150–52) is set to the word “mortuorum (the dead)”; after the bifocal transition, the M8M progression introduces the new phrase in the relative D major (m. 153) on the word “vitam (life).” Whereas in Example 19, the CM expresses death-to-life transcendence more abstractly, outlining the general idea of dramatic contrast and wonder. The CM leads into a new section of the Requiem with the text “Rex tremendae majestatis” (m. 130), underscoring the marvel of the “king of tremendous majesty.” Although the contrast between death and life is masked here,⁽²⁸⁾ the CM highlights the text’s sense of marvel and awe.

[4.2] While Examples 11–19 all feature sacred texts where the notion of death-to-life transcendence is particularly pertinent, the semantic use of M8M progressions arising from bifocal transitions extends to other repertoires. Here I offer an operatic example, which reinforces the connection between CMs from the Baroque period and the wealth of examples from nineteenth-century opera (e.g., Example 5). Example 20 comes from “Voi che sapete,” Cherubino’s arietta from Wolfgang Amadeus Mozart’s The Marriage of Figaro.⁽²⁹⁾ Cherubino is a lovesick teenage page boy experiencing the torment of unfulfilled desires, and this arietta “details the unfamiliar bodily sensations of his sexual awakening” (Ho 2018). In the example, a Phrygian HC (mm. 35–36) accompanies Cherubino’s exclamation of the torment (“martir”) of his yearning, abstracting the conventional death association of the Phrygian cadence into a broader connotation of emotional suffering. Subsequently, a bifocal transition portrays a sudden change in his sensations as he cries “I freeze” (“Gelo”; m. 37). The resulting M8M progression (C+ → A♭+) signifies the startling contrast in Cherubino’s sensory experience, capturing what Wye Jamison Allanbrook (1983, 108) describes as “the fire and ice of infatuation.” While Allanbrook (1983, 108) characterizes this bifocal transition and the M8M progression as a “strange modulation [that] is suited to the text,”⁽³⁰⁾ my preceding discussion elucidates the conventional origin of the semantic use of this CM: Baroque composers have established the practice of signifying death-to-life transcendence and other dramatic contrasts by juxtaposing Phrygian HC and bifocal transition, and Mozart employs this musical signifier in this example to represent Cherubino’s abrupt shift in bodily sensations. Collectively, Examples 18–20 show how Classical composers embrace and expand upon the Baroque convention of using M8M progressions to convey a range of dramatic effects.

[4.3] In the preceding Baroque and Classical examples, M8M progressions always arise from the juxtaposition of Phrygian HC and bifocal transition. Nonetheless, as this CM progression gains conventional status as a musical signifier, the original context becomes dispensable for activating its semantic connotation of death-to-life transcendence. Some Classical composers retain the semantic connotation of M8M progressions in bifocal transitions while substituting the Phrygian HC with a non-Phrygian one—i.e., without a half-step descent in the bass. This practice is exemplified in Example 21, excerpted from the oratorio version of Joseph Haydn’s The Seven Last Words of Christ. This example concerns a subject matter featured in several previous examples—the Crucifixion of Jesus. This example differs from previous ones as the text depicting Jesus’s death is set to a non-Phrygian HC. The cadential arrival at the final dominant of the HC occurs at m. 10, with the bass approaching from $\hat{1}$. Although a German augmented sixth—and thus a ♭$\hat{6}$ in the bass—might be implied in m. 12.4, that chord functions as an expansion of the cadential dominant rather than the actual penultimate harmony of the HC. On a structural level, the entire span from m. 10 to m. 14 constitutes a post-cadential dominant prolongation, with the implied augmented sixth serving an embellishing function. Moreover, the final iteration of the dominant degree in the bass (m. 13) is immediately preceded by C♯3 rather than E♭3, concealing and undermining the essential ♭$\hat{6}$–$\hat{5}$ motion of a Phrygian HC. Nonetheless, despite the absence of a Phrygian HC, the M8M progression resulting from the bifocal transition still evokes death-to-life transcendence, as in previous examples (especially Examples 11, 12, and 17, which also relate to the Crucifixion). The passage preceding the bifocal transition is set to the text “Es ist vollbracht (It is finished)” (mm. 13–14), Jesus’s final cry as he draws his last breath. Afterwards, as B♭+ enters as the second triad of the CM pair (m. 15), the soprano solo proclaims humanity’s redemption through Jesus’s Passion.⁽³¹⁾ By writing a non-Phrygian HC before the bifocal transition, Haydn shows that CMs that result from the Baroque model have become sufficiently and independently emblematic of death-to-life transcendence, such that the same semantic connotation can still be effectively conveyed by M8M progressions that do not follow a Phrygian HC.

[4.4] Similarly, in Examples 22 and 23, the semantic use of M8M progressions occurs with a bifocal transition following a non-Phrygian HC. Example 22 features another excerpt from Joseph Haydn’s The Seven Last Words of Christ, depicting the conversation between Jesus and a criminal crucified alongside him. Although the M8M progression is not introduced with a Phrygian HC, it still carries the connotation of death-to-life transcendence: over a i–V half-cadential progression (mm. 20–21), the criminal pleads for Jesus’s mercy as they face death. A bifocal transition then leads into Jesus’s reassuring reply (m. 22), promising the criminal forgiveness and entry into the paradise. The recurring theme of salvation after death is again portrayed with an M8M progression in this example, even without a Phrygian HC.⁽³²⁾ In Example 23, drawn from a setting of Psalm 111 by Michael Haydn (Joseph’s younger brother), the M8M progression is introduced after a non-Phrygian HC and carries the broader semantic connotation of the marvelous rather than death-to-life transcendence. After an HC approached from ii^o6 (mm. 10–12), a bifocal transition leads to a new verse celebrating the greatness of God’s work. The arrival of C+, the second triad of the CM pair (m. 13), coincides with the adjective “magna (great)” in the text, carrying the semantic connotation of the marvelous. This example shows how Classical composers adapted the semantic use of M8M progressions beyond the Baroque context: the Phrygian HC is no longer required, and the semantic range of the M8M progression has expanded beyond death-to-life transcendence to encompass broader notions.

[4.5] The Classical examples introduced in this section illustrate the continuation and evolution of the Baroque convention of juxtaposing Phrygian HC and bifocal transition. Examples 18–20 demonstrate how Classical composers recognize the semantic connotation of M8M progressions derived from the Baroque convention and continue to incorporate them in vocal works. In contrast, Examples 21–23 feature a new phase of the semantic evolution of CMs, where M8M progressions arise from non-Phrygian HC and thus operate outside the original Baroque context. The following section will explore how the semantic use of M8M progressions further evolved in works of Classical composers.

