{"id":9140,"date":"2024-06-07T13:22:49","date_gmt":"2024-06-07T13:22:49","guid":{"rendered":"https:\/\/theory.esm.rochester.edu\/integral\/?page_id=9140"},"modified":"2025-08-16T14:19:19","modified_gmt":"2025-08-16T14:19:19","slug":"fankhauser","status":"publish","type":"page","link":"https:\/\/theory.esm.rochester.edu\/integral\/37-2024\/fankhauser\/","title":{"rendered":"Displaced Cadential Six-Four Chords"},"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>Gabriel Fankhauser<\/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>Building on research into the efficacy of inverted cadential six-four chords, this article proposes that some unconventional harmonies function as cadential six-fours. Considering a cadential six-four chord\u2019s syntactical role more than its surface harmony or voice leading, this article identifies remarkable treatments that defy traditional analysis. Some examples of chromatically displaced cadential six-four chords seem harmonically strange yet continue to support underlying conventional function. As a result, a conflict forms between a chord\u2019s grammatical clarity or syntax (the function of the chord in a progression) and its morphology (the chord\u2019s pitch content and vertical arrangement). Analysis of excerpts from diverse styles\u2014including examples from Wagner, Brahms, the Beatles, and the Eagles\u2014illustrates how alterations of the cadential six-four chord help maintain its relevance in post-Classical music. More notable displacement in music by Liszt, Prokofiev, and Shostakovich exhibit idiomatic usage that intertwines conventional syntax and structure with innovative grammar and expression.<\/p>\n\n\n\n<p><a href=\"https:\/\/theory.esm.rochester.edu\/integral\/?page_id=9142\" data-type=\"URL\" data-id=\"https:\/\/theory.esm.rochester.edu\/integral\/?page_id=9142\">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>: cadential six-four chords, harmonic function, chromatic harmony, enharmonicism, syntax, hypermeter, clich\u00e9, Wagner, Brahms, Liszt, Shostakovich, Prokofiev<\/p>\n\n\n\n<h2 class=\"wp-block-heading\">1. <strong>The Cadential Six-Four Chord Controversy<\/strong><\/h2>\n\n\n\n<p class=\"has-drop-cap\">Few basic topics in music theory are as controversial as the cadential six-four chord. Even the question of whether the cadential six-four chord stems from dominant or tonic harmony seems to remain as heated today as it was 250 years ago, when Johann Kirnberger responded to what he already considered an \u201ceternal dispute\u201d by asserting definitively that the <em>bass<\/em> of the cadential six-four chord is the <em>root<\/em> and that the chord contains linear, dissonant embellishments of the dominant harmony. In his 1773 treatise, he proclaimed:<\/p>\n\n\n\n<blockquote class=\"wp-block-quote is-layout-flow wp-block-quote-is-layout-flow\">\n<p>The real root of this dissonant six-four chord is the bass note. Since the sixth as well as the fourth in this chord are non-essential dissonances, they can neither be introduced freely, nor be doubled.\u00a0.\u00a0. And thus an end would finally be put to the eternal dispute .\u00a0.\u00a0.\u00a0about which so many written wars have been waged with unspeakable bitterness without anything having been settled (Beach and Thym 1979, 176).<\/p>\n<\/blockquote>\n\n\n\n<p><span style=\"font-weight: 400;\">Kirnberger\u2019s narrow eighteenth-century definition is challenged throughout the musical literature, in which examples double fourths or \u201cfreely\u201d introduce the sixth or fourth. Still, his interpretation continues to be embraced today. While modern pedagogy in North America tends to clarify that the cadential six-four chord functions more as a dominant than as a tonic, the chord is often introduced as a second-inversion tonic triad\u2014a \u201cone six-four.\u201d Part of the justification is heuristic. Inverted triads require no contextual analysis and are therefore more easily grasped than suspensions or other linear embellishments.<span id='easy-footnote-1-9140' class='easy-footnote-margin-adjust'><\/span><span class='easy-footnote'><a href='https:\/\/theory.esm.rochester.edu\/integral\/37-2024\/fankhauser\/#easy-footnote-bottom-1-9140' title='The widely used textbook by Kostka and Payne (2013), for example, introduces the cadential six-four in Chapter 9 (135) with no mention of suspensions or any \u201cnon-chord tones,\u201d which are introduced two chapters later (175) without mention of the cadential six-four. Even Aldwell and Schachter\u2019s 2011 textbook, which more strongly advocates linear considerations and underlying harmonic function, only mildly dissuades the vertical interpretation in its introduction to the six-four, stating that the \u201c$$^{6}_{4}$$ should perhaps not even be labeled I$$^{6}_{4}$$\u201d (140).'><sup>1<\/sup><\/a><\/span><\/span><\/p>\n\n\n\n<p><span style=\"font-weight: 400;\">The conflict of tonic-vs.-dominant function has continued for centuries. The simpler, vertical, \u201csecond inversion\u201d tonic analysis (I$$^{6}_{4}$$\u2013V) may be associated with Wilhelm Friedrich Marpurg and Abb\u00e9 Vogler\u2019s eighteenth-century harmonic emphasis on chords, largely in isolation, while the more linear and contextual analysis (V$$^{6\u20135}_{4\u20133}$$) maintains a Viennese tradition including the mid-nineteenth- and early twentieth-century theories of Simon Sechter and Heinrich Schenker.<span id='easy-footnote-2-9140' class='easy-footnote-margin-adjust'><\/span><span class='easy-footnote'><a href='https:\/\/theory.esm.rochester.edu\/integral\/37-2024\/fankhauser\/#easy-footnote-bottom-2-9140' title='See Wason (1985, Chapters 2\u20138) and Beach (1967).'><sup>2<\/sup><\/a><\/span> A significant part of the problem lies with the meaning or application of Roman numeral labels. Do they signify chords (pitch content) or function (in context)? While scholarship today understandably favors the latter interpretation, an analytical approach adopted in this article may pull the preference uncomfortably toward the former\u2014toward a simplistic vertical description, despite an understood, underlying dominant function.<span id='easy-footnote-3-9140' class='easy-footnote-margin-adjust'><\/span><span class='easy-footnote'><a href='https:\/\/theory.esm.rochester.edu\/integral\/37-2024\/fankhauser\/#easy-footnote-bottom-3-9140' title='White and Quinn (2018) address the differing views of how harmonic function relies on content (pitches) or context (syntax).'><sup>3<\/sup><\/a><\/span>&nbsp;<\/span><\/p>\n\n\n\n<p><span style=\"font-weight: 400;\">The linear, double suspension or appoggiatura analysis applies most readily to music composed in the late eighteenth and early nineteenth century. The behavior of the sixth and fourth as suspensions can be demonstrated by isolating and resolving each interval above the bass: compare V$$^{6\u20135}_{4\u20133}$$ to the isolated suspensions V$$^{6\u20135}$$ and V$$^{4\u20133}$$. Resolution of pre-dominant harmonies to the cadential six-four bolsters its function as an embellished dominant, rather than an inverted tonic.&nbsp;<\/span><\/p>\n\n\n\n<p><span style=\"font-weight: 400;\">In opposition to viewing the six-four figures as linear embellishments, interpretation of the cadential six-four as a second inversion tonic can be demonstrated by replacing any V$$^{6\u20135}_{4\u20133}$$ (or I$$^{6}_{4}$$\u2013V) with root-position I\u2013V. Even when the I\u2013V replacement follows strong pre-dominant harmony\u2014like V$$^{6}_{5}$$\/V, vii$$^{\\circ7}$$\/V, or Gr$$^{+6}$$\u2014the momentary root-position tonic causes little interference in the harmonic progression toward the cadential dominant.<\/span><span id='easy-footnote-4-9140' class='easy-footnote-margin-adjust'><\/span><span class='easy-footnote'><a href='https:\/\/theory.esm.rochester.edu\/integral\/37-2024\/fankhauser\/#easy-footnote-bottom-4-9140' title='My decision to use \u201clower case\u201d Roman numerals in this article supports my goal to clarify localized harmony and chord quality, unlike the goal of the &lt;em&gt;Stufen&lt;\/em&gt; tradition, which uses only upper case (I, II, III, .&amp;nbsp;.&amp;nbsp;.) to clarify function.'><sup>4<\/sup><\/a><\/span>\n\n\n\n<p><span style=\"font-weight: 400;\"> Some analysts may maintain that this preservation of function from a strong predominant to the dominant demonstrates the underlying <\/span><i><span style=\"font-weight: 400;\">dominant function<\/span><\/i><span style=\"font-weight: 400;\"> that is preserved behind the apparent tonic harmony\u2014that the functional root continues to be $$\\hat{5}$$ even if the bass is $$\\hat{3}$$ or $$\\hat{1}$$. Their arguments, to be clarified below, offer an important step toward appreciating both the robust essence of the cadential six-four chord as dominant in function as well as the chord\u2019s surprising variability on the surface.&nbsp;<\/span><\/p>\n\n\n\n<p><span style=\"font-weight: 400;\">In music from the mid-nineteenth century and later, the cadential six-four may have become more harmonically conceived. In some examples, the chord seems less dependent on adjacent harmonies\u2014as from pre-dominant chords with pitches suspending and then resolving into the cadential dominant\u2014and more harmonically independent. That is, the cadential six-four became an increasingly separable term in the vocabulary of Western tonal harmony. Complex examples later in this article show how the harmonic conception and independence of cadential six-four chords developed into the twentieth century.&nbsp;<\/span><\/p>\n\n\n\n<p><span style=\"font-weight: 400;\">This article considers surface flexibility of the cadential six-four through what may be a natural development in the maturation of the singular harmony. Adopting an alternative, rhetorical perspective may circumscribe and inform the perennial tonic-vs.-dominant controversy by highlighting how the cadential six-four is defined more by its context in a cadential progression than by either its isolated harmonic components or its melodic-contrapuntal connections.<\/span><\/p>\n\n\n\n<p><span style=\"font-weight: 400;\">Motivated in part by the heuristic efficiency of identifying the cadential six-four chord as a \u201csecond-inversion tonic triad,\u201d Leonard Meyer (2000\/1992) views the chord as part of a conventional gesture that is best represented as tonic in function. While he \u201cgrants the plausibility\u201d of the interpretation of a double appoggiatura over dominant harmony, he \u201cfinds it more convenient&nbsp;.&nbsp;.&nbsp;. to cling to the more traditional (conventional?) interpretation and symbology\u201d (230, fn. 9, sic). Using a somewhat narrow definition, Meyer searched for examples throughout the <\/span><i><span style=\"font-weight: 400;\">Norton Scores<\/span><\/i><span style=\"font-weight: 400;\"> and found that usage of the cadential six-four progression reached a sharp but short-lived peak in the Classic era. His findings are summarized in <strong>Figure 1<\/strong>. Meyer\u2019s data show that usage increased most notably with the music of Domenico&nbsp;Scarlatti and then waned, most notably with the music of Hector Berlioz, who, Meyer says, rejected the six-four progression as the \u201cepitome of conventionality\u201d (248).<\/span><span id='easy-footnote-5-9140' class='easy-footnote-margin-adjust'><\/span><span class='easy-footnote'><a href='https:\/\/theory.esm.rochester.edu\/integral\/37-2024\/fankhauser\/#easy-footnote-bottom-5-9140' title='My Figure 1 combines calculations from Meyer\u2019s Figure 1, p.&amp;nbsp;241, and Appendix Table A3, p.&amp;nbsp;261. The general trend in Meyer\u2019s Figure 1 appears to peak with Schubert, who perhaps surprisingly is more represented than Beethoven or Haydn. Other data may be similarly surprising, such as a greater usage found in Wagner and Wolf than in Mendelssohn, Chopin, or Schumann. Meyer\u2019s sampling is small, of course\u2014drawn from one edition of the &lt;em&gt;Norton Scores&lt;\/em&gt;\u2014but a greater problem lies with his rules (239\u2013240), which are quite restrictive and contextually insensitive. For example, he requires that the six-four chord be \u201cpreceded by a pre-dominant\u201d\u2014though what he means by that is not clear\u2014and he assigns numeric values somewhat arbitrarily to yield certain statistical results. Still, his general conclusions are persuasive and would not likely be altered greatly by a more open or contextual definition.'><sup>5<\/sup><\/a><\/span> Romantic composers may have avoided the chord, because, as Meyer adds, \u201cthe very sonic salience that made the cadential six-four progression such a forceful signal [of closure] made it seem routine and commonplace.\u201d For composers aiming to avoid tonal formulas and predictability, the cadential six-four became outdated or obsolete.<\/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\/fankhauser-vol37-figure-1\/\"><img loading=\"lazy\" decoding=\"async\" width=\"2560\" height=\"1169\" src=\"https:\/\/theory.esm.rochester.edu\/integral\/wp-content\/uploads\/2024\/06\/fankhauser-vol37-figure-1-scaled.jpg\" alt=\"Fankhauser, Figure 1\" class=\"wp-image-9322\" style=\"width:512px;height:224px\" srcset=\"https:\/\/theory.esm.rochester.edu\/integral\/wp-content\/uploads\/2024\/06\/fankhauser-vol37-figure-1-scaled.jpg 2560w, https:\/\/theory.esm.rochester.edu\/integral\/wp-content\/uploads\/2024\/06\/fankhauser-vol37-figure-1-300x137.jpg 300w, https:\/\/theory.esm.rochester.edu\/integral\/wp-content\/uploads\/2024\/06\/fankhauser-vol37-figure-1-1024x468.jpg 1024w, https:\/\/theory.esm.rochester.edu\/integral\/wp-content\/uploads\/2024\/06\/fankhauser-vol37-figure-1-768x351.jpg 768w, https:\/\/theory.esm.rochester.edu\/integral\/wp-content\/uploads\/2024\/06\/fankhauser-vol37-figure-1-1536x701.jpg 1536w, https:\/\/theory.esm.rochester.edu\/integral\/wp-content\/uploads\/2024\/06\/fankhauser-vol37-figure-1-2048x935.jpg 2048w\" sizes=\"auto, (max-width: 706px) 89vw, (max-width: 767px) 82vw, 740px\" \/><\/a><figcaption class=\"wp-element-caption\"><b>Figure 1.<\/b> Percentage of Cadential Six-Four Use by Era (based on Meyer 2000\/1992).<\/figcaption><\/figure>\n<\/div>\n\n\n<p><span style=\"font-weight: 400;\">If the cadential six-four generally became viewed as an unappealing conventional gesture, then a decline in usage would not be surprising. However, compositional devices that are viewed as clich\u00e9s can, after some period of disuse, sow seeds for revival, often with fresh approaches. Rhetorical clich\u00e9s result when expressions that were novel at one time suffer from overuse, either losing their original meaning or becoming conspicuously predictable. The meaning of a clich\u00e9 derives not solely from the words or parts themselves but more from a collective complex of meanings tied to its usage. English clich\u00e9s like \u201cthe tip of the iceberg\u201d or \u201cthinking outside the box\u201d are often considered signs of sophomoric writing to be avoided in scholarship, but an exception arises when an author purposefully or poetically uses the phrase to allude to a second or deeper meaning\u2014a subtle, intentionally rhetorical usage.