Bach’s Inve Bach’ Invention ntions: s: Figur Figuration, ation, Regis Register ter,, Structur Structure, e, and the “Clear Way to Develop Inventions Properly” olli väisälä Bach’s 15 two-part Inventions are viewed from the Schenkerian perspective, perspective, focusing on three main topics: (1) the significance of figuration (design) and register as structural determinants, determinants, (2) the enlargement of characteristic surface figures, and (3) the significance of the Ursatz for actual musical events. It is argued that these three topics pertain pertain crucially to the musical organization in the Inventions and also offer significant viewpoints for the justification of Schenkerian analysis in Bach research. Keywords: Keywo rds: Bach Bach,, Inven Invention tions, s, Sche Schenkeri nkerian an analy analysis, sis, figura figuration, tion, regi register ster,, enla enlargeme rgements nts
B
ach’s 15 two-part inventions belong to the very best known repertoire of Western Western art music. Written for pedagogical pedagogical purposes, purposes, they still hold hold a standard position in both keyboard and counterpoint pedagogy. They have also frequently serve served d as analyti analytical cal examples of contrap cont rapunta untall devices devices,, moti motivic vic devel developme opment, nt, and form. form.1 Several have doubtless also considered their harmony and voice leading, but they have not featured prominently in
1
the most significant significant Schenkerian literature. literature. The present present study aims to fill in this gap, suggesting that the Inventions constitute an instructive corpus also for giving a “strong foretaste” of the clarity clarity and imaginativenes imaginativenesss of Bach’ Bach’ss voice-leading voice-lead ing structures. str uctures. Three general topics, each of which has significance for Bach’ss music and its analysis, will be my focus. Bach’ focus. The first deals with the role of figuration and register as structural determinants and as analytical criteria. The second topic is Bach’s tendency to develop characteristic foreground figures by enlarging them as larger structural frameworks. frameworks. The third addresses the relationship relationship between the “axiomatic” background of Schenkerian Schenkerian analysis analysis,, the Urlinie , and the actua actuall musical musical means by events. The first of these topics topics addresses the means by which the composition expresses the multilevel structures that Schenkerian analysis seeks to elucidate. elucidate. While each level depends on the fundamental principles of harmony and voice leading, I will be be emphasizing that the determination determination of structural weight—which element belongs to which level— is largely based on quite different factors, such as figuration
In this paper, I shall allude to Bach’s preamble to the Inventions according to the translation translation of the Wiener Urtext Edition (ed. Erwin Ratz and Karl Heinz Heinz Füssl, trans. unknown unknown): ): “A sincere guide, in which which lovers of keyboard music, music, and particularly particularly those desiring desiring to learn, are shown a clear way not only only (1) how to play play faultlessly faultlessly in 2 parts, but also, upon further progress, (2) how to treat three obbligato parts correctly and well; and at the same time not only to be inspired with good inventions but to develop them properly; properly; and most of all to achieve a cantabile manner manner of playing and to gain a strong foretaste of composition.” I am indebted to Lauri Suurpää for his valuable comments on a draft of this article. See, for example, Derr (1981) for discussion discussion on such aspects.
101
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and register.2 The second and third topics identify two contents of sources for the musical contents of such structures: piece-specific figures, figures, on the one hand, and the general general striving for the Urlinie descen Urlinie descent, t, on the other. While none of these topics is by any means original, a speciall attention specia attention to them is, is, I believe, believe, highly beneficia beneficiall for our understanding both of Bach’s musical organization and of the value of Schenkerian analysis in its illumination. While several analysts—Rothgeb (1971) and Oster (1961) being classic examples—have pointed out the impacts of figuration (or design) and register for structural clarification, the significance of these factors seems not always to be fully realized in analytical practice (as I have discussed in Väisälä 2008). 2008 ). Motiv Motivee enlargements enlargements are, are, of course, course, a familiar familiar topic in the Schenkerian literature (see, for instance, Burkhart 1978), 1978), and my contribution in this respect is confined to illuminating its particular significance for the present repertoire.
while the examples of section 1 serve ser ve primarily pri marily to illustrate i llustrate the structure-determining significance of figuration and register,, I will also pay attention to the structures they help register to determine, determine, including the the background background level. Similar interintertwinementt of topics is evident in all the sections. Figuration twinemen and register will retain their significance as analytical criteria throughout the analyses, including those focusing focusing on figure enlargements (which are not based on the desire to find such enlargements). enlargements). Finally Finally,, besides illuminating illuminating Bach’s musical language, language, I will suggest that these topics also offer significant arguments for defending the value of the Schenkerian approach approach in Bach research. research. Such arguments will be outlined in section secti on 4. abbreviations and analytical symbols
The article indentifies each Invention by key in boldface:
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while the examples of section 1 serve ser ve primarily pri marily to illustrate i llustrate the structure-determining significance of figuration and register,, I will also pay attention to the structures they help register to determine, determine, including the the background background level. Similar interintertwinementt of topics is evident in all the sections. Figuration twinemen and register will retain their significance as analytical criteria throughout the analyses, including those focusing focusing on figure enlargements (which are not based on the desire to find such enlargements). enlargements). Finally Finally,, besides illuminating illuminating Bach’s musical language, language, I will suggest that these topics also offer significant arguments for defending the value of the Schenkerian approach approach in Bach research. research. Such arguments will be outlined in section secti on 4.
