{"id":9120,"date":"2024-06-09T21:54:08","date_gmt":"2024-06-09T21:54:08","guid":{"rendered":"https:\/\/theory.esm.rochester.edu\/integral\/?page_id=9120"},"modified":"2025-08-16T14:20:15","modified_gmt":"2025-08-16T14:20:15","slug":"bilik","status":"publish","type":"page","link":"https:\/\/theory.esm.rochester.edu\/integral\/37-2024\/bilik\/","title":{"rendered":"Key Duality and Melody-Bass Disjunction in Faur\u00e9 and Durufl\u00e9"},"content":{"rendered":"\n\n\n\n\n<script type=\"text\/x-mathjax-config\"> \n\t\tMathJax.Hub.Config({ \n\t\t  messageStyle: \"none\" \n}); \n<\/script>\n\n\n\n<p><strong>Matthew Bilik<\/strong><\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Abstract<\/h3>\n\n\n\n<blockquote class=\"wp-block-quote is-layout-flow wp-block-quote-is-layout-flow\">\n<p>This paper explicates how the sensation of two active keys, known as key duality or tonal pairing, often results as disjunction between the melody and bass in the music of Gabriel Faur\u00e9 and Maurice Durufl\u00e9. In Faur\u00e9\u2019s late chamber works, a distinct type of key duality arises not as a juxtaposition of two keys but from the superposition of two. Faur\u00e9\u2019s use of key duality is mirrored by other twentieth-century French composers; Durufl\u00e9 echoes a similar type of duality, albeit to a greater extent. Employing motivic segmentation and voice-leading analysis, I adapt the research of Peter Smith (1997 and 2013), Kaminsky (2004), and Ferrandino (2022), among others, to illustrate how the sensation of two tonal centers emerges when the tonal outline of a melody or bass projects its own center separate from that of other voices. Attention to outer voices sheds light on Faur\u00e9 and Durufl\u00e9\u2019s tonal sleight of hand\u2014a topic many have noticed but few have illuminated.<\/p>\n\n\n\n<p><a href=\"https:\/\/theory.esm.rochester.edu\/integral\/?page_id=9122\" data-type=\"URL\" data-id=\"https:\/\/theory.esm.rochester.edu\/integral\/?page_id=9122\">View PDF<\/a><br><a href=\"https:\/\/theory.esm.rochester.edu\/integral\/37-2024\/\" data-type=\"page\" data-id=\"9044\">Return to Volume 37<\/a><\/p>\n<\/blockquote>\n\n\n\n<p><strong>Keywords and Phrases<\/strong>: Faur\u00e9, key duality, disjunction, Durufl\u00e9, tonal pairing<\/p>\n\n\n\n<p class=\"has-drop-cap\">As a preliminary demonstration of key duality in Gabriel Faur\u00e9\u2019s late chamber works, I present an excerpt from the Violin Sonata no. 2 (1916) with the bass line omitted in <strong>Example 1<\/strong>. Survey the B major melody with its emphasis on $$\\hat{5}$$ (<nobr>F$$\\sharp$$<\/nobr>), the dominant-tonic leap across mm. 35<em>\u2013<\/em>36, as well as the B downbeats in mm. 36 and 42. Note the accompanying inner voices that support the B major tonic, as well: the upper (SAT) parts articulate B major triads on the downbeats of mm. 34, 37, and 38, cycling through a syntactic <nobr>vii$$^{\\circ6}$$\/IV-IV-V$$^{7}$$\/V<\/nobr> thereafter.<\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full is-resized\"><a href=\"https:\/\/theory.esm.rochester.edu\/integral\/bilik-vol37-example-1\/\"><img loading=\"lazy\" decoding=\"async\" width=\"936\" height=\"200\" src=\"https:\/\/theory.esm.rochester.edu\/integral\/wp-content\/uploads\/2024\/06\/bilik-vol37-example-1.png\" alt=\"Bilik, Example 1\" class=\"wp-image-9347\" style=\"width:512px;height:117px\" srcset=\"https:\/\/theory.esm.rochester.edu\/integral\/wp-content\/uploads\/2024\/06\/bilik-vol37-example-1.png 936w, https:\/\/theory.esm.rochester.edu\/integral\/wp-content\/uploads\/2024\/06\/bilik-vol37-example-1-300x64.png 300w, https:\/\/theory.esm.rochester.edu\/integral\/wp-content\/uploads\/2024\/06\/bilik-vol37-example-1-768x164.png 768w\" sizes=\"auto, (max-width: 706px) 89vw, (max-width: 767px) 82vw, 740px\" \/><\/a><figcaption class=\"wp-element-caption\"><b>Example 1.<\/b> Faur\u00e9, Violin Sonata no. 2, op. 108\/3, mm. 34\u201342. B major melody with upper (SAT) parts. Bass line omitted.<\/figcaption><\/figure>\n<\/div>\n\n\n<p><span style=\"font-weight: 400;\">However, the excerpt eschews a tidy B major interpretation due to a rogue bass. <\/span><b>Example 2<\/b><span style=\"font-weight: 400;\"> presents the passage in its entirety, now including the bass which outlines <nobr>G$$\\sharp$$<\/nobr> minor. Examine the <nobr>G$$\\sharp$$<\/nobr> stress on the downbeats of mm. 34 and 38\u2014the beginning of each phrase\u2014as well as the tonic-dominant leaps between <nobr>G$$\\sharp$$<\/nobr> and <nobr>D$$\\sharp$$.<\/nobr> More than simply adding color or dissonance to the sonic B major surface, the <nobr>G$$\\sharp$$<\/nobr> profile of the bass suggests that two simultaneous keys are in play. That is, the linear presentation of <nobr>G$$\\sharp$$<\/nobr> minor in the bass argues for a <nobr>G$$\\sharp$$<\/nobr> minor reading, rather than viewing the bass as an under-seventh of a more structural B major foreground harmony. As we will see, the ambiguity of a single key\u2014caused by the interaction of two tonal centers at once\u2014is characteristic of Faur\u00e9\u2019s later works, where key duality becomes more pronounced. Moreover, duality of this sort endures in the music of Maurice Durufl\u00e9, who engages it with grander scope and breadth.&nbsp;<\/span><\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full is-resized\"><a href=\"https:\/\/theory.esm.rochester.edu\/integral\/bilik-vol37-example-2\/\"><img loading=\"lazy\" decoding=\"async\" width=\"936\" height=\"270\" src=\"https:\/\/theory.esm.rochester.edu\/integral\/wp-content\/uploads\/2024\/06\/bilik-vol37-example-2.png\" alt=\"Bilik, Example 2\" class=\"wp-image-9348\" style=\"width:512px;height:148px\" srcset=\"https:\/\/theory.esm.rochester.edu\/integral\/wp-content\/uploads\/2024\/06\/bilik-vol37-example-2.png 936w, https:\/\/theory.esm.rochester.edu\/integral\/wp-content\/uploads\/2024\/06\/bilik-vol37-example-2-300x87.png 300w, https:\/\/theory.esm.rochester.edu\/integral\/wp-content\/uploads\/2024\/06\/bilik-vol37-example-2-768x222.png 768w\" sizes=\"auto, (max-width: 706px) 89vw, (max-width: 767px) 82vw, 740px\" \/><\/a><figcaption class=\"wp-element-caption\"><b>Example 2.<\/b> Faur\u00e9, Violin Sonata no. 2, op. 108\/3, mm. 34\u201342. Key duality between B major melody and <nobr>G$$\\sharp$$<\/nobr> minor bass line. <\/figcaption><\/figure>\n<\/div>\n\n\n<p><span style=\"font-weight: 400;\">This article explores how similar instances of duality between keys occurs as a disjunction between the melody and bass in four other chamber pieces by Faur\u00e9: the Piano Quintet no. 2 (1921), Cello Sonata no. 2 (1921), Piano Quintet no. 1 (1906), and Piano Trio (1923). It concludes with the Requiem, op. 9 (1947) by Durufl\u00e9, who heightens the sensation of key duality. In one situation, the tonal profile of the melody is so robust that it furnishes its own center separate from the accompaniment.<\/span><span id='easy-footnote-1-9120' class='easy-footnote-margin-adjust'><\/span><span class='easy-footnote'><a href='https:\/\/theory.esm.rochester.edu\/integral\/37-2024\/bilik\/#easy-footnote-bottom-1-9120' title='When speaking of the accompaniment versus the melody, I mean the accompaniment &lt;em&gt;with &lt;\/em&gt;the bass unless stated otherwise. However, as we will see, inner voices can support the tonal center of the melody, bass, or both.'><sup>1<\/sup><\/a><\/span><span style=\"font-weight: 400;\"><\/span> When this arises, the composer may elevate the structural role of the upper parts to convey a distinct center or key. However, in the other circumstance, the tonal fingerprint of the <i><span style=\"font-weight: 400;\">bass<\/span><\/i><span style=\"font-weight: 400;\"> suggests a second tonic layered beneath the other. That is, the bass outlines a center or key separate from that of the upper parts. I recast theories of tonal pairing and melodic-harmonic divorce that, while abundant, have not been combined in this type of repertoire. On the other hand, I maintain that key duality in Faur\u00e9 and Durufl\u00e9 often proceeds from a divorce between tonal profiles of the melody and bass\u2014a perspective that has been largely undertheorized outside of popular music. As preface to my analyses, a brief overview of tonal pairing and melodic-harmonic divorce unfurls below.&nbsp;<\/span><\/p>\n\n\n\n<h2 class=\"wp-block-heading\"><strong>Tonal Pairing and Stratification<\/strong><\/h2>\n\n\n\n<p><span style=\"font-weight: 400;\">Previous theorists have investigated the sensation of two simultaneous tonics in play, or tonal pairing. Known also as the \u201cdouble-tonic complex\u201d according to Robert Bailey (1985), this phenomenon typically refers to two active tonics a third apart, juxtaposed but existing on an equal structural level. Peter Smith (2013) locates prescient instances of tonal pairing in common practice Germanic music, revealing how 5\u20136 exchanges at higher levels create hierarchical ambiguity between keys a third apart (e.g., a tonic and its submediant). Viewed in this fashion, tonal pairing may be the consequence of shifting tonal focus within a 5\u20136 exchange.<span id='easy-footnote-2-9120' class='easy-footnote-margin-adjust'><\/span><span class='easy-footnote'><a href='https:\/\/theory.esm.rochester.edu\/integral\/37-2024\/bilik\/#easy-footnote-bottom-2-9120' title='One might also consider these relationships as neo-Riemannian R or L transformations.'><sup>2<\/sup><\/a><\/span> Other extant literature on key duality focuses on a single composer. Boyd Pomeroy (2004) tracks the severity of dueling tonics in Debussy, while Ellen Bakulina (2018) invokes key duality when talking about \u201cproto-harmonic\u201d structures in Rachmaninoff.<\/span><span id='easy-footnote-3-9120' class='easy-footnote-margin-adjust'><\/span><span class='easy-footnote'><a href='https:\/\/theory.esm.rochester.edu\/integral\/37-2024\/bilik\/#easy-footnote-bottom-3-9120' title='In her earlier work on Russian music, Bakulina (2014) culls the nuances of mutability\u2014a uniquely Russian construal of key duality.'><sup>3<\/sup><\/a><\/span> Joseph Straus (1986) traces third-related tonics in Stravinsky around a shifting tonal \u201caxis.\u201d Straus\u2019s work on tonal stratification is applicable to the present study\u2014chiefly, his tenet that for a tonal axis to exist, it must be stated outright as a verticality.<span id='easy-footnote-4-9120' class='easy-footnote-margin-adjust'><\/span><span class='easy-footnote'><a href='https:\/\/theory.esm.rochester.edu\/integral\/37-2024\/bilik\/#easy-footnote-bottom-4-9120' title='See Straus (1982), who shares an example from the &lt;em&gt;Symphony of Psalms&lt;\/em&gt; where the E minor and G major triads appear simultaneously as an arpeggio. However, BaileyShea (2007) points out that Straus never calls this fusion of triads a \u201ctonic\u201d (BaileyShea, 196). '><sup>4<\/sup><\/a><\/span> This is precisely what ensues in Example 2 and the following analyses where the chord at the beginning or end of a phrase is a seventh chord that fuses two dueling tonics into one. I also subscribe to the idea of two active tonics of equal weight, frequently related by thirds. In Faur\u00e9\u2019s late <em>oeuvre<\/em>, the melody or upper (SAT) parts often express a key a third higher than the key expressed by the bass.<span id='easy-footnote-5-9120' class='easy-footnote-margin-adjust'><\/span><span class='easy-footnote'><a href='https:\/\/theory.esm.rochester.edu\/integral\/37-2024\/bilik\/#easy-footnote-bottom-5-9120' title='For instance, in the second movement of Faur\u00e9\u2019s Violin Sonata no. 2, the opening theme teeters between A major (I) and &lt;nobr&gt;C$$\\sharp$$&lt;\/nobr&gt; minor (iii) due to the &lt;nobr&gt;C$$\\sharp$$-D$$\\sharp$$-E&lt;\/nobr&gt; melodic statements.'><sup>5<\/sup><\/a><\/span> In addition, I view these individual tonal centers as superimposed rather than juxtaposed, in the vein of polytonality.<span id='easy-footnote-6-9120' class='easy-footnote-margin-adjust'><\/span><span class='easy-footnote'><a href='https:\/\/theory.esm.rochester.edu\/integral\/37-2024\/bilik\/#easy-footnote-bottom-6-9120' title='The aural perceptibility of polytonality has been long contested. Thompson and Mor (1992) admit that in the face of two competing tonal centers (\u201ctextures\u201d), the listener elects one, declaring the other \u201cineffective\u201d\u2014a source of dissonance in the principal key.'><sup>6<\/sup><\/a><\/span>I resort to the term key duality rather than double-tonic complex, because in some excerpts the melody or bass alludes to tonal relationships (e.g., i-v) in a key.<span id='easy-footnote-7-9120' class='easy-footnote-margin-adjust'><\/span><span class='easy-footnote'><a href='https:\/\/theory.esm.rochester.edu\/integral\/37-2024\/bilik\/#easy-footnote-bottom-7-9120' title='A key implies a general network of tonal associations oriented around a \u201csingle, maximally stable pitch class\u201d (Nobile 2020, 209).'><sup>7<\/sup><\/a><\/span> That said, many passages do simply involve a double-tonic complex solely by means of two tonics unfolding.<\/p>\n\n\n\n<p><span style=\"font-weight: 400;\">Matthew BaileyShea (2007) removes the haze surrounding the double-tonic complex by categorizing the salience of a dual tonic.<\/span><span id='easy-footnote-8-9120' class='easy-footnote-margin-adjust'><\/span><span class='easy-footnote'><a href='https:\/\/theory.esm.rochester.edu\/integral\/37-2024\/bilik\/#easy-footnote-bottom-8-9120' title='BaileyShea\u2019s primary task is to connect the D major and F$$\\sharp$$ minor duality of the music to the poetic text in Wolf\u2019s &lt;em&gt;Auf eine Christblume&lt;\/em&gt;.'><sup>8<\/sup><\/a><\/span><span style=\"font-weight: 400;\"> In the first category, \u201cvacillation between two keys\u201d is more of a juxtaposition than a simultaneous overlapping of two keys. This is different from the second category, \u201ctonal collision,\u201d where keys may substitute for one another or coincide at the same time (194).<span id='easy-footnote-9-9120' class='easy-footnote-margin-adjust'><\/span><span class='easy-footnote'><a href='https:\/\/theory.esm.rochester.edu\/integral\/37-2024\/bilik\/#easy-footnote-bottom-9-9120' title='In the latter sense, category two shares features with category three.'><sup>9<\/sup><\/a><\/span> The third category contends that this fusion of dual tonics can act as structural tonic, like the conflation of a C major and A minor tonic into an <nobr>Amm$$^{7}$$<\/nobr> tonic. Crucially, BaileyShea argues that these dual utterances need not be far-reaching\u2014they do not \u201crequire analysis of an entire piece\u201d\u2014but may play out over smaller spans of time within more traditional monotonal works (194).