The Double-Tonic Complex and Yavorsky’s Mutability
by
Chad Scarborough, B.A.
A Thesis
In
Music Theory
Submitted to the Graduate Faculty of Texas Tech University in Partial Fulfillment of the Requirements for the Degree of
MASTER OF MUSIC
Approved
David Forrest, PhD. Chair of Committee
Matthew Santa, PhD.
Peter Martens, PhD.
Mark Sheridan Dean of the Graduate School
May, 2019
Copyright 2019, Chad Scarborough
Texas Tech University, Chad Scarborough, May 2019
Table of Contents
Abstract ...... iv
List of Tables ...... v
List of Figures ...... vi
List of Abbreviations ...... ix
CHAPTER I: Introduction ...... 1
Literature Review...... 2
Limitations of Roman-numeral analysis ...... 5
CHAPTER II: Yavorsky’s Theory of Modal Rhythm ...... 7
Harmonic aspects Yavorsky’s theory ...... 7
Benefits of Yavorsky’s system in Russian music ...... 16
Limitations of Yavorsky’s system in Popular music ...... 21
CHAPTER III: Neo-Yavorskian Theory ...... 26
Problems with Yavorsky’s theory ...... 26
Details of the neo-Yavorskian system ...... 29
The neo-Yavorskian system and the basic phrase model ...... 37
A note about tonicization of non-tonic chords ...... 43
More than two tonics ...... 44
CHAPTER IV: Long-Form Analysis...... 48
“Блажен Муж (Blessed is the Man)” from All-Night Vigil by Sergei Rachmaninoff ...... 48
“Trisagion” by Georgy Sviridov ...... 56
“Oh Sherrie” by Steve Perry ...... 62
“Building a Mystery” by Sarah McLachlan...... 71 ii
Texas Tech University, Chad Scarborough, May 2019
Conclusion ...... 74
Bibliography ...... 76
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Texas Tech University, Chad Scarborough, May 2019
Abstract
Robert Bailey (1985) uses the term “double-tonic complex” to describe a pairing of two relative keys into one larger sense of tonic. Scholars have explored this topic, along with multiple closely related topics, in the realms of Russian art music (Bakulina
2014, Brown 2009, DeVoto 1995, McQuere 2009) as well as Western Popular music
(Nobile 2017, Richards 2017, Spicer 2017). In this paper, I discuss the idea of the double- tonic complex (also known as “mutability,” “emergent tonic”) in the context of both
Russian art music and Western Popular music. I then develop and demonstrate a theory of analysis based on the harmonic aspects of Boleslav Yavorsky’s Theory of Modal
Rhythm.
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Texas Tech University, Chad Scarborough, May 2019
List of Tables
3.1: Equivalent labels and terms in Yavorskian and neo-Yavorskian systems...... 27
4.1: “Блажен Муж” – Graph of tonics present (* = аллилуйиа refrain) ...... 49
4.2: “Trisagion” – Tonics present across each strophe ...... 57
4.3: Formal chart of “Oh Sherrie” V = Verse; PC = Pre-chorus; C = Chorus ...... 63
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Texas Tech University, Chad Scarborough, May 2019
List of Figures
1.1: Sergei Rachmaninoff – All-Night Vigil mvt. 3, “Блажен Муж (Blessed is the Man)” m. 1 ...... 5
2.1: Single Symmetrical System ...... 8
2.2: Double Symmetrical System ...... 9
2.3: Elementary combinations and modes ...... 10
2.4: McQuere’s realization of Yavorsky’s resolutions ...... 13
2.5: Glinka, A Life for the Tsar, Act I, Introduction, mm. 8-22...... 18
2.6: Variable Mode 1 ...... 18
2.7: Variable Mode 2 ...... 19
2.8: Sergei Rachmaninoff – All-Night Vigil mvt. 3, “Блажен Муж (Blessed is the Man)” m. 14 ...... 20
2.9: Changing function relative to register ...... 21
2.10: “One of Us” chorus, transc. By Mark Richards ...... 22
2.11: Analysis of Axis progression ...... 24
2.12: The mode implied by the Axis progression according to Yavorsky’s system...... 24
3.1: Axis progression – A-form with Yavorskian analysis ...... 28
3.2: Tension formula ...... 31
3.3: Example resolution ...... 32
3.4: Chords with dominant-function labels ...... 33
3.5: Dominant function in major and minor keys ...... 34
3.6: Two possible harmonic progressions ...... 37
3.7: Aleksandr Borodin – “Polovetsian Dances” from Prince Igor, mm. 16-19 ...... 38
3.8: The Beatles – “She Loves You” intro ...... 41
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3.9: Aleksandr Borodin – “Солнцу Красному Слава” mm. 126-132 ...... 42
3.10: Analysis of progression with secondary dominant chords ...... 44
3.11: Circle of Thirds ...... 45
3.12: Sergei Rachmaninoff – All-Night Vigil, “Blazehn Muzh,” m. 14 ...... 46
3.13: Circle of Thirds representation of tonic motion from Figure 3.12 ...... 47
4.1: “Блажен Муж,” m. 1 ...... 50
4.2: “Блажен Муж,” m. 2 ...... 51
4.3: “Блажен Муж,” m. 6 ...... 52
4.4: “Блажен Муж,” m. 8 ...... 53
4.5: “Блажен Муж,” m. 10 ...... 54
4.6: “Блажен Муж,” m. 14 ...... 55
4.7: “Блажен Муж,” m. 17 ...... 56
4.8: “Trisagion” Strophe 1 (mm. 1-4) ...... 58
4.9: “Trisagion” Strophe 2 (mm. 5-8) ...... 59
4.10: “Trisagion” Strophe 3 (mm. 9-12) ...... 59
4.11: “Trisagion” Strophe 4 (mm. 13-16) ...... 60
4.12: “Trisagion” Strophe 5 (mm. 17-20) ...... 61
4.13: “Trisagion” Strophe 6 (mm. 21-24) ...... 62
4.14: “Oh Sherrie” – Chorus ...... 64
4.15: “Oh Sherrie” – Verse 2 ...... 65
4.16: “Oh Sherrie” – Verse 1 ...... 66
4.17: “Oh Sherrie” – Pre-chorus ...... 68
4.18: “Oh Sherrie” – Verse 3 ...... 69
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4.19: “Oh Sherrie” – Introduction ...... 71
4.20: “Building a Mystery” – Verse ...... 73
4.21: “Building a Mystery” – Chorus ...... 73
4.22: “Building a Mystery” – Pre-chorus ...... 73
4.23: “Building a Mystery” structural reduction based on Nobile 2019...... 74
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List of Abbreviations
D – Dominant (Yavorsky)/Major Dominant (neo-Yavorsky) d – Subdominant (Yavorsky)/Minor Dominant (neo-Yavorsky)
DSS – Double Symmetrical System
S - Subtonic
SSS – Single Symmetrical System
T – Tonic (Yavorsky)/Major Tonic (neo-Yavorsky) t – Minor Tonic
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The Double-Tonic Complex and Yavorsky’s Mutability
CHAPTER I
Introduction
The common system of Roman-numeral analysis works well for music in the
Western common-practice style. It allows for a fairly deep understanding of music for a process so relatively simple due to that style’s consistent reliance on a single tonic.
However, there exists music—particularly in the Russian tradition as well as in Western popular music—which does not always display such a simple concept of tonic, and which instead suggests a richer tonic complex. This complex most often appears in the form of overlapping triads a third apart. Roman-numeral analysis can reveal important harmonic information about these musics, but its usefulness is limited by the necessary condition that a single tonic be chosen for the analysis. To address this issue, I propose an alternate analysis system based on the work of Russian music theorist, Boleslav Yavorsky. In this neo-Yavorskian system, tonic function can be assigned to multiple triads a diatonic third apart from each other, and all other sonorities are classified based on the relative strengths of their resolutions, and potential resolutions, to those tonics. The result is a system which can identify patterns in these musics previously invisible to the Roman- numeral analysis system.
In this paper, I argue for the value of such a system by demonstrating the relevant flaws of Roman-numeral analysis in certain passages, describing in detail the inner
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Texas Tech University, Chad Scarborough, May 2019 workings of the neo-Yavorskian system, and demonstrating its utility through analysis of both 19th-century Russian music and Western Popular music. Chapter 1 reviews the current scholarship on the topic of double-tonic complexes and demonstrates the limitations of Roman-numeral analysis in certain musical examples. Chapter 2 describes
Yavorsky’s original theory as a useful starting point for the analysis of double-tonic complexes and demonstrates aspects of the system which need improvement. Chapter 3 adapts Yavorsky’s theory into a neo-Yavorskian system which is equally capable of analyzing both Russian music and Western popular music. Chapter 4 demonstrates the capabilities of this neo-Yavorskian system through practical analyses of several pieces of music which feature double-tonic complexes.
The neo-Yavorskian theory proposed here will address a significant gap in the current theoretical scholarship surrounding both Russian music and Western Popular music. Both sets of scholarship have acknowledged the existence of music featuring some form of double-tonic complex, and I have designed the neo-Yavorskian system to be an equally appropriate analytical system for both styles. Therefore, this paper will serve as a bridge linking two previously disparate fields of scholarship with a common analytical system.
Literature Review
The analytical system I propose is built on two streams of scholarship: one dealing with Russian music and one dealing with Western Popular music. Both streams of research cite Robert Bailey’s analysis of Richard Wagner’s Prelude and
Transfiguration from Tristan and Isolde, which describes the idea of a “double-tonic
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Texas Tech University, Chad Scarborough, May 2019 complex.”1 According to Bailey, a double-tonic complex is a pairing of two relative keys in such a way that they articulate a broader sense of tonal center than either individual key. Bailey limits this phenomenon to two keys, and only keys which serve as each other’s relative major/minor. The neo-Yavorskian system I propose here expands on
Bailey’s work by allowing any number of keys may be connected to each other, so long as they are all related by diatonic third.