and register.2 The second and third topics identify two contents of sources for the musical contents of such structures: piece-specific figures, figures, on the one hand, and the general general striving for the Urlinie descen Urlinie descent, t, on the other. While none of these topics is by any means original, a speciall attention specia attention to them is, is, I believe, believe, highly beneficia beneficiall for our understanding both of Bach’s musical organization and of the value of Schenkerian analysis in its illumination. While several analysts—Rothgeb (1971) and Oster (1961) being classic examples—have pointed out the impacts of figuration (or design) and register for structural clarification, the significance of these factors seems not always to be fully realized in analytical practice (as I have discussed in Väisälä 2008). 2008 ). Motiv Motivee enlargements enlargements are, are, of course, course, a familiar familiar topic in the Schenkerian literature (see, for instance, Burkhart 1978), 1978), and my contribution in this respect is confined to illuminating its particular significance for the present repertoire. Finally,, while Schenkerian analysts are always concerned Finally concerned with the relationsh relationship ip between the Urlinie and the actual music, the existing literature would seem to lack illumination of this topic based on systematic studies of well-defined but sufficiently extensive extensive corpuses corpuses of basic repertoire. repertoire. The 15 Inventions provide an opportunity for outlining how such a study may be conducted. I shall proceed by first discussing selected analytical examples for illuminating the first two topics in sections 1 and 2. In section section 3, I shall take take a more more comprehensive comprehensive look at the third third topic. topic. Howe However ver,, sinc sincee a single Inven Invention tion may may, of course, pertain to all three three topics, topics, it would be impractical impractical to keep the topics strictly strictly separate in the discussion. discussion. Hence,
2
abbreviations and analytical symbols
The article indentifies each Invention by key in boldface: major keys are given given in majuscule; majuscule; minor in minuscule. minuscule. The abbreviations are used both in the text and in the analytical examples. example s. There are two symbols used for special purposes in the analytical examples: an asterisk denotes voice-leading voice-leading relationships relations hips clarified by parallelism parallelism of figuration; and an accent sign (>) denotes special emphasis pertinent for structural hierarchy. contrapuntal design and form
Although I shall concentrate on the voice-leading structure rather than contrapuntal design or form, some notions concerning the latter two aspects will be necessary for my discussion. Most Inventions fall into two basic types with respect to thematic style and the nature of the opening imitation. Inventions of Type 1 (C, D, d, e, G, an and d a ) open with a statement of a short theme figure in the right hand alone or accompanied by a simple left-hand gesture to establish the tonic. This statement is followed followed by by imitation in the left left hand. Inventions of Type 2 (E , E, f , A , B , an and d b) open with a longer theme combined combined with a countersubject, countersubject, followed by
I discuss this in greater length in Väisälä 2008, in which I identify four significant structural determinants that are logically independent of the norms of harmony and voice-leading: design (including figuration), register,, meter register meter,, and rhetorical/gestural rhetorical/gestural devices. All these factors pertain pertain to the present analyses, even though the greatest greatest explicit attention is paid to the first two.
bach’ bac h’s inventio inventions: ns: figu figura ratio tion, n, reg registe ister, r, str struct uctur ure, e, and the the “cle “clear ar way way to to develo developp invent invention ionss proper properly” ly”
another statement with inverted voices.3 A special variant of Typee 2 is g , in which two countersubje Typ countersubjects cts alternate alternate in thematic statements. The remaining remaining Inventions, c and F , op open en with canons, but, on the basis of the right-hand material preceding the left-hand entrance, F comes closer to Type 1 and c to Type Type 2 (despite its one-voice opening). A central formal consideration concerns recapitulation. Most Type Type 1 Inventions ( C, d, e, an and d a ) lack an unequivocal recapitulation, if we define define this as requiring the concurrent concurrent return of the structural tonic and of the theme at the original level. Howeve Howeverr, d and a contain salient “recapitulation gestures,” theme statements at the original level but prior to the structural tonic return.4 Most Type 2 Inventions ( E , f , A , B , and b), alo along ng with with G and c, close with with a short unequivo unequivocal cal recapitulation recapi tulation:: a tonic return marked marked by a thematic thematic statement or two in the original key. 5 Such statements often in volve adaptations with crucial structural significance; hence
103
Each invention subdivides according to thematic and key design. Sections are usually (but not always) concluded by a cadence and opened by a thematic statement in a key that differs from that in the beginning of the preceding section. In middleground readings, measure lines are employed to indicate sectional borders. Another significant kind of formal entity is the retransition, by which I mean any passage leadleading from the last strongly tonicized non-tonic scale degree to the tonic return. 1. figuration and register as structural structural determinants
a : retransitional v – prolongation clarified by uniform figuration, figuration, with a “failed” “failed” recapitulation gesture as a digression
102
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while the examples of section 1 serve ser ve primarily pri marily to illustrate i llustrate the structure-determining significance of figuration and register,, I will also pay attention to the structures they help register to determine, determine, including the the background background level. Similar interintertwinementt of topics is evident in all the sections. Figuration twinemen and register will retain their significance as analytical criteria throughout the analyses, including those focusing focusing on figure enlargements (which are not based on the desire to find such enlargements). enlargements). Finally Finally,, besides illuminating illuminating Bach’s musical language, language, I will suggest that these topics also offer significant arguments for defending the value of the Schenkerian approach approach in Bach research. research. Such arguments will be outlined in section secti on 4.