<span id='easy-footnote-10-9120' class='easy-footnote-margin-adjust'><\/span><span class='easy-footnote'><a href='https:\/\/theory.esm.rochester.edu\/integral\/37-2024\/bilik\/#easy-footnote-bottom-10-9120' title='Certain moments of the &lt;nobr&gt;D\/F$$\\sharp$$&lt;\/nobr&gt; double-tonic complex in BaileyShea\u2019s analyses are incredibly isolated. For instance, he labels a lower-level, contrapuntal D augmented triad as a manifestation of a D major and &lt;nobr&gt;F$$\\sharp$$&lt;\/nobr&gt; major complex. Elsewhere, he describes a D minor chord\u2014passing in the middle of an omnibus progression\u2014as an \u201cespecially poignant\u201d moment of the &lt;nobr&gt;D\/F$$\\sharp$$&lt;\/nobr&gt; complex. Thus, for BaileyShea, instances of the double-tonic complex may be quite local, even lasting for two beats within \u201cmore conventional linear patterns\u201d (201).'><sup>10<\/sup><\/a><\/span>&nbsp;<\/span><\/p>\n\n\n\n<p><span style=\"font-weight: 400;\">Drew Nobile (2020) contrasts tonal pairing with the double-tonic complex, although in both neither dual tonic is superior to the other. Tonal pairing, he writes, involves oscillation between two keys\u2014a \u201cjuxtaposition of two monotonal frameworks\u201d\u2014that may incite tonal conflict between two incompatible keys (207).<\/span><span id='easy-footnote-11-9120' class='easy-footnote-margin-adjust'><\/span><span class='easy-footnote'><a href='https:\/\/theory.esm.rochester.edu\/integral\/37-2024\/bilik\/#easy-footnote-bottom-11-9120' title='Nobile explicates the distinction between tonal pairing and the double-tonic complex by comparing the two to linguistic ambiguity and linguistic indeterminacy, respectively. The former entails a \u201csemantic problem in need of a solution,\u201d such as the cognitive confusion between two homographs, like the word \u201cbear,\u201d while the latter simply conveys \u201cvagueness or generality\u201d but still gets the semantic meaning across (222\u201324).'><sup>11<\/sup><\/a><\/span> The double-tonic complex, instead, is more of an abstract tonality that conjoins two tonics to create a new governing tonality. Nobile defends this more contentious view of tonality as a conflation of two keys, explaining that in the double-tonic complex, neither key is dissonant with the other because they stem from the same abstract, fused tonality; the four-note sonority (such as an <nobr>Amm$$^{7}$$<\/nobr>) is <em>generative<\/em>, not <em>the<\/em> tonic for a piece (210).<span id='easy-footnote-12-9120' class='easy-footnote-margin-adjust'><\/span><span class='easy-footnote'><a href='https:\/\/theory.esm.rochester.edu\/integral\/37-2024\/bilik\/#easy-footnote-bottom-12-9120' title='In his expert justification of the double-tonic complex, Nobile does not ignore experiential interpretations and cites \u201crapid reorientations from hearing one center to the other\u201d (216).'><sup>12<\/sup><\/a><\/span> For Nobile, a four-note controlling sonority is critical for the double-tonic complex to exist, which will inevitably blur the distinction between the two paired keys and the notion of a single tonal center, as well. Consequently, two essential points emerge in a true double-tonic complex: 1) centricity to a single key is not required, and 2) the listener does not necessarily hear two keys at once but may hear one or the other depending on contextual factors. Like Nobile, I reiterate the latter in the hopes of allaying skepticism surrounding the double-tonic complex. In the forthcoming examples containing a \u201ctonic\u201d seventh chord, I stress linear phenomena as a vital contextual factor.&nbsp;&nbsp;&nbsp;<\/p>\n\n\n\n<p><span style=\"font-weight: 400;\">Tonal stratification, or the layering of tonal centers separated by register and texture, is indirectly related to key duality. Duality may contain vestiges of tonal stratification, but stratification is by no means a requirement of duality. Specifically, tonal stratification evokes the concept of polytonality via superimposed tonal strata. In his work on Ravel, Peter Kaminsky (2004) reframes the presence of polytonality, arguing that listeners \u201cprioritize\u201d<\/span> <span style=\"font-weight: 400;\">one tonal center at a time based on the surrounding musical context. He describes how the bass may either 1) assimilate the dissonant upper voices into one tonal center or 2) elicit a \u201cdual prioritization\u201d when the tonal weight of the treble voices establish a primary or secondary center.<\/span><span id='easy-footnote-13-9120' class='easy-footnote-margin-adjust'><\/span><span class='easy-footnote'><a href='https:\/\/theory.esm.rochester.edu\/integral\/37-2024\/bilik\/#easy-footnote-bottom-13-9120' title='Kaminsky (2004) points out that Ravel\u2019s tendency to use \u201cunresolved\u201d appoggiaturas is an example of the first category, where the bass subsumes the treble voices under its tonal purview. Kaminsky\u2019s idea of strata prioritization is pertinent to this study; turning attention to either the bass or soprano may shade listening.'><sup>13<\/sup><\/a><\/span> Other authors, like Philip Rupprecht (1996), allow stratification to signify a tension (in his words, a \u201cdiscrepancy\u201d) between two \u201cfocal pitches,\u201d not necessarily two triads or keys (312 and 320).<span id='easy-footnote-14-9120' class='easy-footnote-margin-adjust'><\/span><span class='easy-footnote'><a href='https:\/\/theory.esm.rochester.edu\/integral\/37-2024\/bilik\/#easy-footnote-bottom-14-9120' title='Rupprecht shows how these discrete pitches, especially in the lower register, can still imply a tonal, or harmonic, structure.'><sup>14<\/sup><\/a><\/span> To him, how the voices are registrally delineated becomes a principal factor in the strength of strata. Such sensitivity to texture has great payoff in Faur\u00e9 and Durufl\u00e9; the fact that the <em>outer<\/em> voices partake in duality makes tonal disjunction more prominent.<span id='easy-footnote-15-9120' class='easy-footnote-margin-adjust'><\/span><span class='easy-footnote'><a href='https:\/\/theory.esm.rochester.edu\/integral\/37-2024\/bilik\/#easy-footnote-bottom-15-9120' title='Both Kaminsky and Rupprecht take Milhaud\u2019s idea of polytonality as a point of departure but apply it to their work quite differently.'><sup>15<\/sup><\/a><\/span>&nbsp;<\/p>\n\n\n\n<h2 class=\"wp-block-heading\"><strong>Melodic-Harmonic Divorce<\/strong><\/h2>\n\n\n\n<p><span style=\"font-weight: 400;\">Pulling apart the tonal layers of music has elucidated opaque or dissonant harmonic phenomena, especially those in pop and rock. Authors have detected a melodic-harmonic divorce in popular music,<\/span><span id='easy-footnote-16-9120' class='easy-footnote-margin-adjust'><\/span><span class='easy-footnote'><a href='https:\/\/theory.esm.rochester.edu\/integral\/37-2024\/bilik\/#easy-footnote-bottom-16-9120' title='Allan Moore (1995) coined the term melodic-harmonic divorce. De Clercq (2019) notes that Moore recognized three \u201cfunctional layers\u201d in pop and rock: bass, melody, and harmony.'><sup>16<\/sup><\/a><\/span> where the \u201cindependence or stratification of musical layers\u201d generate unusual dissonances (de Clercq 2019, 273). As David Temperley (2007) and Nobile (2015) point out, melody and harmony each have potential to express a different level of formal or harmonic structure in diverging ways.<span id='easy-footnote-17-9120' class='easy-footnote-margin-adjust'><\/span><span class='easy-footnote'><a href='https:\/\/theory.esm.rochester.edu\/integral\/37-2024\/bilik\/#easy-footnote-bottom-17-9120' title='De Clercq (2019) reworks Nobile\u2019s categories of melodic-harmonic divorce to fashion his categories of harmonic-bass divorce.'><sup>17<\/sup><\/a><\/span> Although more common in the popular music sphere, a general theory of separate tonal layers need not be style-bound or repertoire-specific. I do not advocate drawing false parallels between popular music and that of Faur\u00e9 and Durufl\u00e9, let alone believe in committing Nobile\u2019s categories of hierarchy, syntax, and loop divorce to classical music. Nevertheless, we can observe a similar type of disjunction between musical layers in Faur\u00e9 and Durufl\u00e9 that facilitates varied shadings of the passage depending on the tonal strength of each stratum. In Example 2, we may hear B major or <nobr>G$$\\sharp$$<\/nobr> minor depending on whether we follow the melody or bass, respectively. It is important to note that while ideas of stratification and divorce share conceptual proximity, their application is not interchangeable. For instance, a divorce between melody and harmony does not necessarily mean that stratification of pitch or key exists.<span id='easy-footnote-18-9120' class='easy-footnote-margin-adjust'><\/span><span class='easy-footnote'><a href='https:\/\/theory.esm.rochester.edu\/integral\/37-2024\/bilik\/#easy-footnote-bottom-18-9120' title='Divorce in popular music often refers explicitly to divorce of &lt;em&gt;function; &lt;\/em&gt;see, for example, Drew Nobile (2015).'><sup>18<\/sup><\/a><\/span>\n\n\n\n<p><span style=\"font-weight: 400;\">My present work more closely mirrors that of Matthew Ferrandino (2022) and his idea of multi-centric complexes in pop and rock. In these complexes, diverse performing forces (i.e., bass, singer\/melody, and guitar\/keyboard) may imply a tonal center distinct from the others. His example from \u201cDreams,\u201d by Fleetwood Mac, ensconces two tonal streams: an F major bass line that lands on F every two bars and an A minor\u2014or even C major\u2014vocal line which begins each phrase on A or C while accentuating the pitches A, C, and E.<\/span><span id='easy-footnote-19-9120' class='easy-footnote-margin-adjust'><\/span><span class='easy-footnote'><a href='https:\/\/theory.esm.rochester.edu\/integral\/37-2024\/bilik\/#easy-footnote-bottom-19-9120' title='Nobile (2020) also calls attention to the harmonic corollary of two tonal strata. As mentioned earlier, he shows how an A minor bass line and C major vocal line produce a four-note \u201ctonic\u201d sonority at the beginning of the chorus in Hall and Oates\u2019 \u201cPrivate Eyes.\u201d As the generative tonic of a true double-tonic complex, neither A minor nor C major is \u201cstructurally superior\u201d to the other (Nobile 2020, 210).'><sup>19<\/sup><\/a><\/span> However, like Nobile, he does not profess that listeners hear both tonal threads but acknowledges how they might shift from one to the other (30). In his examples as well as mine to come, stratification imparts either 1) a sense of ambiguity of one center or 2) a fluctuation of competing centers. My choice of word, \u201cdisjunction,\u201d hopes to highlight the autonomy of the melodic and bass layers even more. In fact, such musical agency is not limited to outer voices; I show how inner voices assert their own musical agency at times, strengthening the role of the bass or melody in the interpretation. I take my definition of agency from Edward Klorman (2016), who defines multiple agency as an interaction between independent musical roles or ideas, enacted by performers who influence the actions of one another in a \u201cseemingly spontaneous\u201d manner (122).<span id='easy-footnote-20-9120' class='easy-footnote-margin-adjust'><\/span><span class='easy-footnote'><a href='https:\/\/theory.esm.rochester.edu\/integral\/37-2024\/bilik\/#easy-footnote-bottom-20-9120' title='Although Klorman does not analyze tonal layers, his work on musical agency in classical music grapples (quite abstractly) with how listeners interpret the dynamic dialogue of a string quartet.'><sup>20<\/sup><\/a><\/span>\n\n\n\n<h2 class=\"wp-block-heading\"><strong>Role of Bass<\/strong><\/h2>\n\n\n\n<p><span style=\"font-weight: 400;\">The ebb and flow of disputing tonal centers raises questions about the function and, thus, the structural level of each voice. For instance, if the soprano melody projects the leading key, the bass may function as color tones. In these cases, we might view the bass as the added sixth of the chord, appearing a third below the root of the structural triad.<\/span><span id='easy-footnote-21-9120' class='easy-footnote-margin-adjust'><\/span><span class='easy-footnote'><a href='https:\/\/theory.esm.rochester.edu\/integral\/37-2024\/bilik\/#easy-footnote-bottom-21-9120' title='The presence of key duality from melody or bass disjunction may have been a symptom of Faur\u00e9\u2019s auditory issues, which drastically distorted his pitch perception. According to Nectoux (2004), Faur\u00e9 \u201cheard bass notes a third higher and treble notes a third lower\u201d (293). Nectoux quotes Faur\u00e9 as early as 1907 lamenting his faulty hearing. Listening to his compositions after he wrote them was particularly cruel for this reason, as described by Catrena Flint (1997, 3\u20134). Faur\u00e9 was known to compose away from the piano as a result.'><sup>21<\/sup><\/a><\/span> For example, an <nobr>Emm$$^{7}$$<\/nobr> chord may be read as a G major triad with an added sixth (E) in the bass voice.<span id='easy-footnote-22-9120' class='easy-footnote-margin-adjust'><\/span><span class='easy-footnote'><a href='https:\/\/theory.esm.rochester.edu\/integral\/37-2024\/bilik\/#easy-footnote-bottom-22-9120' title='See Tait (1986). Tait also identifies more major chords with added sixths during Faur\u00e9\u2019s late period (Tait, 64\u201365).'><sup>22<\/sup><\/a><\/span> Although he does not focus on key duality, Andrew Pau (2016) uses bass supposition to disentangle a Parisian repertoire so saturated by seventh chords. Even when the musical surface states a root-position seventh chord, Pau occasionally takes the third of the chord as the fundamental bass to clarify the root motion of the phrase. This is akin to hearing the bass as an \u201cunder-seventh\u201d <em>or<\/em> as an added sixth in the bass voice\u2014either way, a dissonance in relation to the structural upper triad.<span id='easy-footnote-23-9120' class='easy-footnote-margin-adjust'><\/span><span class='easy-footnote'><a href='https:\/\/theory.esm.rochester.edu\/integral\/37-2024\/bilik\/#easy-footnote-bottom-23-9120' title='This is, admittedly, a dualist reading. Pau (2016) cites dualist perspectives from Cohn and d\u2019Indy, the latter of which \u201cmediated\u201d the dualist teachings of Riemann in France (Pau, 84).'><sup>23<\/sup><\/a><\/span> Similarly, in Example 2, if the B major of the soprano sounds stronger, then we might hear the bass as a color tone meant to enrich the texture.<\/p>\n\n\n\n<p><span style=\"font-weight: 400;\">It stands to reason that the bass can take a front seat as harmonic driver or a back seat as harmonic color. In the first case, the bass conforms to expectations of a tonal progression via a syntactical phrase: a T-S-D-T phrase model or at least a T-D-T outline.