In the realm of Russian music, the most valuable resource for my research has been the work of Gordon McQuere. McQuere’s chapter, “The Theories of Boleslav
Yavorsky,” effectively summarizes Yavorsky’s Theory of Modal Rhythm while his doctoral dissertation serves as the first complete English translation of Yavorsky’s theory.23 This paper uses McQuere’s work as a starting point for developing the neo-
Yavorskian system. Two more valuable resources regarding multiple tonics are Ellen
Bakulina’s doctoral dissertation and Marc DeVoto’s article, “The Russian Submediant in the Nineteenth Century.”45 Both of these sources provide in-depth descriptions of the nature of various types of multiple tonics in Russian music. Bakulina’s dissertation, much like McQuere’s chapter, discusses Yavorsky’s theories regarding the construction of
1 Robert Bailey, Richard Wagner: Prelude and Transfiguration from “Tristan and Isolde” (New York: Norton, 1985), 121-2. 2 Gordon McQuere, “The Theories of Boleslav Yavorsky,” in Russian Theoretical Thought in Music, ed. Gordon McQuere (Ann Arbor: University of Michigan Press 1983), 109-164. 3 Sergeĭ Protopopov and Gordon McQuere, The Elements of the Structure of Musical Speech (Iowa City: University of Iowa Press 1978). The word “rhythm” in this context does not necessarily refer to rhythm in the way it is commonly understood. Rather, it refers to Yavorsky’s system for understanding tension and resolution. 4 Ellen Bakulina, The Problem of Tonal Disunity in Sergei Rachmaninoffs "All-Night Vigil," Op. 37. (New York: City University of New York Press 2015). Bakulina transliterates Yavorsky’s name differently from how it is presented in this paper, opting to use “Iavorskiĭ” instead. 5 Marc DeVoto, “The Russian Submediant in the Nineteenth Century” in Current Musicology 59 (1995): 48-76. 3
Texas Tech University, Chad Scarborough, May 2019 modes with multiple tonics. DeVoto’s article demonstrates multiple ways in which
Russian composers have emphasized the submediant in their music in such a way that it has become a defining characteristic of the Russian musical ethos. This paper borrows some of their terminology and examples in the discussion of double-tonic complexes in
Russian music.
Drew Nobile’s article “Double-Tonic Complexes in Rock Music” applies the same ideas present in Russian music scholarship to Western Popular music.6 An early version of this article served as the inspiration to combine Russian and Western Popular music research under a unified theory. This article is one of the strongest voices for the analysis of double-tonic complexes in Popular music. Another important resource for this project has been Mark Richards’ article, “Tonal Ambiguity in Popular Music’s Axis
Progressions.”7 This article describes tonality in some popular music in a way that resonates with the Russian scholarship cited above. It suggests that common progressions in Popular music can contribute to tonal ambiguity between relative keys. Adding to
Richards’ observations, the neo-Yavorskian system provides a useful method for explaining the tonal intricacies of the Axis progression. Nicole Biamonte describes chord progressions in rock music which diverge from common-practice norms.8 Her discussion of these progressions opens the door for recognizing dominant function in a variety of chords other than V and viio. This paper expands this idea into a full hierarchy of strength
6 Drew Nobile, “Double-Tonic Complexes in Rock Music” in Music Theory Spectrum, forthcoming. 7 Mark Richards, “Tonal Ambiguity in Popular Music’s Axis Progression” in Music Theory Online, 23, no. 3 (2017), http://mtosmt.org/issues/mto.17.23.3/mto.17.23.3.richards.html. 8 Nicole Biamonte, “Triadic Modal and Pentatonic Patterns in Rock Music” in Music Theory Spectrum 32, no. 2 (2010), 95-110. doi:10.1525/mts.2010.32.2.95. 4
Texas Tech University, Chad Scarborough, May 2019 in terms of dominant function, allowing all non-tonic chords to demonstrate dominant function to some degree.
Limitations of Roman-numeral analysis
A clear example of a double-tonic complex presents itself in the first measure of the third movement of Sergei Rachmaninoff’s All-Night Vigil (Figure 1.1). This measure represents a tonal peculiarity which is present throughout the entire movement—a sort of coexistence of F major and D Aeolian (which I hereafter refer to as D minor for the sake of simplicity). This peculiarity exposes the limitations of Roman-numeral analysis. The analyses below the staves help to demonstrate the analytical challenges in this passage.
Figure 1.1: Sergei Rachmaninoff - All-Night Vigil mvt. 3, "Блажен Муж (Blessed is the Man)" m.1
The D-minor analysis, shown in the first line below the staves in Figure 1.1, appears promising because the phrase begins and ends on the tonic chord. However, the phrase spends most of its time alternating between VII and III, two of the most distant diatonic chords from tonic. The significant amount of time spent around these chords weakens the sense of D minor tonality. These chords are much more at home in the key of F major, where they simply alternate between dominant and tonic function. One might 5
Texas Tech University, Chad Scarborough, May 2019 also notice that the melody in the upper alto line suggests an F-major center, beginning and ending on F and taking all of its melodic pitches from the F major pentachord. These points build a strong argument for F major being the tonal center of the phrase, but for the initial and final D-minor chords. A third option would be to analyze modulations between
D minor and F major. However, this passage seems to display less of a tension or journey between D and F than a marriage of the two. The excerpt never arrives at F major, but rather passes through it between the initial and final instances of D minor, never reaching a cadence in F major. As such, the tonality never truly switches from D minor to F major and back again. Individually the D-minor and the F-major interpretations can each effectively describe different parts of the phrase, but neither captures the harmonic syntax of the phrase as a whole. As mentioned above, this tonal peculiarity continues for the entirety of the movement. The problem of analyzing this piece and others like it lies not in the music, but rather in our analytical systems. Roman- numeral analysis forces the analyst to choose a single tonal center in the form of a major or minor triad in order to analyze a given piece of music. This approach works well for most Western common-practice music, but it has the potential to break down once the sense of tonic becomes more complex. The Rachmaninoff piece excerpted in Figure 1.1, for example, exhibits a richer sense of tonic than D minor or F major alone convey. The neo-Yavorskian approach described in this thesis is specifically designed to address these analytical challenges.
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Texas Tech University, Chad Scarborough, May 2019
CHAPTER II
Yavorsky’s Theory of Modal Rhythm
Harmonic aspects Yavorsky’s theory
In order to understand the neo-Yavorskian system, this chapter will describe
Yavorsky’s approach to understanding tonality through the construction of modes. A thorough review of Yavorsky’s theories is beyond the scope of this paper, therefore this chapter will focus on the aspects most relevant to the current thesis. This chapter begins by discussing Yavorsky’s concepts of harmonic function via the symmetrical systems, followed by a demonstration of his system’s ability to identify multiple tonics in a given piece of music. The chapter concludes by showing various problems with Yavorsky’s system which make it less than ideal for all types of analysis.
Yavorsky’s Theory of Modal Rhythm describes of the construction of modes based on the resolutions of tritones.9 In this system, tritones resolve via one of two methods to either a major third or a minor third. The tritone forms the unstable part of the system, and the resultant major or minor third the stable part. Yavorsky describes modes as an overlapping stack of two or more stable thirds filled in with the unstable tritones which resolve to those thirds. As a result of this structure, the stable tones generally perform tonic function, and the unstable tones generally perform dominant function.
Yavorsky describes two methods of resolving tritones, which he calls the
“symmetrical systems.” The single symmetrical system (SSS) consists of a tritone and its
9 A more thorough description of Yavorsky’s theories can be found in McQuere 2009 and Bakulina 2015. 7
Texas Tech University, Chad Scarborough, May 2019 resolution by half-step in opposite, “symmetrical” directions to either a major third or minor sixth. Yavorsky labels the unstable part of the SSS “D” for “dominant,” which shares its meaning with the same term in common Western parlance. This unstable dominant then resolves to the stable tonic, labelled “T.” In Yavorsky’s system, “T” always represents a major third or its inversion, and is always a part of the SSS. This system is shown in Figure 2.1. The unstable tones are represented by black note heads, and the stable tones are represented by open note heads.
Figure 2.1: Single Symmetrical System10
The double symmetrical system (DSS) consists of a perfect fifth resolving inward symmetrically by whole step to a stable minor third. The unstable portion of the DSS is labelled ‘S’ for “subdominant,” and the stable portion is labelled ‘t,’ read “subtonic.” The complete form of the DSS is shown in Figure 2.2a. Though the perfect fifth is consonant, it is still unstable in Yavorsky’s system because it does not, in this case, perform tonic function. Consonance and stability are not necessarily related. Additionally, one may notice that this system does not produce any overt tritones. The initial perfect fifth resolves inward to a minor third through an enharmonic respelling of a perfect fourth
(spelled as a doubly diminished fifth in Figure 2.2a and 2.2d). However, this resolution
10 This figure and all other figures Demonstrating Yavorsky’s symmetrical systems are adapted from McQuere, Russian Theoretical Thought. 8
Texas Tech University, Chad Scarborough, May 2019 does imply two tritones which each only partially resolve. Each pitch of the intermediary doubly diminished fifth forms a tritone with one of the pitches of the initial perfect fifth.
In Figure 2.2a, the A♭ forms a tritone with the initial D, and the D# forms a tritone with the initial A. Figure 2.2b shows how each of these tritones would normally resolve inward by half-step, each producing one of the pitches belonging to the stable portion of the DSS. The slurs in Figure 2.2b mark pitches which are enharmonically equivalent.
Though the implied tritones do not always appear in real music, Yavorsky believes that we nonetheless perceive them from a functional standpoint. Figure 2.2c shows the DSS as it most commonly appears. Figure 2.2d shows a more idealized version of the DSS, where both initial unstable pitches resolve inward by half-step, mirroring the SSS.
a) b) c) d)
Figure 2.2: Double Symmetrical System
The terms “subdominant” and “subtonic” as they apply to the DSS are unrelated to the same terms in Western music theory. They do not refer to specific scale degrees nor to chords built on those scale degrees. Rather, these terms exist as the DSS analog to
“dominant” and “tonic” as they are used with respect to the SSS. When a symmetrical system resolves to a stable major third, that major third is tonic and the unstable tritone which resolves to it is dominant. Likewise, when a symmetrical system resolves to a stable minor third, that minor third is subtonic, and the unstable sonority which resolves
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Texas Tech University, Chad Scarborough, May 2019 to it is subdominant. This naming system does create some issues, which are discussed in detail later.
Yavorsky combines the stable portions of the single and double systems into a triad. Yavorsky refers to these stable triads as “elementary combinations.” McQuere says
“an elementary combination uses one single and one double system that share a stable tone.” This elementary combination is sufficient to define a heptatonic mode, considering both the stable and unstable portions, as shown in Figure 2.3.
Figure 2.3: Elementary combinations and modes
Figure 2.3 shows how Yavorsky defines the major and minor modes on the top and bottom lines, respectively. As Figure 2.3 demonstrates, the elementary combination results from the combination of two sonorities: one labeled tonic and the other labeled subtonic. Measure 1 shows the SSS—a tritone resolving to a stable major third which therefore acts as tonic (T). Measure 2, likewise, shows two forms of the DSS—a perfect fifth implying two tritones as it resolves to a stable minor third, which is the subtonic. In both lines in Figure 2.3, the tonic and the subtonic overlap by one pitch. In the upper line
(major mode), both stable thirds share the E, and in the lower line (minor mode) they both share the C. Together, they form the aggregate tonic of the constructed mode: C-E-G
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Texas Tech University, Chad Scarborough, May 2019 of the major mode on the top line and A-C-E of the minor mode on the bottom line. But rather than a single consonance, Yavorsky describes each of these sonorities as a combination of tonic and subtonic, each achieved through the resolution of different tritones. This triad represents the complete expression of tonic as a sum of its parts. By combining the tonic elementary combination with the unstable tones of the SSS and DSS, a continuous scale forms, such as in m. 4 of Figure 2.3. The upper line shows the C-major scale as interpreted by Yavorsky’s system. The stable tones are those of the tonic triad: C,
E, and G. All other pitches are unstable and resolve through either the SSS or DSS to one or more of those stable tones. In the same way, the bottom line shows the A-minor scale.