5. Dissociation from the cadential formal function

[5.1] William Caplin (2005, 2014) discusses how musical topics can correlate with formal functions, as first presented in his treatise Classical Form (1998; see also Caplin 2009). Although M8M progressions arising from bifocal transitions are not typically considered topics, the correlation between this progression and its usual formal role informs my current investigation. In the Caplinian sense, the M8M progressions in Examples 11–23 relate to the cadential function, as they originate from HCs. In this section, I present examples of Classical composers using semantically endowed M8M progressions that project other formal functions while still alluding to their semantic derivation in the Baroque period. A list of potential formal contexts of M8M progressions is shown in Example 24.⁽³³⁾ Since this study aims to trace the Baroque origin of the semantic evolution of CMs, the schemata presented in Example 24 are not exhaustive but pertain only to musical examples offered in this paper.⁽³⁴⁾ The following discussion of Classical examples supplements my thesis by establishing the missing link between the Baroque origin of the semantics of CMs and the more widely documented examples from nineteenth-century music, which are found in diverse formal contexts.

[5.2] Let us revisit the example from Rossini’s Tancredi (Example 5), focusing on the formal function of the M8M progression. In this instance, the passage in mm. 94–101 sets up an “active dominant” prolonged by neighboring motion between ${}_4^6$ and ${}_3^5$ figurations (Rothstein 2008, [16]). This lingering dominant ultimately resolves not to F+, but deceptively to A♭+, resulting in an M8M progression (C+ → A♭+). Formally, this example contrasts with previous ones, as the progression arises not from the juxtaposition of an HC and a bifocal transition, but from a deceptive resolution of the dominant (V–♭III ),⁽³⁵⁾ as schematized in Example 24b. By propelling harmonic motion, this M8M progression has a medial formal function within the sentential phrase from m. 94 to m. 105, bridging the presentation and the continuation phrases. Although this progression carries a medial—instead of cadential—formal function, its narrative effect echoes the Baroque context, where M8M progressions are used to depict dramatic junctures in the text by symbolizing the magical and the miraculous. In other words, since the narrative use of bifocal transitions in the Baroque gave M8M progressions sufficient conventional status, later composers were able to recognize their semantic connotation and employ them in non-cadential formal contexts, as seen in Example 5.

[5.3] Example 25 presents another instance where a non-cadential M8M progression marks a significant textual juncture in a Classical composition. This passage is drawn from Salieri’s Requiem at the transition between two stanzas of the Dies irae sequence, where the first stanza ends in G minor and the second begins in F major. Salieri bridges the two stanzas by introducing the new F-major tonic with an A+ triad, which could function as a dominant in D minor. Over the A+ harmony (mm. 33–37), the ${}_5^7$–${}_4^6$–${}_3^5$ inner-voice motion hints at the chord’s dominant quality and alludes to the bifocal transition, in which the first triad of the CM pair functions as the dominant in a Phrygian HC. The new stanza then begins on F+ (m. 37), introducing an M8M progression (A+ → F+). Since the previous section has concluded with a PAC, this progression initiates a new phrase and projects an introductory formal function (schematized in Example 24c).⁽³⁶⁾ This CM pair highlights the marvel of the sounding trumpet from the new line of text, alluding to the Baroque origin of its semantic association despite its non-cadential formal context.

[5.4] In Example 26, which shows a later passage in Salieri’s Requiem, the narrative use of M8M progressions occurs neither at a cadence nor in an introductory prefix, but rather in a medial position of the phrase. Following the phrase’s tonic-prolonging beginning, a ♭VI harmony forms an M8M relation with the initial tonic (m. 81). The formal and harmonic function of the ♭VI remains ambiguous until a D♮ enters in m. 84: the resulting German augmented sixth leads to an HC. This example shows another way of introducing CMs—through the pre-dominant harmonic function with a medial formal function within a phrase (schematized in Example 24d). The F♭+ triad is set to the text “de morte transire ad vitam (to pass from death to life)”; this text-setting choice recalls the semantic origin of CMs in Baroque examples, where M8M progressions from bifocal transitions symbolize death-to-life transcendence. Although the M8M progression in this example is no longer a product of Phrygian HC and bifocal transition, its semantic application persists in another formal context and within a musical syntax typical of the Classical era.

[5.5] Another example of M8M progressions projecting a medial formal function appears in Mozart’s The Magic Flute (Example 27).⁽³⁷⁾ In this example, the M8M progression occurs after a PAC in D major, and the second triad of the progression (B♭+) functions as a pivot for modulating to G minor (schematized in Example 24e). In the opera, this M8M progression comes after Tamino encounters a priest on his voyage to rescue Pamina. As the progression accompanies the priest’s command of “zurück! (turn back)” at Tamino, the modulation in Example 27 is figurative in that Tamino should change paths as the music does. More significantly, the immediate dramatic effect of this CM is to startle Tamino (and the audience) and prevent him from proceeding in the original direction. This M8M progression conveys the element of astonishment and fascination, which derives from the original Baroque usage. Although the subject matter here is no longer directly related to the original semantic content of death-to-life transcendence or supernatural associations, the Baroque convention of employing M8M progressions at critical dramatic junctures has allowed this progression to portray a broader range of effects, including the idea of surprise. This example illustrates how the semantic and formal use of CMs has evolved from its Baroque origin, adapting to different musical and dramatic contexts.

[5.6] After introducing examples of M8M progressions with introductory and medial formal functions (Examples 25–27), I now return to an example with a cadential function. However, unlike examples from sections 3 and 4, where M8M progressions arise from HCs, the one in Example 28 follows a PAC. This example comes from the opening chorus of Salieri’s oratorio Gesù al limbo, which is set to a doxological text. After a PAC in D major (m. 22), a new phrase begins on the new tonic of B♭ major. This phrase modulation thus introduces an M8M CM pair between the cadential tonic of the previous phrase and the on-tonic beginning of the new phrase (schematized in Example 24f). The arrival of the B♭+ triad (m. 23) coincides with the text announcing God as the ruler over the cherub angels, who are portrayed in the bible as “animate supernatural beings” and “divine warriors” who guard the boundary between the earthly and the divine (Wood 2008, 51–61). In this example, the M8M progression bridges two parts of the text that describe God’s dominion over distinct realms: the first part concerns the earthly space and time (mm. 18–22), whereas the second part reaches the heavenly realm through the cherubim (mm. 22–26). This M8M progression conveys the idea of transcendence and the supernatural, and its PAC cadential function demonstrates another instance of how the semantic use of CMs can be found in diverse formal contexts.