<\/span><span id='easy-footnote-24-9120' class='easy-footnote-margin-adjust'><\/span><span class='easy-footnote'><a href='https:\/\/theory.esm.rochester.edu\/integral\/37-2024\/bilik\/#easy-footnote-bottom-24-9120' title='&amp;nbsp;If the bass line articulates a traditional stock segment, such as &lt;nobr&gt;$$\\hat{1}$$-$$\\hat{6}$$-$$\\hat{4}$$-$$\\hat{5}$$&lt;\/nobr&gt; or &lt;nobr&gt;$$\\hat{1}$$-$$\\hat{4}$$-$$\\hat{5}$$-$$\\hat{1}$$&lt;\/nobr&gt;, we may hear it as confirming its own key even without the supporting upper voices. Gilad Rabinovitch (2023), for instance, states that \u201cFaur\u00e9 tends to use the \u2018wrong\u2019 triads or seventh chords above conventional tonal bass schemata\u201d (64). In other words, these \u201ctonally disorientating upper-voice structures, often $$^{6}_{3}$$ substitutions,\u201d bewilder the key expressed by the bass (83).'><sup>24<\/sup><\/a><\/span> In the second case, using the bass for color rather than as a vehicle for harmonic function turns a norm of tonality on its head; that is, the motives and upper parts point to a tonal center while the bass simply adds textural density or harmonic color.<span id='easy-footnote-25-9120' class='easy-footnote-margin-adjust'><\/span><span class='easy-footnote'><a href='https:\/\/theory.esm.rochester.edu\/integral\/37-2024\/bilik\/#easy-footnote-bottom-25-9120' title='If the bass has a dissonance (e.g., chordal seventh) that foregoes typical resolution, context will determine if it is a non-chord tone or a fundamental dissonance.'><sup>25<\/sup><\/a><\/span> A broader issue of chord recognition and overall key finding concerns voice doubling and voice leading. For instance, unconventional voicings may mask the identity of a chord or key. Due to oscillating centricity between two members of a chord (e.g., the root versus the third), the listener may discern more than one key. Part of this is an outgrowth of reversing the hierarchy of root positions over inversions, which may lead to tonal allusions.<span id='easy-footnote-26-9120' class='easy-footnote-margin-adjust'><\/span><span class='easy-footnote'><a href='https:\/\/theory.esm.rochester.edu\/integral\/37-2024\/bilik\/#easy-footnote-bottom-26-9120' title='Likewise, Faur\u00e9 reverses traditional tonal practice whenever he opts for plagal gestures over authentic gestures. For an in-depth dive into allusion in Faur\u00e9, see James Sobaskie (1999). He identifies three forms of allusion: tonal implication, transient tonicization, and modal suggestion. The first refers to \u201cthe allusion to elements of tonal voice-leading structure, either absent, forthcoming, or already past\u201d (163\u2013205). All Sobaskie\u2019s forms of allusion occur in Faur\u00e9 due to unique doublings or voicings that de-center tonal practices, such as stressing the chordal third or fifth rather than the root, as mentioned above.'><sup>26<\/sup><\/a><\/span> Frequently, Faur\u00e9 reinterprets the first part of a cadential $$^{6}_{4}$$ as a consonant tonic <nobr>(I$$^{6}_{4}$$)<\/nobr> arrival, even after a V\/V. The volatile cadential $$^{6}_{4}$$ may imply a <nobr>V$$^{5}_{3}$$<\/nobr>&nbsp; resolution, only later to be reheard as a stable tonic (I) in its own right.&nbsp;<\/p>\n\n\n\n<p><span style=\"font-weight: 400;\">In Faur\u00e9\u2019s and Durufl\u00e9, key duality occurs as a disjunction between the melody and bass.<\/span><span id='easy-footnote-27-9120' class='easy-footnote-margin-adjust'><\/span><span class='easy-footnote'><a href='https:\/\/theory.esm.rochester.edu\/integral\/37-2024\/bilik\/#easy-footnote-bottom-27-9120' title='\u00c9mile Vuillermoz (1969) states that the bass acted as a \u201cgenerating cell for a harmonic creation\u201d for Faur\u00e9 (Vuillermoz, 102). In fact, Faur\u00e9 often asked for strong articulation of the bass during lessons. His gravitation toward bass lines may be related to familiarity with the organ\u2019s foot pedal.'><sup>27<\/sup><\/a><\/span> This transpires when a melody imparts a tonal center or key\u2014usually via melodic unfolding of a structural harmony\u2014that is dissimilar to the accompaniment. Conversely, if the bass espouses a strong tonal profile different enough from the melody, it can imply its own concurrent tonic.<span id='easy-footnote-28-9120' class='easy-footnote-margin-adjust'><\/span><span class='easy-footnote'><a href='https:\/\/theory.esm.rochester.edu\/integral\/37-2024\/bilik\/#easy-footnote-bottom-28-9120' title='The difference in rationalizing away a disparate tonal layer as simply embellishing a primary key lies in the significance of its &lt;em&gt;linear &lt;\/em&gt;presentation. Faur\u00e9\u2019s admirer, Nadia Boulanger, mourned the propensity for vertical interpretations, lamenting that \u201cwe have more or less lost the art of listening to contrapuntal music of following lines rather than chords\u201d (Brooks 2016, 56). Turning our attention to the tonal profile of lines can tell us much about the perplexing chords&lt;em&gt; &lt;\/em&gt;that result from them.'><sup>28<\/sup><\/a><\/span> In this case, the bass might establish a center or key separate from that of the upper parts.<span id='easy-footnote-29-9120' class='easy-footnote-margin-adjust'><\/span><span class='easy-footnote'><a href='https:\/\/theory.esm.rochester.edu\/integral\/37-2024\/bilik\/#easy-footnote-bottom-29-9120' title='In contrast, common-practice music exhibits inner voices working &lt;em&gt;with&lt;\/em&gt; the bass in conveying a single center or key.'><sup>29<\/sup><\/a><\/span> In the first few examples from Faur\u00e9, the relationship between stratified centers is a third, which may be explained via a contrapuntal 5\u20136 exchange. In fact, nearly all the following examples comprise key duality of third-related keys; only the final selections by Faur\u00e9 and Durufl\u00e9 feature disjunction of melody and bass at an interval other than a third. In addition, the final analyses widen the scope of the paper to include another French composer, Durufl\u00e9, who mirrors Faur\u00e9\u2019s application of key duality but exemplifies larger-level manifestations of it.&nbsp;<\/p>\n\n\n\n<h2 class=\"wp-block-heading\"><strong>Faur\u00e9: Piano Quintet no. 2, op. 115 (1921)<\/strong><\/h2>\n\n\n\n<p><b>Example 3<\/b><span style=\"font-weight: 400;\"> depicts a C minor melody from the first movement of Faur\u00e9\u2019s Piano Quintet no. 2. Three musical factors gird the sense of C minor: the prominence of tonic and dominant pitches (C and G), the C-C range of the melody, and the ephemeral G dominant in m. 194. While there is dorian inflection from the <nobr>A$$\\natural$$<\/nobr>, the pitches of the tonic triad remain intact.<span id='easy-footnote-30-9120' class='easy-footnote-margin-adjust'><\/span><span class='easy-footnote'><a href='https:\/\/theory.esm.rochester.edu\/integral\/37-2024\/bilik\/#easy-footnote-bottom-30-9120' title='Often the tonic and the fifth are unchanged but the other notes of the scale\/collection are varied. See James Kurtz (1970). Kurtz observes how a foreground harmony serves simply to harmonize a melodic note with a consonant chord. For example, in G major, an F major chord might support a C in the melody.'><sup>30<\/sup><\/a><\/span> Having presented the same <\/span>C minor melody in m. 35, Faur\u00e9 now endeavors a reharmonization of it over a bass that conveys <nobr>A$$\\flat$$<\/nobr> major. <span style=\"font-weight: 400;\">The preserved, un-transposed C minor theme atop new <nobr>A$$\\flat$$<\/nobr> major harmonies unfolds the C minor tonic over a bass that comes to rest on <nobr>A$$\\flat$$<\/nobr> twice in mm. 199 and 203; <nobr>A$$\\flat$$s<\/nobr> on hypermetrical downbeats reify a reading in <nobr>A$$\\flat$$<\/nobr> major. Bolstering the feeling of <nobr>A$$\\flat$$<\/nobr> major is the <\/span><i><span style=\"font-weight: 400;\">qualia <\/span><\/i><span style=\"font-weight: 400;\">change from <nobr>D$$\\natural$$<\/nobr> to <nobr>D$$\\flat$$<\/nobr> the moment before each <nobr>A$$\\flat$$<\/nobr> major arrival. The disjunction between the C minor melody and the <nobr>A$$\\flat$$<\/nobr> major bass yields a stratification of two distinct tonal centers.<\/span><span id='easy-footnote-31-9120' class='easy-footnote-margin-adjust'><\/span><span class='easy-footnote'><a href='https:\/\/theory.esm.rochester.edu\/integral\/37-2024\/bilik\/#easy-footnote-bottom-31-9120' title='Admittedly, pitch centricity around G is so strong that some listeners may hear G minor as the tonal center of the melody. Because Faur\u00e9 presents the melody in C minor earlier (mm. 35\u201340), I hear it in C minor, although melodic emphasis of $$\\hat{5}$$ is prominent throughout his &lt;em&gt;oeuvre&lt;\/em&gt;.'><sup>31<\/sup><\/a><\/span>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full is-resized\"><a href=\"https:\/\/theory.esm.rochester.edu\/integral\/bilik-vol37-example-3\/\"><img loading=\"lazy\" decoding=\"async\" width=\"936\" height=\"358\" src=\"https:\/\/theory.esm.rochester.edu\/integral\/wp-content\/uploads\/2024\/06\/bilik-vol37-example-3.png\" alt=\"Bilik, Example 3\" class=\"wp-image-9349\" style=\"width:512px;height:197px\" srcset=\"https:\/\/theory.esm.rochester.edu\/integral\/wp-content\/uploads\/2024\/06\/bilik-vol37-example-3.png 936w, https:\/\/theory.esm.rochester.edu\/integral\/wp-content\/uploads\/2024\/06\/bilik-vol37-example-3-300x115.png 300w, https:\/\/theory.esm.rochester.edu\/integral\/wp-content\/uploads\/2024\/06\/bilik-vol37-example-3-768x294.png 768w\" sizes=\"auto, (max-width: 706px) 89vw, (max-width: 767px) 82vw, 740px\" \/><\/a><figcaption class=\"wp-element-caption\"><b>Example 3.<\/b> Faur\u00e9, Piano Quintet no. 2, op. 115\/1, mm. 195\u2013203. Key duality between C minor melody and <nobr>A$$\\flat$$<\/nobr> major accompaniment. <\/figcaption><\/figure>\n<\/div>\n\n\n<p><span style=\"font-weight: 400;\">Key duality resurfaces in <\/span><b>Example 4<\/b><span style=\"font-weight: 400;\"> from the second movement, where the melody unfolds a D minor sonority above a bass that articulates <nobr>B$$\\flat$$<\/nobr> major.<span id='easy-footnote-32-9120' class='easy-footnote-margin-adjust'><\/span><span class='easy-footnote'><a href='https:\/\/theory.esm.rochester.edu\/integral\/37-2024\/bilik\/#easy-footnote-bottom-32-9120' title='Although the D scale is phrygian with &lt;nobr&gt;E$$\\flat$$&lt;\/nobr&gt;, pitches of the D minor triad are unchanged. In later pieces, Faur\u00e9 preserves structural pitches of a melody, such as $$\\hat{1}$$ and $$\\hat{5}$$, but drastically alters the \u201cin-between\u201d notes. See the third movement of the Piano Quintet No. 2, mm. 1\u20139 (not shown), where the tonic and dominant pitches are intact while other notes of the diatonic collection are varied until the cadence.'><sup>32<\/sup><\/a><\/span> The melody highlights the members of the D minor triad, especially the descending A-D perfect fifth in m. 43. Buttressing this D minor melodic frame are the inner voices, which supply D minor triads on the downbeats of mm. 43, 45, and 47. Complicating a single-key interpretation, however, is the bass, which traces a <nobr>B$$\\flat$$<\/nobr> major sonority up the scale from the <nobr>B$$\\flat$$<\/nobr> of m. 43 to the <nobr>B$$\\flat$$<\/nobr> of m. 49. Overall, the listener perceives <nobr>B$$\\flat$$<\/nobr> major due to the logical harmonic syntax and the upcoming <nobr>B$$\\flat$$<\/nobr> major arrival which confirms it, but Faur\u00e9\u2019s voicing invites further scrutiny to explain why D minor sounds so strong.&nbsp;<\/span><\/p>\n\n\n\n<p><span style=\"font-weight: 400;\">The D minor triads in every other measure stagger and weaken a fauxbourdon $$^{6}_{3}$$ sequence, thereby foregrounding D minor despite the momentary 5\u20136 exchange in m. 45. The logic behind the passage is clearly $$^{6}_{3}$$ planing, but the surface presentation rubs against this schema. For example, the chord in m. 48 could be a continuation of the $$^{6}_{3}$$ sequence with the chord <nobr>G-B$$\\flat$$-E<\/nobr>, <\/span><i><span style=\"font-weight: 400;\">or<\/span><\/i><span style=\"font-weight: 400;\"> it could be a G minor triad <nobr>(G-B$$\\flat$$-D)<\/nobr> with E neighbor-tone. The emphasis of root-position triads over inverted ones (and vice versa) where we would typically expect them has the capacity to challenge a monotonal hearing. Whatever interpretation we choose is dependent, in part, on which tonal layer we tune into, which might influence us to hear a $$^{5}_{3}$$ or $$^{6}_{3}$$ chord at any moment. Smith (1997) reminds us that \u201cmotivic process is a form of self-analysis\u201d (180).<span id='easy-footnote-33-9120' class='easy-footnote-margin-adjust'><\/span><span class='easy-footnote'><a href='https:\/\/theory.esm.rochester.edu\/integral\/37-2024\/bilik\/#easy-footnote-bottom-33-9120' title='His analyses embrace a more prolongational attitude rooted in the style of Schenker.'><sup>33<\/sup><\/a><\/span> The stratification of individual lines\u2014those of <nobr>B$$\\flat$$<\/nobr> major and D minor here\u2014frustrate a monotonal hearing, prompting the listener to reevaluate the control of each center or key.&nbsp;<\/span><\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full is-resized\"><a href=\"https:\/\/theory.esm.rochester.edu\/integral\/bilik-vol37-example-4\/\"><img loading=\"lazy\" decoding=\"async\" width=\"936\" height=\"342\" src=\"https:\/\/theory.esm.rochester.edu\/integral\/wp-content\/uploads\/2024\/06\/bilik-vol37-example-4.png\" alt=\"Bilik, Example 4\" class=\"wp-image-9350\" style=\"width:512px;height:187px\" srcset=\"https:\/\/theory.esm.rochester.edu\/integral\/wp-content\/uploads\/2024\/06\/bilik-vol37-example-4.png 936w, https:\/\/theory.esm.rochester.edu\/integral\/wp-content\/uploads\/2024\/06\/bilik-vol37-example-4-300x110.png 300w, https:\/\/theory.esm.rochester.edu\/integral\/wp-content\/uploads\/2024\/06\/bilik-vol37-example-4-768x281.png 768w\" sizes=\"auto, (max-width: 706px) 89vw, (max-width: 767px) 82vw, 740px\" \/><\/a><figcaption class=\"wp-element-caption\"><b>Example 4.<\/b> Faur\u00e9, Piano Quintet no. 2, op. 115\/2, mm. 43\u201349. Key duality between D minor melody and <nobr>B$$\\flat$$<\/nobr> major bass line. Boxed pitches trace members of the unfolding D minor tonic triad.<\/figcaption><\/figure>\n<\/div>\n\n\n<p><span><span style=\"font-weight: 400;\">The fluidity between $$^{6}_{3}$$ and $$^{5}_{3}$$ voicings above a stepwise bass, like in Example 4,<\/span><\/span><span style=\"font-weight: 400;\"> invites a Rule of the Octave (RO) approach.<span id='easy-footnote-34-9120' class='easy-footnote-margin-adjust'><\/span><span class='easy-footnote'><a href='https:\/\/theory.esm.rochester.edu\/integral\/37-2024\/bilik\/#easy-footnote-bottom-34-9120' title='Stepwise bass lines are ubiquitous in Faur\u00e9 and account for much difficulty in extracting a functional bass line due to their contrapuntal nature.'