Both the major and the minor mode can be constructed using Yavorsky’s symmetrical systems. The only difference between the two is the order in which the SSS and DSS are stacked atop one another.
But music is often more complex than the constructed examples shown so far.
Within the subset of diatonic triads (as well as some seventh chords), Yavorsky constructs a chart showing how each of these chords functions within his system as either dominant (D) or subdominant (S) in both the major and minor mode. In addition, he organizes them in terms of the strength of this function measured by their distance from the tonic triad. This distance is determined by a few criteria, namely number of stable tones, number of unstable tones, and which system (SSS or DSS) those unstable tones belong to, both in general and relative to each other. In Yavorsky’s classification, a triad is closer to tonic if its unstable tones belong to the same system rather than different systems. As a result, in C major, a chord consisting of G, B, and F is closer to tonic and therefore of weaker tension than a chord consisting of G, B, and D. The B and F of the
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Texas Tech University, Chad Scarborough, May 2019 former chord form a complete SSS resolving to the tonic C and E. The latter chord, though, contains one tone from each of the symmetrical systems: the B from the SSS and the D from the DSS. As a result, the latter chord is farther from tonic and so resolves more strongly, according to Yavorsky. Despite the tritone in the former chord, the latter chord implies both the single and double system, so the tension is stronger.
Less surprisingly, the unstable tones belonging to the single system are considered to display more tension than the unstable tones of the double system. This tension is primarily due to their half-step resolution versus the double system’s whole-step resolution.
Figure 2.4 reproduces McQuere’s realization of Yavorsky’s diatonic chords and demonstrates their relative tension. The left side of the chart describes chords in the major mode while the right side describes chords in the minor mode. The top measure in each half demonstrates the resolutions that generate each tonic sonority. Below these measures, the chart organizes diatonic sonorities based on their relative stability. These sonorities are organized into columns (displayed as measures), marked by double bar lines. The leftmost columns contain the various subdominant (S) chords; the second columns from the left contain the dominant (D) chords; the remaining columns contain chords that function both as dominant and subdominant because they resolve through both the SSS and DSS. In other words, the dominant/subdominant (DS) chords resolve to both the tonic and subtonic, and in doing so form the complete tonic triad. McQuere makes no distinction left-to-right within the dominant/subdominant chords in terms of relative tension/stability.
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Figure 2.4: McQuere’s realization of Yavorsky’s resolutions11
The following paragraphs describe the nature of Figure 2.4’s numbered rows. The rows are organized such that resolutions from chords in higher numbered rows display more tension than those from lower numbered rows. For example, a Row I chord displays less tension to resolve to tonic than a chord in Row VI. In these descriptions I refer mainly to the major-mode chart, though the logic applies equally to the minor-mode chart.
Row I of the chart contains the chords with the weakest pull towards tonic, five chords that Western music theory would consider suspensions of the I chord. These chords share two stable tones with the tonic (in the examples, C and G, the root and fifth of the triad). The subdominant column contains a D which resolves through the double
11 McQuere, Russian Theoretical Thought, 122. 13
Texas Tech University, Chad Scarborough, May 2019 system to the subtonic stable tone of E, hence its designation as subdominant. Likewise, the dominant column contains an F which resolves down to the tonic stable tone of E through the single system, and thus the chord is labelled as dominant. The dominant/subdominant columns each contain one stable tone plus a D and an F, both of which resolve to E, but through the double system and the single system, respectively.
Because of the equality of this resolution to tonic and subtonic, the chord is labelled as dominant/subdominant.
In Row II, the subdominant and dominant columns again each contain two stable tones of the tonic triad and one unstable tone from the double system and the single system, respectively. In that sense, Row II is exactly like Row I. The difference lies in the fact that, in Row I, the unstable tones resolved to the third E, which Yavorsky clearly views as a weaker resolution than that to the root C or fifth G. The subdominant chord of
Row II resolves its A through the double system down to the fifth G, and the dominant chord resolves its B up through the single system to C. While Yavorsky does not say so explicitly, I believe the reason he thinks of these resolutions to C and G as stronger than the resolutions to E is that, in his system, C is unambiguously part of tonic and G unambiguously part of subdominant, whereas E exists in the overlap between the two and can function as either depending on the resolution by which it is approached. The dominant/subdominant effect is achieved in Row II by combining the resolutions of the dominant and subdominant chords, so the B resolves up to C in the single system and the
A resolves down to G in the double system.
Row III contains complete resolutions of the single and double systems. The subdominant chord resolves its D and A through the double system to the subtonic E and
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G. Likewise, the dominant chord resolves its B and F through the single system to tonic C and E. The dominant/subdominant chords feature this same complete resolution of a symmetrical system, but additionally includes at least one unstable tone from the opposite system to resolve to the remaining stable tone of the tonic triad. This can be seen clearly in the two rightmost chords where a complete system resolves in each and the remaining tone resolves to the final stable tone. The complete seventh chord also features complete resolutions of symmetrical systems to form a stable tonic, but because of the nature of its resolution, it also functions in each of the subsequent rows, indicated by the bracket next to Rows IV, V, and VI. This connection will be discussed in more detail in each of those respective paragraphs.
Row IV contains chords which resolve half of each system in the same direction.
The chord’s status as subdominant or dominant in these cases is determined by the stable third which occurs as a result of the resolutions of the unstable tones. In the subdominant column, the F and A resolve to E and G, respectively. Since these two stable tones form the subtonic third, the chord is considered to be subdominant. Likewise, in the dominant column, the B and D resolve to C and E, respectively, forming the tonic third and designating this chord as dominant. The seventh chord from Row III contains both of these resolutions in this exact form, and so it is able to function on the same level as the other Row IV chords.
Row V functions as a combination of Rows III and IV. The chords in this row contain both complete resolutions of one of the symmetrical systems and a resolution of half of the other symmetrical system. In Row V, these simultaneous resolutions result in either the subtonic or tonic third because the half system (single in subdominant and
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Texas Tech University, Chad Scarborough, May 2019 double in dominant) converges with the complete system as part of its resolution. The subdominant chord resolves a complete double system to E and G, and the F, which is the third of the chord, resolves through the single system to E, which is part of the subtonic third created from the double system resolution. In the same way, the dominant chord resolves its single system of B and F to the tonic C and E, and the D resolves through the double system up to E. The seventh chord from Row III once again contains both of these resolutions in these forms, and so once again functions appropriately on Row V.
The chords in Row VI feature the strongest pull towards tonic. Row VI serves as a near repetition of Row V, but with seventh chords which result in complete versions of the tonic triad. In the case of the subdominant and dominant chords from Row V, Row VI simply adds the missing stable tone from the resolution. The seventh chord from Row III also resolves as a seventh chord to form a complete tonic triad, so it also functions equally on Row VI.
Benefits of Yavorsky’s system in Russian music
Yavorsky’s system is a useful tool for analyzing Russian music which features multiple tonics. The following analyses provide reductions without any expression markings, lyrics, dynamics, etc., for the sake of cleanliness. Above the score, I provide chord symbols in the usual manner, ignoring inversions except in the case of second- inversion tonic chords. Below the score, I provide Yavorsky’s labels of T, D, t, and S, as appropriate to the music.
Figure 2.5 shows an analysis containing both Roman numerals and Yavorskian labels of an excerpt from Mikhail Glinka’s A Life for the Tsar. The Roman-numeral
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Texas Tech University, Chad Scarborough, May 2019 analysis reveals nothing unusual about the harmonic progression. Every motion between chords conforms to common-practice standards and G major is the undisputed tonic. The
Yavorskian labels, though, treat G-major chords as tonic and E-minor chords as subtonic, elevating E minor to a level of equality with G major. This analysis makes sense when one considers where these harmonies occur with respect to phrase boundaries. The excerpt begins with a G-major chord and ends on a half cadence with a D major chord, so treating G major as tonic is perfectly reasonable. However, the first phrase (mm. 8-15) shifts emphasis from G major to E minor, even going so far as to end with a PAC in E minor in m. 14. While both systems recognize this shift to some extent, the Yavorskian analysis does so earlier, considering the D major triad as subdominant (S) to the subtonic
(t) E minor in m. 10. The Roman-numeral analysis, though, does not seem to acknowledge the tonic function of E minor until m. 13 with the B major triad action as
V/vi. The second phrase (beginning in m. 16) also begins with an E-minor sonority before shifting back to G major, further emphasizing the importance of E minor.
Yavorskian labels effectively show this relationship by allowing for multiple tonics to coexist in the same musical space with the emphasis ever shifting between them.
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Figure 2.5: Glinka, A Life for the Tsar, Act I, Introduction, mm. 8-22
Yavorsky’s theories also allow for more than two tonics. As far as Yavorsky’s theory is concerned, a tonic consisting of two parts is the base level of music which can be expanded upon quite easily by stacking three symmetrical systems on top of one another. Yavorsky calls the resulting structures “variable modes,” examples of which are shown in Figures 2.6 and 2.7.12
Figure 2.6: Variable Mode 1
12 McQuere, Russian Theoretical Thought, 117. 18
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Figure 2.7: Variable Mode 2
Figure 2.6 shows an example of variable mode 1, which is comprised of an SSS surrounded on both sides by a DSS. Likewise, Figure 2.7 shows an example of variable mode 2, which is constructed from a DSS surrounded on both sides by an SSS. Unlike the modes discussed previously, the variable modes each have three constituent tonics which overlap with each other. As a result of this overlap, the aggregate tonic of a variable mode takes the form of a seventh chord. In the case of variable mode 1, the tonic is a minor seventh chord, and for variable mode 2 the tonic is a major seventh chord. Though these structures represent the complete form of the tonic of their given modes, the tonic function is rarely expressed in this form. Instead, it will most often shift between the three tonics individually.
Adapting Bailey’s terminology, we could describe these variable modes as a system of three distinct tonics—a “triple-tonic complex.” While the triple-tonic complex is simply an expansion of the previously discussed system, the stability of certain pitches in these variable modes is highly dependent on their contexts. Depending on where a pitch is located in terms of register, it might be stable or unstable. In Figure 2.6, for example, G is stable and has subtonic function in the upper register, but in the lower register it is unstable and wants to resolve to A via the DSS. This change of function will be discussed in more detail in the following example.