&nbsp;<\/span><\/p>\n\n\n\n<p><span style=\"font-weight: 400;\">Like literary clich\u00e9s, cadential six-four chords possess predictability and potential for overuse that may have deterred some nineteenth-century composers. While the strong syntactic power of the cadential six-four to initiate closure may have led to its decline in the late-nineteenth century\u2014a period that saw a decline in well-defined closure and formal divisions\u2014the clarity and simplicity of the chord\u2019s grammatical function may have conversely provided means for subsequent composers to express an individual and innovative harmonic voice. As a clich\u00e9, the cadential six-four could be viewed as an inhibitor of musical originality, but with careful treatment a twisting of the clich\u00e9 could afford composers fresh means for approaching a cadence. A distinctly modified cadential six-four may retain its cadential function as a rhetorical signal for closure, borrowing from Classical syntax, yet be altered in a way that transforms the clich\u00e9 into novelty. Composers today continue to borrow familiar materials from the past in a more individualized, modern context.<\/span><\/p>\n\n\n\n<p><span style=\"font-weight: 400;\">Straddling the threshold between harmonic tradition and innovation, this study supports two main ideas concerning the cadential six-four. The first is that, after conventional use of the cadential six-four reached its peak late in the Classic era, later approaches significantly modified the harmony on the surface while retaining the chord\u2019s underlying rhetorical, cadential function. The second idea is that analysis of those modifications informs our understanding of the cadential six-four chord as separable into two components: its contextual usage, or syntax, and its outward appearance, or morphology. Different musical examples may alter one component more than the other. On one hand, the function of an otherwise conventional cadential six-four may be undermined by its treatment, as by weak-beat placement or by irregular resolution, to the point that its cadential function becomes questionable. On the other hand, examples may retain conventional treatment, particularly in accentuation and resolution, while altering the chord\u2019s outward appearance or pitch content. It is this latter, morphological alteration that lies at the center of this study.<\/span><span id='easy-footnote-6-9140' class='easy-footnote-margin-adjust'><\/span><span class='easy-footnote'><a href='https:\/\/theory.esm.rochester.edu\/integral\/37-2024\/fankhauser\/#easy-footnote-bottom-6-9140' title='This article does not address cadential six-four chords that are constructed conventionally yet behave in odd ways. Instead, focus is on those chords that appear unconventional from the outset. Matthew BaileyShea (2012), for example, discusses remarkable resolutions and questions the forces behind the rising sixth and fourth of the cadential six-four in Mahler\u2019s &lt;em&gt;Kindertotenlieder&lt;\/em&gt;. Poundie Burstein (1999, 72\u201373) analyzes an odd progression leading to a cadential six-four in the first movement of Haydn\u2019s Symphony No. 78 in C minor, in which a cadential six-four is approached chromatically from two \u201cungainly parallel six-fours.\u201d The underlying, conventional progression in E$$\\flat$$ major is expanded by the insertion of two passing six-fours to become, to put literally, if awkwardly, I$$^{6}$$\u2013IV\u2013($$\\flat$$VII$$^{6}_{4}$$\u2013$$\\natural$$VII$$^{6}_{4}$$)\u2013V$$^{6\u20135}_{4\u20133}$$\u2013I. In Haydn\u2019s striking approach to the cadential six-four, structural surprise and semantic surprise merge to invoke humor. For more on the relation between the two, and between wit and humor, see Kidd (1976).'><sup>6<\/sup><\/a><\/span> Focus will be on vertical (pitch) displacement of the cadential six-four, but first consider one example of horizontal (rhythmic) displacement.&nbsp;<\/p>\n\n\n\n<p><span style=\"font-weight: 400;\">Placement of the cadential six-four on a strong beat in relation to its resolution to dominant five-three is a defining characteristic of the cadential six-four chord. The inherent contradiction of a weak-beat cadential six-four chord makes them rare.<span id='easy-footnote-7-9140' class='easy-footnote-margin-adjust'><\/span><span class='easy-footnote'><a href='https:\/\/theory.esm.rochester.edu\/integral\/37-2024\/fankhauser\/#easy-footnote-bottom-7-9140' title='Aldwell and Schachter (1989, 319\u2013320) view these weak-beat, \u201cdeviant\u201d [sic] six-four chords as resulting from an anticipation in the bass to the strong-beat dominant. '><sup>7<\/sup><\/a><\/span> Wagner\u2019s \u201cSong of the Evening Star\u201d from&nbsp;<em>Tannh\u00e4user&nbsp;<\/em>presents an example (<strong>Example 1<\/strong>). In m. 10, the six-four enters on a weak, second hyperbeat, followed by a resolution on the stronger downbeat of m. 11. The only way to hear the six-four fall on a strong hyperbeat would be to hear the opening measure as an anacrusis. The third harmony, an apparent&nbsp;<nobr>$$\\flat$$III$$^{6}$$<\/nobr>, exhibits a weaker association with a cadential six-four, perhaps as a modified V$$^{6\u20135}$$. We will return to this example after examining other displacements of the cadential six-four.<\/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\/ex-1-1200dpi\/\"><img loading=\"lazy\" decoding=\"async\" width=\"2560\" height=\"921\" src=\"https:\/\/theory.esm.rochester.edu\/integral\/wp-content\/uploads\/2024\/06\/Ex-1-1200dpi-scaled.jpg\" alt=\"Fankhauser, Example 1\" class=\"wp-image-9325\" style=\"width:620px;height:222px\" srcset=\"https:\/\/theory.esm.rochester.edu\/integral\/wp-content\/uploads\/2024\/06\/Ex-1-1200dpi-scaled.jpg 2560w, https:\/\/theory.esm.rochester.edu\/integral\/wp-content\/uploads\/2024\/06\/Ex-1-1200dpi-300x108.jpg 300w, https:\/\/theory.esm.rochester.edu\/integral\/wp-content\/uploads\/2024\/06\/Ex-1-1200dpi-1024x368.jpg 1024w, https:\/\/theory.esm.rochester.edu\/integral\/wp-content\/uploads\/2024\/06\/Ex-1-1200dpi-768x276.jpg 768w, https:\/\/theory.esm.rochester.edu\/integral\/wp-content\/uploads\/2024\/06\/Ex-1-1200dpi-1536x553.jpg 1536w, https:\/\/theory.esm.rochester.edu\/integral\/wp-content\/uploads\/2024\/06\/Ex-1-1200dpi-2048x737.jpg 2048w\" sizes=\"auto, (max-width: 706px) 89vw, (max-width: 767px) 82vw, 740px\" \/><\/a><figcaption class=\"wp-element-caption\"><b>Example 1.<\/b> Wagner, \u201cSong of the Evening Star\u201d from Tannh\u00e4user, mm. 5\u201312.<\/figcaption><\/figure>\n<\/div>\n\n\n<figure class=\"wp-block-audio\"><audio controls src=\"https:\/\/theory.esm.rochester.edu\/integral\/wp-content\/uploads\/2024\/06\/fankhauser-vol37-audio-1.mp3\"><\/audio><figcaption class=\"wp-element-caption\"><strong>Example 1 Audio.<\/strong><\/figcaption><\/figure>\n\n\n\n<p><span style=\"font-weight: 400;\">More remarkable deviations from conventional cadential six-four chords lie not with accentuation but with pitch content and arrangements.<span id='easy-footnote-8-9140' class='easy-footnote-margin-adjust'><\/span><span class='easy-footnote'><a href='https:\/\/theory.esm.rochester.edu\/integral\/37-2024\/fankhauser\/#easy-footnote-bottom-8-9140' title='Doublings of the dissonant fourth above the bass are found frequently and early enough in the Baroque that they represent less of a deviation from the repertoire than a deviation from some simplified textbook examples.'><sup>8<\/sup><\/a><\/span><\/span><span style=\"font-weight: 400;\"> The following section examines how the chord itself can be modified, starting with inversion. <\/span><\/p>\n\n\n\n<h2 class=\"wp-block-heading\">2. <strong>Inverted Cadential Six-Four Chords<\/strong><\/h2>\n\n\n\n<p><span style=\"font-weight: 400;\">Placing the cadential six-four chord in inversion alters its outward appearance and increases its resemblance to a consonant tonic triad. Finding support in Schenker\u2019s earlier, unpublished version of <\/span><i><span style=\"font-weight: 400;\">Der freie Satz<\/span><\/i><span style=\"font-weight: 400;\">, William Rothstein (2006, 268\u2013272) observes how an apparent root-position or first-inversion tonic may function as a cadential six-four. <strong>Example&nbsp;2<\/strong> shows his analysis of a passage from Mozart\u2019s Horn Concerto in D, K. 412. While the original voice leading shown in (a) has an F$$\\sharp$$ in the bass ($$\\hat{3}$$) in m.&nbsp;28, Rothstein shows (in b) how A ($$\\hat{5}$$) remains as an imagined or underlying <\/span><i><span style=\"font-weight: 400;\">Stufe<\/span><\/i><span style=\"font-weight: 400;\">. Mozart\u2019s inversion of the cadential six-four is required to resolve the preceding (surface) V$$^{4}_{2}$$ and to avoid parallel octaves with the melody\u2019s local ascent from G4 to A4, $$\\hat{4}$$ to $$\\hat{5}$$.<\/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\/fankhauser-vol37-example-2\/\"><img loading=\"lazy\" decoding=\"async\" width=\"3411\" height=\"2058\" src=\"https:\/\/theory.esm.rochester.edu\/integral\/wp-content\/uploads\/2024\/06\/fankhauser-vol37-example-2.png\" alt=\"Fankhauser, Example 2\" class=\"wp-image-9326\" style=\"width:512px;height:308px\" srcset=\"https:\/\/theory.esm.rochester.edu\/integral\/wp-content\/uploads\/2024\/06\/fankhauser-vol37-example-2.png 3411w, https:\/\/theory.esm.rochester.edu\/integral\/wp-content\/uploads\/2024\/06\/fankhauser-vol37-example-2-300x181.png 300w, https:\/\/theory.esm.rochester.edu\/integral\/wp-content\/uploads\/2024\/06\/fankhauser-vol37-example-2-1024x618.png 1024w, https:\/\/theory.esm.rochester.edu\/integral\/wp-content\/uploads\/2024\/06\/fankhauser-vol37-example-2-768x463.png 768w, https:\/\/theory.esm.rochester.edu\/integral\/wp-content\/uploads\/2024\/06\/fankhauser-vol37-example-2-1536x927.png 1536w, https:\/\/theory.esm.rochester.edu\/integral\/wp-content\/uploads\/2024\/06\/fankhauser-vol37-example-2-2048x1236.png 2048w\" sizes=\"auto, (max-width: 706px) 89vw, (max-width: 767px) 82vw, 740px\" \/><\/a><figcaption class=\"wp-element-caption\"><b>Example 2<\/b><strong>.<\/strong> Mozart, Concerto in D for Horn, K. 412, I, mm. 26\u201329 (based on Rothstein 2006, 277, Example 24).<\/figcaption><\/figure>\n<\/div>\n\n\n<figure class=\"wp-block-audio\"><audio controls src=\"https:\/\/theory.esm.rochester.edu\/integral\/wp-content\/uploads\/2024\/06\/fankhauser-vol37-audio-2.mp3\"><\/audio><figcaption class=\"wp-element-caption\"><strong>Example 2 Audio.<\/strong><\/figcaption><\/figure>\n\n\n\n<p><span style=\"font-weight: 400;\">The concept of inverted six-four chords introduces an analytical challenge. First, it implies that a suspended note\u2014namely $$\\hat{3}$$ or $$\\hat{1}$$ of a cadential six-four\u2014is placed in the bass and then skips up into the following root-position dominant ($$\\hat{5}$$). Rothstein\u2019s omission of Roman numerals below his analysis avoids confusing the chord\u2019s underlying dominant function on one hand\u2014shown between the staves in (a) and below the normalization in (b)\u2014and the apparent inverted tonic triad on the other, indicated by the figured bass 6 below the staves.&nbsp;<\/span><\/p>\n\n\n\n<p><span style=\"font-weight: 400;\">For a surface Roman numeral analysis like I$$^{6}$$ to conflict with the underlying bass <\/span><i><span style=\"font-weight: 400;\">Stufe<\/span><\/i><span style=\"font-weight: 400;\"> like $$\\hat{5}$$ indicates a contradiction between two levels of analysis. Rothstein\u2019s \u201cV$$^{6\u20137}_{4\u20133}$$\u201d analysis in (a) more accurately addresses harmonic function in the third measure, even if \u201cI$$^{6}$$\u2013$$^{5}_{3}$$\u2013V$$^{6\u20137}_{4\u20133}$$\u201d more accurately describes the surface harmony. Since dominant function remains an essential characteristic of the cadential six-four, it would follow that cadential six-fours should be associated with the dominant using the label \u201cV.\u201d The problem is that that label requires multiple levels of interpretation: the apparent I$$^{6}$$ inverts a conventional cadential six-four, which displaces the third and fifth of a dominant. Analysis of more unusual examples may benefit from using the more specific morphological or basic harmonic (vertical) description, following the heuristic of the \u201cone six-four\u201d (I$$^{6}_{4}$$) literal description, even if that analysis remains comparatively on the surface and in conflict with the harmony\u2019s underlying function, which remains understood as dominant, V$$^{6\u20137}_{4\u20133}$$. Analytical examples add a bracket to couple each modified cadential six-four with the dominant.&nbsp;<\/span><\/p>\n\n\n\n<p><span style=\"font-weight: 400;\">Timothy Culter (2009) has investigated how inverted cadential six-fours result from voice exchanges, while Eric Wen has shown how a first inversion tonic triad can serve more as a replacement for a cadential six-four chord (1999, 288). As new as these concepts may seem, however, both Cutler and David Damschroder have noted that the concept of the inverted cadential six-four can be traced to Koch\u2019s harmony treatise of 1811, in which I and I$$^{6}$$ chords are shown to be dissonant in relation to their resolution to dominant.<\/span><span id='easy-footnote-9-9140' class='easy-footnote-margin-adjust'><\/span><span class='easy-footnote'><a href='https:\/\/theory.esm.rochester.edu\/integral\/37-2024\/fankhauser\/#easy-footnote-bottom-9-9140' title='Cutler (2009, 196, fn. 8) cites Damschroder\u2019s discussion (2008, 43\u201345) on how similar arguments about these types of six-four chords were made in Koch\u2019s &lt;em&gt;Handbuch bey dem Studium der Harmonie&lt;\/em&gt; 1811 (col 132, fig. 5).'><sup>9<\/sup><\/a><\/span> One benefit of their more recent studies, therefore, is to challenge modern assumptions and pedagogy regarding the identity of the cadential six-four chord and to broaden our understanding of its usage.<\/p>\n\n\n\n<p><span style=\"font-weight: 400;\">One notable example of an inverted cadential six-four that remains unanalyzed in the literature, as far as I know, enters near the beginning of the fourth movement of Brahms\u2019s Symphony No. 4. The familiar opening theme of the chaconne derives from the last movement \u201cMeine Tage in dem Leide\u201d from Bach\u2019s Cantata <\/span><i><span style=\"font-weight: 400;\">Nach dir, Herr, verlanget mich<\/span><\/i><span style=\"font-weight: 400;\">, BWV150, but, in typical Brahmsian style, alteration of the subject\u2019s structure obscures harmonic function (<strong>Example 3<\/strong>). Each step of an ascending melody pushes toward the climax, which coincides with a modified cadential six-four in m.