><sup>34<\/sup><\/a><\/span> Drawing on the work of Smith (1997) and his ideas of motivic $$^{6}_{3}$$ chords,<span id='easy-footnote-35-9120' class='easy-footnote-margin-adjust'><\/span><span class='easy-footnote'><a href='https:\/\/theory.esm.rochester.edu\/integral\/37-2024\/bilik\/#easy-footnote-bottom-35-9120' title='Smith (1997) questions whether the voice-leading exchange from the fifth of a chord (I) to its sixth creates a new harmony (vi) or not. He unpacks two types of $$^{6}_{3}$$ substitutions: those that commence via 5\u20136 motion and those that are simply triads in first inversion. In general, he explores how this procedure might be executed on the tonic triad, therefore blurring the boundary between tonic and submediant. Although Smith does not comment on key duality, he nonetheless shows how these $$^{6}_{3}$$ substitutions could account for an essence of key duality between the tonic and submediant (Smith, 191).'><sup>35<\/sup><\/a><\/span> Gilad Rabinovitch (2023) demonstrates how Faur\u00e9 enjoys \u201cconflating $$^{6}_{3}$$ and $$^{5}_{3}$$ sonorities with one another in positions across the bass scale where the other sonority is expected\u201d (Rabinovitch, 59).<\/span> <span style=\"font-weight: 400;\">Guided by a RO framework, he maintains that one reason for harmonic ambiguity springs from Faur\u00e9\u2019s constant reinterpretation of scalar bass segments.<span id='easy-footnote-36-9120' class='easy-footnote-margin-adjust'><\/span><span class='easy-footnote'><a href='https:\/\/theory.esm.rochester.edu\/integral\/37-2024\/bilik\/#easy-footnote-bottom-36-9120' title='As Rabinovitch shows, the RO may have been fresh in Faur\u00e9\u2019s mind as part of the partimenti tradition. Partimenti considered bass harmonization in very localized terms. Such view is antithetical to many theories seeking to champion long-range tonal coherence. Hence, it may be tougher to detect substitutions along the RO in these short segments and judge how they might contribute to key duality. Nevertheless, we have a delightful \u201cposition finding game along the RO\u201d which encourages us to reflect on possible tonal directions (Rabinovitch, 73).'><sup>36<\/sup><\/a><\/span> This is evident in the substitution of $$^{5}_{3}$$ for $$^{6}_{3}$$ chords, which tempts us to hear the former as conveying the more stable center; in <\/span><b>Example 5<\/b><span style=\"font-weight: 400;\">, the substitution of a root-position E minor triad in m. 91 for a C major one injects conflicting information. Even if C major is ingrained from the earlier I$$^{6}$$ chords, we might hear a tug-of-war due to the stronger $$^{5}_{3}$$ voicings of the ancillary E minor key. In parallel passages to come, $$^{5}_{3}$$ triads freely supersede $$^{6}_{3}$$ ones.&nbsp;&nbsp;<\/span><\/p>\n\n\n\n<h2 class=\"wp-block-heading\"><strong>Faur\u00e9: Cello Sonata no. 2, op. 117 (1921)<\/strong><\/h2>\n\n\n\n<p><span style=\"font-weight: 400;\">Chamber works from this period spotlight how deft 5\u20136 exchanges tip the balance between two keys related by third. <strong>Example 5<\/strong>, from the slow movement of the Cello Sonata no. 2, shows the piano bass and cello melody partaking in 5\u20136 exchanges that toggle between C major and E minor. Over mm. 92\u201394, the soprano motive<\/span> <span style=\"font-weight: 400;\">points to C major (G-C-G) as the bass motive outlines E minor (E-B-E). Throughout the global C major environment, E minor interjects in mm. 86 and 91 as well. The Roman numerals favor the former due to the constant restarting on <nobr>I$$^{6}$$<\/nobr> in mm. 85, 87, 90, and 92; however, the <nobr>F$$\\sharp$$s<\/nobr> tonicize E minor with fleeting plagal gestures that efface C major\u2014see beats three and four in mm. 92\u201393. Depending on how entrenched in C major the listener is, the <nobr>F$$\\sharp$$s<\/nobr> may sound like lydian inflections.<\/span><span id='easy-footnote-37-9120' class='easy-footnote-margin-adjust'><\/span><span class='easy-footnote'><a href='https:\/\/theory.esm.rochester.edu\/integral\/37-2024\/bilik\/#easy-footnote-bottom-37-9120' title=' The I-iii sidestep via $$\\sharp\\hat{4}$$ is a staple of Faur\u00e9\u2019s &lt;em&gt;oeuvre&lt;\/em&gt;. It shows up earlier in mm. 46\u201347, when &lt;nobr&gt;D$$\\natural$$&lt;\/nobr&gt; carries the music from &lt;nobr&gt;A$$\\flat$$&lt;\/nobr&gt; major to C minor. Overall, the shift to iii is often a case of the sixth in a &lt;nobr&gt;I$$^{6}$$&lt;\/nobr&gt; sliding down a half step to the leading tone.'><sup>37<\/sup><\/a><\/span>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full is-resized\"><a href=\"https:\/\/theory.esm.rochester.edu\/integral\/bilik-vol37-example-5\/\"><img loading=\"lazy\" decoding=\"async\" width=\"936\" height=\"504\" src=\"https:\/\/theory.esm.rochester.edu\/integral\/wp-content\/uploads\/2024\/06\/bilik-vol37-example-5.png\" alt=\"Bilik, Example 5\" class=\"wp-image-9351\" style=\"width:512px;height:276px\" srcset=\"https:\/\/theory.esm.rochester.edu\/integral\/wp-content\/uploads\/2024\/06\/bilik-vol37-example-5.png 936w, https:\/\/theory.esm.rochester.edu\/integral\/wp-content\/uploads\/2024\/06\/bilik-vol37-example-5-300x162.png 300w, https:\/\/theory.esm.rochester.edu\/integral\/wp-content\/uploads\/2024\/06\/bilik-vol37-example-5-768x414.png 768w\" sizes=\"auto, (max-width: 706px) 89vw, (max-width: 767px) 82vw, 740px\" \/><\/a><figcaption class=\"wp-element-caption\"><b>Example 5.<\/b> Faur\u00e9, Cello Sonata no. 2, op. 117\/2, mm. 85\u201395. Key duality between C major soprano and E minor bass in mm. 92\u201394, interpreted as a 5\u20136 exchange over an E pedal.<\/figcaption><\/figure>\n<\/div>\n\n\n<p><span style=\"font-weight: 400;\">In the third movement, <\/span><b>Example 6<\/b><span style=\"font-weight: 400;\"> illustrates how two disparate tonal strands imbue the music with key duality, often in tandem with contrapuntal 5\u20136 substitutions. Over mm. 64\u201371, the soprano melody hints at an <nobr>E$$\\flat$$<\/nobr> major tonic while the bass unfolds a G minor one. The <nobr>B$$\\flat$$<\/nobr> dominant seventh in m. 63 sets the listener up to hear <nobr>E$$\\flat$$<\/nobr> major in m. 64, and the descending <nobr>E$$\\flat$$<\/nobr> major scale four measures later confirms this. However, the tonal profile of the bass traverses the G minor pentachord over mm. 64\u201369, its D apex marked by a perplexing arrival on D minor (v). This harmonization\u2014no doubt a result of Faur\u00e9 substituting a <nobr>D $$^{5}_{3}$$<\/nobr> minor triad for a <nobr>B $$\\flat^{6}_{3}$$<\/nobr> major triad\u2014favors G minor.<span id='easy-footnote-38-9120' class='easy-footnote-margin-adjust'><\/span><span class='easy-footnote'><a href='https:\/\/theory.esm.rochester.edu\/integral\/37-2024\/bilik\/#easy-footnote-bottom-38-9120' title='A similar instance of duality between G minor and &lt;nobr&gt;E$$\\flat$$&lt;\/nobr&gt; major, caused by the substitution of the pitch D for &lt;nobr&gt;E$$\\flat$$,&lt;\/nobr&gt; appears in the second movement of the Piano Quintet no. 2 in mm. 107\u2013120.'><sup>38<\/sup><\/a><\/span> Four measures later, the bass answers $$\\hat{5}$$, D, with an arrival on G in m. 71, at which point the soprano melody corroborates this tonal center with a G minor arpeggio. Yet the G minor arrival at m. 71 is thwarted by an <nobr>E$$\\flat$$<\/nobr> inner voice that stands in for D. At this point in the phrase, the two tonal layers swap; the soprano leaps among members of the G minor triad (see especially the D-G leap upward on a hypermetrical strong beat in m. 76),<span id='easy-footnote-39-9120' class='easy-footnote-margin-adjust'><\/span><span class='easy-footnote'><a href='https:\/\/theory.esm.rochester.edu\/integral\/37-2024\/bilik\/#easy-footnote-bottom-39-9120' title='Frequently, reading a motive separately from the harmony\u2014not together as a complete entity\u2014can expose a separate tonal layer. Recognizing motive and harmony as two separate musical forces, cooperating only occasionally, may also explain why various harmonic notes do not behave as expected. In the presence of harmonic dissonances (like added sevenths), it is wise to consider the melody and accompaniment separately to explain tendency tones that do not resolve traditionally; there may be two rivaling tonal centers.'><sup>39<\/sup><\/a><\/span> as the bass emphasizes <nobr>E$$\\flat$$<\/nobr> major rather than G minor now. Faur\u00e9\u2019s perpetual denial of a single tonal center at structural points in the phrase\u2014every four measures or so\u2014keeps the tonal pendulum swinging. When, in m. 76, the cello enters on G at the start of the phrase and the piano leaps up D-G <nobr>($$\\hat{5}$$-$$\\hat{1}$$)<\/nobr>, the bass maneuvers to <nobr>E$$\\flat$$.<\/nobr> Thus, the trajectory of the bass line delineates a different key from that of the melody at any given time, affording a second tonal center.&nbsp;<\/span><\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full is-resized\"><a href=\"https:\/\/theory.esm.rochester.edu\/integral\/bilik-vol37-example-6\/\"><img loading=\"lazy\" decoding=\"async\" width=\"936\" height=\"510\" src=\"https:\/\/theory.esm.rochester.edu\/integral\/wp-content\/uploads\/2024\/06\/bilik-vol37-example-6.png\" alt=\"Bilik, Example 6\" class=\"wp-image-9352\" style=\"width:512px;height:279px\" srcset=\"https:\/\/theory.esm.rochester.edu\/integral\/wp-content\/uploads\/2024\/06\/bilik-vol37-example-6.png 936w, https:\/\/theory.esm.rochester.edu\/integral\/wp-content\/uploads\/2024\/06\/bilik-vol37-example-6-300x163.png 300w, https:\/\/theory.esm.rochester.edu\/integral\/wp-content\/uploads\/2024\/06\/bilik-vol37-example-6-768x418.png 768w\" sizes=\"auto, (max-width: 706px) 89vw, (max-width: 767px) 82vw, 740px\" \/><\/a><figcaption class=\"wp-element-caption\"><b>Example 6.<\/b> Faur\u00e9, Cello Sonata no. 2, op. 117\/3, mm. 61\u201377. Key duality between <nobr>E$$\\flat$$<\/nobr> major soprano and G minor bass in mm. 64\u201371, at which point they swap tonal profiles. Internal brackets highlight G minor triad unfolding in mm. 71<em>\u2013<\/em>72 and 75<em>\u2013<\/em>77 at the beginnings of phrases. <\/figcaption><\/figure>\n<\/div>\n\n\n<h2 class=\"wp-block-heading\"><strong>Faur\u00e9: Piano Quintet no. 1, op. 89 (1906)<\/strong><\/h2>\n\n\n\n<p><span style=\"font-weight: 400;\">The final movement of the Piano Quintet no. 1 in <\/span><b>Example 7a<\/b><span style=\"font-weight: 400;\"> portrays how a B minor melody resists the D major center of the bass due to changing surface emphasis on A and B. The harmonization of the pitch B in mm. 1<em>\u2013<\/em>2 with <nobr>F$$\\sharp$$<\/nobr> and D (members of the B minor triad) underpins a B tonic, followed by neighbor-tone motions around B in m. 4. After constant spinning around B, the <nobr>F$$\\sharp$$<\/nobr> at the end of the phrase anchors B minor with what sounds like a half cadence on $$\\hat{5}$$. At the same time, the sonic <nobr>F$$\\sharp$$<\/nobr> minor residue of m. 3 bleeds over to the following measure, backing the impression of a half cadence on <nobr>F$$\\sharp$$<\/nobr> in m. 4 (see dotted line). In fact, the melody exerts such weight over the passage that the progression might be heard beginning off-tonic as <nobr>III-iv$$^{7}$$-v<\/nobr> in B minor with a <nobr>D-C$$\\sharp$$<\/nobr> anacrusis. If, however, we cede our attention to the bass, we may hear the D major tonic pillars that enclose each four-measure phrase. The second system tonicizing G major and the final cadence in m. 16 brings the D major of the bass into better focus. Until then, the melodic foregrounding of B, $$\\hat{6}$$, has the power to supplant A, $$\\hat{5}$$, as the stronger tone. <\/span><\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full is-resized\"><a href=\"https:\/\/theory.esm.rochester.edu\/integral\/bilik-vol37-example-7a\/\"><img loading=\"lazy\" decoding=\"async\" width=\"936\" height=\"444\" src=\"https:\/\/theory.esm.rochester.edu\/integral\/wp-content\/uploads\/2024\/06\/bilik-vol37-example-7a.png\" alt=\"Bilik, Example 7a\" class=\"wp-image-9353\" style=\"height:243px\" srcset=\"https:\/\/theory.esm.rochester.edu\/integral\/wp-content\/uploads\/2024\/06\/bilik-vol37-example-7a.png 936w, https:\/\/theory.esm.rochester.edu\/integral\/wp-content\/uploads\/2024\/06\/bilik-vol37-example-7a-300x142.png 300w, https:\/\/theory.esm.rochester.edu\/integral\/wp-content\/uploads\/2024\/06\/bilik-vol37-example-7a-768x364.png 768w\" sizes=\"auto, (max-width: 706px) 89vw, (max-width: 767px) 82vw, 740px\" \/><\/a><figcaption class=\"wp-element-caption\"><b>Example 7a.<\/b> Faur\u00e9, Piano Quintet no. 1, op. 89\/3, mm. 1\u201316. Key duality between B minor soprano and D major bass in mm. 1\u201316, interpreted as a 5\u20136 exchange over a D pedal. Roman numerals synthesize the sonic surface.<\/figcaption><\/figure>\n<\/div>\n\n\n<p><span style=\"font-weight: 400;\">The wobble between D major and B minor persists through the movement; B minor reappears with increasing fervor, inhabiting the ear of the listener more and more. In <\/span><b>Example 7b<\/b><span style=\"font-weight: 400;\">, mm. 49<\/span><em>\u2013<\/em><span style=\"font-weight: 400;\">53, Faur\u00e9 paints the earlier motive with bolder B minor, amplifying the feeling of half cadence on <nobr>F$$\\sharp$$<\/nobr> minor (v) with accidentals <nobr>G$$\\sharp$$<\/nobr> and <nobr>E$$\\sharp$$.<\/nobr><span id='easy-footnote-40-9120' class='easy-footnote-margin-adjust'><\/span><span class='easy-footnote'><a href='https:\/\/theory.esm.rochester.edu\/integral\/37-2024\/bilik\/#easy-footnote-bottom-40-9120' title='Granted, one may hear the tonicization of &lt;nobr&gt;F$$\\sharp$$&lt;\/nobr&gt; minor now as part of a D major\/&lt;nobr&gt;F$$\\sharp$$&lt;\/nobr&gt; minor complex. I tend to perceive the F# minor as a minor dominant (v) in B minor, albeit \u201csuper-charged,\u201d due to its earlier B minor context and the following &lt;nobr&gt;F$$\\sharp$$-D&lt;\/nobr&gt; leap which had occurred before.'><sup>40<\/sup><\/a><\/span> The tonicized dominant of B minor now affects what comes immediately afterward; the leap <nobr>F$$\\sharp$$-D<\/nobr> now sounds even more like <nobr>$$\\hat{5}$$-$$\\hat{3}$$<\/nobr> in B minor. Analogous tonicization of <nobr>F$$\\sharp$$<\/nobr> minor (v) in B minor looms over mm. 186\u2013193 later in the movement, with <nobr>E$$\\sharp$$<\/nobr> and <nobr>G$$\\sharp$$<\/nobr> participating in a V\/v-v (not shown).