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An example of variable mode 1 in practice can be found in Rachmaninoff’s All-
Night Vigil, Movement 3: “Блажен Муж” (“Blessed is the Man”), shown in Figure 2.8.
In this excerpt, Rachmaninoff sequences the same melodic figure three times: the first time over Dm – Am – Dm, then B♭ – F7 – B♭, then Gm – D – Gm. The Yavorskian analysis below these moments shows that they alternate between double- and single- symmetrical systems while descending in diatonic thirds, and thus together form Variable
Mode 1.
Figure 2.8: Rachmaninoff - All-Night Vigil mvt. 3 "Блажен Муж (Blessed is the Man)” m.14
Interesting to note in this example is the shift in function based on register for the
F in the melody. The initial F functions as a stable tone, whereas at the end of the measure its function changes so that the F becomes an F# to fulfill its function as an unstable tone to resolve to G. A diagram of this change in function is shown in Figure
2.9. In the upper register, F is stable; in the lower register, it is not. Even were it left as an
F as opposed to becoming an F#, its function would still differ from that which it has at
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Texas Tech University, Chad Scarborough, May 2019 the beginning of the phrase, as it would form a DSS with an implied C (the 7th of an implied D7 or, in this case, Dm7), to resolve to the G-B♭ subtonic.
Figure 2.9: Changing function relative to register
Limitations of Yavorsky’s system in Popular music
Despite its effectiveness in the analysis of Russian music, Yavorsky’s system often does not work well with Western Popular music. Some of the clearest examples of the double-tonic complex in Popular music come from what Mark Richards calls the
“Axis Progression.”13 This type of progression encompasses multiple different transpositions and rotations, all of which derive from the following: Am – F – C – G.
Richards discusses at length the tonal ambiguity which can result from such a progression, citing as a specific example Joan Osborne’s “One of Us” (Figure 2.10).
13 Richards, “Tonal Ambiguity.” 21
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Figure 2.10: "One of Us" chorus, transc. by Mark Richards
Richards describes how the tonalities of F# minor and A major are equally emphasized by both the melody and the harmony because of qualities such as metric and hypermetric placement. F# minor’s place as the first chord of the four-chord loop affords it some priority in terms of being heard as tonic. Additionally, the melody in the first measure and a half in Figure 2.10 arpeggiates F# minor, further emphasizing that harmony. However, this F# minor arpeggiation is immediately overlapped by an arpeggiation of A major in the second measure. A major is further strengthened by the placement of the pitch A in the melody as the highest pitch and as the first note of the four-chord loop. To quote Richards’ conclusions about this excerpt:
Thus, F Aeolian and A major are both emphasized enough to be heard as viable tonics throughout the passage. In such cases, one may hear an ambiguous mix of the two tonalities, one or more vacillations between the two, or some combination of these hearings.
Though Richards never uses the term “double-tonic complex,” the relationship between F# minor and A major easily fits into that category, just as did the relationship between G major and E minor in the excerpt from A Life for the Tsar (Figure 2.5). It
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Texas Tech University, Chad Scarborough, May 2019 would be logical to assume, then, that the same system by which the double-tonic nature of certain Russian music can be identified can also be used on music which contains, for example, the Axis progression. However, Yavorsky’s method of classifying tonics causes significant problems when analyzing this progression.
Yavorsky defines the difference between “tonic” and “subtonic” based on the method by which they are approached—via the single or double symmetrical system. The former yields a tonic and the latter a subtonic. In the Axis progression described above, both the F#-minor and A-major chords are approached by the double-symmetrical system
(i.e. whole-step resolutions instead of half-stem resolutions), thus Yavorsky would label both chords as subtonic.
Figure 2.11 shows the progression from the Osborne excerpt reduced to triadic whole notes. The Roman-numeral analysis below the staff shows that the A-major triad is approached by its IV chord and that the F# minor triad is approached by its ♭VII chord.
Since Yavorsky created a chart defining many different resolutions to both tonic and subtonic (Figure 2.4), we can see that Yavorsky considers both resolutions to be of the form S → t. The resolutions of both the ♭VII chord and the IV chord are, in Yavorsky’s system, DSS resolutions, and therefore resolve to subtonic. It is important to remember that the quality of the stable triad is practically irrelevant when determining the difference between tonic and subtonic in Yavorsky’s system. What is important is the voice leading of the resolution. The E-major chord resolves through DSS to the F# and A of the F# minor chord. The D major chord, though it resolves to a major chord, resolves via DSS to the C# and E of the A major chord, which is a minor third and, therefore, subtonic.
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Figure 2.11: Analysis of Axis progression
The explanation that both A major and F# minor are subtonic in this case is unintuitive and at least somewhat confusing to our modern sense of aural chord-root indexing. It is made more so when one considers that Yavorsky’s analysis is used to describe the construction of modes. The mode Yavorsky’s system describes in this case is one which does not overlap itself and which is made of two practically unrelated double symmetrical systems. This mode is shown in Figure 2.12.
Figure 2.12: The mode implied by the Axis progression, according to Yavorsky's system
To analyze the Axis progression in this way is unintuitive and unhelpful. In the
Russian music analyses, the labels of tonic and subtonic tend to coincide with the qualities of the chords in question such that major chords tend to function as tonic and minor chords as subtonic. Stable sonorities a third apart would overlap in the Yavorskian analysis of the underlying mode. A major and F# minor clearly overlap much more strongly than Yavorsky’s system can show in this case. Thus, despite the tonal similarities between double-tonic complexes in Russian music and those in Popular 24
Texas Tech University, Chad Scarborough, May 2019 music, Yavorsky’s system is only practically equipped to effectively analyze the former.
Thus, I have decided to adapt Yavorsky’s model in such a way that allows it to analyze both styles of music with equal effectiveness.
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CHAPTER III
Neo-Yavorskian Theory
Problems with Yavorsky’s theory
Yavorsky’s system, while useful for discussing certain music in the Russian tradition, carries with it some issues which prevent it from being completely effective in the universal context he sought to describe. These difficulties range from simple labelling issues to fundamental questions of how to define tonic. This chapter addresses these issues individually, adapting them as necessary into a modernized version of Yavorsky’s system. This modernization will include changes ranging from updated terminology to alterations of some of Yavorsky’s fundamental assumptions. I then describe the details of the updated neo-Yavorskian system and how it overcomes various analytical challenges.
I will first discuss the issue of labelling. The neo-Yavorskian system proposed here retains Yavorsky’s original labels ‘T’ and ‘t’ for the two types of tonic. The names for these functions, however, are changed from “tonic” and “subtonic” to “major tonic” and “minor tonic,” respectively. Likewise, the subdominant label is changed from ‘S’ to
‘d,’ while the dominant label is maintained as ‘D.’ In the same way that the names for the tonic functions changed, so too have the names for the dominant functions. “Dominant” becomes “major dominant,” and “subdominant” becomes “minor dominant.” These changes address issues with nomenclature and labelling consistency. The names
“subdominant” and “subtonic” already have commonly understood meanings in Western music theory, so to have those same terms with different meanings in this system is unnecessarily confusing. Additionally, the label ‘S’ is changed to ‘d’ in order to maintain
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Texas Tech University, Chad Scarborough, May 2019 consistency within the system. This label change makes the relationship between all four functions much clearer: capital letters refer to major functions, and lower-case letters refer to minor functions. Tonic sonorities are labelled with some form of ‘T’ and dominant sonorities with some form of ‘D’ according to quality.
Table 3.1 serves as a translation table for all equivalent terms and labels between the Yavorskian and neo-Yavorskian systems.
Table 3.1: Equivalent labels and terms in Yavorskian and neo-Yavorskian systems Yavorsky Neo-Yavorsky
T Tonic T Major tonic
t Subtonic t Minor tonic
D Dominant D Major dominant
S Subdominant d Minor dominant
A much more fundamental issue with Yavorsky’s theory stems from his method of defining tonic versus subtonic, or, to use my own labels (as I will from this point forward), major tonic versus minor tonic. According to Yavorsky, the difference between major tonic and minor tonic lies entirely in the resolution to that tonic, either by the single or double symmetrical system, respectively. For example, in the key of C major, the progression G→C would be labelled D→T, since G resolves to C mostly via the SSS.
Likewise, the progression F→C would be labelled d→t because F resolves to C mostly via the DSS. In both cases, the tonic chord is C major; the only difference between the two is the chord which resolves to the tonic. More specifically, the difference lies in
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Texas Tech University, Chad Scarborough, May 2019 whether the target of the resolution is the C-E dyad via SSS or the E-G dyad via DSS.
This difference, according to Yavorsky’s system, is sufficient to change how the tonic chord is classified.
Consider, for example, the a-form of the Axis progression shown in Figure 3.1.14
Under the Yavorskian system the A-minor triad would be considered a minor tonic because, as the progression loops, the G-major triad resolves to A minor mostly through the DSS—i.e. G and D resolve by whole-step to A and C. However, the Yavorskian analysis also considers C major, in this context, to be a minor tonic despite its major quality. The A of the F major resolves via the DSS to G in the C major, while the F resolves via SSS to the E. In cases where both systems are applied to a single resolution, the resolution to 5^ takes precedence over the resolution to 3^. Since the resolution to 5^, in this case, is via DSS to the E-G dyad, C major is considered a minor tonic in the
Yavorskian system.
Figure 3.1: Axis progression - A-form with Yavorskian analysis
The neo-Yavorskian system addresses this issue by omitting Yavorsky’s principle that a tonic’s quality is a result of the resolution from which it results. Instead, in the neo-
Yavorskian system, quality is inherent to the full tonic-function triad. A major triad with
14 Richards “Tonal Ambiguity.” 28
Texas Tech University, Chad Scarborough, May 2019 tonic function will always be a major tonic, and a minor triad with tonic function will always be a minor tonic. Since major and minor status are inherent to the chords themselves, there is no longer any need to distinguish SSS and DSS. The point of those systems in Yavorsky’s system is to define major and minor tonic based on the resolutions to those chords. Since those systems are no longer necessary to define tonic quality, there is no need to include them in the theory, thus dramatically simplifying the process of analysis.
Details of the neo-Yavorskian system
In addition to the previously discussed alterations to Yavorsky’s theory, the neo-
Yavorskian system includes a new analytical tool based on an existing tool from
Yavorsky’s theory. The chart from Figure 2.4 shows Yavorsky’s classifications of chords based on their proximity to tonic. Put another way, this chart classifies chords according to the amount of tension they have to resolve to tonic. The neo-Yavorskian system reworks this tool into one which is directly applied to analysis by determining the amount of tension present in a given sonority relative to a given tonic.