[5.7] The above examples illustrate that semantically endowed M8M progressions can display various formal functions beyond the HC cadential function from which they originate. Although the narrative meaning of M8M progressions in Baroque examples initially arises from distinct compositional devices with contrasting semantic connotations, their conventional usage has solidified their status as coherent and independent musical signifiers. Over time, the presence of Phrygian HC and bifocal transition becomes unnecessary for the semantic use of M8M progressions. Consequently, composers could extract these progressions from the bifocal transition and transplant them to other formal contexts, while maintaining their semantic connotations.

Conclusion and further considerations

[6.1] I would like to point out some caveats regarding my account of the semantic evolution of CMs and present these as starting points of further investigation. The first issue concerns the type of CMs involved in my discussion. As defined in paragraph [1.7], this study has focused on the M8M type of CMs. Consequently, a reasonable question arises as to whether this account could explain the semantic use of other types of CMs. This speculation invites further examination through a more systematic survey of theoretical writings and musical examples—for instance, through a corpus study of CMs⁽³⁸⁾—in order to present a more comprehensive overview of the semantic evolution of all types of CMs.

[6.2] Second, this paper examine CMs on the foreground level, meaning that their semantic effect comes from the immediate succession of CM triads on the musical surface.⁽³⁹⁾ In contrast, some scholars have examined CM relations on the middleground level, not as successive triads but rather as adjoining key areas (Cinnamon 1986; Clark 2011; Klorman 2014; Kopp 2002; 2011; Krebs 1980; MacKay 2018; Rothstein 2023; Somer 1995). Despite this difference in approaches, I acknowledge that CMs may operate on a middleground level to achieve similar semantic effects and that the semantics of middleground CMs prior to the nineteenth century could be a rewarding line of inquiry.

[6.3] Finally, I would like to draw attention to Salieri’s role in advancing the use of CMs. As shown in Examples 18, 19, 25, 26, and 28, Salieri’s compositions incorporate M8M progressions in various formal contexts and with different shades of meaning. The existing literature typically attributes the pioneering use of within-phrase CMs to composers such as Ludwig van Beethoven and Franz Schubert (Bretherton 2019, 241; Kopp 2002, 18; Taruskin 2010, 69; Tischler 1958), who studied composition with Salieri in Vienna (Gibbs 2003, 117–27; Hettrick and Rice 2001). Striving to decenter this historical-theoretical discussion from Austro-German composers, Rothstein (2008, [7]) suggests that “in chromatic third-relations it was Rossini who set the pattern for the rest of Europe to follow.” Since Salieri was a pivotal composer of Italian operas during the late eighteenth century, his compositions were likely studied by Rossini, who visited Vienna in 1822 and met Salieri (Rice 1998, 596; Swenson 1974, 308). Therefore, given Salieri’s connection to prominent composers of the next generation, a closer study of his musical language could illuminate both the semantic/syntactic evolution of CMs and the broader stylistic developments around the turn into the nineteenth century.

[6.4] In this article, I outline the semantic evolution of CMs, which ultimately influences the harmonic language of the nineteenth century. By illuminating this diachronic connection, the study enhances our understanding of the historical development of the M8M progression and underscores the lasting impact of CMs on Western music theory and practice.

Jason Yin Hei Lee
Schulich School of Music
McGill University
555 Sherbrooke Street West
Montreal, Quebec H3A 1E3
jason.yh.lee@mail.mcgill.ca

Works Cited

Agawu, V. Kofi. 1991. Playing with Signs: A Semiotic Interpretation of Classic Music. Princeton University Press. https://doi.org/10.1515/9781400861835.

—————. 2008. Music as Discourse: Semiotic Adventures in Romantic Music. Oxford University Press. https://doi.org/10.1093/acprof:oso/9780195370249.001.0001.

Allanbrook, Wye Jamison. 1983. Rhythmic Gesture in Mozart: Le nozze di Figaro & Don Giovanni. University of Chicago Press. https://doi.org/10.7208/chicago/9780226437712.001.0001.

Anson-Cartwright, Mark. 2000. “Haydn’s Hidden Homage to Mozart: Echoes of ‘Voi che sapete’ in Opus 64, No. 3.” Intégral 14/15: 121–36.

Bauer, Laurie. 2008. “Exocentric Compounds.” Morphology 18 (1): 51–74. https://doi.org/10.1007/s11525-008-9122-5.

Beach, David. 1983. “A Recurring Pattern in Mozart’s Music.” Journal of Music Theory 27 (1): 1–29.

Benczes, Réka. 2010. “Setting Limits on Creativity in the Production and Use of Metaphorical and Metonymical Compounds.” In Cognitive Perspectives on Word Formation, ed. Alexander Onysko and Sascha Michel, 217–42. De Gruyter Mouton. https://doi.org/10.1515/9783110223606.217.

Biamonte, Nicole. 2012. “Variations on a Scheme: Bach’s ‘Crucifixus’ and Chopin’s and Scriabin’s E-Minor Preludes.” Intégral 26: 47–89.

Bowling, Daniel. 2013. “A Vocal Basis for the Affective Character of Musical Mode in Melody.” Frontiers in Psychology 4: Article 464. https://doi.org/10.3389/fpsyg.2013.00464.

Bretherton, David. 2019. “The Musico-Poetics of the Flat Submediant in Schubert’s Songs.” Journal of the Royal Musical Association 144 (2): 239–86. https://doi.org/10.1080/02690403.2019.1651495.

Bribitzer-Stull, Matthew. 2006. “The A♭–C–E Complex: The Origin and Function of Chromatic Major Third Collections in Nineteenth-Century Music.” Music Theory Spectrum 28 (2): 167–90. https://doi.org/10.1525/mts.2006.28.2.167.

—————. 2012. “From Nibelheim to Hollywood: The Associativity of Harmonic Progression.” In The Legacy of Richard Wagner: Convergences and Dissonances Aesthetics and Reception, ed. Luca Sala, 157–84. Brepols.

Buch, David J. 2008. Magic Flutes and Enchanted Forests: The Supernatural in Eighteenth-Century Musical Theater. University of Chicago Press. https://doi.org/10.7208/chicago/9780226078113.001.0001.

Burns, Lori. 1995. Bach’s Modal Chorales. Harmonologia Series No. 9. Pendragon.