&nbsp;6. What appears on the surface as a first-inversion tonic functions as an inverted cadential six-four chord, supported both by the preceding, intensifying melodic drive from $$\\hat{1}$$ up to $$\\hat{5}$$ and by the harmonic drive toward the dominant via the subdominant iv$$^{6}$$ in m.&nbsp;4 through V$$^{7}$$\/V in m.&nbsp;5.<\/span><span id='easy-footnote-10-9140' class='easy-footnote-margin-adjust'><\/span><span class='easy-footnote'><a href='https:\/\/theory.esm.rochester.edu\/integral\/37-2024\/fankhauser\/#easy-footnote-bottom-10-9140' title='Hearing the i$$^{6}$$ in m.&amp;nbsp;6 as a deceptive resolution of V$$^{7}$$\/V to a modified vi, or iv$$^{6}$$\/V, misses the greater syntactical role of the chord as &lt;em&gt;increasing&lt;\/em&gt; drive toward the cadence, as a modified cadential six-four, not thwarting or evading it.'><sup>10<\/sup><\/a><\/span> Gestures associated with cadential six-four resolutions remain present here as well but inverted: the octave drop from a high $$\\hat{5}$$ to a lower $$\\hat{5}$$ typical of the bass falls instead in the melody, while the bass descends by step, $$\\hat{3}$$\u2013$$\\flat\\hat{2}$$\u2013$$\\hat{1}$$. This linear descent is more typical of melodic closure, in this case reversing the opening motive in mm.&nbsp;1\u20133 as well as the $$\\hat{1}$$\u2013$$\\flat\\hat{2}$$\u2013$$\\hat{3}$$ (E\u2013F$$\\natural$$\u2013G) opening of the second movement.<\/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\/fankhauser-vol37-example-3\/\"><img loading=\"lazy\" decoding=\"async\" width=\"2560\" height=\"1243\" src=\"https:\/\/theory.esm.rochester.edu\/integral\/wp-content\/uploads\/2024\/06\/fankhauser-vol37-example-3-scaled.jpg\" alt=\"Fankhauser, Example 3\" class=\"wp-image-9308\" style=\"width:512px;height:249px\" srcset=\"https:\/\/theory.esm.rochester.edu\/integral\/wp-content\/uploads\/2024\/06\/fankhauser-vol37-example-3-scaled.jpg 2560w, https:\/\/theory.esm.rochester.edu\/integral\/wp-content\/uploads\/2024\/06\/fankhauser-vol37-example-3-300x146.jpg 300w, https:\/\/theory.esm.rochester.edu\/integral\/wp-content\/uploads\/2024\/06\/fankhauser-vol37-example-3-1024x497.jpg 1024w, https:\/\/theory.esm.rochester.edu\/integral\/wp-content\/uploads\/2024\/06\/fankhauser-vol37-example-3-768x373.jpg 768w, https:\/\/theory.esm.rochester.edu\/integral\/wp-content\/uploads\/2024\/06\/fankhauser-vol37-example-3-1536x746.jpg 1536w, https:\/\/theory.esm.rochester.edu\/integral\/wp-content\/uploads\/2024\/06\/fankhauser-vol37-example-3-2048x994.jpg 2048w\" sizes=\"auto, (max-width: 706px) 89vw, (max-width: 767px) 82vw, 740px\" \/><\/a><figcaption class=\"wp-element-caption\"><b>Example 3.<\/b> Brahms, Symphony No. 4, IV (1885), mm. 1\u20138.<\/figcaption><\/figure>\n<\/div>\n\n\n<figure class=\"wp-block-audio\"><audio controls src=\"https:\/\/theory.esm.rochester.edu\/integral\/wp-content\/uploads\/2024\/06\/fankhauser-vol37-audio-3.mp3\"><\/audio><figcaption class=\"wp-element-caption\"><strong>Example 3 Audio.<\/strong><\/figcaption><\/figure>\n\n\n\n<p><span style=\"font-weight: 400;\">The octave leap and $$\\hat{3}$$\u2013$$\\flat\\hat{2}$$\u2013$$\\hat{1}$$ descent alone support hearing an inverted cadential six-four in m.&nbsp;6, but connections to Bach\u2019s original Chaconne (<strong>Example 4<\/strong>) offer rare insight into Brahms\u2019s thinking. In the opening of this last movement of Bach\u2019s cantata, the bass rises $$\\hat{1}$$\u2013$$\\hat{2}$$\u2013$$\\hat{3}$$\u2013$$\\hat{4}$$\u2013$$\\hat{5}$$ in mm.&nbsp;1\u20134, followed by a $$\\hat{3}$$\u2013$$\\hat{2}$$\u2013$$\\hat{1}$$ melodic descent toward the cadence. At the intersection of those lines lies the cadential six-four in m.&nbsp;4. Brahms\u2019s invertible counterpoint inverts the cadential six-four by placing $$\\hat{3}$$ in the bass and $$\\hat{5}$$ in the melody. The retrogressive opening three harmonies (iv$$^6$$\u2013ii$$^{\\circ6}$$\u2013i) from the outset also hint at Brahms\u2019s attraction to \u201cinverting\u201d traditional tonal syntax.<\/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\/fankhauser-vol37-example-4\/\"><img loading=\"lazy\" decoding=\"async\" width=\"2560\" height=\"984\" src=\"https:\/\/theory.esm.rochester.edu\/integral\/wp-content\/uploads\/2024\/06\/fankhauser-vol37-example-4-scaled.jpg\" alt=\"Fankhauser, Example 4\" class=\"wp-image-9309\" style=\"width:512px;height:197px\" srcset=\"https:\/\/theory.esm.rochester.edu\/integral\/wp-content\/uploads\/2024\/06\/fankhauser-vol37-example-4-scaled.jpg 2560w, https:\/\/theory.esm.rochester.edu\/integral\/wp-content\/uploads\/2024\/06\/fankhauser-vol37-example-4-300x115.jpg 300w, https:\/\/theory.esm.rochester.edu\/integral\/wp-content\/uploads\/2024\/06\/fankhauser-vol37-example-4-1024x394.jpg 1024w, https:\/\/theory.esm.rochester.edu\/integral\/wp-content\/uploads\/2024\/06\/fankhauser-vol37-example-4-768x295.jpg 768w, https:\/\/theory.esm.rochester.edu\/integral\/wp-content\/uploads\/2024\/06\/fankhauser-vol37-example-4-1536x590.jpg 1536w, https:\/\/theory.esm.rochester.edu\/integral\/wp-content\/uploads\/2024\/06\/fankhauser-vol37-example-4-2048x787.jpg 2048w\" sizes=\"auto, (max-width: 706px) 89vw, (max-width: 767px) 82vw, 740px\" \/><\/a><figcaption class=\"wp-element-caption\"><b>Example 4<\/b>. Bach, Nach dir, Herr, verlanget mich, BWV 150: VII. \u201cCiacona: Meine Tage in dem Leide\u201d (1707), mm. 1\u20135.<\/figcaption><\/figure>\n<\/div>\n\n\n<figure class=\"wp-block-audio\"><audio controls src=\"https:\/\/theory.esm.rochester.edu\/integral\/wp-content\/uploads\/2024\/06\/fankhauser-vol37-audio-4.mp3\"><\/audio><figcaption class=\"wp-element-caption\"><strong>Example 4 Audio.<\/strong><\/figcaption><\/figure>\n\n\n\n<p><span style=\"font-weight: 400;\">Identifying the inversion of the progression from Bach\u2019s chaconne to Brahms\u2019s symphony demonstrates that the inverted cadential six-four is more than a speculative interpretation of a particular harmony and more than an example of a late nineteenth-century composer\u2019s innovative treatment of an early eighteenth-century trope. In this case, Brahms\u2019s inverted cadential six-four derives from a specific historical example of a conventional cadential six-four, offering a rare glimpse of an innovative compositional process.&nbsp;<\/span><\/p>\n\n\n\n<p><span style=\"font-weight: 400;\">The cadential six-four chord is commonly associated with the Western classical tradition and the previous two examples draw a direct link from Bach to Brahms, but the harmony may be found in other styles. Some rock music has been shown to adhere at least loosely to Classical harmonic syntax and to use cadential six-four chords specifically.<span id='easy-footnote-11-9140' class='easy-footnote-margin-adjust'><\/span><span class='easy-footnote'><a href='https:\/\/theory.esm.rochester.edu\/integral\/37-2024\/fankhauser\/#easy-footnote-bottom-11-9140' title='For more on the cadential six-four\u2019s use in rock music, see Everett (2009, 208-209) and Nobile (2016, 167\u2013172), who shows how harmonic function depends more on syntax than on pitch content.'><sup>11<\/sup><\/a><\/span><\/span> <span style=\"font-weight: 400;\"> Consider the chorus of the Eagles\u2019s \u201cHeartache Tonight\u201d (Example 5). The rising chromatic bass line increases drive toward the cadential dominant, but that dominant is displaced by root-position tonic harmony.<\/span><span id='easy-footnote-12-9140' class='easy-footnote-margin-adjust'><\/span><span class='easy-footnote'><a href='https:\/\/theory.esm.rochester.edu\/integral\/37-2024\/fankhauser\/#easy-footnote-bottom-12-9140' title='William Drabkin (1996, 152) addresses the structural role of the tonic when it falls between the subdominant and cadential dominant: I\u2013IV\u2013I\u2013V\u2013I. He cites Schenker\u2019s graph (&lt;em&gt;Der freie Satz&lt;\/em&gt;, Fig.&amp;nbsp;22b) as showing harmonic support of a consonant passing tone, I IV (I) V I.'><sup>12<\/sup><\/a><\/span> After playing $$\\sharp\\hat{4}$$ (C$$\\sharp$$), the bass plays the tonic (G) before resolving up to the dominant (D), forming an inverted cadential six-four chord. Substitution of \u201cI\u2013V\u201d in place of the cadential dominant or V$$^{6\u20135}_{4\u20133}$$ following vii$$^{\\circ7}$$\/V is common in American bluegrass and other popular styles.<span id='easy-footnote-13-9140' class='easy-footnote-margin-adjust'><\/span><span class='easy-footnote'><a href='https:\/\/theory.esm.rochester.edu\/integral\/37-2024\/fankhauser\/#easy-footnote-bottom-13-9140' title='The same progression, including the vii$$^{\\circ7}$$\/V\u2013I\u2013V, is found in other popular songs, including Arlo Guthrie\u2019s \u201cAlice\u2019s Restaurant Massacree\u201d (1967) and Phish\u2019s \u201cPoor Heart\u201d (1992). While one could hear the vii$$^{\\circ7}$$\/V as a common-tone diminished seventh resolving to tonic, I find that hearing to be overly localized and disengaged from the larger progression. \u201cWhen the Saints Go Marching In\u201d has a similar progression with a \u201croot-position\u201d cadential six-four:&amp;nbsp; I\u2013V$$^{4}_{2}$$\/IV\u2013IV$$^{6}$$\u2013iv$$^{6}$$\u2013I\u2013V\u2013I.'><sup>13<\/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\/fankhauser-vol37-example-5\/\"><img loading=\"lazy\" decoding=\"async\" width=\"4292\" height=\"1210\" src=\"https:\/\/theory.esm.rochester.edu\/integral\/wp-content\/uploads\/2024\/06\/fankhauser-vol37-example-5.png\" alt=\"Fankhauser, Example 5\" class=\"wp-image-9310\" style=\"width:620px;height:174px\" srcset=\"https:\/\/theory.esm.rochester.edu\/integral\/wp-content\/uploads\/2024\/06\/fankhauser-vol37-example-5.png 4292w, https:\/\/theory.esm.rochester.edu\/integral\/wp-content\/uploads\/2024\/06\/fankhauser-vol37-example-5-300x85.png 300w, https:\/\/theory.esm.rochester.edu\/integral\/wp-content\/uploads\/2024\/06\/fankhauser-vol37-example-5-1024x289.png 1024w, https:\/\/theory.esm.rochester.edu\/integral\/wp-content\/uploads\/2024\/06\/fankhauser-vol37-example-5-768x217.png 768w, https:\/\/theory.esm.rochester.edu\/integral\/wp-content\/uploads\/2024\/06\/fankhauser-vol37-example-5-1536x433.png 1536w, https:\/\/theory.esm.rochester.edu\/integral\/wp-content\/uploads\/2024\/06\/fankhauser-vol37-example-5-2048x577.png 2048w\" sizes=\"auto, (max-width: 706px) 89vw, (max-width: 767px) 82vw, 740px\" \/><\/a><figcaption class=\"wp-element-caption\"><b>Example 5.<\/b> Eagles, \u201cHeartache Tonight\u201d (1979), 1:58\u20132:14.<\/figcaption><\/figure>\n<\/div>\n\n\n<p><span style=\"font-weight: 400;\">Conventional analysis interprets the $$\\hat{5}$$ bass as the root of the cadential six-four, but in the inverted cadential six-fours described by Rothstein and Cutler (the apparent I or I$$^{6}$$ chords), the $$\\hat{5}$$ root lies a fifth or third above the bass. In subsequent, more chromatic examples that retain six-four figures (like \u201c$$\\flat$$VI$$^{6}_{4}$$\u201d), I will use Roman numerals to designate the fourth above the bass as the triadic root. A seeming contradiction in cadential six-four analysis stems from the difference between emphasizing harmonic function\u2014by definition, an underlying dominant function for all cadential six-four chords\u2014and triadic formulation, a literal description of the pitches that lie above the bass.<\/span><\/p>\n\n\n\n<p><span style=\"font-weight: 400;\">Countering traditional Schenkerian-<\/span><i><span style=\"font-weight: 400;\">Stufen<\/span><\/i><span style=\"font-weight: 400;\"> theory, David Temperley (2017) argues that some contexts justify the use of Roman numerals to indicate localized harmony. His use of the label \u201cI$$^{6}_{4}$$\u201d applies \u201ca concept that is often implicit in modern music theory but rarely defined explicitly: what we might call a surface-level harmony, or (hereafter) simply a harmony\u201d (4). In any conventional example, adopting the narrow \u201cI$$^{6}_{4}$$\u201d label over the more functional and linear V$$^{6\u20135}_{4\u20133}$$ interpretation might seem trite, but the vertical description is more justified in examples that significantly modify the cadential six-four to create uncanny harmonic relations.<\/span><\/p>\n\n\n\n<p><span style=\"font-weight: 400;\">The difference between a triad\u2019s root and its bass may seem evident enough, but Daniel Harrison (1994, 48) makes a further distinction between a root and a <\/span><i><span style=\"font-weight: 400;\">base<\/span><\/i><span style=\"font-weight: 400;\">. An unfortunate homonym with \u201cbass,\u201d a base refers not to the lowest note but a more conceptual foundation. He views the assertion that the cadential six-four is dominant in function (as in V$$^{6\u20135}_{4\u20133}$$) to mean not that $$\\hat{5}$$ is the root but more precisely that it is the base. Whereas a root is determined by restacking a triad, a base is determined by the context of the key. In cadential six-four chords that are inverted to I$$^{6}$$, the lowest note ($$\\hat{3}$$) is the bass. Vertical restacking of the triad determines the (surface) root ($$\\hat{1}$$) simply enough, while $$\\hat{5}$$ remains the functional <\/span><i><span style=\"font-weight: 400;\">base<\/span><\/i><span style=\"font-weight: 400;\">, a quasi-root. Using Harrison\u2019s distinction, we may view the cadential i$$^{6}$$ in Brahms\u2019s Symphony (Example 3, above) to present G as the bass, E as the root, and B as the base, which, while placed in an inner voice, still plays the greatest harmonic role in the context of the progression. Conventional cadential six-fours do not require this distinction, but in the inverted examples discussed earlier and in the more harmonically displaced examples that follow, equating the chord\u2019s base\u2014not necessarily its root or its bass\u2014with the chord\u2019s dominant function helps to elucidate the taxonomic problem, when a chord\u2019s spelling conflicts with its function. If \u201c$$\\flat$$VI$$^{6}_{4}$$\u201d were to function as a cadential six-four, for example, its surface root would be $$\\flat\\hat{6}$$, and its bass would be $$\\flat\\hat{3}$$, but its <\/span><i><span style=\"font-weight: 400;\">base<\/span><\/i><span style=\"font-weight: 400;\"> would remain $$\\hat{5}$$, an interpreted, absent functional root.