and register.2 The second and third topics identify two contents of sources for the musical contents of such structures: piece-specific figures, figures, on the one hand, and the general general striving for the Urlinie descen Urlinie descent, t, on the other. While none of these topics is by any means original, a speciall attention specia attention to them is, is, I believe, believe, highly beneficia beneficiall for our understanding both of Bach’s musical organization and of the value of Schenkerian analysis in its illumination. While several analysts—Rothgeb (1971) and Oster (1961) being classic examples—have pointed out the impacts of figuration (or design) and register for structural clarification, the significance of these factors seems not always to be fully realized in analytical practice (as I have discussed in Väisälä 2008). 2008 ). Motiv Motivee enlargements enlargements are, are, of course, course, a familiar familiar topic in the Schenkerian literature (see, for instance, Burkhart 1978), 1978), and my contribution in this respect is confined to illuminating its particular significance for the present repertoire. Finally,, while Schenkerian analysts are always concerned Finally concerned with the relationsh relationship ip between the Urlinie and the actual music, the existing literature would seem to lack illumination of this topic based on systematic studies of well-defined but sufficiently extensive extensive corpuses corpuses of basic repertoire. repertoire. The 15 Inventions provide an opportunity for outlining how such a study may be conducted. I shall proceed by first discussing selected analytical examples for illuminating the first two topics in sections 1 and 2. In section section 3, I shall take take a more more comprehensive comprehensive look at the third third topic. topic. Howe However ver,, sinc sincee a single Inven Invention tion may may, of course, pertain to all three three topics, topics, it would be impractical impractical to keep the topics strictly strictly separate in the discussion. discussion. Hence,
2
abbreviations and analytical symbols
The article indentifies each Invention by key in boldface: major keys are given given in majuscule; majuscule; minor in minuscule. minuscule. The abbreviations are used both in the text and in the analytical examples. example s. There are two symbols used for special purposes in the analytical examples: an asterisk denotes voice-leading voice-leading relationships relations hips clarified by parallelism parallelism of figuration; and an accent sign (>) denotes special emphasis pertinent for structural hierarchy. contrapuntal design and form
Although I shall concentrate on the voice-leading structure rather than contrapuntal design or form, some notions concerning the latter two aspects will be necessary for my discussion. Most Inventions fall into two basic types with respect to thematic style and the nature of the opening imitation. Inventions of Type 1 (C, D, d, e, G, an and d a ) open with a statement of a short theme figure in the right hand alone or accompanied by a simple left-hand gesture to establish the tonic. This statement is followed followed by by imitation in the left left hand. Inventions of Type 2 (E , E, f , A , B , an and d b) open with a longer theme combined combined with a countersubject, countersubject, followed by
I discuss this in greater length in Väisälä 2008, in which I identify four significant structural determinants that are logically independent of the norms of harmony and voice-leading: design (including figuration), register,, meter register meter,, and rhetorical/gestural rhetorical/gestural devices. All these factors pertain pertain to the present analyses, even though the greatest greatest explicit attention is paid to the first two.