Burstein, L. Poundie. 2014. “The Half Cadence and Other Such Slippery Events.” Music Theory Spectrum 36 (2): 203–27. https://doi.org/10.1093/mts/mtu010.

—————. 2015. “The Half Cadence and Related Analytical Fictions.” In What Is a Cadence? Theoretical and Analytical Perspectives on Cadences in the Classical Repertoire, ed. Markus Neuwirth and Pieter Bergé, 85–116. Leuven University Press. https://doi.org/10.2307/j.ctt14jxt45.6.

—————. 2020. Journeys through Galant Expositions. Oxford University Press. https://doi.org/10.1093/oso/9780190083991.001.0001.

Caplin, William E. 1998. Classical Form: A Theory of Formal Functions for the Instrumental Music of Haydn, Mozart, and Beethoven. Oxford University Press. https://doi.org/10.1093/oso/9780195104806.001.0001.

—————. 2005. “On the Relation of Musical Topoi to Formal Function.” Eighteenth Century Music 2 (1): 113–24. https://doi.org/10.1017/S1478570605000278.

—————. 2009. “What Are Formal Functions?” In Musical Form, Forms, and Formenlehre: Three Methodological Reflections, ed. Pieter Bergé, 21–40. Leuven University Press. https://doi.org/10.2307/j.ctt9qf01v.5.

—————. 2014. “Topics and Formal Functions: The Case of the Lament.” In The Oxford Handbook of Topic Theory, ed. Danuta Mirka, 415–49. Oxford University Press. https://doi.org/10.1093/oxfordhb/9780199841578.013.0016.

—————. 2024. Cadence: A Study of Closure in Tonal Music. Oxford University Press. https://doi.org/10.1093/oso/9780190056445.001.0001.

Chafe, Eric. 1991. Tonal Allegory in the Vocal Music of J. S. Bach. University of California Press. https://doi.org/10.1525/9780520419896.

—————. 2014. J. S. Bach’s Johannine Theology: The St. John Passion and the Cantatas for Spring 1725. Oxford University Press. https://doi.org/10.1093/acprof:oso/9780199773343.001.0001.

Chandler, Daniel. 2022. Semiotics: The Basics. 4th ed. Routledge. https://doi.org/10.4324/9781003155744.

Cinnamon, Howard. 1986. “Tonic Arpeggiation and Successive Equal Third Relations as Elements of Tonal Evolution in the Music of Franz Liszt.” Music Theory Spectrum 8 (1): 1–24. https://doi.org/10.2307/746067.

Clark, Suzannah. 2011. “On the Imagination of Tone in Schubert’s Liedesend (D473), Trost (D523), and Gretchens Bitte (D564).” In The Oxford Handbook of Neo-Riemannian Music Theories, ed. Edward Gollin and Alexander Rehding, 294–318. Oxford University Press. https://doi.org/10.1093/oxfordhb/9780195321333.013.0010.

Clarke, Howard. 2003. The Gospel of Matthew and Its Readers: A Historical Introduction to the First Gospel. Indiana University Press.

Cohn, Richard. 1996. “Maximally Smooth Cycles, Hexatonic Systems, and the Analysis of Late-Romantic Triadic Progressions.” Music Analysis 15 (1): 9–40. https://doi.org/10.2307/854168.

—————. 2004. “Uncanny Resemblances: Tonal Signification in the Freudian Age.” Journal of the American Musicological Society 57 (2): 285–324. https://doi.org/10.1525/jams.2004.57.2.285.

—————. 2012a. Audacious Euphony: Chromaticism and the Triad’s Second Nature. Oxford University Press.

—————. 2012b. “Peter, the Wolf, and the Hexatonic Uncanny.” In Tonality 1900–1950: Concept and Practice, ed. Felix Wörner, Ullrich Scheidler, and Philip Rupprecht, 47–62. Franz Steiner Verlag.

Cone, Edward T. 1982. “Schubert’s Promissory Note: An Exercise in Musical Hermeneutics.” 19th-Century Music 5 (3): 233–41. https://doi.org/10.2307/746462.

Cumming, Naomi. 1997. “The Subjectivities of ‘Erbarme dich.’” Music Analysis 16 (1): 5–44. https://doi.org/10.2307/854112.

Deutscher, Guy. 2005. The Unfolding of Language: An Evolutionary Tour of Mankind’s Greatest Invention. Metropolitan Books.

Dowd, Sharyn, and Elizabeth Struthers Malbon. 2006. “The Significance of Jesus’ Death in Mark: Narrative Context and Authorial Audience.” Journal of Biblical Literature 125 (2): 271–97. https://doi.org/10.2307/27638361.

Downes, Edward O. D. 1961. “Secco Recitative in Early Classical Opera Seria (1720–80).” Journal of the American Musicological Society 14 (1): 50–69. https://doi.org/10.2307/829465.

Forrest, David L. 2017a. “Britten and the Supernatural.” In Essays on Benjamin Britten from a Centenary Symposium, ed. David L. Forrest, Quinn Patrick Ankrum, Stacey Jocoy, and Emily Ahrens Yates, 181–206. Cambridge Scholars Publishing.

—————. 2017b. “PL Voice Leading and the Uncanny in Pop Music.” Music Theory Online 23 (4). https://doi.org/10.30535/mto.23.4.6.

—————. 2022. “Kate Bush’s Uncanny Harmonic Language.” In The Routledge Handbook of Women’s Work in Music, ed. Rhiannon Mathias, 228–37. Routledge. https://doi.org/10.4324/9780429201080-23.

Fritz, Thomas, Sebastian Jentschke, Nathalie Gosselin, Daniela Sammler, Isabelle Peretz, Robert Turner, Angela D. Friederici, and Stefan Koelsch. 2009. “Universal Recognition of Three Basic Emotions in Music.” Current Biology 19 (7): 573–76. https://doi.org/10.1016/j.cub.2009.02.058.

Gasparini, Francesco. 1708. L’armonico pratico al cimbalo. Bologna. Petrucci Music Library (IMSLP #33595).

Gibbs, Christopher H. 2003. “Writing Under the Influence? Salieri and Schubert’s Early Opinion of Beethoven.” Current Musicology 75: 117–44.

Greenberg, Yoel. 2022. How Sonata Forms: A Bottom-Up Approach to Musical Form. Oxford University Press. https://doi.org/10.1093/oso/9780197526286.001.0001.

Hatten, Robert S. 1994. Musical Meaning in Beethoven: Markedness, Correlation, and Interpretation. Indiana University Press.