&nbsp;<\/span><\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full is-resized\"><a href=\"https:\/\/theory.esm.rochester.edu\/integral\/bilik-vol37-example-7b\/\"><img loading=\"lazy\" decoding=\"async\" width=\"936\" height=\"460\" src=\"https:\/\/theory.esm.rochester.edu\/integral\/wp-content\/uploads\/2024\/06\/bilik-vol37-example-7b.png\" alt=\"Bilik, Example 7b\" class=\"wp-image-9354\" style=\"width:512px;height:252px\" srcset=\"https:\/\/theory.esm.rochester.edu\/integral\/wp-content\/uploads\/2024\/06\/bilik-vol37-example-7b.png 936w, https:\/\/theory.esm.rochester.edu\/integral\/wp-content\/uploads\/2024\/06\/bilik-vol37-example-7b-300x147.png 300w, https:\/\/theory.esm.rochester.edu\/integral\/wp-content\/uploads\/2024\/06\/bilik-vol37-example-7b-768x377.png 768w\" sizes=\"auto, (max-width: 706px) 89vw, (max-width: 767px) 82vw, 740px\" \/><\/a><figcaption class=\"wp-element-caption\"><b>Example 7b.<\/b> Faur\u00e9, Piano Quintet no. 1, op. 89\/3, mm. 49\u201353. Heightened presence of B minor due to tonicization of <nobr>F$$\\sharp$$<\/nobr> minor (v) in mm. 51\u201352 and subsequent leaps from <nobr>F$$\\sharp$$<\/nobr> up to D, falling back to B.<\/figcaption><\/figure>\n<\/div>\n\n\n<p><span style=\"font-weight: 400;\">Comparable instances of key duality over longer swaths of music commence in the third movement of the Piano Quartet no. 2 (1887), in <\/span><b>Example 8a<\/b><span style=\"font-weight: 400;\">. Although much earlier, this vignette also exhibits a tension between two keys related by third, <nobr>E$$\\flat$$<\/nobr> major and G minor, over a greater expanse. The right hand and bass line articulate <nobr>E$$\\flat$$-G,<\/nobr> but the sense of <nobr>E$$\\flat$$<\/nobr> major is made murky by the recalcitrant G-D perfect fifth that advances a G minor center. A burgeoning G minor materializes in mm. 3<em>\u2013<\/em>5 with a G minor piano arpeggio and G minor viola melody. Still, in <\/span><b>Example 8b<\/b><span style=\"font-weight: 400;\">, emphasis tilts to <nobr>E$$\\flat$$<\/nobr> major by m. 38, as a <nobr>B$$\\flat$$<\/nobr> dominant seventh coalesces to confirm the new key. Although the G minor arpeggio returns in m. 41, a firm <nobr>E$$\\flat$$<\/nobr> major rolled chord continues to frame the next few measures in <nobr>E$$\\flat$$.<\/nobr> The result is a fluid tonal center a third away\u2014the result of another contrapuntal 5\u20136 exchange that penetrates the movement.&nbsp;&nbsp;<\/span><\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full is-resized\"><a href=\"https:\/\/theory.esm.rochester.edu\/integral\/bilik-vol37-example-8a-1\/\"><img loading=\"lazy\" decoding=\"async\" width=\"700\" height=\"510\" src=\"https:\/\/theory.esm.rochester.edu\/integral\/wp-content\/uploads\/2024\/06\/bilik-vol37-example-8a-1.png\" alt=\"Bilik, Example 8a (1\/2)\" class=\"wp-image-9355\" style=\"width:512px;height:373px\" srcset=\"https:\/\/theory.esm.rochester.edu\/integral\/wp-content\/uploads\/2024\/06\/bilik-vol37-example-8a-1.png 700w, https:\/\/theory.esm.rochester.edu\/integral\/wp-content\/uploads\/2024\/06\/bilik-vol37-example-8a-1-300x219.png 300w\" sizes=\"auto, (max-width: 700px) 100vw, 700px\" \/><\/a><figcaption class=\"wp-element-caption\"><b>Example 8a (1\/2).<\/b> Faur\u00e9, Piano Quartet no. 2, op. 45\/3, mm. 1\u20137. Duality between <nobr>E$$\\flat$$<\/nobr> major and G minor. Strong accentuation of G minor in piano and viola in mm. 3\u20135.<\/figcaption><\/figure>\n<\/div>\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full is-resized\"><a href=\"https:\/\/theory.esm.rochester.edu\/integral\/bilik-vol37-example-8a-2\/\"><img loading=\"lazy\" decoding=\"async\" width=\"696\" height=\"486\" src=\"https:\/\/theory.esm.rochester.edu\/integral\/wp-content\/uploads\/2024\/06\/bilik-vol37-example-8a-2.png\" alt=\"Bilik, Example 8a (2\/2)\" class=\"wp-image-9356\" style=\"width:512px;height:358px\" srcset=\"https:\/\/theory.esm.rochester.edu\/integral\/wp-content\/uploads\/2024\/06\/bilik-vol37-example-8a-2.png 696w, https:\/\/theory.esm.rochester.edu\/integral\/wp-content\/uploads\/2024\/06\/bilik-vol37-example-8a-2-300x209.png 300w\" sizes=\"auto, (max-width: 696px) 100vw, 696px\" \/><\/a><figcaption class=\"wp-element-caption\"><b>Example 8a (2\/2).<\/b><\/figcaption><\/figure>\n<\/div>\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full is-resized\"><a href=\"https:\/\/theory.esm.rochester.edu\/integral\/bilik-vol37-example-8b-1\/\"><img loading=\"lazy\" decoding=\"async\" width=\"690\" height=\"520\" src=\"https:\/\/theory.esm.rochester.edu\/integral\/wp-content\/uploads\/2024\/06\/bilik-vol37-example-8b-1.png\" alt=\"Bilik, Example 8b (1\/2)\" class=\"wp-image-9357\" style=\"width:512px;height:386px\" srcset=\"https:\/\/theory.esm.rochester.edu\/integral\/wp-content\/uploads\/2024\/06\/bilik-vol37-example-8b-1.png 690w, https:\/\/theory.esm.rochester.edu\/integral\/wp-content\/uploads\/2024\/06\/bilik-vol37-example-8b-1-300x226.png 300w\" sizes=\"auto, (max-width: 690px) 100vw, 690px\" \/><\/a><figcaption class=\"wp-element-caption\"><b>Example 8b (1\/2).<\/b> Faur\u00e9, Piano Quartet no. 2, op. 45\/3, mm. 38<em>\u2013<\/em>42. Duality between <nobr>E$$\\flat$$<\/nobr> major and G minor. Stronger accentuation of <nobr>E$$\\flat$$<\/nobr> major now via <nobr>V$$^{7}$$<\/nobr> in m. 39 and <nobr>E$$\\flat$$<\/nobr> major arrival in m. 42. <\/figcaption><\/figure>\n<\/div>\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full is-resized\"><a href=\"https:\/\/theory.esm.rochester.edu\/integral\/bilik-vol37-example-8b-2\/\"><img loading=\"lazy\" decoding=\"async\" width=\"670\" height=\"490\" src=\"https:\/\/theory.esm.rochester.edu\/integral\/wp-content\/uploads\/2024\/06\/bilik-vol37-example-8b-2.png\" alt=\"Bilik, Example 8b (2\/2)\" class=\"wp-image-9358\" style=\"width:512px;height:375px\" srcset=\"https:\/\/theory.esm.rochester.edu\/integral\/wp-content\/uploads\/2024\/06\/bilik-vol37-example-8b-2.png 670w, https:\/\/theory.esm.rochester.edu\/integral\/wp-content\/uploads\/2024\/06\/bilik-vol37-example-8b-2-300x219.png 300w\" sizes=\"auto, (max-width: 670px) 100vw, 670px\" \/><\/a><figcaption class=\"wp-element-caption\"><b>Example 8b (2\/2).<\/b><\/figcaption><\/figure>\n<\/div>\n\n\n<h2 class=\"wp-block-heading\"><strong>Faur\u00e9: Piano Trio, op. 120 (1923)<\/strong><\/h2>\n\n\n\n<p><span style=\"font-weight: 400;\">In <\/span><b>Example 9<\/b><span style=\"font-weight: 400;\">, the finale of the Piano Trio announces key duality at the outset, except now the interval of disjunction is no longer a third but a fifth, as the cadence of the consequent (mm. 10<em>\u2013<\/em>12) answers that of the antecedent (mm. 7<em>\u2013<\/em>9) a perfect fifth lower. Tonal ears may readily grasp the underlying period structure. The key signature and tonal skeleton of the melody evince D minor, embodied in the first cadence on the dominant (A) and the second cadence on tonic (D). Yet the bass confronts this tonic with a competing G minor tonic. That is, the D in m. 8 to the terminal G in m. 12 implies G minor\u2014a familiar v-i tonal structure. Strengthening a G minor reading is the <nobr>E$$\\flat$$<\/nobr> of the iv<sup>(add6)<\/sup>, the break in texture after the G minor arrival, and motion from <nobr>E$$\\flat$$-D<\/nobr> afterward which is more traditionally interpreted as <nobr>$$\\flat\\hat{6}$$-$$\\hat{5}$$.<\/nobr> As a result, an air of ambiguity emerges from two contending keys. Crucially, the cadence in m. 12 features a four-note sonority\u2014a fused G minor\/D minor tonic.&nbsp;&nbsp;<\/span><\/p>\n\n\n\n<p><span style=\"font-weight: 400;\">The merging of D minor and G minor casts an unmistakable modal hue. The outcome of key duality for the listener may be the perception of modalism\u2014a trait so often ascribed to Faur\u00e9\u2019s works.<\/span><span id='easy-footnote-41-9120' class='easy-footnote-margin-adjust'><\/span><span class='easy-footnote'><a href='https:\/\/theory.esm.rochester.edu\/integral\/37-2024\/bilik\/#easy-footnote-bottom-41-9120' title='&amp;nbsp;James Kidd (1973) explores how nineteenth-century chant accompaniment played a role in Faur\u00e9\u2019s proclivity for modalism. Taylor Greer (1991), when speaking of Faur\u00e9\u2019s \u201cmodal\u201d language, refers explicitly to modal mixture and how flat mediants or flat submediants function within the confines of traditional syntax.'><sup>41<\/sup><\/a><\/span> With Kaminsky\u2019s ideas in mind, we may prioritize the D minor melody or the G minor bass, but the simultaneous <em>interaction<\/em> of the two strata creates a modal synthesis for the listener. For example, I can hear D phrygian at first due to the combination of the D minor melody with the C and <nobr>E$$\\flat$$<\/nobr> bass, which by itself sounds more traditionally like $$\\hat{4}$$ and $$\\flat\\hat{6}$$ in G minor. This D phrygian changes slightly to D aeolian with the presence of <nobr>E$$\\natural$$<\/nobr> in m. 11. However, given the period-like structure and melodic trajectory of the bass, I can also hear G aeolian at first, changing slightly to G dorian with the <nobr>E$$\\natural$$<\/nobr> in m. 11. Thus, the D minor profile of the melody is made modal (e.g., phrygian) due to the G minor elements in the bass, and the G minor cadence in the bass is made modal (e.g., dorian) due to the D minor components in the melody.&nbsp;<\/p>\n\n\n\n<p><span style=\"font-weight: 400;\">This excerpt attests to the difficulty in analyzing polyphonic passages. Plural function stems from the tonal fingerprint of each voice: is the final chord in m. 12 the D minor tonic (privileging the soprano) or a <nobr>i$$^{7}$$<\/nobr> chord in G minor (privileging the bass)? A reasonable place to start when encountering plural-function harmonies is the contrapuntal motion, or confluence, of parts.<\/span><span id='easy-footnote-42-9120' class='easy-footnote-margin-adjust'><\/span><span class='easy-footnote'><a href='https:\/\/theory.esm.rochester.edu\/integral\/37-2024\/bilik\/#easy-footnote-bottom-42-9120' title='For a richer investigation of plural harmonic function, see Kevin Swinden (2005). When faced with a problematic passage, we would do well to see if melodic resolutions do or do not correspond with harmonic ones; for example, the D tonic arrival in m. 12 is complicated by a G wedged in the bass\u2014a clear case of tonal disjunction.'><sup>42<\/sup><\/a><\/span> Try playing the passage twice, listening first to the soprano and then to the bass to hear the harmonic palette change.<\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full is-resized\"><a href=\"https:\/\/theory.esm.rochester.edu\/integral\/bilik-vol37-example-9\/\"><img loading=\"lazy\" decoding=\"async\" width=\"936\" height=\"284\" src=\"https:\/\/theory.esm.rochester.edu\/integral\/wp-content\/uploads\/2024\/06\/bilik-vol37-example-9.png\" alt=\"Bilik, Example 9\" class=\"wp-image-9359\" style=\"width:512px;height:155px\" srcset=\"https:\/\/theory.esm.rochester.edu\/integral\/wp-content\/uploads\/2024\/06\/bilik-vol37-example-9.png 936w, https:\/\/theory.esm.rochester.edu\/integral\/wp-content\/uploads\/2024\/06\/bilik-vol37-example-9-300x91.png 300w, https:\/\/theory.esm.rochester.edu\/integral\/wp-content\/uploads\/2024\/06\/bilik-vol37-example-9-768x233.png 768w\" sizes=\"auto, (max-width: 706px) 89vw, (max-width: 767px) 82vw, 740px\" \/><\/a><figcaption class=\"wp-element-caption\"><b>Example 9.<\/b> Faur\u00e9, Piano Trio, op. 120\/3, mm. 1\u201312. Key duality between D minor melody and G minor bass in mm. 7\u201312. <\/figcaption><\/figure>\n<\/div>\n\n\n<p><span style=\"font-weight: 400;\">The same phenomenon ensues in <\/span><b>Example 10<\/b><span style=\"font-weight: 400;\">, when Faur\u00e9 presents the melody in canon. Faur\u00e9 forges his harmony from the layering of motives. There are no block chords; instead, Faur\u00e9 opts for three distinct polyphonic voices. In a nod to medieval counterpoint, he gives the listener two voices in imitation above a steady \u201ctenor.\u201d The motive engineers much of the dissonance, complicating the passing harmonies in mm. 122<em>\u2013<\/em>123. While the outer voices and harmonies come together at harmonic goalposts (see measures with Roman numerals), neither are clear en route. For example, the F bass in m. 123 passes up to the following G, while the <nobr>B$$\\flat$$<\/nobr> soprano above anticipates the following G minor harmony. Despite all that, the outer voices do bare a period form akin to the beginning of the movement in mm. 7<em>\u2013<\/em>12; here, v in C minor (m. 124) is answered a perfect fifth lower by i in C minor (m. 127). Although the violin melody suggests <nobr>E$$\\flat$$<\/nobr> major, the listener intuits C minor from the bass.<span id='easy-footnote-43-9120' class='easy-footnote-margin-adjust'><\/span><span class='easy-footnote'><a href='https:\/\/theory.esm.rochester.edu\/integral\/37-2024\/bilik\/#easy-footnote-bottom-43-9120' title='Like Example 4, the members of the &lt;nobr&gt;E$$\\flat$$&lt;\/nobr&gt; tonic triad are fixed despite the momentary Lydian inflection in m. 123. See also Example 15.'><sup>43<\/sup><\/a><\/span> Like the previous passage, the melody and bass have a tonal profile resolute enough to communicate their own contrasting key.<span id='easy-footnote-44-9120' class='easy-footnote-margin-adjust'><\/span><span class='easy-footnote'><a href='https:\/\/theory.esm.rochester.edu\/integral\/37-2024\/bilik\/#easy-footnote-bottom-44-9120' title='I have assimilated the G minor alto melody into the C minor\/&lt;nobr&gt;E$$\\flat$$&lt;\/nobr&gt; major realm of the outer voices. However, the pianist might experiment bringing out this line for fun during rehearsal.'><sup>44<\/sup><\/a><\/span> And, as before, the merging of two tonic harmonies at the cadence transmits a sense of modalism.&nbsp;<\/span><\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full is-resized\"><a href=\"https:\/\/theory.esm.rochester.edu\/integral\/bilik-vol37-example-10\/\"><img loading=\"lazy\" decoding=\"async\" width=\"936\" height=\"272\" src=\"https:\/\/theory.esm.rochester.edu\/integral\/wp-content\/uploads\/2024\/06\/bilik-vol37-example-10.png\" alt=\"Bilik, Example 10\" class=\"wp-image-9360\" style=\"width:512px;height:149px\" srcset=\"https:\/\/theory.esm.rochester.edu\/integral\/wp-content\/uploads\/2024\/06\/bilik-vol37-example-10.png 936w, https:\/\/theory.esm.rochester.edu\/integral\/wp-content\/uploads\/2024\/06\/bilik-vol37-example-10-300x87.png 300w, https:\/\/theory.esm.rochester.edu\/integral\/wp-content\/uploads\/2024\/06\/bilik-vol37-example-10-768x223.png 768w\" sizes=\"auto, (max-width: 706px) 89vw, (max-width: 767px) 82vw, 740px\" \/><\/a><figcaption class=\"wp-element-caption\"><b>Example 10.