To determine which sonorities create the most tension in relation to a given tonic,
I have created a simple formula based on two simple criteria. 1) Notes which resolve by half-step to a stable tone create more tension than notes which resolve by whole-step to a stable tone, and 2) resolutions to the root of the tonic triad are stronger than resolutions to the fifth which, in turn, are stronger than resolutions to the third.
Criterion 1 is derived from Yavorsky’s principle that harmonic progression results from resolving tritones. The SSS is formed by a tritone resolving in contrary motion by
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Texas Tech University, Chad Scarborough, May 2019 half-step to two stable tones. Meanwhile, the DSS is formed by an unstable perfect fifth resolving in contrary motion by whole-step to two stable tones. Yavorsky justifies the
DSS as a proper tritone resolution by positing that the motion from perfect fifth to minor third implies two intermediary tritones, each of which half-resolves by half-step. His insistence that all resolutions are the result of tritones moving by half-step in contrary motion implies that, in the Yavorskian system, half-step motions are superior to whole- step motions in terms of creating and resolving tension. Therefore, the neo-Yavorskian system maintains this principle in the form of Criterion 1.
Criterion 2 is similarly derived from Yavorsky’s original theory. Figure 2.4 shows
Yavorsky’s delineation of chords in terms of distance from tonic. Row I contains the chords which are closest to tonic, moving farther away until Row VI which contains the chords which are farthest from tonic. In this chart, Rows I and II are identical in the sense that both rows contain chords which resolve one half of either the SSS or DSS to a single stable tone. The difference between the two rows is that, in Row I, the unstable tones resolve to what would be the third of the tonic triad, and in Row II the unstable tones resolve to either the root or fifth. Therefore, according to Yavorsky’s theory, resolutions to the third of the tonic triad are weaker than resolutions to the root or fifth. However,
Yavorsky seems to consider resolutions to the root and fifth of a tonic triad to be approximately equivalent. In Criterion 2, I expand this idea to fit with the common
Western sensibility that resolutions to the root of a tonic triad are inherently stronger than resolutions to the fifth.
From these two criteria comes this formula (Figure 3.2) for determining the amount of tension present in a given unstable sonority:
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6: half-step to root
5: whole-step to root
4: half-step to fifth
3: whole-step to fifth
2: half-step to third
1: whole-step to third
0: common tone with tonic triad
Figure 3.2: Tension formula
The numbers next to each type of resolution represent a numerical amount of tension present in their respective resolutions. Higher numbers mean greater amounts of tension. For example, a whole-step resolution to the fifth of the tonic triad contains more tension (3) than a half-step resolution to the third (2). Therefore, the former resolution is stronger.
Each unstable sonority in the neo-Yavorskian system is assigned a tension value according to the combined tension values of its constituent pitches.15 To determine the amount of tension a chord possesses in relation to a given tonic, one hypothetically resolves that chord to the tonic chord via the smoothest possible voice leading. Then, the
15 This philosophy of determining chord function based on the combined functions of a chord’s constituent tones has been discussed at great length in Daniel Harrison, Harmonic Function in Chromatic Music (Chicago: University of Chicago Press 1994). Though Harrison’s theory and the neo-Yavorskian system are similar in this regard, Harrison’s focus rests primarily on the scale degrees which form chords of various function while the neo-Yavorskian system focuses primarily on assumed resolutions from any given sonority to one or more tonics. 31
Texas Tech University, Chad Scarborough, May 2019 tension values associated with each of these resolutions are added together, resulting in the tension value for that unstable chord.
For the purposes of determining tension within the neo-Yavorskian system,
“smoothest possible voice leading” is generally achieved via a three-step process: 1) common tones do not move, 2) strong tendency tones resolve first, and 3) when appropriate, all other tones fill in the remaining voices of the tonic triad. Figure 3.3 shows an example of a typical V7 → I resolution in C major. Each voice in the V7 chord moves with the smoothest voice leading to a tone in the I chord, as shown by the arrows. The common G does not move, according to rule 1. B and F are both strong tendency tones in
G7 and so resolve accordingly, following rule 2. At this point, D has yet to resolve, and there are no missing voices in the tonic triad. D must therefore follow more conventional rules of voice leading, doubling the root of the tonic triad which is generally more appropriate than doubling the third.
The numbers adjacent to each arrow represent the amount of tension associated with each resolution, as defined by the formula above. F → E is a half-step to 3^, and so has a tension value of 2. D → C is a whole-step to 1^, and so has a tension value of 5. B →
C is a half-step to 1^, and so has a tension value of 6. G → G is a common tone with the tonic triad, and so has a tension value of 0. Adding these values together yields a final tension value of 13.
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Figure 3.3: Example resolution
Dominant chords receive two labels: ‘D’ or ‘d’ to indicate the quality of the tonic to which they resolve, and their tension value in the form of a subscript. As an example,
7 the G chord from Figure 3.3 would receive the label ‘D13.’ The upper-case ‘D’ represents its resolution to a major tonic, and the subscript ‘13’ represents the tension value associated with each of its constituent chord tones’ resolutions to the tonic triad, according to the tension formula. To illustrate this point more broadly, Figure 3.4 lists common chords, translating their Roman-numeral labels into neo-Yavorskian labels with respect to major and minor tonics. These chords are not the only possibilities; any non- tonic sonority within a progression has dominant function, and its tension can be determined using the formula in Figure 3.2.
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Figure 3.4: Chords with dominant-function labels
Whether the major or minor side of the chart in Figure 3.4 is referenced depends on the quality of the local tonic. Any time the local tonic is major, the dominant-function labels used correspond with those shown in the major side of Figure 3.4. Likewise, any time the local tonic is minor, the dominant-function labels used correspond with those shown on the minor side. This relationship between tonic quality and dominant-function labels is more clearly shown in Figure 3.5.16 Notice that the same G7 chord receives a slightly different subscript depending on whether it resolves to C major or C minor, since the half-step resolution F-E in the major version becomes a whole step F-Eb in the minor.
16 I intentionally ignore chord inversions in my analyses with the exception of cadential 6/4 chords because, within the neo-Yavorskian theory, they are largely irrelevant for measuring tension. 34
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Figure 3.5: Dominant function in major and minor keys
Of course, in order to label some sonorities as stable and others as unstable, there must be some system for identifying tonic sonorities within a given musical context. For this purpose, I rely on the four methods of asserting tonic function described by Daniel
Harrison, including one additional method specific to the neo-Yavorskian system, resulting in a total of five indicators of tonic function:
1) “Tonic function ends a composition”
2) “Tonic begins compositional sections”
3) “Harmonic stasis and immobility attract Tonic function”
4) “Thematic exposition is heard in a Tonic context”
17 5) Strong resolutions (D/d11+) indicate at least temporary tonic function.
17 1-4 taken directly from Harrison, Harmonic Function, 76-83. 35
Texas Tech University, Chad Scarborough, May 2019
It should be noted that these five indicators of tonic function are not exhaustive; there may be other qualities of specific pieces of music which cause a given sonority to function more or less as tonic.
Both major and minor tonics can be expressed at the same time, most often in the form of a minor seventh chord, as we have previously seen in Figure 1.1. These double tonics are labeled “Tt.” Additionally, preceding dominant chords should be labelled Dd to show that the chord functions with respect to both tonics. For example, the progression D
7 7 → Em should be labelled as D11d10 → Tt. Considering Em to be the combined form of
G major and E minor, both functioning as tonic, the composite label for the D major chord should capture its relationship to both tonics. With regards to G major, D major is a
V chord, and so receives the label D11; relative to E minor, D major is a ♭VII chord, and so receives the label d10. Combining these two functions, since the tonic is combined as well, results in the label ‘D11d10’ for the D major chord.
Analyzing longer progressions proceeds in much the same way. All dominant chords receive dominant-function labels as though they resolve to tonic via the smoothest possible voice leading, and all tonic chords receive their appropriate tonic labels. Figure
3.6 shows two potential progressions. The first progression follows the standard common-practice model of pre-dominant → dominant → tonic. Since common-practice music tends to feature tension and release as the primary force for harmonic motion, it should come as no surprise that the tension values in a ii → V → I progression gradually increase from D10 to D11, representing how tension builds across the progression before it ultimately resolves to tonic. The second progression demonstrates what is known as the
36
Texas Tech University, Chad Scarborough, May 2019 double-plagal progression.18 While rare in common-practice literature, the double-plagal progression is very common in popular music. This progression, unlike the previous example, decreases tension until it reaches tonic. Progressions which approach tonic through a decrease in tension are discussed in more detail later.
Figure 3.6: Two possible harmonic progressions
The neo-Yavorskian system and the basic phrase model
Tracking the growth and decay of tension, as denoted by the subscript tension values, can lead to some useful observations about how a phrase is harmonically structured. In general, the strength of the unstable chords tends to increase as a resolution is approached.19 Traditional Western music theory describes this phenomenon as pre-
18 Walter Everett, “Rock’s Tonal Systems,” in Music Theory Online 10, 4 (2004), http://www.mtosmt.org/issues/mto.04.10.4/mto.04.10.4.w_everett.html 19 This approach to describing harmonic progression in terms of increasing and decreasing tension within the chords themselves is reminiscent of Paul Hindemith, The Craft of Musical Composition, trans. Arthur Mendel (New York: Associated Music Publishers, 1945). 37
Texas Tech University, Chad Scarborough, May 2019 dominant harmony moving through dominant and eventually resolving to tonic. This pattern is shown in the neo-Yavorskian system through the general increase in the strength of tension, as denoted by the subscript D values. Indeed, the chords listed with
D1-10 in Figure 3.4 are those chords typically labeled “pre-dominant” while the
“dominant” chords have tension values of 11 or greater. The benefit of labelling chords in accordance with their inherent tension as opposed to the more traditional “pre-dominant – dominant” system is three-fold. First, the neo-Yavorskian labelling system provides a more tangible method of comparing the strengths of cadences relative to each other by providing a metric for directly comparing the tension associated with different chords. As a result, the standard model of a period, for example, in which the final cadence is supposed to be the strongest, can be quantitatively shown to be the strongest, should that be the case. Second, the progression of a given phrase is clearer because all chords are labelled according to the amount of tension, and the general trends of a phrase to increase, decrease, or maintain tension can more quickly and accurately be observed.
Third, the label “pre-dominant” can be misleading in many cases because the name itself implies the chord attached to it necessarily resolves to some dominant chord, despite that these chords are completely capable of resolving directly to tonic without an intermediary dominant chord. Removing the pre-dominant label alleviates this potential misdirection regarding the functions of certain chords, especially in contemporary popular music.