bach’ bac h’s inventio inventions: ns: figu figura ratio tion, n, reg registe ister, r, str struct uctur ure, e, and the the “cle “clear ar way way to to develo developp invent invention ionss proper properly” ly”
another statement with inverted voices.3 A special variant of Typee 2 is g , in which two countersubje Typ countersubjects cts alternate alternate in thematic statements. The remaining remaining Inventions, c and F , op open en with canons, but, on the basis of the right-hand material preceding the left-hand entrance, F comes closer to Type 1 and c to Type Type 2 (despite its one-voice opening). A central formal consideration concerns recapitulation. Most Type Type 1 Inventions ( C, d, e, an and d a ) lack an unequivocal recapitulation, if we define define this as requiring the concurrent concurrent return of the structural tonic and of the theme at the original level. Howeve Howeverr, d and a contain salient “recapitulation gestures,” theme statements at the original level but prior to the structural tonic return.4 Most Type 2 Inventions ( E , f , A , B , and b), alo along ng with with G and c, close with with a short unequivo unequivocal cal recapitulation recapi tulation:: a tonic return marked marked by a thematic thematic statement or two in the original key. 5 Such statements often in volve adaptations with crucial structural significance; hence
103
Each invention subdivides according to thematic and key design. Sections are usually (but not always) concluded by a cadence and opened by a thematic statement in a key that differs from that in the beginning of the preceding section. In middleground readings, measure lines are employed to indicate sectional borders. Another significant kind of formal entity is the retransition, by which I mean any passage leadleading from the last strongly tonicized non-tonic scale degree to the tonic return. 1. figuration and register as structural structural determinants
a : retransitional v – prolongation clarified by uniform figuration, figuration, with a “failed” “failed” recapitulation gesture as a digression
bach’ bac h’s inventio inventions: ns: figu figura ratio tion, n, reg registe ister, r, str struct uctur ure, e, and the the “cle “clear ar way way to to develo developp invent invention ionss proper properly” ly”
another statement with inverted voices.3 A special variant of Typee 2 is g , in which two countersubje Typ countersubjects cts alternate alternate in thematic statements. The remaining remaining Inventions, c and F , op open en with canons, but, on the basis of the right-hand material preceding the left-hand entrance, F comes closer to Type 1 and c to Type Type 2 (despite its one-voice opening). A central formal consideration concerns recapitulation. Most Type Type 1 Inventions ( C, d, e, an and d a ) lack an unequivocal recapitulation, if we define define this as requiring the concurrent concurrent return of the structural tonic and of the theme at the original level. Howeve Howeverr, d and a contain salient “recapitulation gestures,” theme statements at the original level but prior to the structural tonic return.4 Most Type 2 Inventions ( E , f , A , B , and b), alo along ng with with G and c, close with with a short unequivo unequivocal cal recapitulation recapi tulation:: a tonic return marked marked by a thematic thematic state5 ment or two in the original key. Such statements often in volve adaptations with crucial structural significance; hence such sections actually do much more than just “recapitulate,” but I shall call them recapitulations for the sake of simplicity. simplicity. A longer recapitulation, containing a counterpart for all parts of the opening opening section, section, is to be found in D and E. In the these se cases, the stretch stretch leading to the dominant dominant in the opening opening section is transposed at the lower fifth in the recapitulation so as to redirect redirect the music to the tonic. Finally, a comparable lower-fifth transposition, but without without any any preceding return at 6 the tonic, tonic, is evident evident in F and g .
3 4
5
6
104
Each invention subdivides according to thematic and key design. Sections are usually (but not always) concluded by a cadence and opened by a thematic statement in a key that differs from that in the beginning of the preceding section. In middleground readings, measure lines are employed to indicate sectional borders. Another significant kind of formal entity is the retransition, by which I mean any passage leadleading from the last strongly tonicized non-tonic scale degree to the tonic return. 1. figuration and register as structural structural determinants
In B , the countersubject countersubject is slightly varied in these these two statements. statements. In b, the countersubject is first presented as an unfigurated skeleton. In a , there are two two such gestures, the latter of which which (measure 22) is ac6 6 companied by the I of a I –V–I auxiliary cadence and thus anticipates the tonic while not yet establishing it (Example 1[a]). In several cases (E , f , b, G), the effect of the tonic tonic return is softened by a local I6 whose bass represents the goal 3 of a large-scale 5–4–3 top voice progression. In most cases ( E , b, an and d G), th thee 3 returns shortly to its due top-voice location above I. In F , measures 4–12 correspond correspond to measure measuress 26–34. In g, measure measuress 1–3 correspond to measures 13–15 and measures 5–9 correspond to measures 163–212. How However ever,, whe wherea reass F shows a straightforward lower-fifth
a : retransitional v – prolongation clarified by uniform figuration, figuration, with a “failed” “failed” recapitulation gesture as a digression
The retransitional events in a offer an excellent introduction to the structure-determining impact of figuration, also illustrating the participation of register in structural clarification. A central analytical problem problem in this Invention concerns the structural functions of its two recapitulation gestures (measures 18 and 22); Example 1(a) provides an annotated annotated score. scor e. For a meaningful meaningful solution solution to this problem, problem, let us examine how each of these gestures relates with surrounding figuration. The first recapitulation gesture (measure 18) occurs after four sequential measures measures (measures 14–17), which follow the cadence caden ce to V (E minor). While this recapitulati recapitulation on gesture momentarily interrupts the sequential sequential pattern, the right-hand part of this pattern is resumed immediately after this gesture (measure (meas ure 19). At this point, point, the left hand also also participates participates in transposition of the entire entire passage, in g the correspondence is varied in several ways, rendering it perceptually less salient. These cases also relate differently differently with structure, since measure 26 in F begins a large subdominant prolongation but measure 13 in g only prepares for such prolongation (Examples 6[c] and 7[c]).
music theory spectrum 31 (2009)
*
retransition begins
15
*
*
*
6 5
V
*
1st recap. gesture
“I” 6
retransition figure resumed
103
20
*
104
music theory spectrum 31 (2009)
*
*
15
retransition begins
*
*
6 5
V
20
*
*
retransition figure resumed
1st recap. gesture
“I” 6
2nd recap. gesture theme figure extended
5 3
[ ]
VII 7
V
I6 aux. cad.