<\/b> Faur\u00e9, Piano Trio, op. 120\/3, mm. 121\u2013127. Key duality between <nobr>E$$\\flat$$<\/nobr> major melody and C minor bass. <\/figcaption><\/figure>\n<\/div>\n\n\n<p><span style=\"font-weight: 400;\">The other tonal layers and motivic statements in canon obscure a holistic harmonic analysis but are nonetheless synthesized once again below the staff with Roman numerals. The C minor reading from the bass is reinforced by the tonicized half cadence\u2014the applied <nobr>D$$^{7}$$<\/nobr> setup in m. 121 that moves to G minor in m. 124.<span id='easy-footnote-45-9120' class='easy-footnote-margin-adjust'><\/span><span class='easy-footnote'><a href='https:\/\/theory.esm.rochester.edu\/integral\/37-2024\/bilik\/#easy-footnote-bottom-45-9120' title='The &lt;nobr&gt;D$$^{7}$$&lt;\/nobr&gt; is preceded by a six-measure D major harmony. Measure 128 begins a sequence upward that transports the music to G major (V of C minor).'><sup>45<\/sup><\/a><\/span> Alternatively, the Eb major reading gives the soprano melody more credence. The duality between the two keys is what makes Faur\u00e9\u2019s late music distinct.&nbsp;<\/span><\/p>\n\n\n\n<p><span style=\"font-weight: 400;\">Our last Faur\u00e9 example, the ninth song of the 1906<em>\u2013<\/em>10 song cycle <\/span><i><span style=\"font-weight: 400;\">La chanson d\u2019Eve<\/span><\/i><span style=\"font-weight: 400;\">, op. 95, \u201cCr\u00e9puscule,\u201d stages an unabashed melding of D minor and F major, seen in <\/span><b>Example 11<\/b><span style=\"font-weight: 400;\">. The recurring D minor melody, plucked from his suite Pell\u00e9as et M\u00e9lisande (\u201cLa mort de M\u00e9lisande\u201d), coexists peacefully with its D minor context at first, entraining the listener to hear D minor. However, beginning in m. 15, a protruding C pedal sounds in the bass, supporting F major triads (in second inversion) at the beginning and ends of each two-measure phrase. To tonal ears, this harmony suggests a standing on the dominant, C, in F major. Together with the D minor profile of the melody, one may hear the composite harmony as an F major triad with added sixth, D, above.<span id='easy-footnote-46-9120' class='easy-footnote-margin-adjust'><\/span><span class='easy-footnote'><a href='https:\/\/theory.esm.rochester.edu\/integral\/37-2024\/bilik\/#easy-footnote-bottom-46-9120' title=' The &lt;nobr&gt;G$$\\sharp$$s&lt;\/nobr&gt; in the inner voice resolve to A, the reciting tone of both F major (mode 6) and D minor (mode 1). I am grateful for the anonymous reviewer that brought this to my attention.'><sup>46<\/sup><\/a><\/span> Yet affirmation of F major never arrives, and the song ends in D major, the parallel key in which it began. The compound F major\/D minor tonic, a <nobr>Dmm$$^{7}$$<\/nobr> sonority in third inversion, is content to simply exist over mm. 15<em>\u2013<\/em>20. As an example of BaileyShea\u2019s third and most radical category of the double-tonic complex, the passage also foreshadows Durufl\u00e9\u2019s practice of tonal stratification to generate key duality.&nbsp;<\/span><\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full is-resized\"><a href=\"https:\/\/theory.esm.rochester.edu\/integral\/bilik-vol37-example-11\/\"><img loading=\"lazy\" decoding=\"async\" width=\"818\" height=\"594\" src=\"https:\/\/theory.esm.rochester.edu\/integral\/wp-content\/uploads\/2024\/06\/bilik-vol37-example-11.png\" alt=\"Bilik, Example 11\" class=\"wp-image-9361\" style=\"width:512px;height:372px\" srcset=\"https:\/\/theory.esm.rochester.edu\/integral\/wp-content\/uploads\/2024\/06\/bilik-vol37-example-11.png 818w, https:\/\/theory.esm.rochester.edu\/integral\/wp-content\/uploads\/2024\/06\/bilik-vol37-example-11-300x218.png 300w, https:\/\/theory.esm.rochester.edu\/integral\/wp-content\/uploads\/2024\/06\/bilik-vol37-example-11-768x558.png 768w\" sizes=\"auto, (max-width: 706px) 89vw, (max-width: 767px) 82vw, 740px\" \/><\/a><figcaption class=\"wp-element-caption\"><b>Example 11.<\/b> Faur\u00e9, La chanson d\u2019Eve, op. 95\/9, mm. 13\u201320. Disjucntion between D minor melody and F major bass that stands on the dominant, C.<\/figcaption><\/figure>\n<\/div>\n\n\n<h2 class=\"wp-block-heading\"><strong>Durufl\u00e9: Requiem, op. 9 (1947, rev. 1961)<\/strong><\/h2>\n\n\n\n<p><span style=\"font-weight: 400;\">We have now ventured from BaileyShea\u2019s second category of the double-tonic complex to the third, which also brings us closer to Nobile\u2019s true double-tonic complex characterized by a fundamental four-note tonic sonority. Key duality of this sort in twentieth-century French music comes to a head in the music of Durufl\u00e9. Considering Durufl\u00e9\u2019s interest in chant reharmonization, it is not surprising that his melodies emit tonal ambiguity between a chant line and its harmony. Although analytical writings on Durufl\u00e9 have recognized the significance of reharmonization in his works, they have also skirted the idea of key duality, opting to reduce a tonic seventh chord to a structural triad with extensions (Harrison 2016) or view chords as part of an evolving macroharmony (Chiu 2021).<\/span><span id='easy-footnote-47-9120' class='easy-footnote-margin-adjust'><\/span><span class='easy-footnote'><a href='https:\/\/theory.esm.rochester.edu\/integral\/37-2024\/bilik\/#easy-footnote-bottom-47-9120' title='Harrison (2016) notes the preponderance of conflated tonics in French Impressionism. Chiu (2021) positions his analysis along mathematical lines, using the discrete Fourier transform (DFT) to explain octatonic and hexatonic shifts.'><sup>47<\/sup><\/a><\/span> The end of Domine Jesu Christe, from the Requiem, op. 9, maintains a delicate equilibrium between <nobr>F$$\\sharp$$<\/nobr> major and <nobr>D$$\\sharp$$<\/nobr> minor\u2014specifically, <nobr>D$$\\sharp$$<\/nobr> aeolian and <nobr>D$$\\sharp$$<\/nobr> dorian\u2014in <strong>Example 12<\/strong>. Initially, the first-inversion <nobr>F$$\\sharp$$<\/nobr> major triad in the instrumental accompaniment and the <nobr>A$$\\sharp$$\/F$$\\sharp$$<\/nobr> dyad between the soprano and alto situate the passage in <nobr>F$$\\sharp$$<\/nobr> major. However, the falling alto line to <nobr>D$$\\sharp$$<\/nobr> in m. 163 veers in the direction of <nobr>D$$\\sharp$$<\/nobr> minor, persuading the soprano to follow accordingly. As the soprano encircles the <nobr>D$$\\sharp$$<\/nobr> minor tonic over mm. 163<em>\u2013<\/em>166, the accompaniment steps up from <nobr>C$$\\sharp$$<\/nobr> to share the soprano <nobr>D$$\\sharp$$<\/nobr> in m. 165, fueling the ongoing 5<em>\u2013<\/em>6 exchanges.<span id='easy-footnote-48-9120' class='easy-footnote-margin-adjust'><\/span><span class='easy-footnote'><a href='https:\/\/theory.esm.rochester.edu\/integral\/37-2024\/bilik\/#easy-footnote-bottom-48-9120' title='Typical of Durufl\u00e9\u2019s works, the cadence in the melody precedes the cadence in the accompaniment.'><sup>48<\/sup><\/a><\/span> The <nobr>D$$\\sharp$$<\/nobr> confirmation sets the closing melody in <nobr>D$$\\sharp$$<\/nobr> minor over mm. 166<em>\u2013<\/em>168. Not content with a simple <nobr>F$$\\sharp$$<\/nobr> to <nobr>D$$\\sharp$$<\/nobr> narrative, though, Durufl\u00e9 alerts the listener to the dual presence of <nobr>F$$\\sharp$$<\/nobr> major via a staunch <nobr>F$$\\sharp$$<\/nobr> drone. At last, both tonics coalesce into a seventh chord in mm. 168<em>\u2013<\/em>169, heard either as an <nobr>F$$\\sharp$$<\/nobr> major triad with added sixth <nobr>(D$$\\sharp$$)<\/nobr> or a revoiced <nobr>D$$\\sharp$$<\/nobr> minor triad with added seventh <nobr>(C$$\\sharp$$).<\/nobr><span id='easy-footnote-49-9120' class='easy-footnote-margin-adjust'><\/span><span class='easy-footnote'><a href='https:\/\/theory.esm.rochester.edu\/integral\/37-2024\/bilik\/#easy-footnote-bottom-49-9120' title='The final of the chant often ends a third above the root of the harmony; in the fifth movement, \u201cPie Jesu,\u201d the voices conclude by repeating the C final over an &lt;nobr&gt;A$$\\flat$$&lt;\/nobr&gt; major triad.'><sup>49<\/sup><\/a><\/span> The beauty of the passage lies not just in the sonorous bodies of conjoined tonics but the careful attention to what<em> creates<\/em> those wonderful sounds. In this form of active listening, our interpretation is shaped by what voice, timbre, or register we prioritize.&nbsp;<\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full is-resized\"><a href=\"https:\/\/theory.esm.rochester.edu\/integral\/bilik-vol37-example-12-1\/\"><img loading=\"lazy\" decoding=\"async\" width=\"842\" height=\"408\" src=\"https:\/\/theory.esm.rochester.edu\/integral\/wp-content\/uploads\/2024\/06\/bilik-vol37-example-12-1.png\" alt=\"Bilik, Example 12 (1\/2).\" class=\"wp-image-9362\" style=\"width:512px;height:248px\" srcset=\"https:\/\/theory.esm.rochester.edu\/integral\/wp-content\/uploads\/2024\/06\/bilik-vol37-example-12-1.png 842w, https:\/\/theory.esm.rochester.edu\/integral\/wp-content\/uploads\/2024\/06\/bilik-vol37-example-12-1-300x145.png 300w, https:\/\/theory.esm.rochester.edu\/integral\/wp-content\/uploads\/2024\/06\/bilik-vol37-example-12-1-768x372.png 768w\" sizes=\"auto, (max-width: 706px) 89vw, (max-width: 767px) 82vw, 740px\" \/><\/a><figcaption class=\"wp-element-caption\"><b>Example 12 (1\/2).<\/b> Score excerpt from Durufl\u00e9, Requiem, op. 9\/3, mm.159\u2013169. Duality between <nobr>D$$\\sharp$$<\/nobr> minor melody and <nobr>F$$\\sharp$$<\/nobr> major bass sounded as aggregate in the final three measures.<\/figcaption><\/figure>\n<\/div>\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full is-resized\"><a href=\"https:\/\/theory.esm.rochester.edu\/integral\/bilik-vol37-example-12-2\/\"><img loading=\"lazy\" decoding=\"async\" width=\"874\" height=\"366\" src=\"https:\/\/theory.esm.rochester.edu\/integral\/wp-content\/uploads\/2024\/06\/bilik-vol37-example-12-2.png\" alt=\"Bilik, Example 12 (2\/2)\" class=\"wp-image-9363\" style=\"width:512px;height:214px\" srcset=\"https:\/\/theory.esm.rochester.edu\/integral\/wp-content\/uploads\/2024\/06\/bilik-vol37-example-12-2.png 874w, https:\/\/theory.esm.rochester.edu\/integral\/wp-content\/uploads\/2024\/06\/bilik-vol37-example-12-2-300x126.png 300w, https:\/\/theory.esm.rochester.edu\/integral\/wp-content\/uploads\/2024\/06\/bilik-vol37-example-12-2-768x322.png 768w\" sizes=\"auto, (max-width: 706px) 89vw, (max-width: 767px) 82vw, 740px\" \/><\/a><figcaption class=\"wp-element-caption\"><b>Example 12 (2\/2).<\/b><\/figcaption><\/figure>\n<\/div>\n\n\n<p><span style=\"font-weight: 400;\">The beginning of the first and fourth movements contain similar occurrences of key duality due to Durufl\u00e9\u2019s chant harmonization. These movements are notable for their greater degree of duality. Where Faur\u00e9 may implement duality for 8<em>\u2013<\/em>16 measures, Durufl\u00e9 might indulge in duality for most of a movement. <\/span><b>Example 13<\/b><span style=\"font-weight: 400;\">, the beginning of the Introit, pits a D minor bass against an F major choir.<\/span><span id='easy-footnote-50-9120' class='easy-footnote-margin-adjust'><\/span><span class='easy-footnote'><a href='https:\/\/theory.esm.rochester.edu\/integral\/37-2024\/bilik\/#easy-footnote-bottom-50-9120' title='The Introit of Faur\u00e9\u2019s &lt;em&gt;Requiem &lt;\/em&gt;also brandishes duality between F major and D minor. For a transformational reading of this work, see Cohn (2012, 54\u201356).'><sup>50<\/sup><\/a><\/span> The D bass pedal and sustained D\/F dyad across bar lines reifies the D center of the accompaniment, while the Fs in the choir at the beginning and ends of phrases (mm. 2, 5, 7, and 11) solidify an F center. At two of these junctures, mm. 5 and 11, the upper voices also fill out the F major triad upon entering. The mingling of these two tonal centers appears in the sixteenth-note arpeggios, which outlines a <nobr>Dmm$$^{7}$$<\/nobr> seventh chord. It is as if Durufl\u00e9 verticalizes the characteristic notes of the chant, which would be $$\\hat{1}$$, $$\\hat{3}$$, $$\\hat{5}$$, and $$\\natural\\hat{7}$$ in dorian. The disjunction between tonal layers fluctuates in kaleidoscopic fashion within each phrase; the C pedal over mm. 8<em>\u2013<\/em>10, doubled in the bass before m. 11, is poised for an authentic cadence in F major, only to sidestep to D minor.<span id='easy-footnote-51-9120' class='easy-footnote-margin-adjust'><\/span><span class='easy-footnote'><a href='https:\/\/theory.esm.rochester.edu\/integral\/37-2024\/bilik\/#easy-footnote-bottom-51-9120' title='A varied statement of the mm. 8\u201311 melodic line occurs over mm. 16\u201319, but the vocal ending on F is harmonized with an F major triad this time after a plagal cadence (not shown).'><sup>51<\/sup><\/a><\/span> Later in the movement, at m. 72 (not shown), Durufl\u00e9 resurrects the same melodic-bass disjunction: harmonic motion to D minor is tailed by an A dominant bass pedal in mm. 51<em>\u2013<\/em>54, but it quickly dissolves to another plagal cadence in F to close the movement.<span id='easy-footnote-52-9120' class='easy-footnote-margin-adjust'><\/span><span class='easy-footnote'><a href='https:\/\/theory.esm.rochester.edu\/integral\/37-2024\/bilik\/#easy-footnote-bottom-52-9120' title='The orchestra cadences in m. 56, but the voice does not cadence on F until m. 58. In fact, contrapuntal motion in the choir often evades what would otherwise be a closed cadence in the bass, and vice versa. See, for instance, the second and fifth movements.'><sup>52<\/sup><\/a><\/span> Overall, in both the outer sections of the ternary form, Durufl\u00e9 makes key duality a salient feature to be resolved by the end of each section. Unlike the previous example, this one resolves the opening key duality by the end of the movement. <span id='easy-footnote-53-9120' class='easy-footnote-margin-adjust'><\/span><span class='easy-footnote'><a href='https:\/\/theory.esm.rochester.edu\/integral\/37-2024\/bilik\/#easy-footnote-bottom-53-9120' title='In the Introit, the F final is harmonized with an F major triad; in the Sanctus, the D final is harmonized with a D minor triad.'><sup>53<\/sup><\/a><\/span>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full is-resized\"><a href=\"https:\/\/theory.esm.rochester.edu\/integral\/bilik-vol37-example-13-1\/\"><img loading=\"lazy\" decoding=\"async\" width=\"792\" height=\"506\" src=\"https:\/\/theory.esm.rochester.edu\/integral\/wp-content\/uploads\/2024\/06\/bilik-vol37-example-13-1.png\" alt=\"Bilik, Example 13 (1\/3)\" class=\"wp-image-9364\" style=\"width:512px;height:327px\" srcset=\"https:\/\/theory.esm.rochester.edu\/integral\/wp-content\/uploads\/2024\/06\/bilik-vol37-example-13-1.png 792w, https:\/\/theory.esm.rochester.edu\/integral\/wp-content\/uploads\/2024\/06\/bilik-vol37-example-13-1-300x192.png 300w, https:\/\/theory.esm.rochester.edu\/integral\/wp-content\/uploads\/2024\/06\/bilik-vol37-example-13-1-768x491.png 768w\" sizes=\"auto, (max-width: 706px) 89vw, (max-width: 767px) 82vw, 740px\" \/><\/a><figcaption class=\"wp-element-caption\"><b>Example 13 (1\/3)<\/b><strong>.