—————. 1996. “Grounding Interpretation: A Semiotic Framework for Musical Hermeneutics.” The American Journal of Semiotics 13: 25–42. https://doi.org/10.5840/ajs1996131/43.

—————. 2006. “A Theory of Musical Gesture and Its Application to Beethoven and Schubert.” In Music and Gesture, ed. Elaine King, 1–23. Routledge. https://doi.org/10.4324/9781315091006-2.

Heetderks, David. 2015. “From Uncanny to Marvelous: Poulenc’s Hexatonic Pole.” Theory and Practice 40: 177–204.

Heine, Erik. 2018. “Chromatic Mediants and Narrative Context in Film.” Music Analysis 37 (1): 103–32. https://doi.org/10.1111/musa.12106.

Hepokoski, James, and Warren Darcy. 2006. Elements of Sonata Theory: Norms, Types, and Deformations in the Late-Eighteenth-Century Sonata. Oxford University Press. https://doi.org/10.1093/acprof:oso/9780195146400.001.0001.

Hettrick, Jane Schatkin, and John A. Rice. 2001. “Salieri, Antonio.” Grove Music Online. https://doi.org/10.1093/gmo/9781561592630.article.24378.

Hill, David. 1996. “The Time of the Sign: ‘O Haupt voll Blut und Wunden’ in Bach’s St. Matthew Passion.” The Journal of Musicology 14 (4): 514–43. https://doi.org/10.2307/764071.

Ho, Jocelyn. 2018. “Emulating Cherubino’s Sexual Awakening: A Bodily-Based Approach to Adelina Patti’s ‘Voi che sapete.’” Presented at the Annual Meeting of the Society for Music Theory, San Antonio. https://osf.io/h4f5p/.

Horn, Katelyn, and David Huron. 2015. “On the Changing Use of the Major and Minor Modes 1750–1900.” Music Theory Online 21 (1). https://doi.org/10.30535/mto.21.1.4.

Hunt, Graham G. 2007. “David Lewin and Valhalla Revisited: New Approaches to Motivic Corruption in Wagner’s Ring Cycle.” Music Theory Spectrum 29 (2): 177–96. https://doi.org/10.1525/mts.2007.29.2.177.

Huron, David. 2006. Sweet Anticipation: Music and the Psychology of Expectation. The MIT Press. https://doi.org/10.7551/mitpress/6575.001.0001.

Hynes-Tawa, Liam. 2020. “How the Phrygian Final Lost Its Finality.” PhD diss., Yale University.

Judd, Cristle Collins. 1992. “Modal Types and Ut, Re, Mi Tonalities: Tonal Coherence in Sacred Vocal Polyphony from about 1500.” Journal of the American Musicological Society 45 (3): 428–67. https://doi.org/10.2307/831714.

Kassler, Jamie Croy. 1983. “Heinrich Schenker’s Epistemology and Philosophy of Music: An Essay on the Relations Between Evolutionary Theory and Music Theory.” In The Wider Domain of Evolutionary Thought, ed. David Oldroyd and Ian Langham, 221–60. D. Reidel. https://doi.org/10.1007/978-94-009-6986-5_8.

Kimmel, William. 1980. “The Phrygian Inflection and the Appearances of Death in Music.” College Music Symposium 20 (2): 42–76.

Kirnberger, Johann Philipp. 1771. The Art of Strict Musical Composition [Die Kunst des reinen Satzes in der Musik]. Translated by David Beach and Jürgen Thym. Yale University Press.

Klorman, Edward. 2014. “On the Slow Movement of Brahms’s F-Minor Clarinet Sonata: Thirds-Cycles, Diatonie, and Todesangst.” Gamut 7 (1): 126–49.

Kopp, David. 2002. Chromatic Transformations in Nineteenth-Century Music. Cambridge University Press. https://doi.org/10.1017/CBO9780511481932.

—————. 2011. “Chromaticism and the Question of Tonality.” In The Oxford Handbook of Neo-Riemannian Music Theories, ed. Edward Gollin and Alexander Rehding, 400–414. Oxford University Press. https://doi.org/10.1093/oxfordhb/9780195321333.013.0014.

Korsakova-Kreyn, Marina, and W. Jay Dowling. 2014. “Emotional Processing in Music: Study in Affective Responses to Tonal Modulation in Controlled Harmonic Progressions and Real Music.” Psychomusicology: Music, Mind, and Brain 24 (1): 4–20. https://doi.org/10.1037/pmu0000029.

Krebs, Harald. 1980. “Third Relation and Dominant in Late 18th- and Early 19th-Century Music.” PhD diss., Yale University.

LaRue, Jan. (1957) 2001. “Bifocal Tonality: An Explanation for Ambiguous Baroque Cadences.” The Journal of Musicology 18 (2): 283–94. https://doi.org/10.1525/jm.2001.18.2.283.

Lawson, Matt, and Lawrence E. MacDonald. 2018. 100 Greatest Film Scores. Rowman & Littlefield.

Lehman, Frank. 2013. “Transformational Analysis and the Representation of Genius in Film Music.” Music Theory Spectrum 35 (1): 1–22. https://doi.org/10.1525/mts.2013.35.1.1.

—————. 2018. Hollywood Harmony: Musical Wonder and the Sound of Cinema. Oxford University Press. https://doi.org/10.1093/oso/9780190606398.001.0001.

Lerdahl, Fred, and Ray S. Jackendoff. 1983. A Generative Theory of Tonal Music. The MIT Press.

Lloyd, Rebecca. 2007. “Bach: Luther’s Musical Prophet?” Current Musicology 83: 5–32.

Long, Megan Kaes. 2020. Hearing Homophony: Tonal Expectation at the Turn of the Seventeenth Century. Oxford University Press. https://doi.org/10.1093/oso/9780190851903.001.0001.

MacKay, James S. 2018. “Another Look at Chromatic Third-Related Key Relationships in Late Haydn: Parallel Keys and Remote Modulation in Selected String Quartet Minuets.” HAYDN: Online Journal of the Haydn Society of North America 8 (2): Article 4.

—————. 2020. “Fuzzy Boundaries in Classical Sonata Expositions: The Main Theme→Transition Thematic Complex.” Indiana Theory Review 36 (1/2): 56–85. https://doi.org/10.2979/inditheorevi.36.1-2.03.

Malawey, Victoria. 2020. “Chromatic Mediants in Popular Music.” In The Routledge Companion to Music Theory Pedagogy, ed. Leigh VanHandel, 350–54. Routledge. https://doi.org/10.4324/9780429505584-59.