IV
25
IV 7
V
I
example 1(a). a: measur measures es 14–25, annot annotated ated score score
bach’ bac h’s inventio inventions: ns: figu figura ratio tion, n, reg registe ister, r, str struct uctur ure, e, and the the “cle “clear ar way way to to develo developp invent invention ionss proper properly” ly” 13 21 22
^2
13
18
22
^2
N
V IV 7 V
V
6 5
13
*
*
*
()
*
V
22
* 1st recap gesture
“I” IV 7 V
18
6 5
105
^2
*
() () *
“I” 6
*
5 7 3 IV V
example 1(b). Measures 14–25, structural derivation
similar figuration, adding to the vigor of of this resumption. resumption. Similar right-hand figuration continues for the next two measures, leading to a semi-cadence V in measure 22.
the local 36 position of the “I” chord chord— bass’s sudden —by the bass’ withdrawal from the low register. The G 2 at the end of the sequence of measures 14– 14 –17 creates an expectation of an A2,
bach’ bac h’s inventio inventions: ns: figu figura ratio tion, n, reg registe ister, r, str struct uctur ure, e, and the the “cle “clear ar way way to to develo developp invent invention ionss proper properly” ly” 13 21 22
^2
13
18
22
13
^2
*
N
V IV 7 V
*
*
()
* 1st recap gesture
“I” IV 7 V
22
*
6 5
V
18
6 5
V
105
^2
*
() () *
*
“I” 6
5 7 3 IV V
example 1(b). Measures 14–25, structural derivation
similar figuration, adding to the vigor of of this resumption. resumption. Similar right-hand figuration continues for the next two measures, leading to a semi-cadence V in measure 22. Figuration suggests thus that the “attempted attempted”” recapitulation in measure 18 “fails fails”” and is only a temporary digression within an other otherwise wise uni unifi fied pattern connecting the V in measure 13 with the V in measure 22.7 Registral features support suppo rt such a perc perceptio eption. n. As circled circled in Examp Example le 1(a), 1(a), a stepwise descending line is formed by the high points of the top voice, voice, except for for measure measure 21, in which the the C4 occurs one octave “too low.” low.” (The D5–C4 relationship is clarifi clarified by dissonance treatment.) Since the first of these these high high points, points, B 5, is not supported by the V but represents a chromatic passing tone, the descent descent may be interpreted interpreted as a filled-in octave from an implicit B5 to B4. As for for the bass bass,, the effe effect ct of the the recapitulation gesture (measure 18) is weakened— weakened—apart from
the local 36 position of the “I” chord chord— bass’s sudden —by the bass’ withdrawal from the low register. The G 2 at the end of the sequence of measures 14– 14 –17 creates an expectation of an A2, which is only ful fulfi measure 21. The bass motion confilled in measure tinues to D 2, which suggests suggests a registral registral connect connection ion and a neighboring relationship with the original E2 (measure 14). In all, the low register register notes notes form an unfolding unfolding figure in which E2–G 2 is answered by A2–D 2. Example 1(b) clarifi clarifies the structural derivation of this passag pas sage. e. The “I” of the “failed failed”” recapitulation gesture has its basis in the neighboring motion B– B–C–B above the retransitional V – prolongation.8 Example 1(c) shows glimpses of two other Inventions— Inventions—d and e—indicating that such “I” chords are not unique to a .9 The octave desce descent nt from 2 to 2 (F 5–F 4) in e resem resembles, bles, in certain respects respects,, that in a and might be viewed as a simplifi simplified model for it. On the other hand, d, is another interesting example in which the “I” is exploited
the first recapitulation gesture as a digression relates sug7 The notion of the gestively to the compositional process of a , as this gesture is is among the material that Bach interpolated to the music after the preliminary verBach ). In sion of a (found in Clavierbüchlein vor Wilhelm Friedemann Bach) my analysis, the two versions of this Invention show a basically basically similar structure, struct ure, as opposed opposed to Neumeyer (1981), (1981), who regards regards the first recapitulation gesture as a structural tonic.