A significant amount of music tends to increase tension throughout its phrases before finally reaching a cadence. This model of generally increasing tension can be clearly seen in the initial period of the first dance from Aleksandr Borodin’s “Polovetsian
Dances,” from Prince Igor (Figure 3.7). The excerpt contains two phrases forming a
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Texas Tech University, Chad Scarborough, May 2019 parallel period within an A major/F# minor double-tonic complex, with each phrase focusing on one of the two tonal centers present. The first phrase consists of a D10 → D13
→ T motion in A major, while the second phrase consists of a d5 → d16 → t motion in the relative F# minor. Both phrases demonstrate a definite increase in tension within the dominant chords before resolving to their respective tonics. This model equates well with the standard concept in Western music of tension and release—the idea that music builds tension over time and then resolves it away to release it. The increase in the level of tension within a progression is a quantifiable way to measure this tension as it approaches its resolution.
Figure 3.7: Aleksandr Borodin - "Polovetsian Dances" from Prince Igor, mm. 16-19
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Because of this more specific method of measuring tension, it is possible to more precisely compare the relative strengths of two different cadences by comparing the tension associated with their respective final unstable chords. Figure 3.7 provides an example of the benefit of this more finely tuned harmonic analysis. Part of the definition of a period is that the second phrase has a stronger cadence than the first phrase. In traditional analysis, both cadences in Figure 3.7 would be labeled as imperfect authentic cadences (IAC) since they both exhibit dominant-to-tonic progression, yet neither consists of root position V→I motion with tonic in the soprano voice on the final chord.
Therefore, traditional analysis would not recognize the phrases in Figure 3.7 as a period, saying nothing of the fact that the two phrases are in two different keys. However, the neo-Yavorskian voice-leading model for the strength of dominant function shows that the second cadence is stronger than the first, thus recognizing the antecedent-consequent relationship between the phrases in Figure 3.7. Additionally, the approach by the relatively weak d5 emphasizes the strength of the penultimate d16 chord, as opposed to the somewhat more static D10 → D13 motion in the first phrase, thus further strengthening the final cadence of the period.
Popular music sometimes avoids strong resolutions and instead focuses on weaker motions, resolving D(d)1-8 to their respective tonics instead of building tension and then releasing it. As a part of this pattern of weak resolutions, songs in this style might slowly decrease tension as they approach tonic. If one thinks of a chord’s strength of tension as a measure of its distance from tonic, then it becomes apparent that a decrease of this tension over time might constitute a slow resolution. As the tension decreases, the harmony slowly approaches tonic, since the distance of the harmony from tonic decreases
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Texas Tech University, Chad Scarborough, May 2019 with its tension. An example of this decrease in tension can be seen in the intro to the
Beatles’ “She Loves You” (Figure 3.8).
Figure 3.8: The Beatles – “She Loves You” intro20
In this example, though the final tonic is in fact a compound tonic, the strength of tension toward both tonics decreases through the progression. Relative to the minor tonic, the excerpt shows a d6 → d4 → t progression, and relative to the major tonic a D9 → D5
→ T progression. Both progressions show a clear, fairly slow descent into tonic as opposed to a strong release of tension as one might expect in the Western classical tradition. Neither traditional labels of pre-dominant and dominant nor Roman numeral analysis would clearly show this decrease in tension. Instead, these forms of labelling chords would provide a vague sense that the progression shown is unorthodox. The neo-
Yavorskian system, though, is able demonstrate the functional relationships of all the chords within the progression and reveal the overall decrease in tension as an inherent part of the phrase structure. Put another way, describing this passage as a slow, gentle
20 Transcription by the author. 41
Texas Tech University, Chad Scarborough, May 2019 release of tension focuses on reading the passage on its own terms and avoiding needlessly pejorative terms such as “retrogression.”
The third benefit of this system is that it breaks down the occasionally misleading label of “pre-dominant.” Theorists traditionally consider the ii chord a pre-dominant harmony. This, indeed, is very often how it functions. As a result, though, one might assume that ii → I is a sort of plagal motion akin to IV → I. However, the strength of 2^
→ 1^, especially in the outer voices, is strong enough nearly on its own to qualify ii → I as an authentic motion (consider, for example, a Schenkerian Urlinie, which necessarily ends with 2^→ 1^ motion). A good example of the strength of ii is the ending of the chorus which opens Borodin’s Prince Igor, shown in Figure 3.9.
Figure 3.9: Aleksandr Borodin - "Солнцу Красному Слава" mm. 126-132
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To refer to weaker unstable chords, such as ii, as “pre-dominant,” as is often done in traditional Western theory, can be misleading, as it implies that their primary function is to precede “dominant” chords while ignoring their potential to resolve to tonic on their own.
By labelling all non-tonic chords according to their inherent tension relative to a given tonic, musics underserved by existing analysis methods (Popular music and
Russian music, to name but two examples) receive the benefit of being understood more closely to their own terms rather than the terms of an arbitrary, 18th-century, European classical norm. Having a wide range of classifications for unstable chords allows us to more accurately understand progressions within a phrase, whether they function according to a more traditional framework or not; quantify the relative strengths of cadences; and more accurately determine the functions of chords which are potentially mislabeled by the existing pre-dominant → dominant → tonic system.
A note about tonicization of non-tonic chords
In cases where non-tonic chords are temporarily tonicized by, for example, a secondary dominant chord, the analysis proceeds on two different levels, as shown in
Figure 3.10. On the lower level and set off by parentheses, the secondary dominant-tonic relationship is shown with the tonicized chord acting as the local tonic. On the upper line, the secondary dominant chord is skipped and the tonicized chord is labelled according to
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Texas Tech University, Chad Scarborough, May 2019 its relationship to the deeper tonic.21 In this way, the progression can be understood on two different levels, each describing an important aspect of function.
Figure 3.10: Analysis of progression with secondary dominant chords
More than two tonics
Yavorsky allows for modes with three tonics, which he calls “variable modes” or
“mutable modes.” These modes are constructed in much the same way as their double- tonic counterparts: by stacking diatonic thirds atop one another. The neo-Yavorskian theory I propose also allows for such musical constructs, but with no upper limit on the number of tonics which might be present, so long as those tonics are related by diatonic third. I represent this relationship with a Circle of Thirds.
The Circle of Thirds pictured in Figure 3.11 models tonic centricity in the neo-
Yavorskian system. In this graph, all possible tonal centers (excluding certain enharmonic spellings) are shown in relation to the tonal centers a third away. Any two adjacent tonal centers pictured in the Circle of Thirds can be combined to create an
21 I choose to skip the secondary dominant chords in cases such as this because they typically do not function in relation to the local tonic. Their primary function is to establish a temporary secondary tonic which, itself, functions as part of the progression. Assigning these secondary dominant chords dominant-function labels on the same level as the other chords would tend to disrupt the pattern of increasing or decreasing tension established by the primary chords of the progression. 44
Texas Tech University, Chad Scarborough, May 2019 aggregate tonic in the form of a seventh chord because all adjacent triads share two common pitches.
Figure 3.11: Circle of Thirds
Most of the pieces under examination in this thesis employ just two tonal centers, adjacent to each other on the Circle of Thirds. While it is more common for the lower of the two tonal centers to be minor and the upper to be major, this is not always true, and the system works no matter the arrangement, so long as the tonal centers involved are adjacent on the Circle of Thirds.
Because of the ability of tonal centers to work together in this way, it is possible to shift by multiple degrees around the Circle within a piece or, sometimes, within a single phrase, such as in Figure 3.12. This phrase contains four different tonics. For clarity, Figure 3.12 adds the appropriate letter name as a subscript to each ‘T’ or ‘t’ to identify the root of the chord it labels.
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Figure 3.12: Sergei Rachmaninoff - All-Night Vigil, "Blazhen Muzh," m. 14
The tonic-function labels in Figure 3.12 reveal a progression around the Circle of
Thirds. The phrase begins with an F-major chord and then begins to proceed counter- clockwise around the Circle to D minor, B♭ major, and finally to G minor, traversing a full four spaces on the Circle of Thirds in the span of a single phrase, as shown in Figure
3.13.
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Figure 3.13: Circle of Thirds representation of tonic motion from Figure 3.12
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CHAPTER IV
Long-form Analysis
In this chapter, I directly apply the neo-Yavorskian system to the analysis of complete works in order to demonstrate its effectiveness as an analytical tool. This chapter consists of a total of four analyses: two pieces from the Russian tradition and two pieces of Western Popular music.
“Блажен Муж (Blessed is the Man)” from All-Night Vigil by Sergei Rachmaninoff22
The third movement of Sergei Rachmaninoff’s All-Night Vigil, “Блажен Муж
(Blessed is the Man),” has served as an example for multiple concepts throughout this paper. As such, the piece serves as a demonstrative vehicle for the application of the neo-
Yavorskian system. Hence, I provide below a full analysis of the movement, using neo-
Yavorskian analysis to reveal some of its harmonic nuances. The neo-Yavorskian analysis of this piece reveals the interplay of independent patterns in melody and harmony as a unifying device for the whole movement.
This piece can be understood in terms of which tonics it emphasizes in each phrase as the piece unfolds. While the primary tonics of the piece are D minor and F major, multiple other tonics are emphasized at various points throughout. Table 4.1 demonstrates which tonics are present in each measure of the piece. The tonics on the
22 The piece to which this movement belongs is discussed in great detail in Bakulina, The Problem of Tonal Disunity. 48
Texas Tech University, Chad Scarborough, May 2019 left-hand side of the chart are listed in order of the Circle of Thirds. Cells which contain an ‘X’ indicate that their respective tonic occurs in their respective measure.
Table 4.1: "Блажен Муж" - Graph of tonics present (* = “аллилуйиа” refrain)
Measure Number
1 2* 3 4* 5 6* 7 8* 9 10* 11 12* 13 14 15* 16* 17*
C X
a X
F X X X X X X X X X X X X
d X X X X X X X X X X X X TonicsPresent B♭ X X X X
g X X X X
Measure 1 of the movement, shown in Figure 4.1, has been discussed previously in Figure 1.1.23 I include it here in this analysis to serve as a model for all following measures. Measure 1 begins and ends solidly in D minor, as shown by the lowercase functional labels at the beginning and the end of the measure, whereas in the middle of the measure it centers more on F major. This pattern of beginning and ending the phrase around one tonic and shifting to the other tonic in the middle of the phrase is consistent throughout most of the movement. The neo-Yavorskian functional labels make this pattern clear by showing a shift from minor function to major function and back again.