<span id='easy-footnote-14-9140' class='easy-footnote-margin-adjust'><\/span><span class='easy-footnote'><a href='https:\/\/theory.esm.rochester.edu\/integral\/37-2024\/fankhauser\/#easy-footnote-bottom-14-9140' title='To allow for an absence of the hypothetical base from a chord extends Harrison\u2019s theory but logically elucidates the problem of the displaced cadential six-four.'><sup>14<\/sup><\/a><\/span><\/span><\/p>\n\n\n\n<h2 class=\"wp-block-heading\"><strong>3. Definition of the Cadential Six-Four Chord<\/strong><\/h2>\n\n\n\n<p><span style=\"font-weight: 400;\">Table 1 isolates properties of the cadential six-four. Characteristics 1\u20133 are essential, defining features: (1) cadential six-fours have strong metric accentuation in relation to their resolution to a dominant in the approach to the cadence\u2014typically falling on hyperbeat 3 of a four-hyperbeat phrase, (2) they contain intervals of a sixth and fourth above the bass\u2014forming an apparent triad with the fifth in the bass, and (3) they include pitches from the tonic triad\u2014though these pitches may be altered chromatically. Characteristics 4\u20136 are better considered as common treatments than as defining characteristics. They describe the doubling of the bass, the downward resolution of the sixth and fourth (6\u20135 and 4\u20133), and the holding of the bass $$\\hat{5}$$ into the cadential dominant.<span id='easy-footnote-15-9140' class='easy-footnote-margin-adjust'><\/span><span class='easy-footnote'><a href='https:\/\/theory.esm.rochester.edu\/integral\/37-2024\/fankhauser\/#easy-footnote-bottom-15-9140' title='The move from a cadential six-four to a V$$^{4}_{2}$$, as in an evaded cadence, is common enough not to be considered a deviation. Ascending fourths above the bass ($$\\hat{1}$$\u2013$$\\hat{2}$$) are also not rare. David Lodewyckx (2015) examines cadential six-fours in which the fourth ascends, yielding $$\\hat{1}$$\u2013$$\\hat{2}$$\u2013$$\\hat{1}$$ voice-leading motion. He credits Marpurg as the first to identify this \u201cgalant cadence.\u201d'><sup>15<\/sup><\/a><\/span> Deviations from Characteristics 4\u20136, while somewhat uncommon, pose no challenge to the function or identity of the chord.<\/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\/fankhauser-vol37-table-1\/\"><img loading=\"lazy\" decoding=\"async\" width=\"1690\" height=\"1075\" src=\"https:\/\/theory.esm.rochester.edu\/integral\/wp-content\/uploads\/2024\/06\/fankhauser-vol37-table-1.jpg\" alt=\"Fankhauser, Table 1\" class=\"wp-image-9394\" style=\"width:512px;height:326px\" srcset=\"https:\/\/theory.esm.rochester.edu\/integral\/wp-content\/uploads\/2024\/06\/fankhauser-vol37-table-1.jpg 1690w, https:\/\/theory.esm.rochester.edu\/integral\/wp-content\/uploads\/2024\/06\/fankhauser-vol37-table-1-300x191.jpg 300w, https:\/\/theory.esm.rochester.edu\/integral\/wp-content\/uploads\/2024\/06\/fankhauser-vol37-table-1-1024x651.jpg 1024w, https:\/\/theory.esm.rochester.edu\/integral\/wp-content\/uploads\/2024\/06\/fankhauser-vol37-table-1-768x489.jpg 768w, https:\/\/theory.esm.rochester.edu\/integral\/wp-content\/uploads\/2024\/06\/fankhauser-vol37-table-1-1536x977.jpg 1536w\" sizes=\"auto, (max-width: 706px) 89vw, (max-width: 767px) 82vw, 740px\" \/><\/a><figcaption class=\"wp-element-caption\"><b>Table 1.<\/b> Characteristics of the Cadential Six-Four and Potential Deviations.<\/figcaption><\/figure>\n<\/div>\n\n\n<p><span style=\"font-weight: 400;\">Isolating these defining characteristics will help in the study of some unusual musical examples. Each defining characteristic invites a specific compositional challenge: how might an unconventional cadential six-four counter a given characteristic while preserving underlying, functional identity? Potential deviations are listed in the middle column, and a musical example for each deviation is listed to the right. Each listed example deviates in some respect from conventional usage but all satisfy two out of the three most essential criteria. Challenging criterion 3\u2014that the cadential six-four consists of pitches from the tonic triad\u2014lies at the heart of this study.<span id='easy-footnote-16-9140' class='easy-footnote-margin-adjust'><\/span><span class='easy-footnote'><a href='https:\/\/theory.esm.rochester.edu\/integral\/37-2024\/fankhauser\/#easy-footnote-bottom-16-9140' title='My definition of a cadential six-four chord does not require the presence of all members of the tonic triad, $$\\hat{1}$$, $$\\hat{3}$$, and $$\\hat{5}$$. Yet, I find it notable that all examples do contain some form of $$\\hat{3}$$\u2014either diatonic, chromatic, or enharmonic. The consistency of $$\\hat{3}$$&lt;\/span&gt; &lt;span style=&quot;font-weight: 400;&quot;&gt;as the only scale degree found in cadential six-fours throughout this article may raise its status as an essential component, seemingly more than $$\\hat{1}$$ or $$\\hat{5}$$, and offers odd support for Allen Cadwallader\u2019s (1992, 194) assertion, \u201cThe cadential six-four support for scale-degree 3 represents a perfectly logical union of harmony and counterpoint.\u201d David Beach (1992), Cadwallader (1992), and Joel Lester (1992) offer differing views on how the cadential six-four may or may not provide harmonic support for $$\\hat{3}$$. An odd exception to the scale degree tendency may be found in Night Ranger\u2019s \u201cWhen You Close Your Eyes\u201d (1983), 3:18\u20133:25. The progression of the first phrase of the chorus, I$$^{6}$$\u2013IV\u2013vi\u2013vii$$^{\\circ}$$$$^{6}_{4}$$\u2013IV (or IV$$^{6\u20135}_{4\u20133}$$), concludes with two harmonies that displace both a cadential six-four and the dominant, which are both shifted down a step and then corrected in the subsequent phrase. My definition excludes the double suspension above a tonic, I$$^{6\u20135}_{4\u20133}$$ (\u201cIV$$^{6}_{4}$$\u201d to I) as a cadential six-four, despite some similarities. Measure 8 of Mozart\u2019s Symphony No. 41 in C major, K. 551 \u201cJupiter\u201d (1788) contains an example.'><sup>16<\/sup><\/a><\/span><\/span><\/p>\n\n\n\n<p><span style=\"font-weight: 400;\">To understand the theoretical origin of cadential six-four chords with non-tonic pitches and the remarkable excerpts listed to the right of criterion 3, reconsider the use of Roman numerals and Arabic numerals. Arabic numerals originally simply indicated intervals above the bass (figured bass), with little or no consideration of triadic harmony. Roman numerals were affixed significantly later, in the early nineteenth century. If certain aspects of the cadential six-four chord can be categorized as primarily contrapuntal on one hand, with voice leading and inversions denoted by figured bass, or harmonic-syntactic on the other, based on the pitches and harmonic context, then the two commonly used analytical symbols may be separated into two potential means for deviation: the apparent \u201cI\u201d and the \u201csix-four\u201d (Figure 2). The cadential six-four\u2019s composition of pitches from the tonic triad is such an integral part of its identity that we see more flexibility with figured bass or inversions.<\/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\/fankhauser-vol37-figure-2\/\"><img loading=\"lazy\" decoding=\"async\" width=\"3998\" height=\"799\" src=\"https:\/\/theory.esm.rochester.edu\/integral\/wp-content\/uploads\/2024\/06\/fankhauser-vol37-figure-2.png\" alt=\"Fankhauser, Figure 2\" class=\"wp-image-9323\" style=\"width:512px;height:102px\" srcset=\"https:\/\/theory.esm.rochester.edu\/integral\/wp-content\/uploads\/2024\/06\/fankhauser-vol37-figure-2.png 3998w, https:\/\/theory.esm.rochester.edu\/integral\/wp-content\/uploads\/2024\/06\/fankhauser-vol37-figure-2-300x60.png 300w, https:\/\/theory.esm.rochester.edu\/integral\/wp-content\/uploads\/2024\/06\/fankhauser-vol37-figure-2-1024x205.png 1024w, https:\/\/theory.esm.rochester.edu\/integral\/wp-content\/uploads\/2024\/06\/fankhauser-vol37-figure-2-768x153.png 768w, https:\/\/theory.esm.rochester.edu\/integral\/wp-content\/uploads\/2024\/06\/fankhauser-vol37-figure-2-1536x307.png 1536w, https:\/\/theory.esm.rochester.edu\/integral\/wp-content\/uploads\/2024\/06\/fankhauser-vol37-figure-2-2048x409.png 2048w\" sizes=\"auto, (max-width: 706px) 89vw, (max-width: 767px) 82vw, 740px\" \/><\/a><figcaption class=\"wp-element-caption\"><b>Figure 2.<\/b> Isolation of the Cadential Six-Four Chord\u2019s Harmonic vs. Contrapuntal Potential for Deviation.<\/figcaption><\/figure>\n<\/div>\n\n\n<p><span style=\"font-weight: 400;\">As Meyer suggested, the inherent predictability of the cadential six-four chord likely led some nineteenth-century composers to avoid it. Other composers, however, may have seen potential for flexibility in its <\/span><i><span style=\"font-weight: 400;\">harmony<\/span><\/i><span style=\"font-weight: 400;\"> through complete transposition of the chord\u2014a drastic alteration counterbalanced by rigid restriction of the figures to six-four. In this latter means of deviation, the six-four figured bass is retained while the pitch content\u2014most efficiently represented by a Roman numeral\u2014is varied. Transposition of the whole chord offers a greater potential for variety than inversion. <\/span><\/p>\n\n\n\n<h2 class=\"wp-block-heading\">4. <strong>Harmonic Deviations in the Cadential Six-Four<\/strong><\/h2>\n\n\n\n<p><span style=\"font-weight: 400;\">A hypothetical spectrum of cadential six-four deviations\u2014from the conventional through the contrapuntal to what may seem quite harmonically bizarre\u2014is offered in <strong>Example 6<\/strong>. Compared to the conventional usage in Example 6a, the deviations in Examples 6b and 6c demonstrate contrapuntal flexibility while retaining the pitch content of the tonic triad. These are the types of deviation discussed by Rothstein and Cutler.<\/span><\/p>\n\n\n\n<p><span style=\"font-weight: 400;\">Examples&nbsp;6d and 6e, however, present notably different alterations, which retain the intervals of a sixth and fourth of the conventional six-four while shifting the entire chord vertically. The remarkable iii$$^{6}_{4}$$ in Example&nbsp;6d and even more unusual <nobr>$$\\flat$$I$$^{6}_{4}$$<\/nobr> in Example&nbsp;6e are but two of the possible transpositions of the cadential six-four. These five hypothetical examples vary in their intervals or basses, but all maintain some defining characteristics as they displace the cadential V$$^{7}$$ from a strong beat in the context of a basic progression. Each example also supports the conventional $$\\hat{3}$$\u2013$$\\hat{2}$$\u2013$$\\hat{1}$$ melodic gesture in the upper voice. While the surface analyses of each downbeat of m.&nbsp;3 vary widely in their Roman numerals, all of the cadential six-fours in Example&nbsp;6 maintain an underlying syntactical role and association with<\/span><i><span style=\"font-weight: 400;\"> dominant function<\/span><\/i><span style=\"font-weight: 400;\">, regardless of substantial alterations on the surface.<\/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\/fankhauser-vol37-example-6\/\"><img loading=\"lazy\" decoding=\"async\" width=\"2214\" height=\"2560\" src=\"https:\/\/theory.esm.rochester.edu\/integral\/wp-content\/uploads\/2024\/06\/fankhauser-vol37-example-6-scaled.jpg\" alt=\"Fankhauser, Example 6\" class=\"wp-image-9311\" style=\"width:512px;height:592px\" srcset=\"https:\/\/theory.esm.rochester.edu\/integral\/wp-content\/uploads\/2024\/06\/fankhauser-vol37-example-6-scaled.jpg 2214w, https:\/\/theory.esm.rochester.edu\/integral\/wp-content\/uploads\/2024\/06\/fankhauser-vol37-example-6-259x300.jpg 259w, https:\/\/theory.esm.rochester.edu\/integral\/wp-content\/uploads\/2024\/06\/fankhauser-vol37-example-6-886x1024.jpg 886w, https:\/\/theory.esm.rochester.edu\/integral\/wp-content\/uploads\/2024\/06\/fankhauser-vol37-example-6-768x888.jpg 768w, https:\/\/theory.esm.rochester.edu\/integral\/wp-content\/uploads\/2024\/06\/fankhauser-vol37-example-6-1328x1536.jpg 1328w, https:\/\/theory.esm.rochester.edu\/integral\/wp-content\/uploads\/2024\/06\/fankhauser-vol37-example-6-1771x2048.jpg 1771w\" sizes=\"auto, (max-width: 706px) 89vw, (max-width: 767px) 82vw, 740px\" \/><\/a><figcaption class=\"wp-element-caption\"><b>Example 6.<\/b> Hypothetical Cadential Six-Fours of Increasing Deviation.<\/figcaption><\/figure>\n<\/div>\n\n\n<p><span style=\"font-weight: 400;\">An example of a iii$$^{6}_{4}$$ acting as a displaced cadential six-four (Example 6d, above) enters near the beginning of The Beatles\u2019s \u201cJulia\u201d (<strong>Example 7<\/strong>, below).<span id='easy-footnote-17-9140' class='easy-footnote-margin-adjust'><\/span><span class='easy-footnote'><a href='https:\/\/theory.esm.rochester.edu\/integral\/37-2024\/fankhauser\/#easy-footnote-bottom-17-9140' title='The iii$$^{6}_{4}$$ chord has been specifically eschewed by theory instructors. In 2008, readers of the AP Theory exam made T-shirts bearing an anti-iii$$^{6}_{4}$$ emblem. This emphatic rejection was partly in jest, yet the reaction is understandable given: (1) the iii$$^{6}_{4}$$\u2019s overuse by students in fundamentals courses who indiscriminately combine triads with triadic inversion, (2) its rareness in practice, and (3) its functional ambiguity, sharing two pitches with both tonic and dominant triads.'><sup>17<\/sup><\/a><\/span> John Lennon plays two second-inversion mediants in the opening of his song. He uses a picking technique on the guitar that presents off-beat bass arpeggiations down to the fifth of the opening chords, but these initial, arpeggiating six-fours do not alter the underlying inversion. In the first two measures, the first bass note is more structural and holds the harmony to root position. The third chord alters the pattern, however, as the C$$\\sharp$$ in the bass represents the fifth of a mediant triad to form a iii$$^{6}_{4}$$ substitute for a more conventional V$$^{6}$$. The $$\\hat{1}$$\u2013$$\\hat{6}$$\u2013$$\\hat{7}$$ (D\u2013B\u2013C$$\\sharp$$) bass line in the opening phrase sits uncomfortably on the leading tone until it leaves the iii$$^{6}_{4}$$ to pass back up to the tonic at the start of the next phrase. Following the return of the iii$$^{6}_{4}$$ near the end of the second phrase, a briefly inserted $$\\hat{5}$$ (A) in the bass ($$\\hat{1}$$ \u2013$$\\hat{6}$$ \u2013$$\\hat{7}$$ \u2013$$\\hat{5}$$ \u2013$$\\hat{1}$$) alters the chord\u2019s harmonic role to become cadential as it resolves into a root-position dominant. The reappearance of the chord thereby carries more syntactical weight as a cadential six-four.