McCreless, Patrick. 1996. “An Evolutionary Perspective on Nineteenth-Century Semitonal Relations.” In The Second Practice of Nineteenth-Century Tonality, ed. William Kinderman and Harald Krebs, 87–113. University of Nebraska Press.

McDowell, Laura Pollie. 1991. “Death in the Renaissance: Musical Symbols and Styles in Commemorative Motets, 1460–1539.” PhD diss., Florida State University.

Mirka, Danuta. 2014. “Introduction.” In The Oxford Handbook of Topic Theory, ed. Danuta Mirka, 1–57. Oxford University Press. https://doi.org/10.1093/oxfordhb/9780199841578.013.002.

Monelle, Raymond. 1992. Linguistics and Semiotics in Music. Routledge.

—————. 2000. The Sense of Music: Semiotics Essays. Princeton University Press.

—————. 2006. The Musical Topic: Hunt, Military and Pastoral. Indiana University Press.

Murphy, Scott. 2014a. “Scoring Loss in Some Recent Popular Film and Television.” Music Theory Spectrum 36 (2): 295–314. https://doi.org/10.1093/mts/mtu014.

—————. 2014b. “Transformational Theory and the Analysis of Film Music.” In The Oxford Handbook of Film Music Studies, ed. David Neumeyer, 470–99. Oxford University Press. https://doi.org/10.1093/oxfordhb/9780195328493.013.019.

—————. 2023. “An Eightfold Taxonomy of Harmonic Progressions, and Its Application to Triads Related by Major Third and Their Significance in Recent Screen Music.” Journal of Music Theory 67 (1): 141–69. https://doi.org/10.1215/00222909-10232093.

—————. 2024. “Tracking Progressions of Heroic Chord Progressions in Recent Popular Screen Media.” In Film Music Analysis: Studying the Score, ed. Frank Lehman, 46–62. Routledge. https://doi.org/10.4324/9781003001171-3.

Nattiez, Jean-Jacques. 1990. Music and Discourse: Toward a Semiology of Music. Translated by Carolyn Abbate. Princeton University Press.

—————. 2021. Musical Analyses and Musical Exegesis: The Shepherd’s Melody in Richard Wagner’s Tristan and Isolde. Translated by Joan Huguet. University of Rochester Press. https://doi.org/10.1017/9781800103634.

Novack, Saul. 1977. “The Significance of the Phrygian Mode in the History of Tonality.” Miscellanea Musicologica: Adelaide Studies in Musicology 9: 82–127.

Parncutt, Richard. 2014. “The Emotional Connotations of Major versus Minor Tonality: One or More Origins?” Musicae Scientiae 18 (3): 324–53. https://doi.org/10.1177/1029864914542842.

Peirce, Charles Sanders. 1960. “The Icon, Index, and Symbol.” In Elements of Logic, ed. Charles Hartshorne and Paul Weiss, II: 156–73. The Collected Papers of Charles Sanders Peirce. The Belknap Press of Harvard University Press.

Pelikan, Jaroslav, and Walter A. Handen, eds. 1968. Lectures on Titus, Philemon, and Hebrews. Vol. 29. Luther’s Works. Concordia.

Powers, Harold. (1998) 2014. “From Psalmody to Tonality.” In Tonal Structures in Early Music, ed. Cristle Collins Judd, 275–340. Routledge.

Pritchard, Brian W. 2015. Liner notes for Morte e sepoltura di Christo by Antonio Caldara, with the Stavanger Symphony Orchestra, conducted by Fabio Biondi, Glossa GCD 923403, compact disc.

Ratner, Leonard G. 1980. Classic Music: Expression, Form and Style. Schirmer.

Rice, John A. 1998. Antonio Salieri and Viennese Opera. University of Chicago Press. https://doi.org/10.7208/chicago/9780226711270.001.0001.

Rosand, Ellen. 1979. “The Descending Tetrachord: An Emblem of Lament.” Musical Quarterly 65 (3): 346–59. https://doi.org/10.1093/mq/LXV.3.346.

Rosen, Charles. 1988. Sonata Forms. Rev. ed. W. W. Norton.

—————. 1997. The Classical Style: Haydn, Mozart, Beethoven. Rev. ed. W. W. Norton.

Rothstein, William. 1989. Phrase Rhythm in Tonal Music. Schirmer.

—————. 2008. “Common-Tone Tonality in Italian Romantic Opera.” Music Theory Online 14 (1). https://doi.org/10.30535/mto.14.1.3.

—————. 2023. The Musical Language of Italian Opera, 1813–1859. Oxford University Press. https://doi.org/10.1093/oso/9780197609682.001.0001.

Sánchez-Kisielewska, Olga. 2016. “Interactions between Topics and Schemata: The Case of the Sacred Romanesca.” Theory and Practice 41: 47–80.

Schachter, Carl. 1995. “The Triad as Place and Action.” Music Theory Spectrum 17 (2): 149–69. https://doi.org/10.2307/745869.

Schellhous, Rosalie Athol. 1985. “Form and Spirituality in Bach’s St. Matthew Passion.” The Musical Quarterly 71 (3): 295–326. https://doi.org/10.1093/mq/LXXI.3.295.

Senici, Emanuele, ed. 2004. The Cambridge Companion to Rossini. Cambridge University Press. https://doi.org/10.1017/CCOL9780521807364.

Sheinberg, Esti, and William P. Dougherty, eds. 2020. The Routledge Handbook of Music Signification. Routledge. https://doi.org/10.4324/9781351237536.

Somer, Avo. 1995. “Chromatic Third-Relations and Tonal Structure in the Songs of Debussy.” Music Theory Spectrum 17 (2): 215–41. https://doi.org/10.2307/745872.

Steblin, Rita. 2002. A History of Key Characteristics in the Eighteenth and Early Nineteenth Centuries. 2nd ed. University of Rochester Press.

Stillings, Frank S., trans. 1963. The Practical Harmonist at the Harpsichord. By Francesco Gasparini. Edited by David L. Burrows. Yale School of Music.

Suurpää, Lauri. 1999. “Programmatic Aspects of the Second Sonata of Haydn’s Seven Last Words.” Theory and Practice 24: 29–55.

Swain, Joseph P. 1997. Musical Languages. W. W. Norton.

Swenson, Edward Elmgren. 1974. “Antonio Salieri: A Documentary Biography.” PhD diss., Cornell University.

Tarasti, Eero. 2016. “Musical Semiotics—a Discipline, Its History and Theories, Past and Present.” Recherches Sémiotiques/Semiotic Inquiry 36 (3): 19–51. https://doi.org/10.7202/1051395ar.