<\/strong> Score excerpt from Durufl\u00e9, Requiem, op. 9\/1, mm. 1\u201311. F major melody against D minor bass.<\/figcaption><\/figure>\n<\/div>\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full is-resized\"><a href=\"https:\/\/theory.esm.rochester.edu\/integral\/bilik-vol37-example-13-2\/\"><img loading=\"lazy\" decoding=\"async\" width=\"790\" height=\"432\" src=\"https:\/\/theory.esm.rochester.edu\/integral\/wp-content\/uploads\/2024\/06\/bilik-vol37-example-13-2.png\" alt=\"Bilik, Example 13 (2\/3)\" class=\"wp-image-9365\" style=\"width:512px;height:280px\" srcset=\"https:\/\/theory.esm.rochester.edu\/integral\/wp-content\/uploads\/2024\/06\/bilik-vol37-example-13-2.png 790w, https:\/\/theory.esm.rochester.edu\/integral\/wp-content\/uploads\/2024\/06\/bilik-vol37-example-13-2-300x164.png 300w, https:\/\/theory.esm.rochester.edu\/integral\/wp-content\/uploads\/2024\/06\/bilik-vol37-example-13-2-768x420.png 768w\" sizes=\"auto, (max-width: 706px) 89vw, (max-width: 767px) 82vw, 740px\" \/><\/a><figcaption class=\"wp-element-caption\"><b>Example 13 (2\/3).<\/b><\/figcaption><\/figure>\n<\/div>\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full is-resized\"><a href=\"https:\/\/theory.esm.rochester.edu\/integral\/bilik-vol37-example-13-3\/\"><img loading=\"lazy\" decoding=\"async\" width=\"818\" height=\"468\" src=\"https:\/\/theory.esm.rochester.edu\/integral\/wp-content\/uploads\/2024\/06\/bilik-vol37-example-13-3.png\" alt=\"Bilik, Example 13 (3\/3)\" class=\"wp-image-9366\" style=\"width:512px;height:293px\" srcset=\"https:\/\/theory.esm.rochester.edu\/integral\/wp-content\/uploads\/2024\/06\/bilik-vol37-example-13-3.png 818w, https:\/\/theory.esm.rochester.edu\/integral\/wp-content\/uploads\/2024\/06\/bilik-vol37-example-13-3-300x172.png 300w, https:\/\/theory.esm.rochester.edu\/integral\/wp-content\/uploads\/2024\/06\/bilik-vol37-example-13-3-768x439.png 768w\" sizes=\"auto, (max-width: 706px) 89vw, (max-width: 767px) 82vw, 740px\" \/><\/a><figcaption class=\"wp-element-caption\"><b>Example 13 (3\/3).<\/b><\/figcaption><\/figure>\n<\/div>\n\n\n<p><span style=\"font-weight: 400;\">A familiar wash of key duality occurs in the fourth movement, shown in <\/span><b>Example 14<\/b><span style=\"font-weight: 400;\">. Here, though, the interval of disjunction between the two tonal centers is not a third but a second\u2014a G minor bass and F major choir. The constant F major triads at the beginning of each measure rub against the G bass downbeats. The G minor bass materializes with the assistance of the D dominant upbeats and what sounds like a half cadence in G in m. 6. The composite key, if one were to lean toward a monotonal hearing, might be D minor due to the D minor arpeggios which mediate the disjunction of G minor and F major. A possibility for D minor is to hear an out-of-sync iv<sup>(add6)<\/sup>-i in D minor, with the G bass connected to the <nobr>B$$\\flat$$-E-G<\/nobr> chord in the upper part. This ostensible D minor reading takes some effort, as the metric accent prioritizes G, not D. However, Durufl\u00e9 confirms the potential of this <\/span><i><span style=\"font-weight: 400;\">third <\/span><\/i><span style=\"font-weight: 400;\">tonal layer when he transposes the first six measures up a perfect fifth, furnishing a close on D minor in m. 22 after the voices end on a phrygian half cadence on A two measures beforehand (not shown).&nbsp;<\/span><\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full is-resized\"><a href=\"https:\/\/theory.esm.rochester.edu\/integral\/bilik-vol37-example-14-1\/\"><img loading=\"lazy\" decoding=\"async\" width=\"876\" height=\"448\" src=\"https:\/\/theory.esm.rochester.edu\/integral\/wp-content\/uploads\/2024\/06\/bilik-vol37-example-14-1.png\" alt=\"Bilik, Example 14 (1\/2)\" class=\"wp-image-9367\" style=\"width:512px;height:262px\" srcset=\"https:\/\/theory.esm.rochester.edu\/integral\/wp-content\/uploads\/2024\/06\/bilik-vol37-example-14-1.png 876w, https:\/\/theory.esm.rochester.edu\/integral\/wp-content\/uploads\/2024\/06\/bilik-vol37-example-14-1-300x153.png 300w, https:\/\/theory.esm.rochester.edu\/integral\/wp-content\/uploads\/2024\/06\/bilik-vol37-example-14-1-768x393.png 768w\" sizes=\"auto, (max-width: 706px) 89vw, (max-width: 767px) 82vw, 740px\" \/><\/a><figcaption class=\"wp-element-caption\"><b>Example 14 (1\/2).<\/b> Score excerpt from Durufl\u00e9, Requiem, op. 9\/4, mm. 1\u20136. F major melody against G minor bass.<\/figcaption><\/figure>\n<\/div>\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full is-resized\"><a href=\"https:\/\/theory.esm.rochester.edu\/integral\/bilik-vol37-example-14-2\/\"><img loading=\"lazy\" decoding=\"async\" width=\"880\" height=\"446\" src=\"https:\/\/theory.esm.rochester.edu\/integral\/wp-content\/uploads\/2024\/06\/bilik-vol37-example-14-2.png\" alt=\"Bilik, Example 14 (2\/2)\" class=\"wp-image-9368\" style=\"width:512px;height:259px\" srcset=\"https:\/\/theory.esm.rochester.edu\/integral\/wp-content\/uploads\/2024\/06\/bilik-vol37-example-14-2.png 880w, https:\/\/theory.esm.rochester.edu\/integral\/wp-content\/uploads\/2024\/06\/bilik-vol37-example-14-2-300x152.png 300w, https:\/\/theory.esm.rochester.edu\/integral\/wp-content\/uploads\/2024\/06\/bilik-vol37-example-14-2-768x389.png 768w\" sizes=\"auto, (max-width: 706px) 89vw, (max-width: 767px) 82vw, 740px\" \/><\/a><figcaption class=\"wp-element-caption\"><b>Example 14 (2\/2).<\/b><\/figcaption><\/figure>\n<\/div>\n\n\n<h2 class=\"wp-block-heading\"><strong>Role of Inner Voices<\/strong><\/h2>\n\n\n\n<p><span style=\"font-weight: 400;\">There is something to be said for how inner voices contribute to a sense of key duality. <\/span><b>Example 15<\/b><span style=\"font-weight: 400;\">, from the second movement of Faur\u00e9\u2019s Piano Quintet no. 2, serves as a snapshot of how inner voices bewilder a single-key interpretation. The soprano outlines <nobr>E$$\\flat$$<\/nobr> lydian with its emphasis on <nobr>E$$\\flat$$<\/nobr> and <nobr>B$$\\flat$$<\/nobr> on beats one, two, and three; the <nobr>$$\\hat{1}$$-$$\\hat{2}$$-$$\\hat{3}$$-$$\\hat{2}$$-$$\\hat{1}$$<\/nobr> fragment in mm. 3<em>\u2013<\/em>4 likewise confirms <nobr>E$$\\flat$$,<\/nobr> now with a phrygian inflection.<span id='easy-footnote-54-9120' class='easy-footnote-margin-adjust'><\/span><span class='easy-footnote'><a href='https:\/\/theory.esm.rochester.edu\/integral\/37-2024\/bilik\/#easy-footnote-bottom-54-9120' title='The lydian &lt;nobr&gt;A$$\\natural$$&lt;\/nobr&gt; does not destroy the impression of &lt;nobr&gt;E$$\\flat$$,&lt;\/nobr&gt; nor the fact that &lt;nobr&gt;C$$\\sharp$$-D&lt;\/nobr&gt; would make more sense as scale degrees &lt;nobr&gt;$$\\sharp$$4-5&lt;\/nobr&gt; rather than &lt;nobr&gt;$$\\sharp$$6-7.&lt;\/nobr&gt; On the other hand, hearing &lt;nobr&gt;C$$\\sharp$$-D&lt;\/nobr&gt; as &lt;nobr&gt;$$\\sharp\\hat{4}$$-$$\\hat{5}$$&lt;\/nobr&gt; underscores the sway of G minor.'><sup>54<\/sup><\/a><\/span> Further reinforcing <nobr>E$$\\flat$$<\/nobr> is the <nobr>E$$\\flat$$-E$$\\flat$$<\/nobr> range of the soprano in mm. 3<em>\u2013<\/em>4. Yet the alto voice defies this <nobr>E$$\\flat$$<\/nobr> center at first with a sturdy G-D perfect fifth and G downbeat.<span id='easy-footnote-55-9120' class='easy-footnote-margin-adjust'><\/span><span class='easy-footnote'><a href='https:\/\/theory.esm.rochester.edu\/integral\/37-2024\/bilik\/#easy-footnote-bottom-55-9120' title='The G phrygian motion of the alto (&lt;nobr&gt;A$$\\flat$$-G&lt;\/nobr&gt; in mm. 1\u20132) is echoed in the &lt;nobr&gt;E$$\\flat$$&lt;\/nobr&gt; phrygian of the soprano (&lt;nobr&gt;E$$\\flat$$-F$$\\flat$$&lt;\/nobr&gt; in mm. 3\u20134).'><sup>55<\/sup><\/a><\/span> Faur\u00e9 plants the seeds of key duality, where the bass and soprano convey <nobr>E$$\\flat$$<\/nobr> while the inner voice articulates G minor for the first two measures. The added reading in C minor takes the <nobr>A$$\\flat$$-G<\/nobr> in the alto as <nobr>$$\\flat\\hat{6}$$-$$\\hat{5}$$<\/nobr> and privileges the C minor triadic leaps in the bass. In this light, the bass could promote a C minor reading or back the <nobr>E$$\\flat$$<\/nobr> center of the soprano with strong <nobr>E$$\\flat$$<\/nobr> downbeats.&nbsp;<\/span><\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full is-resized\"><a href=\"https:\/\/theory.esm.rochester.edu\/integral\/bilik-vol37-example-15\/\"><img loading=\"lazy\" decoding=\"async\" width=\"936\" height=\"292\" src=\"https:\/\/theory.esm.rochester.edu\/integral\/wp-content\/uploads\/2024\/06\/bilik-vol37-example-15.png\" alt=\"Bilik, Example 15\" class=\"wp-image-9369\" style=\"width:512px;height:127px\" srcset=\"https:\/\/theory.esm.rochester.edu\/integral\/wp-content\/uploads\/2024\/06\/bilik-vol37-example-15.png 936w, https:\/\/theory.esm.rochester.edu\/integral\/wp-content\/uploads\/2024\/06\/bilik-vol37-example-15-300x94.png 300w, https:\/\/theory.esm.rochester.edu\/integral\/wp-content\/uploads\/2024\/06\/bilik-vol37-example-15-768x240.png 768w\" sizes=\"auto, (max-width: 706px) 89vw, (max-width: 767px) 82vw, 740px\" \/><\/a><figcaption class=\"wp-element-caption\"><b>Example 15.<\/b> Faur\u00e9, Piano Quintet no. 2, op. 115\/2, mm. 1\u20135. Tonal centers of <nobr>E$$\\flat$$<\/nobr> lydian, G minor, and possibly C minor in flux.<\/figcaption><\/figure>\n<\/div>\n\n\n<p><span style=\"font-weight: 400;\">Finally, <\/span><b>Example 16<\/b><span style=\"font-weight: 400;\"> from the third movement models how a certain line might nudge the music to a new center or key. Harmonies spring from canonic statements of the motive over mm. 35<em>\u2013<\/em>39. Trailing a <nobr>i-iv-$$\\flat$$II<\/nobr> progression in E minor (not shown), this passage projects an E minor center from the tonic unfolding of the soprano. Besides the E minor scalar collection, the downbeats come to rest on tonic (E) and dominant (B). (The preceding half cadence in m. 35 is muddled by a stalwart E that hampers the B minor (v) sonority, even though the bass jumps in to salvage it.) The persistent E in the alto also tethers the listener to E minor in mm. 37<em>\u2013<\/em>38. However, the bass disrupts the E minor tonic, ferrying the music to G major via staggered parallel thirds with the soprano from mm. 36<em>\u2013<\/em>38 (see dotted lines). Thus, Faur\u00e9 validates E minor only after subverting it through 1) an equivocal half cadence in m. 35 and 2) a bass that harmonizes the soprano in G major.<span id='easy-footnote-56-9120' class='easy-footnote-margin-adjust'><\/span><span class='easy-footnote'><a href='https:\/\/theory.esm.rochester.edu\/integral\/37-2024\/bilik\/#easy-footnote-bottom-56-9120' title='The &lt;nobr&gt;C$$\\sharp$$&lt;\/nobr&gt; of m. 35 aside, the bass outlines G major with parallel tenths above, inserting an element of key duality within the overarching E minor.'><sup>56<\/sup><\/a><\/span> Amid the harmonic fog, the E minor soprano may be a beacon through hearing the excerpt.&nbsp;&nbsp;<\/span><\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full is-resized\"><a href=\"https:\/\/theory.esm.rochester.edu\/integral\/bilik-vol37-example-16\/\"><img loading=\"lazy\" decoding=\"async\" width=\"936\" height=\"314\" src=\"https:\/\/theory.esm.rochester.edu\/integral\/wp-content\/uploads\/2024\/06\/bilik-vol37-example-16.png\" alt=\"Bilik, Example 16\" class=\"wp-image-9370\" style=\"width:512px;height:172px\" srcset=\"https:\/\/theory.esm.rochester.edu\/integral\/wp-content\/uploads\/2024\/06\/bilik-vol37-example-16.png 936w, https:\/\/theory.esm.rochester.edu\/integral\/wp-content\/uploads\/2024\/06\/bilik-vol37-example-16-300x101.png 300w, https:\/\/theory.esm.rochester.edu\/integral\/wp-content\/uploads\/2024\/06\/bilik-vol37-example-16-768x258.png 768w\" sizes=\"auto, (max-width: 706px) 89vw, (max-width: 767px) 82vw, 740px\" \/><\/a><figcaption class=\"wp-element-caption\"><b>Example 16.<\/b> Faur\u00e9, Piano Quintet no. 2, op. 115\/3, mm. 35\u201338. Motive in canon. Key duality from E minor soprano and G major bass. <\/figcaption><\/figure>\n<\/div>\n\n\n<h2 class=\"wp-block-heading\"><strong>Concluding Thoughts and Directions<\/strong><\/h2>\n\n\n\n<p><span style=\"font-weight: 400;\">In Faur\u00e9 and Durufl\u00e9&#8217;s music, key duality often occurs between tonal centers separated by a third. While relations by third are the norm when it comes to tonal pairing and double-tonic complexes, the distinctiveness of their key duality lies in the disjunction, or \u201cdivorce,\u201d between a melody and a bass that express dissimilar tonal centers. When related by thirds, these stratified tonal centers often arise via contrapuntal 5<em>\u2013<\/em>6 exchanges. Finally, the amalgamation of two tonal layers conjures a quintessential modal landscape, often in the form of a tonic seventh chord formed from the union of two tonics. Faur\u00e9\u2019s influence on French modernism is well-known, and his use of key duality is magnified in the works of Durufl\u00e9. Overall, Durufl\u00e9 employs it with wider formal breadth and intervals of disjunction beyond a third, as seen in Example 14<\/span><\/p>\n\n\n\n<p><span style=\"font-weight: 400;\">Throughout this article, my analyses have espoused a broader attention to individual voices, especially outer ones. Because these chords like the ones in Example 10 are in transit, assigning a clean harmonic label can be challenging and counterproductive. Extoling Faur\u00e9\u2019s mastery of counterpoint, James Kurtz (1970) prefers to downplay a vertical chord-by-chord interpretation. He concurs that \u201croot movement is subordinate to the behavior of individual voices\u201d in Faur\u00e9 and continues: \u201cthe means of establishing its [the tonic\u2019s] priority is more often to be found through the use of contrapuntal motions and melodic relationship rather than traditional tonal function [of harmonies]\u2026Most vertical sonorities come into being though a confluence of moving parts\u201d<\/span> (183)<span style=\"font-weight: 400;\">.<span id='easy-footnote-57-9120' class='easy-footnote-margin-adjust'><\/span><span class='easy-footnote'><a href='https:\/\/theory.esm.rochester.edu\/integral\/37-2024\/bilik\/#easy-footnote-bottom-57-9120' title='Certainly, the plethora of unresolved dominant sevenths in the accompaniment points the listener to another potential source of tonal coherence: the melody. '><sup>57<\/sup><\/a><\/span> In addition, he underscores the autonomous role of the bass as an independent line that partakes in more than root progressions. William Thomson (2006) also argues for melodic agency in progressions: \u201cThe pitch simultaneities of chords add an immediate and significant shaping dimension; sometimes they confirm, sometimes they are at odds with melodic shaping\u201d<\/span> (94)<span style=\"font-weight: 400;\">.