8
9
According to this reading, the C bass of the first recapitulation gesture is a transferred upper-voice tone. This function is concretized concretized by the correspondence between the left-hand figure of measure 19 and the right-hand figure of measure 21. Whereas the “I” is subordinate to IV IV 7 (= VII7 of V) in a , it forms forms the the main support for the neighboring tone in e and d.
music theory spectrum 31 (2009)
106 13 15
19
14 15
16
^2
e
V “I”
18 19
^1
38 46 47
d
“I” V
“I”6 53 V 7
46 47
38
44
^5
( ) ( )
V “I” V 7 V
38
^5
^4
V 8 (“I”) 7
^5
^4
V 8
(“I”) 7
V 8
46 47 48
^4
( )
(recap gesture)
(“I” 6
5) 7 3
example 1(c). Comparable retransitional V – progressions
for creating a non-structural recapitulation gesture; I shall return to this example in section 2 below in connection with Example 5. My identification of the first recapitulation gesture in
figuration. As if to repel any such possibility, the figuration pattern of the theme is extended so as to occupy fi ve quarters (measures 223–23 3). The remaining music also sustains a constant motion in invariant time values in each hand, creat-
music theory spectrum 31 (2009)
106 13 15
19
14 15
16
^2
e
V “I”
18 19
38 46 47
^1
“I”6 53 V 7
“I” V
46 47
38
44
46 47 48
^5
d
( ) ( )
V “I” V 7 V
38
^5
^4
V 8 (“I”) 7
^5
^4
^4
V 8
(“I”) 7
V 8
( )
(recap gesture)
(“I” 6
5) 7 3
example 1(c). Comparable retransitional V – progressions
for creating a non-structural recapitulation gesture; I shall return to this example in section 2 below in connection with Example 5. My identification of the first recapitulation gesture in a as “failed” is not meant to belittle its significance for the retransitional events. While figuration and register support perceiving this gesture as a digression within a dominant-framed span, it associates strongly with the upcoming tonic and also buttresses the feeling of the tonic key (which, characteristically, arrives much before the structural tonic harmony). Both of these contrasting aspects are significant for the musical effect, but a much more meaningful picture of prolongational relationships emerges if we follow the clues given by figuration and register and do not regard this gesture as a structural tonic.10 Example 1(d) illustrates how the retransitional events relate with the overall structure. The significance of the B5–B4 octave descent is clarified by its registral association with an earlier salient coupling C5–C6. Together these couplings elaborate degrees 3 and 2 in the 5-Urlinie . The second recapitulation gesture (measure 223), in contrast to the first, is followed by no return to the preceding 10
figuration. As if to repel any such possibility, the figuration pattern of the theme is extended so as to occupy fi ve quarters (measures 223–23 3). The remaining music also sustains a constant motion in invariant time values in each hand, creating the impression of a single relentless sweep up to the final tonic. As indicated in Examples 1(a) and 1(d), such an impression may be aptly described in terms of the auxiliary cadence I6–IV –V –I.11 Since the bass of this I6 lies an octave lower (C3) than that of the first recapitulation gesture (C4), register also contributes to the impression of the second gesture as the more decisive of the two. As indicated in Example 1(d), the top voice of this auxiliary cadence descends from 5 to 1, repeating the earlier 5–2 motion in a compressed form and delaying the eventual arrival at 1. The 11
In addition to Neumeyer (1981), Travis (1976) and Adrian (1985) regard this gesture as a structural tonic.
The details of this reading may call for some clari fication. Reading the I6 as the governing harmony at the second recapitulation gesture is based on its occurrence at the third beats of measures 22 and 23, the framing points of the uniform right-hand figuration and strong points in the perceived meter (notwithstanding the measure lines). The ensuing IV chord (measure 234) is marked, despite its metrical weakness, by the change in right-hand figuration and by the lack of registral continuation in the bass at the subsequent strong beat. The return to the IV (measure 24 4) is underlined by the extreme registral position of its bass (D 2).
bach’s inventions: figuration, register, structure, and the “clear way to develop inventions properly” 3
6
^5
^4
6 4 6 4 6 6 6 6 6 2 5 2 5 4 5 4 5
I
13
14
18
retrans.
1st retrans. recap. figure gesture resumed
^3
(C: II 64
9
6 V 5
22
^2
23
25
2nd recap. gesture
^1
( ) () () ( ) ( ) * * * *
III
(e: II
4 3
V
I)
V
^3 ^ 2
* *
*
I)
^5 ^ 4
(“I”6
example 1(d). Overall sketch
*
5 7 3 ) IV V
I6
IV
aux. cad. to
IV 7 V I I
107
bach’s inventions: figuration, register, structure, and the “clear way to develop inventions properly” 3
6
^5
9
^4
13
14
18
retrans.