Taruskin, Richard. 2010. Music in the Nineteenth Century. Oxford University Press.

Temperley, David. 2001. The Cognition of Basic Musical Structures. The MIT Press.

Terrigno, Loretta. 2021. “Emergent Modality: Minor-to-Major Progressions as ‘Tragic-to-Transcendent’ Narratives in Brahms’s Solo Songs.” Music Theory Online 27 (3). https://doi.org/10.30535/mto.27.3.3.

Tischler, Hans. 1958. “Re: Chromatic Mediants—A Facet of Musical Romanticism.” Journal of Music Theory 2 (1): 94–97.

Ulansey, David. 1991. “The Heavenly Veil Torn: Mark’s Cosmic Inclusio.” Journal of Biblical Literature 110 (1): 123–25. https://doi.org/10.2307/3267155.

Virtala, Paula, and Mari Tervaniemi. 2017. “Neurocognition of Major-Minor and Consonance-Dissonance.” Music Perception 34 (4): 387–404. https://doi.org/10.1525/mp.2017.34.4.387.

Waldman, Nahum M. 1974. “Some Notes on Malachi 3:6; 3:13; and Psalm 42:11.” Journal of Biblical Literature 93 (4): 543–49. https://doi.org/10.2307/3263831.

Williams, Peter. 1997. The Chromatic Fourth During Four Centuries of Music. Clarendon Press. https://doi.org/10.1093/oso/9780198165637.001.0001.

Wood, Alice. 2008. Of Wings and Wheels: A Synthetic Study of the Biblical Cherubim. Walter de Gruyter. https://doi.org/10.1515/9783110211214.