<span id='easy-footnote-18-9140' class='easy-footnote-margin-adjust'><\/span><span class='easy-footnote'><a href='https:\/\/theory.esm.rochester.edu\/integral\/37-2024\/fankhauser\/#easy-footnote-bottom-18-9140' title='I interpret the C$$\\sharp$$ ($$\\hat{7}$$) presented on the downbeat as the primary bass note, which continues the pattern from the opening chords and yields the odd iii$$^{6}_{4}$$. To interpret the subsequent F$$\\sharp$$ in the same measure not as an embellishing arpeggiation of the bass but as more structural would place the mediant in root position. While this analysis would make the chord not a six-four but a five-three (root-position) chord, the chord\u2019s syntactical function could still be connected directly to that of a cadential six-four.'><sup>18<\/sup><\/a><\/span> This subtle redirection of the chord as initially passing or unresolved as it accompanies the word \u201cmeaningless\u201d toward more defined syntactical closure as it accompanies the word \u201cJulia\u201d coincides with a stretching of the phrase rhythm as Lennon sings the name of his mother, who was killed in a car accident when he was seventeen years old.&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\/fankhauser-vol37-example-7\/\"><img loading=\"lazy\" decoding=\"async\" width=\"4063\" height=\"994\" src=\"https:\/\/theory.esm.rochester.edu\/integral\/wp-content\/uploads\/2024\/06\/fankhauser-vol37-example-7.png\" alt=\"Fankhauser, Example 7\" class=\"wp-image-9312\" style=\"width:512px;height:125px\" srcset=\"https:\/\/theory.esm.rochester.edu\/integral\/wp-content\/uploads\/2024\/06\/fankhauser-vol37-example-7.png 4063w, https:\/\/theory.esm.rochester.edu\/integral\/wp-content\/uploads\/2024\/06\/fankhauser-vol37-example-7-300x73.png 300w, https:\/\/theory.esm.rochester.edu\/integral\/wp-content\/uploads\/2024\/06\/fankhauser-vol37-example-7-1024x251.png 1024w, https:\/\/theory.esm.rochester.edu\/integral\/wp-content\/uploads\/2024\/06\/fankhauser-vol37-example-7-768x188.png 768w, https:\/\/theory.esm.rochester.edu\/integral\/wp-content\/uploads\/2024\/06\/fankhauser-vol37-example-7-1536x376.png 1536w, https:\/\/theory.esm.rochester.edu\/integral\/wp-content\/uploads\/2024\/06\/fankhauser-vol37-example-7-2048x501.png 2048w\" sizes=\"auto, (max-width: 706px) 89vw, (max-width: 767px) 82vw, 740px\" \/><\/a><figcaption class=\"wp-element-caption\"><b>Example 7.<\/b> The Beatles, \u201cJulia\u201d (1968), 0:00\u20130:14.<\/figcaption><\/figure>\n<\/div>\n\n\n<p><span style=\"font-weight: 400;\">The end of Brahms\u2019s Waltz in E major, op. 39, No. 2 is strikingly similar (<strong>Example 8<\/strong>). The cadential \u201ciii$$^{6}_{4}$$\u201d in m.&nbsp;23 functions as an altered cadential six-four, one whose connection to tonic or dominant harmony is not immediately apparent but whose function is clarified by its context and resolution. Its entrance on a weak hyperbeat, the second measure of the phrase, and $$\\hat{1}$$-to-$$\\hat{7}$$ approach in the bass motion initially make the chord sound passing, as was the earlier correlating E\u2013D$$\\sharp$$ motion in m.&nbsp;6: I\u2013(V$$^{6}$$)\u2013vi\u2013V\/V\u2013V (not shown). The resolution of the six-four directly to the cadential dominant, however, confirms its cadential identity. In Brahms\u2019s waltz, the iii$$^{6}_{4}$$ resembles the first half of a V$$^{6\u20135}$$ motion, but with the chordal third (D$$\\sharp$$, $$\\hat{7}$$) in the bass, which then skips down to the root (B, $$\\hat{5}$$).<\/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\/fankhauser-vol37-example-8\/\"><img loading=\"lazy\" decoding=\"async\" width=\"2560\" height=\"1334\" src=\"https:\/\/theory.esm.rochester.edu\/integral\/wp-content\/uploads\/2024\/06\/fankhauser-vol37-example-8-scaled.jpg\" alt=\"Fankhauser, Example 8\" class=\"wp-image-9313\" style=\"width:512px;height:227px\" srcset=\"https:\/\/theory.esm.rochester.edu\/integral\/wp-content\/uploads\/2024\/06\/fankhauser-vol37-example-8-scaled.jpg 2560w, https:\/\/theory.esm.rochester.edu\/integral\/wp-content\/uploads\/2024\/06\/fankhauser-vol37-example-8-300x156.jpg 300w, https:\/\/theory.esm.rochester.edu\/integral\/wp-content\/uploads\/2024\/06\/fankhauser-vol37-example-8-1024x534.jpg 1024w, https:\/\/theory.esm.rochester.edu\/integral\/wp-content\/uploads\/2024\/06\/fankhauser-vol37-example-8-768x400.jpg 768w, https:\/\/theory.esm.rochester.edu\/integral\/wp-content\/uploads\/2024\/06\/fankhauser-vol37-example-8-1536x801.jpg 1536w, https:\/\/theory.esm.rochester.edu\/integral\/wp-content\/uploads\/2024\/06\/fankhauser-vol37-example-8-2048x1067.jpg 2048w\" sizes=\"auto, (max-width: 706px) 89vw, (max-width: 767px) 82vw, 740px\" \/><\/a><figcaption class=\"wp-element-caption\"><b>Example 8.<\/b> Brahms, Waltz in E major, op. 39, No. 2, mm. 22\u201325.<\/figcaption><\/figure>\n<\/div>\n\n\n<figure class=\"wp-block-audio\"><audio controls src=\"https:\/\/theory.esm.rochester.edu\/integral\/wp-content\/uploads\/2024\/06\/fankhauser-vol37-audio-8.mp3\"><\/audio><figcaption class=\"wp-element-caption\"><strong>Example 8 Audio.<\/strong><\/figcaption><\/figure>\n\n\n\n<p><span style=\"font-weight: 400;\">Unlike Lennon\u2019s example and more like Wagner\u2019s, the weak hypermetric placement of this six-four in relation to the cadential dominant further lessens its cadential quality. It is the simple progression\u2019s syntax, more than the associated harmony or counterpoint, that makes the six-four chord cadential. The chord\u2019s brief harmonic implication as a conventional cadential six-four in G$$\\sharp$$ minor is fostered by the next waltz of the set, which begins with a G$$\\sharp$$-minor tonic.&nbsp;<\/span><\/p>\n\n\n\n<p><span style=\"font-weight: 400;\">Franz Liszt\u2019s \u201cIl penseroso\u201d (<strong>Example 9<\/strong>) contains an apparent submediant cadential six-four chord. The bass in the opening phrase (mm.&nbsp;1\u20134) completes a highly conventional progression: I\u2013VI\u2013IV\u2013V\u2013I. Each harmony after the opening tonic, however, grammatically and dramatically pushes the progression into a mid-nineteenth century chromatic idiom. The second phrase (mm.&nbsp;5\u20138) expresses an equally conservative underlying syntax. Its morphological envelope is pushed further, however, as the modulating progression from C$$\\sharp$$ minor to E minor wrestles through what sounds like a \u201cwrong\u201d cadential six-four chord, labeled below according to its pitch content as a cadential VI$$^{6}_{4}$$. <\/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\/fankhauser-vol37-example-9\/\"><img loading=\"lazy\" decoding=\"async\" width=\"2560\" height=\"1911\" src=\"https:\/\/theory.esm.rochester.edu\/integral\/wp-content\/uploads\/2024\/06\/fankhauser-vol37-example-9-scaled.jpg\" alt=\"Fankhauser, Example 9\" class=\"wp-image-9314\" style=\"width:512px;height:382px\" srcset=\"https:\/\/theory.esm.rochester.edu\/integral\/wp-content\/uploads\/2024\/06\/fankhauser-vol37-example-9-scaled.jpg 2560w, https:\/\/theory.esm.rochester.edu\/integral\/wp-content\/uploads\/2024\/06\/fankhauser-vol37-example-9-300x224.jpg 300w, https:\/\/theory.esm.rochester.edu\/integral\/wp-content\/uploads\/2024\/06\/fankhauser-vol37-example-9-1024x764.jpg 1024w, https:\/\/theory.esm.rochester.edu\/integral\/wp-content\/uploads\/2024\/06\/fankhauser-vol37-example-9-768x573.jpg 768w, https:\/\/theory.esm.rochester.edu\/integral\/wp-content\/uploads\/2024\/06\/fankhauser-vol37-example-9-1536x1146.jpg 1536w, https:\/\/theory.esm.rochester.edu\/integral\/wp-content\/uploads\/2024\/06\/fankhauser-vol37-example-9-2048x1529.jpg 2048w\" sizes=\"auto, (max-width: 706px) 89vw, (max-width: 767px) 82vw, 740px\" \/><\/a><figcaption class=\"wp-element-caption\"><b>Example 9.<\/b> Liszt, <i>Ann\u00e9es de p\u00e8lerinage<\/i> (Years of Pilgrimage): Italia, 2. \u201cIl penseroso\u201d (1839), mm. 1\u20138.<\/figcaption><\/figure>\n<\/div>\n\n\n<figure class=\"wp-block-audio\"><audio controls src=\"https:\/\/theory.esm.rochester.edu\/integral\/wp-content\/uploads\/2024\/06\/fankhauser-vol37-audio-9.mp3\"><\/audio><figcaption class=\"wp-element-caption\"><strong>Example 9 Audio.<\/strong><\/figcaption><\/figure>\n\n\n\n<p><span style=\"font-weight: 400;\">Liszt\u2019s altered cadential six-four in this example suggests a change in nineteenth-century compositional thought. As a clear harbinger of closure, the cadential six-four provides opportunity for manipulation of expectation. Whereas original Baroque usage of the cadential six-four derives from contrapuntal displacement of dominant\u2019s fifth and third, as through suspensions, Classical usage increased harmonic independence. As a strong signal for closure, the cadential six-four saw increased use in common-practice tonality, placing more significance on the chord as a discrete, separable harmonic entity. Increased emphasis on the cadential six-four\u2019s vertical dimension invites expansion not merely through prolongation, as in a cadenza, but of the shape of the chord itself.&nbsp;<\/span><\/p>\n\n\n\n<p><span style=\"font-weight: 400;\">In contrast to the largely linear Baroque usage and even to the more harmonic Classical usage, the six-four in Liszt\u2019s 1839 example, while still following earlier voice-leading conventions, highlights a shift toward even greater harmonic autonomy, in which the cadential six-four chord, like the opening harmonies in \u201cIl penseroso,\u201d is subjected to morphological alteration secured only by a well-defined, underlying tonal syntax.<span id='easy-footnote-19-9140' class='easy-footnote-margin-adjust'><\/span><span class='easy-footnote'><a href='https:\/\/theory.esm.rochester.edu\/integral\/37-2024\/fankhauser\/#easy-footnote-bottom-19-9140' title='Figure 1 (based on Meyer, 2000\/1992,&amp;nbsp;241) shows Liszt\u2019s usage of the cadential six-four to be remarkably low, signifying the composer\u2019s personal attraction to innovative harmony and more generally supporting a general decline of the chord\u2019s usage.'><sup>19<\/sup><\/a><\/span> The result is not simply a change in the color of the harmony, as from major to minor, but a dramatic, seemingly jagged, change in its outward shape. An analogy could be made to painting\u2014the technique being less like the strident color schemes of Henri Matisse\u2019s Fauvist paintings and more like the disfiguration in Pablo Picasso\u2019s Cubist paintings. The outlines of Matisse\u2019s subjects remain intact, if somewhat altered or blurred. Picasso\u2019s subjects, by contrast, experience more dramatic fissures in form, sometimes pushing them to the point of unrecognizability, despite the more precise brush strokes and more defined colors.<\/span><span id='easy-footnote-20-9140' class='easy-footnote-margin-adjust'><\/span><span class='easy-footnote'><a href='https:\/\/theory.esm.rochester.edu\/integral\/37-2024\/fankhauser\/#easy-footnote-bottom-20-9140' title='Compare, for example, Fauvist colors in Henri Matisse\u2019s 1905 &lt;em&gt;The Green Line&lt;\/em&gt;&amp;nbsp;[&lt;em&gt;Portrait of Madame Matisse&lt;\/em&gt;] to Cubist disfiguration in Pablo Picasso\u2019s 1937 &lt;em&gt;Weeping Woman&lt;\/em&gt;.'><sup>20<\/sup><\/a><\/span>\n\n\n\n<p><span style=\"font-weight: 400;\">As a distinct category of chords derived from \u201ccommon practice,\u201d cadential six-fours offer a harmonic resource that is both directly connected with the past yet easily malleable in more modern contexts. To deconstruct cadential six-four chords into contrapuntal, harmonic, and syntactical components allows for a variety of compositional and analytical approaches that at once engage both the conventional and the innovative.<span id='easy-footnote-21-9140' class='easy-footnote-margin-adjust'><\/span><span class='easy-footnote'><a href='https:\/\/theory.esm.rochester.edu\/integral\/37-2024\/fankhauser\/#easy-footnote-bottom-21-9140' title='Harrison (2016, 10) makes a similar point, that innovative approaches to tonal harmony modify some components of conventional \u201ccommon-practice harmony,\u201d which he describes as an \u201cinterlocked system of components that includes conventions of counterpoint and voice leading, rhythm, vertical sonority, and normative syntax.\u201d'><sup>21<\/sup><\/a><\/span><\/span><\/p>\n\n\n\n<p><span style=\"font-weight: 400;\"><strong>Example&nbsp;10<\/strong> shows a reduction of Liszt\u2019s passage, along with a voice-leading analysis and hypothetical normalization, to clarify the simple, underlying grammar of the passage while also revealing the relatively young composer\u2019s harmonic innovation. On the surface, the progression of the closing four harmonies, iv\u2013VI\u2013V\u2013i, seems unremarkable, but the inversion of the submediant to six-four alters its pre-dominant role. Strong placement of any six-four chord on the third hyperbeat of a phrase is one of the first indicators of cadential function. Hearing the pre-dominant relation of the submediant combined with the chord\u2019s potential as a cadential six-four confuses the chord\u2019s harmonic function. Comparing the replacement of the VI$$^{6}_{4}$$ in the progression with the conventional cadential i$$^{6}_{4}$$ (or its inversion i$$^{6}$$) reveals their commonality. The vastly different aural impression created by the original, \u201cwrong\u201d cadential six-four (Example&nbsp;10a) as compared to the normalized diatonic version (Example&nbsp;10c) makes their <\/span><i><span style=\"font-weight: 400;\">similarity<\/span><\/i><span style=\"font-weight: 400;\"> in harmonic function and syntax even more remarkable. <\/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\/fankhauser-vol37-example-10\/\"><img loading=\"lazy\" decoding=\"async\" width=\"2560\" height=\"1904\" src=\"https:\/\/theory.esm.rochester.edu\/integral\/wp-content\/uploads\/2024\/06\/fankhauser-vol37-example-10-scaled.jpg\" alt=\"Fankhauser, Example 10\" class=\"wp-image-9315\" style=\"width:620px;height:461px\" srcset=\"https:\/\/theory.esm.rochester.edu\/integral\/wp-content\/uploads\/2024\/06\/fankhauser-vol37-example-10-scaled.jpg 2560w, https:\/\/theory.esm.rochester.edu\/integral\/wp-content\/uploads\/2024\/06\/fankhauser-vol37-example-10-300x223.jpg 300w, https:\/\/theory.esm.rochester.edu\/integral\/wp-content\/uploads\/2024\/06\/fankhauser-vol37-example-10-1024x762.jpg 1024w, https:\/\/theory.esm.rochester.edu\/integral\/wp-content\/uploads\/2024\/06\/fankhauser-vol37-example-10-768x571.jpg 768w, https:\/\/theory.esm.rochester.edu\/integral\/wp-content\/uploads\/2024\/06\/fankhauser-vol37-example-10-1536x1142.jpg 1536w, https:\/\/theory.esm.rochester.edu\/integral\/wp-content\/uploads\/2024\/06\/fankhauser-vol37-example-10-2048x1523.jpg 2048w\" sizes=\"auto, (max-width: 706px) 89vw, (max-width: 767px) 82vw, 740px\" \/><\/a><figcaption class=\"wp-element-caption\"><b>Example 10.<\/b> Reduction, Voice-Leading Analysis, and Normalization of \u201cIl penseroso,\u201d mm. 1\u20138.