23 The measures of this piece are unusually long and lack a time signature. Rather than indicating meter, barlines in this piece indicate phrase divisions as dictated both by the music and by the text. 49
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Figure 4.1: "Блажен Муж" m. 1
Measure 1 also directly demonstrates its double-tonic nature via the Dm7 chord labelled ‘Tt’ in the middle of the measure. Though this direct juxtaposition of multiple tonics only happens a total of three times within the movement, its occurrence in the first measure serves to set up the double-tonic nature of the entire movement.
Measure 2 (Figure 4.2) introduces the movement’s refrain which sets three consecutive statements of “Аллилуйиа (Alleluia).” This refrain occurs every other measure prior to the climax of the piece (as well as every measure after the climax) and serves to separate verses.24 Harmonically speaking, the refrain is simpler than the verses.
However, the refrain still follows the general D-minor/F-major/D-minor pattern of the first measure. Once again, the neo-Yavorskian labels make these shifts between tonics clear and concise.
24 Specifically, the refrain occurs in mm. 2, 4, 6, 8, 10, 12, 15, 16, and 17: the measures marked ‘*’ in Figure 4.1. 50
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Figure 4.2: "Блажен Муж" m. 2
While the melody in m. 6 (Figure 4.3) is an exact whole-step transposition of mm.
2 and 4, the harmonies are transposed by perfect fourth. As a result, m. 6 exists in a G- minor/B♭-major double-tonic complex: the next two tonics counterclockwise from D minor and F major on the Circle of Thirds. This measure begins a pattern of large-scale ascension within the refrain measures.
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Figure 4.3: "Блажен Муж" m. 6
The following “аллилуйиа” refrain expands on this pattern further. Measure 7 (as shown in Figure 4.4) returns to the now typical D minor/F major double-tonic complex while m. 8 continues the melodic rise of the refrain sections. The melody of m. 8 is once again a direct transposition up one whole step from the previous refrain measure. The harmony for m. 8 is adjusted so that the measure occupies the A minor/C major double- tonic complex which is formed from the two tonics immediately clockwise from D minor and F major on the Circle of Thirds. With this introduction of new tonics, the piece has formed a continuum of six adjacent tonics on the Circle of Thirds within which it can operate.25
25 These tonics are presented in Table 4.1 in the same order in which they would appear on the Circle of Thirds. 52
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Figure 4.4: "Блажен Муж" m. 8
Measure 10 (Figure 4.5) continues the pattern of ascending the refrain melody by step while returning to the G-minor/B♭-major double-tonic complex of measure 6. Unlike measure 6, where the melody emphasized G minor, the melody in measure 10, now raised two steps from measure 6, emphasizes B♭ major. As the melodies of the refrain sections continue their stepwise ascent, the piece explores the previously mentioned continuum of six adjacent tonics.
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Figure 4.5: "Блажен Муж" m. 10
The payoff for all of these harmonic gymnastics comes in m. 14 (Figure 4.6), in which the established harmonic pattern breaks. Unlike every prior measure of the movement, m. 14 features four distinct tonics, and it sequences through them all via the
Circle of Thirds. The measure begins on F major and descends through D minor, B♭ major, and finally G minor. While three tonal shifts is a lot to ask of a listener, each of these tonal areas have been prepared by previous phrases. This measure is undoubtedly the harmonic climax of the piece for this reason, but it also serves as the compositional climax. Along with m. 13, this portion of the piece forms the longest continuous non- refrain text of the piece, and it contains the final instance of non-refrain text. The text for m. 13 even ends with “аминь,” meaning “Amen.”
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Figure 4.6: "Блажен Муж" m. 14
After a short descent in mm. 15 and 16, m. 17 (Figure 4.7) returns to the D minor/F major double-tonic complex from the beginning. One might expect that the piece would end solidly emphasizing one or the other, however, the final measure of this movement behaves the same as any other measure of the movement: emphasizing two tonics. The soprano melody strongly suggests F major; and while the final cadence features a D-minor triad approached by d5, the soprano line denies the descent to D that would solidify that key as the primary tonal center. Instead, both tonal centers are present even within the final chord of the piece, thus refusing to choose one tonic over the other.
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Figure 4.7: "Блажен Муж" m. 17
“Trisagion” by Georgy Sviridov
Georgy Sviridov’s “Trisagion” is a setting of the Russian Orthodox text “Святый
Боже, Святыи Крепкий, Святый Безсмертный, помилуй нас” (Holy God, Holy
Almighty, Holy Immortal, have mercy on us). The entire piece consists of six repetitions of this text with four measures for each repetition. The following analysis takes each 4- bar setting of the text as a strophe. Whereas the previous piece primarily consisted of two tonics (D minor and F major) with brief forays into related tonics, this piece’s form is based largely on continuous motion from D# minor to E major and back again. This journey is shown in detail in Table 4.2.
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Table 4.2: "Trisagion" - Tonics present across each strophe
Strophe 1 Strophe 2 Strophe 3 Strophe 4 Strophe 5 Strophe 6 d# X X X
B (X) X X X g# X X X X
E X
Following the printed breath marks, I divide each strophe into three phrases which align with the text. “Святый Боже,” “Святыи Крепкий,” and “Святый Безсмертный,
помилуй нас” each act as phrases within the larger strophe, especially at the slow tempo of this piece (♪ = 54). Since each of these text units constitutes a phrase, and since there are no apparent half cadences in the piece, I posit that the sonority which ends each phrase has local tonic function.
The first strophe of the piece (Figure 4.8) is strongly situated in D# minor, primarily featuring motion back and forth between the tonic D#m and the dominant A#m
(d7). Though a full D#-minor triad only appears as the final chord of the strophe, the inclusion of the minor v chord as the dominant is enough to imply a minor quality for the otherwise open D# chords.26
26 Chords which lack a third are labelled in parentheses. 57
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Figure 4.8: “Trisagion” Strophe 1 (mm. 1-4)
Strophe 2 (Figure 4.9) is a nearly exact repetition of Strophe 1. The primary difference between the two is the inclusion of the F#-B (D11-TB) motion in the third measure of Strophe 2. This motion serves to briefly introduce B major, foreshadowing B- major cadences in Strophe 3, which begins the piece’s journey from D# minor to E major. I choose to describe B major as a secondary tonic here because, though it is approached by a D11, its placement within the strophe does not afford it the influence necessary to be considered a true tonic. Additionally, it only appears once within the strophe which is otherwise dominated by D# minor. This inclusion of B major against a
D# minor tonic also serves as preparation for the double-tonic nature of later strophes.
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Figure 4.9: “Trisagion” Strophe 2 (mm. 5-8)
Whereas the double-tonic implication in Strophe 2 is subtle, in Strophe 3 it is more overt. As shown in Figure 4.10, Strophe 3 takes the briefly introduced B major from the previous strophe as its initial tonic and by the end of the strophe moves to G# minor.
When considered as a whole, the piece so far exhibits three consecutive tonics from the
Circle of Thirds: D# minor, B major, and G# minor. When combined this way, these three tonics form what Yavorsky calls the “variable mode,” specifically variable mode 1.
Figure 4.10: “Trisagion” Strophe 3 (mm. 9-12)
Strophe 4 (Figure 4.11) reenacts the tonal motion of Strophe 3. Strophe 3 features a broad motion from B major to G# minor; Strophe 4 features the same motion four
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Texas Tech University, Chad Scarborough, May 2019 times. It is important to note that, despite not receiving a proper cadence, B major does serves as a tonic in Strophe 4 because of its function in the previous strophe. The end of
Strophe 3 establishes G# minor as tonic, and Strophe 4 strengthens its status as such by arriving at G# minor four times—once at each punctuation mark in the text. The presence of B major helps to link Strophe 4 back to Strophe 3 and to prepare the tonal motion of
Strophe 5.
Figure 4.11: Strophe 4 (mm. 13-16)
Strophe 5 (Figure 4.12) is the most harmonically interesting of the six strophes.
The first two measures of this strophe contain the only instances of E major in the piece, continuing the path around the Circle of Thirds. From this point onward, the piece begins to work back toward D# minor, the original tonic of the piece.
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Figure 4.12: “Trisagion” Strophe 5 (mm. 17-20)
One might choose to argue that E major does not act in a tonic capacity in this case due to the fact that the dominant chord immediately preceding it has its root a tritone from E. But it is worth considering E major’s position within the strophe as the cadential chord of each of the first two measures. Throughout the piece, every chord which has occupied that position has acted as tonic. This piece is clearly very pattern-based due to its repetitive nature, and so the most logical conclusion is to assume that the pattern holds, even if there are some points of intrigue surrounding E major in this case.
Measuring tonal areas along the Circle of Thirds, E major is the farthest point from the initial D# minor that the piece achieves. Therefore, the first two measures of
Strophe 5 serve as a harmonic climax. It is the apex of the tonal journey, highlighted by the unusual progressions surrounding E major.
Strophe 6 (Figure 4.13) retraces the thirds path back home to D# minor. It begins by once again strongly emphasizing B major. By the third measure, the tonal center has shifted back to G# minor before finally moving back to the initial tonic D# minor at the end of the piece. In the midst of the return journey to D# minor, the piece makes an interesting harmonic move. As the tonal center shifts from B major to G# minor in 61
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measure 23, a D#-minor chord inserts itself in the middle as a d7. Then, as G# minor gives way to D# minor in measures 23-24, a B-major chord appears as a d4. In this way, the three primary tonal centers of the piece come together at the end, each functioning differently with respect to each other.
Figure 4.13: Strophe 6 (mm. 21-24)
“Oh Sherrie” by Steve Perry27
Steve Perry’s “Oh Sherrie” is a good example of a similar type of tonal pairing in
Western Popular music. As such, the song is an excellent vehicle for demonstrating the capabilities of the neo-Yavorskian system with respect to Western Popular music. In general, the verses of “Oh Sherrie” are in D minor while the choruses are in F major. This pattern of minor verses and relative-major choruses is a common tonal plan in popular music that Mark Spicer describes as an “emergent tonic.”28 The following analysis shows the benefits of using neo-Yavorskian labels to describe the phenomenon as a global
27 All popular-music transcriptions are by the author unless otherwise noted. 28 Mark Spicer, “Fragile, Emergent, and Absent Tonics in Pop and Rock Songs,” in Music Theory Online 23, no. 2 (2017), http://mtosmt.org/issues/mto.17.23.2/mto.17.23.2.spicer.html (Accessed April 1, 2019) 62
Texas Tech University, Chad Scarborough, May 2019 double-tonic complex. Table 4.3 provides a broad overview of the song’s form in terms of tonic expression in each formal section.