1st retrans. recap. figure gesture resumed
^3
22
^2
23
107
25
2nd recap. gesture
^1
( ) () () ( ) ( ) * * * *
*
6 V 5
I
I)
4 3
(e: II
V
III
^3 ^ 2
* *
6 4 6 4 6 6 6 6 6 2 5 2 5 4 5 4 5
(C: II 64
^5 ^ 4
*
I)
6
V
5 7 3 ) IV V
(“I”
I6
IV
aux. cad. to
IV 7 V I I
example 1(d). Overall sketch
overall structure may thus be viewed as a variant of the interrupted structure, whose second branch is weakened by its short duration and by the 63 position of its opening tonic. The relationship between figuration and structure in this introductory example illustrates a basically familiar analytical principle. As formulated by John Rothgeb (1971, 231), “changes in surface design usually coincide with crucial structural points, and accordingly such changes must be given the most thoughtful attention in deriving or verifying an analysis.” The first recapitulation gesture suggests a change in surface design, but the suggestion is quickly cancelled, depriving this gesture of structural decisiveness. Only the second gesture effects a permanent change in design, signaling a decisive break with the dominant’s prolongational orbit. Another way to formulate Rothgeb’s principle is by saying that spans of uniform figuration—i.e., those without changes in surface design—tend to correspond with spans relevant to prolongational hierarchy. This principle is of utmost significance for Bach analysis and, as the present example suggests, it is powerful enough to apply even when
the uniformity of figuration is interrupted by a temporary digression. This example also illustrates the structural significance of registral proximity and extremity. The bass-line unfolding (E2–G 2, A2–D 2) is supported by both proximity and extremity, as is the large-scale top-voice coupling (C5–C6, B5–B4). However, whereas figuration or design provides, I would suggest, a virtually unfailing “key to structure” in Bach, we should bear in mind that registral positions involve considerable flexibility. When other factors are suf ficiently strong in determining the structural position of an element, the registral presentation of that element is freer. For example, since the structural position of the dominant in measure 22 is clarified by the expectation created by the preceding °7 chord on D 2 and by the radical change in design, the location of that dominant (E3) an octave higher than expected does not jeopardize structural clarity. In this case, leaving the E2 implicit in measure 22 is aesthetically motivated by the way it adds to the freshness and effectiveness of the explicit D 2–E2 motion in the closing cadence (measure 25).
music theory spectrum 31 (2009)
108 5
9
12
23
^5
25
( ^6 IN
27
^4
31 ^4
^3)
~ ~ ~ P
recap.
(countersubject)
N
I I5
V
I6
VI
II
6
II
(IV)
V 42
I6
V 43
I
5 3
example 2. E : register, figuration, and structure
^3
^2
^1
~ (extension of theme)
P
VII6 (or V 43 )
I6
II 6 V I
music theory spectrum 31 (2009)
108 5
9
12
23
^5
25
( ^6 IN
27
^4
31 4^
^3)
~ ~ ~ recap.
I6
V
I5
VI
II
6
II
(IV)
V 42
I6
V 43
I
1^
(extension of theme)
P
N
I
2^
~
P
(countersubject)
3^
5 3
VII6 (or V 43 )
I6
II 6 V I
example 2. E : register, figuration, and structure
: parallelism of figuration and register
motions. Of these high-register tones, C6 occurs within a countersubject statement but A 5 is marked by the freer employment of similar figuration. Hence, while the B 5–C6 relationship might be viewed as a by-product of the thematic disposition, the appearance of similar figuration to mark A 5 suggests more expressly an impulse to clarify voice-leading relationships as its motivation. B 5, C6, and A 5 participate in a 5–6–4–3 framework, completed at the beginning of the short recapitulation (measure 27) and thus spanning most of the Invention. Whereas the beginning of this framework is registrally uniform, the 4–3 motion involves a registral drop from A 5 to G4 (more locally this motion is transferred to the bass in measures 26–27). Such a registral drop has significant implications for the structure, since it undermines the definitiveness of this initial progression, suggesting that it does not yet form part of the Urlinie proper. And indeed, a more satisfactory 4–3 Urlinie descent, leading to 2–1, follows in the recapitulation once the extended Invention theme has climbed emphatically back to the obligatory high register (A 5 in measure 31). The crucial
e
clarifying top-voice motions
Connections of figuration may clarify voice leading even when involving more widely dispersed details, especially when supported by extreme registral position. Blending structural with musical notation (the latter only in upper stave), Example 2 illustrates how the cooperation of figuration and register highlights top-voice motions in E .The beginning of the Invention theme centers on 3 (G4, measures 1–3), but an “open position” arpeggiation G4–E 5–B 5 leads the top voice to a higher 5, a persistent tone in the countersubject (measures 5–8; Example 2 shows only the beginning of the countersubject). Despite the local V harmony, the extreme register and the persistence of this B 5 attract attention so as to suggest Kopfton status. This suggestion is borne out by subsequent top-voice events, in which C6 (measure 12) and A 5 (measure 25) are highlighted through similar highregister figuration, creating stepwise connections with the B 5 and confirming its role as the point of departure for top-voice
bach’s inventions: figuration, register, structure, and the “clear way to develop inventions properly”
significance of these registral events for structural perception becomes evident if we consider the effects that a high 3 (G5) would have at the beginning of the recapitulation. A 4 (A 5) surrounded by two such high 3s would likely be heard as a neighbor of 3 and could not function as an Urlinie tone. Analogous registral events are evident in the bass, which moves away from the original low register (E 2) at the beginning of the recapitulation (E 3) and returns there so as to underline the Urlinie 4 (F 2). The structure of E is particularly noteworthy because it exemplifies a structural pattern whose variants recur in several other Inventions. I shall return to E for discussing these related cases in section 3, in connection with Example 14.