<\/figcaption><\/figure>\n<\/div>\n\n\n<figure class=\"wp-block-audio\"><audio controls src=\"https:\/\/theory.esm.rochester.edu\/integral\/wp-content\/uploads\/2024\/06\/fankhauser-vol37-audio-10a.mp3\"><\/audio><figcaption class=\"wp-element-caption\"><strong>Example 10a Audio.<\/strong><\/figcaption><\/figure>\n\n\n\n<figure class=\"wp-block-audio\"><audio controls src=\"https:\/\/theory.esm.rochester.edu\/integral\/wp-content\/uploads\/2024\/06\/fankhauser-vol37-audio-10b.mp3\"><\/audio><figcaption class=\"wp-element-caption\"><strong>Example 10c Audio.<\/strong><\/figcaption><\/figure>\n\n\n\n<p><span style=\"font-weight: 400;\">If a voice-leading graph aims to show prolongation through conventional linear and harmonic connections, then displaced or seemingly detached harmonic relations present a challenge. In this case, it is not simply the chromaticism that challenges analysis; it is that traditional <\/span><i><span style=\"font-weight: 400;\">Stufen<\/span><\/i><span style=\"font-weight: 400;\">\u2014scale degrees that possess inherent harmonic meaning\u2014are displaced to sound like other <\/span><i><span style=\"font-weight: 400;\">Stufen<\/span><\/i><span style=\"font-weight: 400;\">. The G$$\\natural$$ bass of the six-four in m.&nbsp;7 most directly associates with $$\\hat{3}$$ in E minor, but due to its strong metric placement, the six-four figures, and its direct association with the cadential dominant, the G$$\\natural$$ functions more like a displaced $$\\hat{5}$$. The dotted slur connecting the G to the B in Example 10b suggests one of two interpretations. The earlier discussion on inverted cadential six-fours might lead one to view the G as an inner voice that is placed low, effectively a i$$^{6}$$ with B displaced by G, which would make the dotted slur an arpeggiation within an underlying voice exchange.&nbsp;<\/span><\/p>\n\n\n\n<p><span style=\"font-weight: 400;\">A competing hearing retains its six-four position, in which VI$$^{6}_{4}$$ in the score functions as a cadential six-four not by inversion of an E minor triad\u2014with a displaced fifth\u2014but by a transposition of the whole underlying cadential six-four: the bass G functions as a shifted or sub-posed B, together representing the same $$\\hat{5}$$ <\/span><i><span style=\"font-weight: 400;\">Stufe<\/span><\/i><span style=\"font-weight: 400;\">. By extension, one might hear the upper voice C function as a displaced $$\\hat{1}$$ (E) and the E as a displaced $$\\hat{3}$$, represented by the G$$\\sharp$$ in the normalized E-major ending. While smooth voice leading supports the earlier hearing as a modified inverted cadential six-four, the harmonic syntax supports the latter, in which the surface six-four is retained and decidedly cadential in function. In that latter hearing, the chord is simply a transposed, \u201cwrong\u201d cadential six-four.<span id='easy-footnote-22-9140' class='easy-footnote-margin-adjust'><\/span><span class='easy-footnote'><a href='https:\/\/theory.esm.rochester.edu\/integral\/37-2024\/fankhauser\/#easy-footnote-bottom-22-9140' title='A third underlying hearing could retain the upper voices (C, E, and G) above an implied bass note B to yield a dominant with $$\\flat$$9, $$\\flat$$6\u20135, and 4\u20133 figuration. That interpretation would hear the dominant function but not the cadential six-four character.'><sup>22<\/sup><\/a><\/span><\/span><\/p>\n\n\n\n<p><span style=\"font-weight: 400;\">With that hearing, the dotted slur in the bass from G$$\\natural$$ to B in Example&nbsp;10b highlights an odd connection. More than a traditional slur showing arpeggiation, the slur makes a syntactical link, like a skewed <\/span><i><span style=\"font-weight: 400;\">tie<\/span><\/i><span style=\"font-weight: 400;\"> that retains function as $$\\hat{5}$$ (as if B-to-B) behind a shift on the surface (G$$\\natural$$ to B). Dotting the slur makes a more nuanced reference to Schenker\u2019s more traditional octave transfer, which represents a preservation of function behind a change in pitch. The dotted slur here represents an obligatory correction of the misplaced cadential six-four bass to the \u201ccorrect\u201d dominant $$\\hat{5}$$ to secure the cadence.&nbsp;<\/span><\/p>\n\n\n\n<p><span style=\"font-weight: 400;\">Liszt\u2019s enharmonic change from C$$\\natural$$ ($$\\flat\\hat{1}$$) to B$$\\sharp$$ ($$\\hat{7}$$) in the opening phrase presents a similar, albeit simpler, shift in function and provides motivic basis for the extraordinary cadence.<\/span><span id='easy-footnote-23-9140' class='easy-footnote-margin-adjust'><\/span><span class='easy-footnote'><a href='https:\/\/theory.esm.rochester.edu\/integral\/37-2024\/fankhauser\/#easy-footnote-bottom-23-9140' title='Richard Cohn (2012) explores enharmonicism in this passage as it relates to the concepts double syntax, double-agent complex (from David Lewin), and &lt;em&gt;Mehrdeutigkeit&lt;\/em&gt;.'><sup>23<\/sup><\/a><\/span> Contrary to Example&nbsp;10b\u2019s dotted slur in m. 7, which connects two different pitches to the same underlying function, the earlier dotted slur in mm. 2\u20133 connects enharmonic pitches with different underlying functions. Working to develop further the salient C$$\\natural$$ tonal problem that is introduced in m. 2 and developed throughout the excerpt, the G$$\\natural$$ bass of the six-four exerts a force commonly associated with C major to pull further from a tonicization of a more normal relative major, E major (shown in Example&nbsp;10c\u2019s normalization), toward that of the minor mediant, E minor. The altered cadential six-four, therefore, serves a greater role than simply an unexpected sonority inserted into a largely conventional grammar. It intensifies a specific tonal-motivic development throughout the passage.&nbsp;<\/p>\n\n\n\n<p><span style=\"font-weight: 400;\">David Damschroder (1990) draws historical connections between Liszt\u2019s composition and several other works, the third movement of Beethoven\u2019s Piano Sonata op. 26 being a more direct inspiration than Michaelangelo\u2019s namesake sculpture. As Damschroder notes, Liszt\u2019s harmonic innovations push beyond those of Beethoven; his \u201cuse of the \u2018G-natural\u2019 tonal area in <\/span><i><span style=\"font-weight: 400;\">Il penseroso<\/span><\/i><span style=\"font-weight: 400;\"> makes Beethoven\u2019s compositional behavior seem almost timid\u201d (12). Yet, Damschroder\u2019s analysis disregards the first strong implication of the G-natural tonal area, which is firmly established in mm.&nbsp;14\u201315: the bass of the \u201cwrong\u201d cadential six-four chord in m. 7. This displaced cadential six-four chord most immediately pulls toward C major, but the tonal problem presented by the G-natural in the bass may inspire the \u201cthinker\u2019s\u201d consideration of foreign tonal areas.<span id='easy-footnote-24-9140' class='easy-footnote-margin-adjust'><\/span><span class='easy-footnote'><a href='https:\/\/theory.esm.rochester.edu\/integral\/37-2024\/fankhauser\/#easy-footnote-bottom-24-9140' title='Damschroder\u2019s voice-leading graph, his Example 6b, shares much in common with mine but more immediately relegates the bass G$$\\natural$$ to an inner voice, corresponding to an inverted cadential six-four.'><sup>24<\/sup><\/a><\/span> Neither Damschroder nor I have proposed what the innovative progression means for Liszt\u2019s \u201cThinker\u201d \u2014not to mention the consistent placement of left-hand chords not on each downbeat but on the (displaced?) second beat of each measure\u2014but these considerations offer initial steps. More evident in this excerpt than in the previous examples of inverted cadential six-four chords is the capacity of the normally well-defined chord to have a distorted shape while retaining syntactical function. Its preservation of function stems from three primary factors: its placement on a strong hyperbeat, its six-four figures, and its immediate resolution to the cadential dominant.<\/span><\/p>\n\n\n\n<h2 class=\"wp-block-heading\">5. <strong>Displaced Cadential Six-Four Chords in Prokofiev and Shostakovich<\/strong><\/h2>\n\n\n\n<p><span style=\"font-weight: 400;\">It may seem spurious to draw connections from specific harmonic techniques of Liszt to those of Prokofiev and Shostakovich, but all three composers incorporate odd chromaticism and jarring harmonic shifts that embrace innovative harmonic treatments on one hand while maintaining direct reference to Classical harmonic syntax on the other. The first two phrases of the Gavotte from Prokofiev\u2019s \u201cClassical\u201d Symphony (Example&nbsp;11) contain quick, colorful harmonic shifts in tonal centers. The most striking shift is the chromatic six-four chord in the third phrase. Unlike harmonic progressions in the opening nine measures, the harmony in m. 10 defies traditional harmonic analysis.<\/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\/fankhauser-vol37-example-11\/\"><img loading=\"lazy\" decoding=\"async\" width=\"2560\" height=\"2417\" src=\"https:\/\/theory.esm.rochester.edu\/integral\/wp-content\/uploads\/2024\/06\/fankhauser-vol37-example-11-scaled.jpg\" alt=\"Fankhauser, Example 11\" class=\"wp-image-9316\" style=\"width:512px;height:483px\" srcset=\"https:\/\/theory.esm.rochester.edu\/integral\/wp-content\/uploads\/2024\/06\/fankhauser-vol37-example-11-scaled.jpg 2560w, https:\/\/theory.esm.rochester.edu\/integral\/wp-content\/uploads\/2024\/06\/fankhauser-vol37-example-11-300x283.jpg 300w, https:\/\/theory.esm.rochester.edu\/integral\/wp-content\/uploads\/2024\/06\/fankhauser-vol37-example-11-1024x967.jpg 1024w, https:\/\/theory.esm.rochester.edu\/integral\/wp-content\/uploads\/2024\/06\/fankhauser-vol37-example-11-768x725.jpg 768w, https:\/\/theory.esm.rochester.edu\/integral\/wp-content\/uploads\/2024\/06\/fankhauser-vol37-example-11-1536x1450.jpg 1536w, https:\/\/theory.esm.rochester.edu\/integral\/wp-content\/uploads\/2024\/06\/fankhauser-vol37-example-11-2048x1933.jpg 2048w\" sizes=\"auto, (max-width: 706px) 89vw, (max-width: 767px) 82vw, 740px\" \/><\/a><figcaption class=\"wp-element-caption\"><b>Example 11.<\/b> Prokofiev, \u201cClassical\u201d Symphony op. 25, III, mm. 1\u201312 (1917).<\/figcaption><\/figure>\n<\/div>\n\n\n<figure class=\"wp-block-audio\"><audio controls src=\"https:\/\/theory.esm.rochester.edu\/integral\/wp-content\/uploads\/2024\/06\/fankhauser-vol37-audio-11-1.mp3\"><\/audio><figcaption class=\"wp-element-caption\"><strong>Example 11 Audio.<\/strong><\/figcaption><\/figure>\n\n\n\n<p><span style=\"font-weight: 400;\">The score shows a C$$\\sharp$$-major six-four, which most immediately forms an unusual <\/span><i><span style=\"font-weight: 400;\">neighboring<\/span><\/i><span style=\"font-weight: 400;\"> six-four between two dominants, defined by the lower-neighbor motion in the bass, A\u2013G$$\\sharp$$\u2013A, with a potential literal analysis of V$$^{7}$$\u2013(VII$$^{6}_{4}$$)\u2013V$$^{7}$$. However, this chord\u2019s function as a chromatically displaced <\/span><i><span style=\"font-weight: 400;\">cadential<\/span><\/i><span style=\"font-weight: 400;\"> six-four is expressed by its strong accentuation and its temporal and harmonic proximity to the cadential dominant, in addition to a chromatic approach that is surprisingly conventional.&nbsp;<\/span><\/p>\n\n\n\n<p><span style=\"font-weight: 400;\">Voice-leading analysis in <strong>Example&nbsp;12<\/strong> shows how this altered six-four at once embodies two normally contradictory functions, with the chord\u2019s salient chromaticism on one hand\u2014a kind of \u201cflat\u201d tonic six-four\u2014and its highly conventional and well-defined tonal syntax on the other. The voice-leading graph respells the V$$^{7}$$ to VII$$^{6}_{4}$$ in D major to fit a more typical motion, Gr$$^{+6}$$ to cadential six-four in D$$\\flat$$ major. Prokofiev\u2019s treatment of the apparent local dominant-seventh as a Gr$$^{+6}$$ signals a cadential six-four function in the flat-tonic region. The dotted tie from the A$$\\flat$$ to A$$\\natural$$ in the bass represents shared dominant function of two different pitches, similar to the transformation in the Liszt example above from G to B.<\/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\/fankhauser-vol37-example-12\/\"><img loading=\"lazy\" decoding=\"async\" width=\"2560\" height=\"1162\" src=\"https:\/\/theory.esm.rochester.edu\/integral\/wp-content\/uploads\/2024\/06\/fankhauser-vol37-example-12-scaled.jpg\" alt=\"Fankhauser, Example 12\" class=\"wp-image-9317\" style=\"width:512px;height:232px\" srcset=\"https:\/\/theory.esm.rochester.edu\/integral\/wp-content\/uploads\/2024\/06\/fankhauser-vol37-example-12-scaled.jpg 2560w, https:\/\/theory.esm.rochester.edu\/integral\/wp-content\/uploads\/2024\/06\/fankhauser-vol37-example-12-300x136.jpg 300w, https:\/\/theory.esm.rochester.edu\/integral\/wp-content\/uploads\/2024\/06\/fankhauser-vol37-example-12-1024x465.jpg 1024w, https:\/\/theory.esm.rochester.edu\/integral\/wp-content\/uploads\/2024\/06\/fankhauser-vol37-example-12-768x348.jpg 768w, https:\/\/theory.esm.rochester.edu\/integral\/wp-content\/uploads\/2024\/06\/fankhauser-vol37-example-12-1536x697.jpg 1536w, https:\/\/theory.esm.rochester.edu\/integral\/wp-content\/uploads\/2024\/06\/fankhauser-vol37-example-12-2048x929.jpg 2048w\" sizes=\"auto, (max-width: 706px) 89vw, (max-width: 767px) 82vw, 740px\" \/><\/a><figcaption class=\"wp-element-caption\"><b>Example 12.<\/b> Voice-Leading Analysis of \u201cClassical\u201d Symphony, III, mm. 9\u201312.<\/figcaption><\/figure>\n<\/div>\n\n\n<p><span style=\"font-weight: 400;\">A normalization that raises the six-four and its preceding \u201cwrong\u201d Gr$$^{+6}$$ up a half step (<strong>Example 13<\/strong>) reveals a more Haydnesque treatment. While the normalization does not account for the remaining weak hypermetric placement of the cadential six-four, the accentuation of the chord is strong and the underlying harmonic progression, beneath the odd surface, is quite conventional, revealing what Richard Bass (1988) might describe as underlying \u201cshadow\u201d structure.<span id='easy-footnote-25-9140' class='easy-footnote-margin-adjust'><\/span><span class='easy-footnote'><a href='https:\/\/theory.esm.rochester.edu\/integral\/37-2024\/fankhauser\/#easy-footnote-bottom-25-9140' title='In 2006, I made an analogy of this harmonic shift to the refraction of light, in which the image of the refracted object\u2014the enclosed passage in Example 12\u2014appears distorted from a hypothetical image of an unrefracted object, as proposed in Example 13. Unlike a shadow, a refracted image represents the \u201ctrue\u201d object only with an apparent shift.'