Table 4.3: Formal chart of "Oh Sherrie" V = Verse; PC = Pre-chorus; C = Chorus
Intro V1 PC C V2 PC C Solo V3 C Solo Outro
F X X X X (X) X X X
?? X X X
d X X
The chorus of “Oh Sherrie” (Figure 4.17) is the most tonally straightforward section of the song, landing itself squarely in the realm of F major. Most of the harmonic progression consists of T-D13-T between F major and C major, with no hint of any other adjacent tonics from the Circle of Thirds (D minor or G minor, in this case). The only other chords besides F major and C major serve to temporarily tonicize B♭, setting up a plagal cadence (D5-T) at the end of each of the chorus’ two phrases. This plagal motion is related to the harmonic progression which dominates the song’s verses.
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Figure 4.14: "Oh Sherrie" - Chorus
Figure 4.15 shows Verse 2 of “Oh Sherrie,” which is the most harmonically stable of the song’s three verses, clearly emphasizing D minor. The entire progression of the verse consists of a motion from D minor to G minor and back (t-d5-t). As mentioned above, this plagal motion is the same as that which ends the chorus, though in this case the chords used are the relative minors of those from the chorus.
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Figure 4.15: "Oh Sherrie" - Verse 2
Though the second verse clearly centers on D minor, the first (Figure 4.16) is significantly more ambiguous owing to its lack of accompaniment until the final two measures (once again, D minor and G minor). The verse begins over a lingering F major chord from the introduction. Very quickly, though, the melody begins to imply D minor as tonic with a higher-level 3^-2^-1^ descent in D minor. The F over “know-” descends through the E over “I” before finally reaching D over “feel”. The entrance of the accompaniment reinforces the sense of D minor, but at the same time the melody shifts to a 3^-2^-1^ in F major, directly juxtaposed against the accompaniment harmony. It is worth 65
Texas Tech University, Chad Scarborough, May 2019 noting that the end of Verse 1 and the end of Rachmaninoff’s “Blessed is the Man” feature the same type of tonal juxtaposition, even involving the same two tonics.
3^ 2^
1^ 3^ 2^ 1^
Figure 4.16: "Oh Sherrie" - Verse 1
Now that we have established the two tonics present in the piece, I will focus on the sections which connect them. Figure 4.17 shows a transcription of the pre-chorus which follows Verse 1. Another pre-chorus which is harmonically identical (though with different lyrics) follows Verse 2. The pre-chorus harmony alternates three times between
B♭ major and C major. This section links the D-minor verses to the F-major chorus by providing equivalent function in both keys without ever leaning toward either. The labels 66
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d4|D5 and d10|D11 show that both chords provide almost equal tension toward both tonics.
Additionally, the tension increases and decreases over the course of the pre-chorus by consistent amounts toward both tonics. Moving from B♭ to C, the tension toward D minor increases by 6, from 4 to 10. Toward F major, the tension changes from 5 to 11, also increasing by 6. In Roman numeral terms, B♭ and C suggest both a ♭VI-♭VII-i progression (also known as the Aeolian progression) and a IV-V-I progression toward D minor and F major, respectively.29 Using the neo-Yavorskian dominant-function labels to describe both progressions simultaneously demonstrates how functionally similar they are to each other, and how a listener could potentially hear either progression in this instance.
29 Biamonte, “Triadic Modal and Pentatonic Patterns.” 67
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Figure 4.17: "Oh Sherrie" - Pre-chorus
Though a pre-chorus follows Verses 1 and 2, Verse 3 moves directly into the chorus, still managing to connect the two tonics in the process. Figure 4.18 shows a transcription of Verse 3. Just like the first two verses, Verse 3 consists almost entirely of alternation between D-minor and G-minor chords. However, the final chord of the verse, which moves directly into the F major chorus, is Dm7. Just as in Figure 4.1 from the
Rachmaninoff analysis above, the Dm7 chord combines both tonics into a single compound tonic marked ‘Tt.’ With this compound tonic, the song can move from D
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Texas Tech University, Chad Scarborough, May 2019 minor to F major without the need of the intermediary pre-chorus section. The motion from G minor to the D-minor portion of the compound tonic has been a consistent element of the verse sections. However, the motion from G minor to the F-major portion of the compound tonic is foreshadowed in the song’s introduction.
Figure 4.18: "Oh Sherrie" - Verse 3
The introduction to “Oh Sherrie” (Figure 4.19) begins in standard Western fashion, featuring alternations between dominant and tonic chords as well as short progressions which increase the amount of tension before finally resolving back to tonic
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(D5-D9-D11-T, in this case). What makes this introduction interesting is the final cadence from G minor to F major. As mentioned above, this cadence foreshadows the compound tonic in Verse 3. This G-minor-to-F-major progression also serves to amplify the tonal ambiguity in the first verse (Figure 4.16). When the G-minor chord appears in Verse 1, D minor is far from established as the local tonic key, partially implying a resolution to F major based on this previous exposure. The verse even partially delivers on this expectation, with the melody centering on F while the accompaniment below moves back to D minor. It is also worth mentioning that D minor never receives a stronger resolution than it does from G minor throughout the entire piece, so D minor never becomes so strongly tonicized that it cannot be easily supplanted by F major, such as at the end of
Verse 3. It would not be a mistake to say that the song’s ability to effectively combine D minor and F major is at least partially due to G minor.
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Figure 4.19: "Oh Sherrie" - Introduction
“Building a Mystery” by Sarah McLachlan30
Sarah McLachlan’s “Building a Mystery” and its apparent tonal ambiguity has been the subject of much discussion among theorists focused on Popular music.31 Drew
Nobile interprets the song through a double-tonic complex of B minor and D major.32
The neo-Yavorskian system developed here demonstrates how the harmonies of each section of the song contributes to this complex.
30 All transcriptions and other figures adapted from Nobile, “Double-Tonic Complexes.” 31 Robin Attas, “Sarah Setting the Terms: Defining Phrase in Popular Music,” in Music Theory Online 17, no. 3 (2011), http://www.mtosmt.org/issues/mto.11.17.3/mto.11.17.3.attas.html (Accessed April 1, 2017). Christopher Doll, “Rockin’ Out: Expressive Modulation in Verse–Chorus Form,” in Music Theory Online 17, no. 3 (2011), http://www.mtosmt.org/issues/mto.11.17.3/mto.11.17.3.doll.html (Accessed April 1, 2019). Trevor de Clercq, "Sections and Successions in Successful Songs: A Prototype Approach to Form in Rock Music” (PhD diss., University of Rochester, 2012), 97. Richards, “Tonal Ambiguity.” Nobile, “Double-Tonic Complexes.” 32 Nobile, “Double-Tonic Complexes.” 71
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The primary difference between “Oh Sherrie” and “Building a Mystery” is that the former contains different primary tonalities for its verse and chorus sections (verse in
D minor; chorus in F major). In the case of “Building a Mystery,” however, both sections sit squarely in the realm of a B minor/D major complex. Rather than functioning as a tonal journey from one key to the other, the pre-chorus “connects the verse and chorus sections with subdominant and dominant sonorities within this double-tonic context.”33
The verse and chorus sections (Figures 4.20 and 4.21, respectively) feature clear instances of Mark Richard’s Axis progression, which, as previously discussed in Figure
2.11, inherently implies a double tonic complex.34 The neo-Yavorskian analysis below the figure demonstrates how both B minor and D major have similar claims of tonic function. G major has a D5 relationship to D major and a d4 relationship to B minor, functioning similarly with respect to both tonics. A major has a D11 relationship to D major and a d10 relationship to B minor. While A major does lean slightly toward D major, the hypermetric placement of B minor within the four-chord loop provides it with enough emphasis to counteract this discrepancy in tension. As such, the two tonics present within the verse section are effectively equal. In the chorus, though the melody much more strongly emphasizes D major than B minor, the progression begins with B minor, thus affording it special influence over the perception of the rest of the progression, tonally speaking.
33 Nobile, “Double-Tonic Complexes.” 34 Richards, “Tonal Ambiguity.” 72
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Figure 4.20: "Building a Mystery" - Verse
Figure 4.21: "Building a Mystery" – Chorus
Just as in “Oh Sherrie,” the pre-chorus section in “Building a Mystery” (Figure
4.22) serves as a harmonic bridge between the verse and chorus sections, asserting weak tension in the direction of both tonics without ever fully committing to either. The neo-
Yavorskian labels beneath the staff in Figure 4.22 clearly show this weak tension for most of the pre-chorus section which finally increases with the A-major chord at the end, leading strongly back into both tonics.
Figure 4.22: "Building a Mystery" - Pre-chorus
The reduction shown in Figure 4.23 demonstrates the harmonic progression within a single instance of the verse – pre-chorus – chorus cycle.35 The verse establishes
35 From Nobile, “Double-Tonic Complexes.” Neo-Yavorskian labels by the author. 73
Texas Tech University, Chad Scarborough, May 2019 the double-tonic complex, the pre-chorus introduces and then escalates tension before resolving back to the double-tonic complex in the chorus. The neo-Yavorskian labels below the figure show that this progression works well with respect to both B minor and
D major. Considering chords to only function against B minor, the overall progression is t-d5-d10-t, and doing the same to D major results in T-D10-D11-T. Both versions of the progression follow the basic pattern of establishing tonic, introducing tension, and resolving that tension. Because this pattern works in both keys, this analysis demonstrates the similarity with which both B minor and D major are simultaneously developed over the course of the song.
Figure 4.23: "Building a Mystery" structural reduction based on Nobile 2019
Conclusion
The neo-Yavorskian system I propose clearly defines the amount of tension a given sonority exhibits toward any number of tonics. By assigning specific tension values to each non-tonic harmony, the system allows for discussion of function on a more specific level than the more general “dominant” and “pre-dominant” labels. It also allows for the understanding of more unorthodox progressions by simply analyzing them in terms of the amount of tension toward tonic present at any given moment instead of comparison to an arbitrary norm.
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The neo-Yavorskian system still has much room for development and application beyond what is discussed above. The most pressing issue for the future development of the neo-Yavorskian system is further codification of the process of determining primary versus secondary tonic function. At the moment, the distinction is purely subjective, making it the only such element of the neo-Yavorskian system.
The system may be developed and applied in other ways, though. Yavorsky’s original theory describes more than just the harmonic aspects of music; it also discusses ideas regarding rhythm and form. Future research might seek to incorporate these aspects into the neo-Yavorskian theory described above. Future research might also seek to expand the neo-Yavorskian system into the realm of reductive analysis, using weaker dominant functions as justification for harmonic reduction. Double-tonic complexes also occur in music outside the scope described above, such as Renaissance music, folk music of various countries, and hymns. Future research might seek to apply this neo-Yavorskian system to these pieces of music to see what information there is to be gained, be it with respect to the music itself, the analysis system, or both. Furthermore, some music features multiple tonics which are not a third apart, but rather a second or a fourth, for example.
Future research might seek to apply the neo-Yavorskian system to these pieces toward the same ends as previously mentioned.
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