<\/span><span id='easy-footnote-58-9120' class='easy-footnote-margin-adjust'><\/span><span class='easy-footnote'><a href='https:\/\/theory.esm.rochester.edu\/integral\/37-2024\/bilik\/#easy-footnote-bottom-58-9120' title='He demonstrates how conflict between foreground and background harmonic structures steers two different interpretations\u2014oriented toward the foreground or middleground\u2014that may not be reconciled into one. While middleground and larger level structures are beyond the scope of this paper, these authors praise the importance of outer voices for clarifying structure. Philips (1993) also pays close attention to contrapuntal lines. In one case, he cites \u201ccounterfeit dominants\u201d that contradict the middleground\u2014dominants that function locally but not structurally as dominants (Phillips, 7). The proliferation of seventh chords places a \u201csmokescreen\u201d over the middleground structure, obfuscating or denying it.'><sup>58<\/sup><\/a><\/span> Essentially, a chord tone may be consonant with its own triad but dissonant in the larger context of melodic unfolding.<\/p>\n\n\n\n<p><span style=\"font-weight: 400;\">The main thrust of this article has foregrounded outer voices as the sculptor of tonal structure in Faur\u00e9 and Durufl\u00e9; in particular, I have focused heavily on linear utterances and their&nbsp; tonal disjunction. In these pieces, both composers permit the melody and bass to establish their own centers, rendering the impression of two operating keys.<span id='easy-footnote-59-9120' class='easy-footnote-margin-adjust'><\/span><span class='easy-footnote'><a href='https:\/\/theory.esm.rochester.edu\/integral\/37-2024\/bilik\/#easy-footnote-bottom-59-9120' title='There are many cases where the bass does not express a harmonic unfolding. In the absence of a tonal profile, we may look to the soprano for a center or key.'><sup>59<\/sup><\/a><\/span> Although unconventional harmonic syntax and added sevenths baffle straightforward analysis, when we attend to the melody and bass, we notice the source of ambiguity in the form of key duality. The superposition of discrete tonal centers reflects the myriad expanded conceptions of tonality of the twentieth century. Sensitivity to the tonal profile of these outer voices helps reveal the origins of key duality in this perplexing twentieth-century repertoire.<\/span><\/p>\n\n\n\n<hr class=\"wp-block-separator has-css-opacity\"\/>\n\n\n\n<h2 class=\"wp-block-heading\"><strong>References<\/strong><\/h2>\n\n\n<p><span style=\"font-weight: 400;\">Bailey, Robert. 1985. \u201cAn Analytical Study of the Sketches and Drafts.\u201d In <\/span><i><span style=\"font-weight: 400;\">Richard Wagner: Prelude and Transfiguration from \u201cTristan and Isolde,\u201d<\/span><\/i><span style=\"font-weight: 400;\"> edited by Robert Bailey. New York: Norton.<\/span><\/p>\n<p><span style=\"font-weight: 400;\">BaileyShea, Matt. 2007. \u201cThe Hexatonic and the Double Tonic: Wolf\u2019s \u2018Christmas Rose.\u2019 \u201d <\/span><i><span style=\"font-weight: 400;\">Journal of Music Theory <\/span><\/i><span style=\"font-weight: 400;\">51, (2 Fall): 187\u2013210.<\/span><\/p>\n<p><span style=\"font-weight: 400;\">Bakulina, Ellen. 2018. \u201cProto-Harmony and The Problem of Tonal Centricity in Rachmaninoff\u2019s All-Night Vigil.\u201d Int\u00e9gral 32 : 15\u201336.&nbsp;<\/span><\/p>\n<p><span style=\"font-weight: 400;\">\u2014 \u2014 \u2014<\/span><span style=\"font-weight: 400;\">. 2014.&nbsp; \u201cThe Concept of Mutability in Russian Theory.\u201d <\/span><i><span style=\"font-weight: 400;\">Music Theory Online <\/span><\/i><span style=\"font-weight: 400;\">20 (3). https:\/\/www.mtosmt.org\/issues\/mto.14.20.3\/mto.14.20.3.bakulina.php.<\/span><\/p>\n<p><span style=\"font-weight: 400;\">Boulanger, Nadia. 1926. \u201cLectures on Modern Music.\u201d <\/span><i><span style=\"font-weight: 400;\">The Rice Institute Pamphlet <\/span><\/i><span style=\"font-weight: 400;\">13 (2): 113\u2013152.&nbsp;&nbsp;<\/span><\/p>\n<p><span style=\"font-weight: 400;\">Brooks, Jeanice. 2016. <\/span><i><span style=\"font-weight: 400;\">The Musical Work of Nadia Boulanger: Performing Past and Future Between the Wars.<\/span><\/i><span style=\"font-weight: 400;\"> Cambridge University Press.&nbsp;<\/span><\/p>\n<p><span style=\"font-weight: 400;\">Caron, Sylvain. 2017. \u201c\u00c9criture tonale et perspectives nouvelles de l\u2019harmonie faur\u00e9enne.\u201d <\/span><i><span style=\"font-weight: 400;\">Canadian University Music Review <\/span><\/i><span style=\"font-weight: 400;\">22 (2): 48\u201376.<\/span><\/p>\n<p><span style=\"font-weight: 400;\">Chiu, Matt. 2021. \u201cMacroharmonic Progressions through the Discrete Fourier Transform: An Analysis from Maurice Durufl\u00e9\u2019s Requiem.\u201d <\/span><i><span style=\"font-weight: 400;\">Music Theory Online 27<\/span><\/i><span style=\"font-weight: 400;\">&nbsp;(3). https:\/\/mtosmt.org\/ issues\/mto.21.27.3\/mto.21.27.3.chiu.html.<\/span><\/p>\n<p><span style=\"font-weight: 400;\">Cohn, Richard. 2012. <\/span><i><span style=\"font-weight: 400;\">Audacious Euphony: Chromatic Harmony and the Triad\u2019s Second Nature<\/span><\/i><span style=\"font-weight: 400;\">. Oxford University Press.<\/span><\/p>\n<p><span style=\"font-weight: 400;\">De Clercq, Trevor. 2019. \u201cThe Harmonic-Bass Divorce in Rock,\u201d <\/span><i><span style=\"font-weight: 400;\">Music Theory Spectrum<\/span><\/i><span style=\"font-weight: 400;\"> 41 (2): 271\u2013284.<\/span><\/p>\n<p><span style=\"font-weight: 400;\">Ferrandino, Matthew. 2022 \u201cMulti-Centric Complexes in Pop-Rock Music.\u201d <\/span><i><span style=\"font-weight: 400;\">Int\u00e9gral <\/span><\/i><span style=\"font-weight: 400;\">35: 27\u201343.<\/span><\/p>\n<p><span style=\"font-weight: 400;\">Greer, Taylor. 1991. \u201cModal Sensibility in Gabriel Faur\u00e9\u2019s Harmonic Language.\u201d <\/span><i><span style=\"font-weight: 400;\">Theory and Practice<\/span><\/i><span style=\"font-weight: 400;\"> 16: 127\u2013142.<\/span><\/p>\n<p><span style=\"font-weight: 400;\">Flint, Catrena<\/span><i><span style=\"font-weight: 400;\">.<\/span><\/i><span style=\"font-weight: 400;\"> 1997.<\/span><i><span style=\"font-weight: 400;\"> La Chanson d\u2019Eve: Counterpoint in the Late Style of Faur\u00e9.<\/span><\/i><span style=\"font-weight: 400;\"> PhD diss., McGill University.<\/span><\/p>\n<p><span style=\"font-weight: 400;\">Harrison, Daniel. 2016. <\/span><i><span style=\"font-weight: 400;\">Pieces of Tradition: An Analysis of Contemporary Tonal Music.<\/span><\/i><span style=\"font-weight: 400;\"> Oxford University Press.<\/span><\/p>\n<p><span style=\"font-weight: 400;\">Kaminsky, Peter. 2004. \u201cRavel\u2019s Late Music and the Problem of \u2018Polytonality.\u2019 \u201d <\/span><i><span style=\"font-weight: 400;\">Music Theory Spectrum<\/span><\/i><span style=\"font-weight: 400;\"> 26 (3): 237\u2013264.<\/span><\/p>\n<p><span style=\"font-weight: 400;\">Klorman, Edward. 2016. <\/span><i><span style=\"font-weight: 400;\">Mozart\u2019s Music of Friends: Social Interplay in the Chamber Works<\/span><\/i><span style=\"font-weight: 400;\">. Cambridge: Cambridge University Press.<\/span><\/p>\n<p><span style=\"font-weight: 400;\">Kurtz, James. 1970. \u201cProblems of Tonal Structure in Songs of Gabriel Faur\u00e9.\u201d PhD diss., Brandeis University.<\/span><\/p>\n<p><span style=\"font-weight: 400;\">Moore, Allan. 1995. \u201cThe So-Called \u2018Flattened Seventh\u2019 in Rock.\u201d <\/span><i><span style=\"font-weight: 400;\">Popular Music <\/span><\/i><span style=\"font-weight: 400;\">14 (2): 185\u2013201.<\/span><\/p>\n<p><span style=\"font-weight: 400;\">Nectoux, Jean-Michel. 2004. <\/span><i><span style=\"font-weight: 400;\">Gabriel Faur\u00e9: A Musical Life<\/span><\/i><span style=\"font-weight: 400;\">. Translated by Roger Nichols. Cambridge University Press.<\/span><\/p>\n<p><span style=\"font-weight: 400;\">Nobile, Drew. 2020. \u201cDouble-Tonic Complexes in Rock Music.\u201d <\/span><i><span style=\"font-weight: 400;\">Music Theory Spectrum<\/span><\/i><span style=\"font-weight: 400;\"> 42 (2): 207\u2013226.<\/span><\/p>\n<p><span style=\"font-weight: 400;\">\u2014 \u2014 \u2014<\/span><span style=\"font-weight: 400;\">. 2015. \u201cUnpacking the \u2018Melodic-Harmonic Divorce.\u201d <\/span><i><span style=\"font-weight: 400;\">Music Theory Spectrum<\/span><\/i><span style=\"font-weight: 400;\"> 37 (2): 189\u2013203.<\/span><\/p>\n<p><span style=\"font-weight: 400;\">Pau, Andrew. 2016. \u201cPlagal Systems in the Songs of Faur\u00e9 and Duparc.\u201d <\/span><i><span style=\"font-weight: 400;\">Theory and Practice<\/span><\/i><span style=\"font-weight: 400;\"> 41: 81\u2013111.<\/span><\/p>\n<p><span style=\"font-weight: 400;\">Phillips, Edward R. 1993. \u201cSmoke, Mirrors and Prisms: Tonal Contradiction in Faur\u00e9.\u201d <\/span><i><span style=\"font-weight: 400;\">Music Analysis<\/span><\/i><span style=\"font-weight: 400;\"> 12 (1): 3\u201324.&nbsp;<\/span><\/p>\n<p><span style=\"font-weight: 400;\">Pomeroy, Boyd. 2004. \u201cTales of Two Tonics: Directional Tonality in Debussy\u2019s Orchestral Music.\u201d <\/span><i><span style=\"font-weight: 400;\">Music Theory Spectrum <\/span><\/i><span style=\"font-weight: 400;\">26<\/span><i><span style=\"font-weight: 400;\"> (1)<\/span><\/i><span style=\"font-weight: 400;\">: 87\u2013118.<\/span><\/p>\n<p><span style=\"font-weight: 400;\">Rabinovitch, Gilad. 2023. \u201cReimagining Faur\u00e9\u2019s Harmony.\u201d<\/span> <i><span style=\"font-weight: 400;\">Int\u00e9gral <\/span><\/i><span style=\"font-weight: 400;\">36: 55\u2013101.<\/span><\/p>\n<p><span style=\"font-weight: 400;\">Rupprecht, Philip. 1996. \u201cTonal Stratification and Uncertainty in Britten\u2019s Music.\u201d <\/span><i><span style=\"font-weight: 400;\">Journal of Music Theory <\/span><\/i><span style=\"font-weight: 400;\">40 (2): 311\u2013346.&nbsp;<\/span><\/p>\n<p><span style=\"font-weight: 400;\">Smith, Peter H. 2013. \u201cTonal Pairing and Monotonality in Instrumental Forms of Beethoven, Schubert, Schumann, and Brahms.\u201d <\/span><i><span style=\"font-weight: 400;\">Music Theory Spectrum <\/span><\/i><span style=\"font-weight: 400;\">16 <\/span><span style=\"font-weight: 400;\">(2)<\/span><span style=\"font-weight: 400;\">: 175\u2013217.<\/span><\/p>\n<p><span style=\"font-weight: 400;\">\u2014 \u2014 \u2014. 1997. \u201cBrahms and Motivic 6\/3 Chords.\u201d<\/span><i><span style=\"font-weight: 400;\"> Music Analysis<\/span><\/i><span style=\"font-weight: 400;\"> 12 (1): 3\u201324.&nbsp;<\/span><\/p>\n<p><span style=\"font-weight: 400;\">Sobaskie, James. 1999. \u201cAllusion in the Music of Gabriel Faur\u00e9.\u201d In <\/span><i><span style=\"font-weight: 400;\">Regarding Faur\u00e9<\/span><\/i><span style=\"font-weight: 400;\">, edited by Tom Gordon. New York: Gordon and Breach.<\/span><\/p>\n<p><span style=\"font-weight: 400;\">Straus, Joseph. 1982. \u201cStravinsky\u2019s Tonal Axis.\u201d <\/span><i><span style=\"font-weight: 400;\">Journal of Music Theory<\/span><\/i><span style=\"font-weight: 400;\"> 26 (2): 261-290.<\/span><\/p>\n<p><span style=\"font-weight: 400;\">Swinden, Kevin, J. 2005. \u201cWhen Functions Collide: Aspects of Plural Function in Chromatic Music.\u201d <\/span><i><span style=\"font-weight: 400;\">Music Theory Spectrum<\/span><\/i><span style=\"font-weight: 400;\"> 27 (2): 249\u2013282.<\/span><\/p>\n<p><span style=\"font-weight: 400;\">Tait, Robin C. 1986. \u201cThe Musical Language of Faur\u00e9.\u201d PhD diss., University of St. Andrews.<\/span><\/p>\n<p><span style=\"font-weight: 400;\">Temperley, David. 2007. \u201cThe Melodic-Harmonic \u2018Divorce\u2019 in Rock.\u201d <\/span><i><span style=\"font-weight: 400;\">Popular Music <\/span><\/i><span style=\"font-weight: 400;\">26 (2): 323\u2013342.<\/span><\/p>\n<p><span style=\"font-weight: 400;\">Thompson, William. 2006. \u201cPitch Frames as Melodic Archetypes.\u201d <\/span><i><span style=\"font-weight: 400;\">Empirical Musicology Review <\/span><\/i><span style=\"font-weight: 400;\">1 (2): 85\u2013102.<\/span><\/p>\n<p><span style=\"font-weight: 400;\">Thompson William and Shulamit Mor. 1992. \u201cA Perceptual Investigation of Polytonality.\u201d <\/span><i><span style=\"font-weight: 400;\">Psychological Research <\/span><\/i><span style=\"font-weight: 400;\">54: 60-71.<\/span><\/p>\n<p><span style=\"font-weight: 400;\">Vuillermoz, \u00c9mile. 1969. <\/span><i><span style=\"font-weight: 400;\">Gabriel Faur\u00e9<\/span><\/i><span style=\"font-weight: 400;\">. Translated by Steven Smolian. Chilton Book Co..<\/span><\/p>","protected":false},"excerpt":{"rendered":"<p>Matthew Bilik Abstract This paper explicates how the sensation of two active keys, known as key duality or tonal pairing, often results as disjunction between the melody and bass in the music of Gabriel Faur\u00e9 and Maurice Durufl\u00e9. In Faur\u00e9\u2019s late chamber works, a distinct type of key duality arises not as a juxtaposition of &hellip; <\/p>\n<p class=\"link-more\"><a href=\"https:\/\/theory.esm.rochester.edu\/integral\/37-2024\/bilik\/\" class=\"more-link\">Continue reading<span class=\"screen-reader-text\"> &#8220;Key Duality and Melody-Bass Disjunction in Faur\u00e9 and Durufl\u00e9&#8221;<\/span><\/a><\/p>\n","protected":false},"author":25,"featured_media":0,"parent":9044,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"_oasis_is_in_workflow":0,"_oasis_original":0,"_exactmetrics_skip_tracking":false,"_exactmetrics_sitenote_active":false,"_exactmetrics_sitenote_note":"","_exactmetrics_sitenote_category":0,"footnotes":""},"class_list":["post-9120","page","type-page","status-publish","hentry"],"_links":{"self":[{"href":"https:\/\/theory.esm.rochester.edu\/integral\/wp-json\/wp\/v2\/pages\/9120","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/theory.esm.rochester.edu\/integral\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/theory.esm.rochester.edu\/integral\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/theory.esm.rochester.edu\/integral\/wp-json\/wp\/v2\/users\/25"}],"replies":[{"embeddable":true,"href":"https:\/\/theory.esm.rochester.edu\/integral\/wp-json\/wp\/v2\/comments?post=9120"}],"version-history":[{"count":27,"href":"https:\/\/theory.esm.rochester.edu\/integral\/wp-json\/wp\/v2\/pages\/9120\/revisions"}],"predecessor-version":[{"id":11712,"href":"https:\/\/theory.esm.rochester.edu\/integral\/wp-json\/wp\/v2\/pages\/9120\/revisions\/11712"}],"up":[{"embeddable":true,"href":"https:\/\/theory.esm.rochester.edu\/integral\/wp-json\/wp\/v2\/pages\/9044"}],"wp:attachment":[{"href":"https:\/\/theory.esm.rochester.edu\/integral\/wp-json\/wp\/v2\/media?parent=9120"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}