><sup>25<\/sup><\/a><\/span><\/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\/fankhauser-vol37-example-13\/\"><img loading=\"lazy\" decoding=\"async\" width=\"2560\" height=\"1036\" src=\"https:\/\/theory.esm.rochester.edu\/integral\/wp-content\/uploads\/2024\/06\/fankhauser-vol37-example-13-scaled.jpg\" alt=\"Fankhauser, Example 13\" class=\"wp-image-9318\" style=\"width:512px;height:207px\" srcset=\"https:\/\/theory.esm.rochester.edu\/integral\/wp-content\/uploads\/2024\/06\/fankhauser-vol37-example-13-scaled.jpg 2560w, https:\/\/theory.esm.rochester.edu\/integral\/wp-content\/uploads\/2024\/06\/fankhauser-vol37-example-13-300x121.jpg 300w, https:\/\/theory.esm.rochester.edu\/integral\/wp-content\/uploads\/2024\/06\/fankhauser-vol37-example-13-1024x414.jpg 1024w, https:\/\/theory.esm.rochester.edu\/integral\/wp-content\/uploads\/2024\/06\/fankhauser-vol37-example-13-768x311.jpg 768w, https:\/\/theory.esm.rochester.edu\/integral\/wp-content\/uploads\/2024\/06\/fankhauser-vol37-example-13-1536x622.jpg 1536w, https:\/\/theory.esm.rochester.edu\/integral\/wp-content\/uploads\/2024\/06\/fankhauser-vol37-example-13-2048x829.jpg 2048w\" sizes=\"auto, (max-width: 706px) 89vw, (max-width: 767px) 82vw, 740px\" \/><\/a><figcaption class=\"wp-element-caption\"><b>Example 13.<\/b> Normalization of \u201cClassical\u201d Symphony, III, mm. 9\u201312.<\/figcaption><\/figure>\n<\/div>\n\n\n<figure class=\"wp-block-audio\"><audio controls src=\"https:\/\/theory.esm.rochester.edu\/integral\/wp-content\/uploads\/2024\/06\/fankhauser-vol37-audio-13.mp3\"><\/audio><figcaption class=\"wp-element-caption\"><strong>Example 13 Audio.<\/strong><\/figcaption><\/figure>\n\n\n\n<p><span style=\"font-weight: 400;\">An example of more extreme morphological deviation enters in Shostakovich\u2019s Piano Prelude op. 34, No.&nbsp;10 (<strong>Example 14<\/strong>). Similar to the Prokofiev example above, the six-four chord in m. 15 functions as a vertically displaced cadential six-four, whose syntactic clarity is obscured only by its chromatic alteration and distance from the tonic. On the surface, the chord pushes toward a brief tonicization of B$$\\flat$$ minor. This foreign key relates to the underlying C$$\\sharp$$ tonic as what might be labeled literally \u201c$$\\flat\\flat$$vii$$^{6}_{4}$$\u201d (Analysis 1) or interpreted as an enharmonic \u201c$$\\sharp$$vi$$^{6}_{4}$$\u201d (Analysis 2), which recalls the tonal-motivic implication of the A$$\\sharp$$ in m.&nbsp;3. However, both of these labels lack sensible harmonic analysis. The obscured context reveals an absence of clear, logical harmonic relations, but the chord\u2019s six-four figures immediately preceding a cadential dominant illuminate a logical analytical path derived from harmonic convention. Correlating the chord to a different enharmonic chord\u2014a triple flat cadential six-four chord \u201c$$\\flat\\flat\\flat\\text{ }$$<\/span>i$$^{6}_{4}$$<span style=\"font-weight: 400;\">\u201d (Analysis 2b)\u2014seems quite dubious. Still, that analysis makes a direct connection to its underlying <\/span><i><span style=\"font-weight: 400;\">diatonic<\/span><\/i><span style=\"font-weight: 400;\"> function as a cadential six-four, if largely by analogy. In addition to the literal and enharmonic interpretations, Analysis 3 hypothesizes a third interpretation of the chord, hearing the chord as a conventional six-four that lacks a root and adds embellishments, notably a B$$\\flat$$ (A$$\\sharp$$) to implied G$$\\sharp$$ ($$\\sharp$$9\u20138). While that hearing brings the underlying dominant function to the surface, I find it even less plausible and farther removed from the chord\u2019s context. Analysis 3 not only lacks the essential dominant root, it also rearranges and confuses the distinct six-four figures. A more musical hearing, I think, draws more from the chord\u2019s syntactical role than its harmonic or voice-leading connections. <\/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\/fankhauser-vol37-example-14\/\"><img loading=\"lazy\" decoding=\"async\" width=\"2388\" height=\"2560\" src=\"https:\/\/theory.esm.rochester.edu\/integral\/wp-content\/uploads\/2024\/06\/fankhauser-vol37-example-14-scaled.jpg\" alt=\"Fankhauser, Example 14\" class=\"wp-image-9319\" style=\"width:512px;height:549px\" srcset=\"https:\/\/theory.esm.rochester.edu\/integral\/wp-content\/uploads\/2024\/06\/fankhauser-vol37-example-14-scaled.jpg 2388w, https:\/\/theory.esm.rochester.edu\/integral\/wp-content\/uploads\/2024\/06\/fankhauser-vol37-example-14-280x300.jpg 280w, https:\/\/theory.esm.rochester.edu\/integral\/wp-content\/uploads\/2024\/06\/fankhauser-vol37-example-14-955x1024.jpg 955w, https:\/\/theory.esm.rochester.edu\/integral\/wp-content\/uploads\/2024\/06\/fankhauser-vol37-example-14-768x823.jpg 768w, https:\/\/theory.esm.rochester.edu\/integral\/wp-content\/uploads\/2024\/06\/fankhauser-vol37-example-14-1433x1536.jpg 1433w, https:\/\/theory.esm.rochester.edu\/integral\/wp-content\/uploads\/2024\/06\/fankhauser-vol37-example-14-1910x2048.jpg 1910w\" sizes=\"auto, (max-width: 706px) 89vw, (max-width: 767px) 82vw, 740px\" \/><\/a><figcaption class=\"wp-element-caption\"><b>Example 14.<\/b> Shostakovich, Piano Prelude op. 34, No. 10 (1932\u201333), mm. 1\u201318<\/figcaption><\/figure>\n<\/div>\n\n\n<figure class=\"wp-block-audio\"><audio controls src=\"https:\/\/theory.esm.rochester.edu\/integral\/wp-content\/uploads\/2024\/06\/fankhauser-vol37-audio-14.mp3\"><\/audio><figcaption class=\"wp-element-caption\"><strong>Example 14 Audio.<\/strong><\/figcaption><\/figure>\n\n\n\n<p><span style=\"font-weight: 400;\">As in previous examples, m. 15\u2019s cadential six-four functions syntactically to signal a drive toward a cadence. Other characteristics support the cadential six-four hearing: (1) the bass\u2019s wide leap down from F$$\\natural$$3 to G$$\\sharp$$2 in mm.&nbsp;15\u201316 resembles a conventional octave leap, and (2) hypermetric accentuation is greater on m.&nbsp;15 than m.&nbsp;16 (strong\u2013weak). Hearing the D$$\\flat$$4 in the displaced cadential six-four as an enharmonic tonic C$$\\sharp$$ reinforces associations with the conventional cadential six-four. At the same time, the displaced six-four chord creates an ephemeral yet deeply dramatic detour that pulls away from the tonic. Example 15 simplifies mm.&nbsp;1\u201318 to highlight the passage\u2019s harmonic derivation from a simple four-chord progression, i\u2013III\u2013V$$^{7}$$\u2013i, along with the varying interpretations of the chromatic chord in m.&nbsp;15.<\/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\/fankhauser-vol37-example-15\/\"><img loading=\"lazy\" decoding=\"async\" width=\"2549\" height=\"1490\" src=\"https:\/\/theory.esm.rochester.edu\/integral\/wp-content\/uploads\/2024\/06\/fankhauser-vol37-example-15.jpg\" alt=\"Fankhauser, Example 15\" class=\"wp-image-9320\" style=\"width:440px;height:257px\" srcset=\"https:\/\/theory.esm.rochester.edu\/integral\/wp-content\/uploads\/2024\/06\/fankhauser-vol37-example-15.jpg 2549w, https:\/\/theory.esm.rochester.edu\/integral\/wp-content\/uploads\/2024\/06\/fankhauser-vol37-example-15-300x175.jpg 300w, https:\/\/theory.esm.rochester.edu\/integral\/wp-content\/uploads\/2024\/06\/fankhauser-vol37-example-15-1024x599.jpg 1024w, https:\/\/theory.esm.rochester.edu\/integral\/wp-content\/uploads\/2024\/06\/fankhauser-vol37-example-15-768x449.jpg 768w, https:\/\/theory.esm.rochester.edu\/integral\/wp-content\/uploads\/2024\/06\/fankhauser-vol37-example-15-1536x898.jpg 1536w, https:\/\/theory.esm.rochester.edu\/integral\/wp-content\/uploads\/2024\/06\/fankhauser-vol37-example-15-2048x1197.jpg 2048w\" sizes=\"auto, (max-width: 706px) 89vw, (max-width: 767px) 82vw, 740px\" \/><\/a><figcaption class=\"wp-element-caption\"><b>Example 15.<\/b> Simplification of Shostakovich, Piano Prelude op. 34, No. 10, mm. 1\u201318.<\/figcaption><\/figure>\n<\/div>\n\n\n<figure class=\"wp-block-audio\"><audio controls src=\"https:\/\/theory.esm.rochester.edu\/integral\/wp-content\/uploads\/2024\/06\/fankhauser-vol37-audio-15.mp3\"><\/audio><figcaption class=\"wp-element-caption\"><strong>Example 15 Audio.<\/strong><\/figcaption><\/figure>\n\n\n\n<p><span style=\"font-weight: 400;\">The interval of transposition of Liszt\u2019s altered cadential six-four (down a major third to VI$$^{6}_{4}$$) is greater than that of Prokofiev (down a half step to $$\\flat$$I$$^{6}_{4}$$) or Shostakovich (down the equivalent of a minor third to $$\\flat\\flat$$vii$$^{6}_{4}$$). Yet, Liszt\u2019s submediant harmonic relation is more closely associated with tonic. By the early nineteenth century, the submediant had already become both a favored harmonic substitute for tonic and an agent of narrative, especially with use of $$\\flat$$VI in context of a major key. The cadential six-four of \u201cIl penseroso,\u201d therefore, crosses the syntax of a conventional cadential six-four with flat-submediant harmony that by 1839 was widely used in developments during heightened textual drama. Unlike the analysis of Prokofiev\u2019s and Shostakovich\u2019s chords as displaced versions of a cadential \u201cI$$^{6}_{4}$$,\u201d the analysis of Liszt\u2019s harmony as a submediant VI$$^{6}_{4}$$, retains a somewhat conventional harmonic relation, thereby fusing (confusing?) the underlying dominant function (V) with surface pre-dominant harmony (VI).<\/span><\/p>\n\n\n\n<p><span style=\"font-weight: 400;\">In the two Russian examples, each modified cadential six-four represents a harmonic relation that reaches farther from the tonic key, despite the smaller interval of transposition. Neither Prokofiev\u2019s nor Shostakovich\u2019s harmonic alteration of the cadential six-four fuses pre-dominant harmony with a conventional cadential dominant. Instead, their treatments sound more abstract and more harmonically detached. As the chords distance themselves from their conventional, functional pedigree, they become more reliant on rhetoric. These modified cadential six-four chords represent specific terms inserted as clich\u00e9s, with clear syntax but strange outward appearance. The mix of conventional syntax and odd vocabulary creates a quirky irony that simultaneously challenges yet satisfies tonal expectation.<\/span><span id='easy-footnote-26-9140' class='easy-footnote-margin-adjust'><\/span><span class='easy-footnote'><a href='https:\/\/theory.esm.rochester.edu\/integral\/37-2024\/fankhauser\/#easy-footnote-bottom-26-9140' title='The cadence in final measure of Prokofiev\u2019s March from &lt;em&gt;The Love for Three Oranges&lt;\/em&gt; op.&amp;nbsp;33 (Act 2, Rehearsal 173) similarly blends traditional syntax with a modified cadential six-four. The chords D\/A\u2013G\/F\u2013C on the surface may appear literally as V$$^{6}_{4}$$\/V\u2013V$$^{4}_{2}$$\u2013I in C major but function syntactically and more deeply as alterations of a conventional cadential six-four progression.'><sup>26<\/sup><\/a><\/span>\n\n\n\n<h2 class=\"wp-block-heading\">6. <strong>Alternative Transformations using Inversion and Transposition<\/strong><\/h2>\n\n\n\n<p><span style=\"font-weight: 400;\">The identity of the displaced cadential six-fours in this study relies heavily on their consistent intervals above the bass. Each chord\u2019s retention of the six-four figures through unusual transpositions from the conventional cadential six-four seems to contrast starkly with previous research into inversions of cadential six-four chords, in which voice leading places $$\\hat{1}$$ or $$\\hat{3}$$ in the bass. Yet, several of the examples above could be explained by taking a third path with two logical steps. This third pathway combines treatments of the two seemingly disparate alterations by first inverting the cadential six-four and then shifting one voice by step.&nbsp;<\/span><\/p>\n\n\n\n<p><span style=\"font-weight: 400;\">The two pathways\u2014a strict transposition of an entire six-four chord versus an inversion of the chord followed by a slight shift\u2014not only represent different means to the same harmonic goal; a difference also lies in the mappings of the individual pitches. Compare how the two logical pathways might derive the cadential six-four from Liszt\u2019s \u201cIl penseroso.\u201d In <strong>Figure 3a<\/strong>, the underlying conventional six-four (i$$^{6}_{4}$$ in E minor) is transposed in entirety down a third (VI$$^{6}_{4}$$), as discussed in Examples 9 and 10a. In <strong>Figure 3b<\/strong>, however, the underlying conventional six-four is first inverted (i$$^{6}_{4}$$ to i$$^{6}$$ in E minor) and then $$\\hat{5}$$ is shifted up to ($$\\flat$$)$$\\hat{6}$$ to yield the apparent VI$$^{6}_{4}$$.<\/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\/fankhauser-vol37-figure-3\/\"><img loading=\"lazy\" decoding=\"async\" width=\"2597\" height=\"1726\" src=\"https:\/\/theory.esm.rochester.edu\/integral\/wp-content\/uploads\/2024\/06\/fankhauser-vol37-figure-3.png\" alt=\"Fankhauser, Figure 3\" class=\"wp-image-9324\" style=\"width:440px;height:292px\" srcset=\"https:\/\/theory.esm.rochester.edu\/integral\/wp-content\/uploads\/2024\/06\/fankhauser-vol37-figure-3.png 2597w, https:\/\/theory.esm.rochester.edu\/integral\/wp-content\/uploads\/2024\/06\/fankhauser-vol37-figure-3-300x199.png 300w, https:\/\/theory.esm.rochester.edu\/integral\/wp-content\/uploads\/2024\/06\/fankhauser-vol37-figure-3-1024x681.png 1024w, https:\/\/theory.esm.rochester.edu\/integral\/wp-content\/uploads\/2024\/06\/fankhauser-vol37-figure-3-768x510.png 768w, https:\/\/theory.esm.rochester.edu\/integral\/wp-content\/uploads\/2024\/06\/fankhauser-vol37-figure-3-1536x1021.png 1536w, https:\/\/theory.esm.rochester.edu\/integral\/wp-content\/uploads\/2024\/06\/fankhauser-vol37-figure-3-2048x1361.png 2048w\" sizes=\"auto, (max-width: 706px) 89vw, (max-width: 767px) 82vw, 740px\" \/><\/a><figcaption class=\"wp-element-caption\"><b>Figure 3.<\/b> Two Pathways to the Displaced Cadential Six-Four in Liszt\u2019s \u201cIl penseroso\u201d<\/figcaption><\/figure>\n<\/div>\n\n\n<p><span style=\"font-weight: 400;\"><strong>Table 2<\/strong> reconsiders some specific examples to determine how this third path leads to each displaced cadential six-four. Similar to the complications discussed in Shostakovich\u2019s Prelude (Example 14) of inferring missing roots and adjusting an upper voice, I find this logic overly complicated and less musical than the simpler syntactical association as vertically displaced cadential six-fours.<\/span><\/p>\n\n\n\n<figure class=\"wp-block-table is-style-regular\"><table><tbody><tr><td><strong>Example<\/strong><\/td><td><strong>Mapping using Inversion and Shift<\/strong><\/td><\/tr><tr><td>Beatles, \u201cJulia\u201d (Example 7)&nbsp;&nbsp;<\/td><td>In D major, invert major cadential I$$^{6}_{4}$$ to I.<br>&nbsp;&nbsp;&nbsp;&nbsp;Then, shift $$\\hat{1}$$ to $$\\hat{7}$$ to create iii$$^{6}_{4}$$.