Footnotes

* I would like to thank Nicole Biamonte, Richard Cohn, Michèle Duguay (via the Engaged Music Theory Mentoring Program), David Forrest, Robert Hasegawa, Edward Klorman, Su Yin Mak, John Roeder, William Rothstein, Peter Schubert, and Leigh VanHandel for their invaluable comments and suggestions at various stages of this study. I am grateful also for the constructive feedback from the anonymous reviewers and the editorial team of MTO.
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1. For example, see Bribitzer-Stull (2012), Lehman (2013, 2018), Murphy (2014a, 2014b), Forrest (2017b, 2022), and Heine (2018). A summary of the connotations is also given in Example 2.
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2. I follow Cohn’s (1996) notational convention of using + and – to indicate major and minor triads respectively.
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3. To avoid straying away from my main arguments, I present only a cursory overview of semiotics in music. For a more comprehensive discussion of this subject, see Agawu (1991, 2008), Hatten (1994, 1996), Monelle (1992, 2000), Nattiez (1990, 2021), Sheinberg and Dougherty (2020), and Tarasti (2016).
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4. Hexatonic poles falls into a category David Kopp (2002) terms “disjunct mediants” instead of CMs, since triads in a hexatonic pole share no common tones. Nonetheless, given the similar semantic effects of chromatic and disjunct mediants and their prototypical relationship, in this paper I consider both types of mediant relations in conjunction. That is, I include hexatonic poles in my discussion of CM relations. This approach is shared by Victoria Malawey (2020).
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5. See Murphy (2014a) for a discussion on how the homology argument can be applied and expanded to explain expressive connotations of non-CM progressions.
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6. See the quote in the first sentence of paragraph [1.4].
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7. Rossini’s first name is sometimes spelled as “Gioacchino” instead of “Gioachino.” The Cambridge Companion to Rossini adopts the spelling of “Gioachino” and suggests that even though “in present-day Italian the correct spelling of Rossini’s forename is ‘Gioacchino,’ Rossini himself eventually [settled] on ‘Gioachino’ in the 1830s. Rossini experts consider ‘Gioachino’ the more accurate form” (Senici 2004, xiv).
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8. Kopp (2002, 8–9) enumerates all sixteen possible mediant relations (i.e., third-related triads) and offers various ways of classifying them. In his theoretical framework, eight of them are CMs: I–III♯, I–♭III, I–VI♯, I–♭VI, i–♮iii, i–♭iii, i–♮vi, i–♭vi. As mentioned in note 3, in this study I also consider the four disjunct mediants (including hexatonic poles) in conjunction with CMs: I–♭iii, I–♭vi, i–♮III, i–♮VI. (The remaining four of the sixteen are called relative mediants: I–iii, I–vi, i–III, and i–♭VI.)
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9. Murphy (2023, 2024) revises this labeling system by introducing the “IRK (inversion, retrograde, and key) scope.” In this expanded system, CM progressions discussed in this article belong to the M8M_K type. See Forrest (2022, 236n4) for the difference between Forrest’s (which I follow) and Murphy’s use of this “MnM” labelling system.
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10. For example, in Example 6.14 from Rothstein (2023, 202–4), the progression from m. 49 to m. 50 features a minor-third-related CM pair (M3M; D♯+ → F♯+ with an added seventh).
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11. This view is supported by Scott Murphy (2014b, 307–8).
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12. For other analogies between music-theoretical inquiry and evolutionary theory, see Kassler 1983, McCreless 1996, and Greenberg 2022. My use of the term “evolution” emphasizes the diachronic—rather than synchronic—nature of the current inquiry. For a discussion on diachronic versus synchronic investigations in music theory, see Greenberg (2022, 27–47) on the evolution of sonata form. Among the three models for describing the evolution of ideas— selective, dialectical, and creative (Kassler 1983)—this investigation aligns with the creative model, where the evolutionary process is driven by conscious choices. My discussion attributes such choices to the composer of the musical examples.
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13. Both Saul Novack (1977, 103–4) and William Kimmel (1980) argue that, because the Phrygian scale degree $\hat{2}$ can be heard as ♭$\hat{2}$ in a major or minor key when the Phrygian final is interpreted as the tonic, the Neapolitan sixth may also evoke the death association of the Phrygian mode.
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14. In this study, I adopt the term “Phrygian HC” as a shorthand for an HC with a semitone descent in the bass. Indeed, the connection between Phrygian modality and HC may appear problematic (Caplin 2024, 104n152), as these two concepts involve different scale-degree interpretations for the Phrygian final (as $\hat{1}$ in the Phrygian mode and $\hat{5}$ in the HC). Nonetheless, as Liam Hynes-Tawa (2020) argues, the function of the Phrygian final as a proper modal tonic is untenable. See also [2.3] for my discussion of the finality of the Phrygian HC.
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15. The V/vi–I progression resulting from bifocal transitions, possibly interpreted as III♯–I, might be related to theoretical views that III♯ could function as an altered dominant with a raised $\hat{5}$ in a major key (Kopp 2002, 16–17).
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16. Regarding the semantic or practical context of these third-related progressions, Gasparini suggests that they can be “found in sacred as well as secular vocal compositions, both for the chamber and for the theater, in which it is used to end an interrogative or exclamatory phrase and then to begin the next; it is usually found in the serious style, or in recitative” (1708, translated in Stillings 1963, 39). It is important to note, however, that Gasparini does not describe these progressions in terms of their narrative uses that I explore in this paper.
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17. During performance of the concerto, the keyboardist may improvise a cadenza before the Phrygian HC of the Adagio. For example, refer to the recordings by Concerto Italiano (directed by Rinaldo Alessandrini, Naïve Classique OP 30412, 2006) and Swiss Baroque Soloists (directed by Andrés Gabetta, Naxos 8.557755, 2006).
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18. Corelli’s contribution to the norm of bifocal transition supports Rothstein’s (2008) argument that the use of CMs originated in Italian rather than Austro-German music.
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19. Discussions of the harmonic strategy can be found in Ratner (1980, 225–28), Cone (1982, 236), Beach (1983), Rosen (1988, 265–72; 1997, 466–82), Caplin (1998, 141), Hepokoski and Darcy (2006, 198–205).
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20. Bifocal tonality can also represent grief and death-to-life transcendence in musical contexts other than the bifocal transition. Consider the “Crucifixus” section of J. S. Bach’s Mass in B Minor, which is based on an ostinato of the chromatic Phrygian tetrachord in E minor and concludes in an IAC in the relative G major, which leads into the next movement “Et resurrexit.” See Biamonte (2012) for a detailed discussion of this example.
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21. David Huron (2006, 225–7) discusses this paradox between familiarity and surprise, which he calls “Wittgenstein’s puzzle.” Similarly, Rothstein (1989, 254–305) examines Richard Wagner’s use of deceptive cadences (often V–vii^o7/V) as a replacement—instead of a deferral—of V–I authentic cadences. Despite its frequent use throughout Wagner’s operas, the “Wagnerian deceptive cadence” continues to produce dramatic effects in various scenes (Rothstein 1989, 254); see, for example, Example 8.5 in Rothstein (1989, 259) and the accompanying discussion.
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22. In both Examples 15 and 16, the Phrygian HCs are set to questions in the text. This compositional practice of setting a question over a Phrygian HC is common in the recitatives in eighteenth-century opera seria (Downes 1961, 60–62).
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23. The other instances of this chorale can be found in nos. 15, 17, 44, and 54 of the Passion. (The numbering is based on Neue Bach-Ausgabe.) All of these settings are harmonized in the major (Ionian) mode. David Hill (1996) offers a detailed comparative analysis of these chorale settings.
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24. Several other authors support Hill’s interpretation. Johann Philipp Kirnberger (1771, 326) and Lori Burns (1995, 231) both identify the chorale tune—without referring to any harmonization in particular—as being in the Phrygian mode. Hynes-Tawa (2020, 95–96) acknowledges that Bach’s harmonization of the chorale in Example 17 poses an analytical problem but concurs that it has a Phrygian ending.
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25. Linguists describe this process of word formation by concatenating multiple words as “compounding” (Benczes 2010), and words like “metaphor” fall under the category of “metaphoric compounds” (Bauer 2008). For an accessible overview of this phenomenon, see Deutscher (2005, 115–43).
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26. For example, its genitive form “metaphoron (μεταφορών)” translates to “Transport” in title of the Ministry of Infrastructure and Transport in today’s Greek government.
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27. I thank anonymous reviewer #1 for introducing these examples to me.
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28. Alternatively, one could interpret “Rex tremendae majestatis” as representing life, akin to the case of “Eja mater” in Example 12. In this view, the preceding question indirectly signifies death through a sense of peril and insecurity. With this interpretation, the CM in this example still conveys the connotation of death-to-life transcendence, though less explicitly.
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29. I thank Edward Klorman for introducing this example to me.
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30. See also Anson-Cartwright (2000) for a discussion on the large-scale harmonic implication of this M8M progression.
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31. James MacKay’s (2020, 66–69) analysis of the instrumental version of the work shows that the bifocal transition in this example concludes a “main theme ⇒ transition” unit in the movement’s sonata form. See also my discussion (para. [2.6]) on the connection between the Baroque model of bifocal transition and formal structure in Classical sonatas.
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32. See also Lauri Suurpää (1999) for a detailed voice-leading, motivic, and formal analysis of the instrumental version of this movement. Suurpää identifies mm. 1–20 of the movement as the “first group” of the sonata-form movement, with a Schenkerian interruption occurring at the bifocal transition.
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33. This classification by formal contexts parallels Forrest’s (2017b) approach of organizing popular-music examples of CMs by musical context.
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34. Due to their general nature, the identification of formal functions is not always straightforward, and ambiguities can arise. While some may challenge my form-functional analyses, my central argument is that CMs have dissociated from their Baroque cadential origin yet retained their semantic connation in other formal contexts. While the labelling of these contexts remains open to re-examination, they are clearly distinguished from the cadential function of the bifocal cadence.
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35. Caplin (2024, 69) emphasizes the distinction between the deceptive resolution of a non-cadential dominant and a genuine deceptive cadence, offering examples of contexts where such non-cadential resolutions occur.
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36. Caplin (1998) offers several interchangeable terms for the formal function of phrase prefixes like this: “before-the-beginning” (15), “introduction function” (15), “introductory function” (15), “initiating function” (4), or in the sonata context, “transitional introduction” (147).
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37. David Buch (2008) offers a thorough discussion of the portrayal of the supernatural in The Magic Flute and other eighteenth-century theatrical or operatic music, though he does not address the use of CMs. For an analysis of the association between Phrygian modality and death in The Magic Flute, see Novack (1977, 103–4).
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38. On a subject related to the current study, Olga Sánchez-Kisielewska (2016) presents a corpus study to demonstrate how the Romanesca schema becomes a signifier of spirituality and transcendence in late eighteenth-century Viennese music. Her methodology could be applied to further investigate the semantic evolution of CMs.
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39. Strictly speaking, my reading of CMs in several examples does involve a degree of reduction of the musical surface. In Examples 18, 23, 27, and 28, my analysis reduces away embellishing tones that function as anacruses, passing tones, or arpeggiations. Nonetheless, these embellishments are transient and do not disrupt the immediate succession of the CM triads.
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