<\/td><\/tr><tr><td>Brahms, Waltz (Example 8)<\/td><td>In E major, invert major cadential I$$^{6}_{4}$$ to I.<br>\u2003Then, shift $$\\hat{1}$$ to $$\\hat{7}$$ to create iii$$^{6}_{4}$$.<\/td><\/tr><tr><td>Liszt, \u201cIl penseroso\u201d <br>\u2003(Examples 9 and 10<br>\u2003and Figure 3)<\/td><td>In E minor, invert minor cadential i$$^{6}_{4}$$ to i$$^{6}$$.<br><nobr>\u2003Then, shift $$\\hat{5}$$ to $$\\hat{6}$$ to create VI$$^{6}_{4}$$.<\/nobr><\/td><\/tr><tr><td><nobr>Shostakovich, Piano Prelude<\/nobr><br>\u2003(Example 14)<\/td><td>In C$$\\sharp$$ minor, invert a major cadential I$$^{6}_{4}$$ to I$$^{6}$$ (E$$\\sharp$$ in bass).<br><nobr>\u2003Then, shift $$\\hat{5}$$ to $$\\sharp\\hat{6}$$ to create $$\\sharp$$vi$$^{6}_{4}$$ and spell enharmonically as $$\\flat\\flat$$vii$$^{6}_{4}$$.<\/nobr><\/td><\/tr><\/tbody><\/table><figcaption class=\"wp-element-caption\"><strong>Table 2.<\/strong> Alternative Transformations in Previous Examples&nbsp; using Inversion and a Shift<\/figcaption><\/figure>\n\n\n\n<h2 class=\"wp-block-heading\"><strong>7. Limits of Cadential Six-Four Deviations<\/strong><\/h2>\n\n\n\n<p><span style=\"font-weight: 400;\">The limits to how an altered chord can function as a cadential six-four are not easily defined, due in part to some overlap between pre-dominant function and cadential six-four function, and, perhaps moreover, due to the dependence of chord function on listener perception. The casual statement that a conventional cadential six-four \u201cresolves to a root-position dominant\u201d is inaccurate. Analysis tends to regard a conventional cadential six-four as a root-position dominant itself with two upper voices displaced (to the sixth and fourth). Displaced cadential six-fours in this article further shift individual voices within the dominant harmony to include other intervals or changes in the bass. Increasing displacement diminishes the apparent dominant function, and, insofar as it delays and leads to a more apparent dominant, it adopts a more pre-dominant role. The fewer of the criteria of the cadential six-four that are satisfied, the less the chord functions as a cadential six-four. The extent to which inverted, non-tonic harmonies are capable of expressing cadential six-four function remains a challenge both to theory and analysis. Complicating the issue is the dependence on the analyst\u2019s perception and attenuation to specific elements of the music.&nbsp;<\/span><\/p>\n\n\n\n<p><span style=\"font-weight: 400;\">Consider two examples. Example 1 showed how the second phrase in Wagner\u2019s \u201cEvening Star\u201d reversed conventional, relative accentuation by placing a cadential six-four on a weak beat prior to its more strongly accented resolution. Similarly, the first phrase presents a chord closely associated with cadential six-four function. A reduction of the phrase is shown in <strong>Example&nbsp;16a<\/strong>. Following supertonic harmony on the second hyperbeat, a chromatic $$\\flat$$III$$^{6}$$ falls on the strong third hyperbeat of the first phrase and resolves to the cadential dominant in the second half (the \u201c&amp;\u201d) of hyperbeat 3. The bass holds the dominant pitch ($$\\hat{5}$$) from the $$\\flat$$III$$^{6}$$ into V, and the melody descends from a sixth to a fifth above the bass ($$\\flat\\hat{3}$$\u2013$$\\hat{2}$$).<\/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\/fankhauser-vol37-example-16\/\"><img loading=\"lazy\" decoding=\"async\" width=\"2935\" height=\"2579\" src=\"https:\/\/theory.esm.rochester.edu\/integral\/wp-content\/uploads\/2024\/06\/fankhauser-vol37-example-16.png\" alt=\"Fankhauser, Example 16\" class=\"wp-image-9321\" style=\"width:512px;height:450px\" srcset=\"https:\/\/theory.esm.rochester.edu\/integral\/wp-content\/uploads\/2024\/06\/fankhauser-vol37-example-16.png 2935w, https:\/\/theory.esm.rochester.edu\/integral\/wp-content\/uploads\/2024\/06\/fankhauser-vol37-example-16-300x264.png 300w, https:\/\/theory.esm.rochester.edu\/integral\/wp-content\/uploads\/2024\/06\/fankhauser-vol37-example-16-1024x900.png 1024w, https:\/\/theory.esm.rochester.edu\/integral\/wp-content\/uploads\/2024\/06\/fankhauser-vol37-example-16-768x675.png 768w, https:\/\/theory.esm.rochester.edu\/integral\/wp-content\/uploads\/2024\/06\/fankhauser-vol37-example-16-1536x1350.png 1536w, https:\/\/theory.esm.rochester.edu\/integral\/wp-content\/uploads\/2024\/06\/fankhauser-vol37-example-16-2048x1800.png 2048w\" sizes=\"auto, (max-width: 706px) 89vw, (max-width: 767px) 82vw, 740px\" \/><\/a><figcaption class=\"wp-element-caption\"><b>Example 16.<\/b> Reduction and Normalization of Wagner, \u201cSong of the Evening Star\u201d (mm. 5\u20138).<\/figcaption><\/figure>\n<\/div>\n\n\n<figure class=\"wp-block-audio\"><audio controls src=\"https:\/\/theory.esm.rochester.edu\/integral\/wp-content\/uploads\/2024\/06\/fankhauser-vol37-audio-16a.mp3\"><\/audio><figcaption class=\"wp-element-caption\"><strong>Example 16a Audio.<\/strong><\/figcaption><\/figure>\n\n\n\n<figure class=\"wp-block-audio\"><audio controls src=\"https:\/\/theory.esm.rochester.edu\/integral\/wp-content\/uploads\/2024\/06\/fankhauser-vol37-audio-16b.mp3\"><\/audio><figcaption class=\"wp-element-caption\"><strong>Example 16b Audio.<\/strong><\/figcaption><\/figure>\n\n\n\n<p><span style=\"font-weight: 400;\">The rise in the accompaniment from the subtonic F$$\\natural$$ to the leading tonic F$$\\sharp$$ in the dominant counters conventional usage. This upward $$\\natural$$3\u2013$$\\sharp$$3 figure above the dominant could be interpreted as a kind of inverted 4\u20133 intervallic motion found in the conventional cadential six-four in the approach to the leading tone, with F$$\\natural$$ substituting for G. The conventional six-four in the subsequent phrase \u201ccorrects\u201d the earlier displaced six-four simply by replacing the upward $$\\natural$$3\u2013$$\\sharp$$3 inner voice motion with 4\u20133 and thereby strengthens their correlation.<\/span><\/p>\n\n\n\n<p><span style=\"font-weight: 400;\">Wagner\u2019s cadential $$\\flat$$III$$^{6}$$ here deviates from conventional cadential six-fours both in harmony, as a chromatically altered mediant, and in voice leading, with the ascending chromatic approach to the third of the dominant. This contrapuntal alteration stems not from inversion of six-four chords as seen in earlier examples, however, but from voice leading in a single inner voice. The F$$\\natural$$ in the line, D\u2013E\u2013F$$\\natural$$\u2013F$$\\sharp$$\u2013G, makes the alteration of six-four necessary. <strong>Example 16b<\/strong> replaces the F$$\\natural$$ with a G (D\u2013E\u2013G\u2013F$$\\sharp$$\u2013G), creating a conventional cadential six-four and, as a result, demonstrating how unsatisfactory that conventional chord would have been. Wagner\u2019s F$$\\natural$$ not only forms a momentary B$$\\flat$$-major triad, which makes the resolution to E$$\\flat$$ ($$\\flat$$VI) less distant or deceptive; the F$$\\natural$$ also makes the inner voice\u2019s line an inversion of the melody (C\u2013B\u2013B$$\\flat$$\u2013A\u2013G), with the two lines converging into the G. <\/span><\/p>\n\n\n\n<p><span style=\"font-weight: 400;\">To include $$\\flat$$III$$^{6}$$ in Example 6 as an inverted displaced cadential six-four chord, such as in the progression I\u2013IV\u2013$$\\flat$$III$$^{6}$$\u2013V\u2013I, may push the connection between the chromatic chord and the conventional cadential six-four chord too far. On one hand, if cadential six-four chords can retain function either under inversion, as previous authors have shown, or under transposition of the whole chord, as I have argued, then it might follow that cadential six-four chords can retain function under both transposition <\/span><i><span style=\"font-weight: 400;\">and<\/span><\/i><span style=\"font-weight: 400;\"> inversion. On the other hand, so many chords would fall into that category that it would stretch the concept of a cadential six-four quite thin. Not every chord that falls on a strong beat relative to the cadential dominant derives from an underlying cadential six-four. Accenting the third chords in the progressions I\u2013IV\u2013vii$$^{\\circ7}$$\/V\u2013V\u2013I or I\u2013IV$$^{6}$$\u2013Gr$$^{+6}$$\u2013V\u2013I, for example, highlights some characteristics shared with cadential six-four chords\u2014all of which include $$\\hat{3}$$\u2013$$\\hat{2}$$ and $$\\hat{1}$$\u2013$$\\hat{7}$$ resolutions!\u2014but to view the cadential six-four as their ancestor expands of the concept widely and perhaps inappropriately. Still, to make the comparison reveals voice-leading and syntactical similarity that transcends Roman numeral analysis. <\/span><\/p>\n\n\n\n<h2 class=\"wp-block-heading\"><strong>8. Partial Closure<\/strong><\/h2>\n\n\n\n<p><span style=\"font-weight: 400;\">All of the altered cadential six-four chords above deviate in some way from convention. Their degree of deviation ranges from minor departures (as in the weak cadential six-four in Wagner\u2019s \u201cEvening Star\u201d in Example 1), to inversions (as in Brahms\u2019s Symphony in Example&nbsp;3), to quite unusual harmonic alterations (as in Liszt\u2019s \u201cIl penseroso,\u201d in Example&nbsp;9). This last category represents the most significant challenge to the definition of the cadential six-four. Lennon\u2019s apparent iii$$^{6}_{4}$$ and Liszt\u2019s apparent VI$$^{6}_{4}$$ function as cadential six-fours despite their transposition and harmonic shift from dominant to other, seemingly non-dominant <\/span><i><span style=\"font-weight: 400;\">Stufen<\/span><\/i><span style=\"font-weight: 400;\">. Six-fours in the Prokofiev and Shostakovich examples similarly preserve underlying conventional syntax and dominant function of the cadential six-four, despite the unusual harmonic relations caused by their chromatic transpositions. The latter examples in particular illustrate the rhetorical power of the cadential six-four chord to persist as a signal of closure even as composers twist conventional tonal syntax nearly to the point of fracture. <\/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\n<p>Aldwell, Edward and Carl Schachter with Allen Cadwallader. 2011. <em>Harmony and Voice Leading<\/em>. 4<sup>th<\/sup> ed. Boston: Schirmer.<\/p>\n\n\n\n<p>BaileyShea, Matthew L. 2012. \u201cMusical Forces and Interpretation: Some Thoughts on a Measure in Mahler.\u201d <em>Music Theory Online<\/em> 18 (3).&nbsp;<\/p>\n\n\n\n<p>Bass, Richard. 1988. \u201cProkofiev\u2019s Technique of Chromatic Displacement.\u201d <em>Music Analysis<\/em> 7 (2): 197\u2013214.<\/p>\n\n\n\n<p>Beach, David. 1967. \u201cThe Functions of the Six-Four Chord in Tonal Music.\u201d<em> Journal of Music Theory<\/em> 11 (1): 2\u201331.<\/p>\n\n\n\n<p>\u2014\u2014\u2014. 1990. \u201cMore on the Six-Four.\u201d <em>Journal of Music Theory<\/em> 34 (2): 281\u2013290.<\/p>\n\n\n\n<p>\u2014\u2014\u2014. 1992. \u201cThe Cadential Six-Four as Support for Scale-Degree Three of the Fundamental Line.\u201d <em>Journal of Music Theory<\/em> 34 (1): 81\u201399.&nbsp;<\/p>\n\n\n\n<p>Brown, Matthew. 1986. \u201cThe Diatonic and the Chromatic in Schenker\u2019s Theory of Harmonic Relations.\u201d <em>Journal of Music Theory<\/em> 30 (1): 1\u201333.<\/p>\n\n\n\n<p>Burstein, L. Poundie. 1999. \u201cComedy and Structure in Haydn\u2019s Symphonies.\u201d In <em>Schenker Studies<\/em> 2, ed. Carl Schachter and Hedi Siegel, 67\u201381. New York: Cambridge University Press.<\/p>\n\n\n\n<p>Cadwallader, Allen. 1992. \u201cMore on Scale Degree Three and the Cadential Six-Four.\u201d <em>Journal of Music Theory<\/em> 36 (1): 187\u2013198.<\/p>\n\n\n\n<p>Cohn, Richard. 2012. <em>Audacious Euphony: Chromaticism and the Triad\u2019s Second Nature.<\/em> New York: Oxford University Press.&nbsp;<\/p>\n\n\n\n<p>Cutler, Timothy. 2009. \u201cOn Voice Exchanges.\u201d <em>Journal of Music Theory<\/em> 53 (2): 191\u2013226.<\/p>\n\n\n\n<p>Damschroder, David. 1990. \u201cLiszt\u2019s Composition Lessons from Beethoven (Florence, 1838-1839): <em>Il penseroso<\/em>.\u201d<em> Journal of the American Liszt Society <\/em>28: 3\u201319.&nbsp;<\/p>\n\n\n\n<p>\u2014\u2014\u2014. 2008. <em>Thinking about Harmony: Historical Perspectives on Analysis<\/em>. New York: Cambridge University Press.<\/p>\n\n\n\n<p>Drabkin, William. 1996. \u201cSchenker, the Consonant Passing Note, and the First-Movement Theme of Beethoven\u2019s Sonata Op. 26.\u201d <em>Music Analysis<\/em> 15 (2\/3): 149\u2013189.&nbsp;<\/p>\n\n\n\n<p>Everett, Walter. 2009. <em>The Foundations of Rock: From \u201cBlue Suede Shoes\u201d to \u201cSuite: Judy Blue Eyes.\u201d<\/em> New York: Oxford University Press.&nbsp;<\/p>\n\n\n\n<p>Fankhauser, Gabriel. 2006. \u201cFlat Primary Triads, Harmonic Refraction, and the Harmonic Idiom of Shostakovich and Prokofiev.\u201d In <em>Musical Currents from the Left Coast<\/em>, ed. Bruce Quaglia and Jack Boss, 202\u2013215. Cambridge: Cambridge Scholars Publishing.&nbsp;<\/p>\n\n\n\n<p>\u2014\u2014\u2014. 2013. \u201cCadential Intervention in the Finale of Shostakovich\u2019s Piano Trio in E Minor, Op.&nbsp;67.\u201d <em>Music Analysis<\/em> 32 (2): 210\u2013250.<\/p>\n\n\n\n<p>Forte, Allen and Steven E. 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New York: Cambridge University Press.White, Christopher WM and Ian Quinn. 2018. \u201cChord Context and Harmonic Function in Tonal Music.\u201d <em>Music Theory Spectrum<\/em> 40, 2: 314\u2013335.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Gabriel Fankhauser Abstract Building on research into the efficacy of inverted cadential six-four chords, this article proposes that some unconventional harmonies function as cadential six-fours. Considering a cadential six-four chord\u2019s syntactical role more than its surface harmony or voice leading, this article identifies remarkable treatments that defy traditional analysis. Some examples of chromatically displaced cadential &hellip; <\/p>\n<p class=\"link-more\"><a href=\"https:\/\/theory.esm.rochester.edu\/integral\/37-2024\/fankhauser\/\" class=\"more-link\">Continue reading<span class=\"screen-reader-text\"> &#8220;Displaced Cadential Six-Four Chords&#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-9140","page","type-page","status-publish","hentry"],"_links":{"self":[{"href":"https:\/\/theory.esm.rochester.edu\/integral\/wp-json\/wp\/v2\/pages\/9140","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=9140"}],"version-history":[{"count":117,"href":"https:\/\/theory.esm.rochester.edu\/integral\/wp-json\/wp\/v2\/pages\/9140\/revisions"}],"predecessor-version":[{"id":11692,"href":"https:\/\/theory.esm.rochester.edu\/integral\/wp-json\/wp\/v2\/pages\/9140\/revisions\/11692"}],"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=9140"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}