: parallelism establishing registral discrepancy and reconciliation
d
109
(measures 47–50). For considering the structural implications of this parallelism, it should first be noted that the former passage begins a large but relatively straightforward prolongation of V and 2, extending all the way to the beginning of the recapitulation (measures 5–42; Example 3[b] provides details of the interpretation). At the end of this prolongation, the F 4–E5 seventh is recomposed on a retransitional V 64-5 -3 framework, reminding us of the original discrepancy (measures 39–42). Now the ascending seventh F 4–E5 naturally creates an expectation of D5 to effect a change in direction in the melodic motion and to satisfy the top voice’s aspiration towards the higher octave. And while the recapitulation begins with the low 3 (F 4, measure 43), which suggests a structural interruption, an ascent to D5 follows shortly (measure 47), pointing to a registral E5–D5 connection over the intervening low 3. On the large scale, the E5–D5 connection is supported by the parallelism
bach’s inventions: figuration, register, structure, and the “clear way to develop inventions properly”
significance of these registral events for structural perception becomes evident if we consider the effects that a high 3 (G5) would have at the beginning of the recapitulation. A 4 (A 5) surrounded by two such high 3s would likely be heard as a neighbor of 3 and could not function as an Urlinie tone. Analogous registral events are evident in the bass, which moves away from the original low register (E 2) at the beginning of the recapitulation (E 3) and returns there so as to underline the Urlinie 4 (F 2). The structure of E is particularly noteworthy because it exemplifies a structural pattern whose variants recur in several other Inventions. I shall return to E for discussing these related cases in section 3, in connection with Example 14.
(measures 47–50). For considering the structural implications of this parallelism, it should first be noted that the former passage begins a large but relatively straightforward prolongation of V and 2, extending all the way to the beginning of the recapitulation (measures 5–42; Example 3[b] provides details of the interpretation). At the end of this prolongation, the F 4–E5 seventh is recomposed on a retransitional V 64-5 -3 framework, reminding us of the original discrepancy (measures 39–42). Now the ascending seventh F 4–E5 naturally creates an expectation of D5 to effect a change in direction in the melodic motion and to satisfy the top voice’s aspiration towards the higher octave. And while the recapitulation begins with the low 3 (F 4, measure 43), which suggests a structural interruption, an ascent to D5 follows shortly (measure 47), pointing to a registral E5–D5 connection over the intervening low 3. On the large scale, the E5–D5 connection is supported by the parallelism shown by the large asterisks, as the D5 is featured by the reappearance of the octave-leap texture that originally established the E5. Design and register thus suggest hearing the D highlighted by the octave leaps i n measures 47–50 as representing 1 in a large-scale 3 – 2– 1 pattern. Such a hearing implies that the features pointing to the interrupted structure as the basis of this Invention should not be taken quite at face value. To be sure, the recapitulation section can be heard as embodying the second branch of the interrupted structure. The octave leaps on 1 are followed by two registrally uniform small-scale 3 – 2 – 1 progressions in both registers pertinent to the initial F 4–E5 discrepancy (F 5–E5–D5 in measures 51–54 and F 4–E4–D4 in measures 56–59), as if to correct the discrepancy. The former 3–2–1 is accompanied by a deceptive cadence and the latter by the final authentic cadence, which completes the second branch. However, the perception of 1 as being already stated before these progressions offers an unusual—and aesthetically satisfactory —perspective for hearing them. Instead of introducing 1, they confirm an earlier 1 . Such a hearing
: parallelism establishing registral discrepancy and reconciliation
d
Figuration and register do not always work neatly in cooperation, but parallelism of figuration may also help to establish a voice-leading connection between registrally noncorrespondent elements. As illustrated by brackets and small asterisks in Example 3(a) (measures 1–5), occurrences of the theme figure and its variant establish a registral discrepancy between a low 3 (F 4) and a high 2 (E5) at the opening of D. This discrepancy is a prominent feature of this Invention and has crucial ramifications for its unusual structure. Apart from the registral discrepancy, this 3–2 motion shows other unusual features that highlight the character of the 2 as a surprise element. 2 and the accompanying tonicized dominant arrive exceptionally early and without preceding modulatory procedures. The dominant key is established only afterwards through a repetitious four-measure passage (measures 5–8) with a dominant pedal activated by octave leaps, a passage with uncharacteristically simple texture for Bach. The large asterisks in Example 3(a) (measures 5 and 47) indicate a parallelism on a larger scale, one between this octave-leap passage and its correspondent in the recapitulation
music theory spectrum 31 (2009)
110
5
^3 (F 4)
10
^2(E5)
*
I
* *
(A: I
IV (V 42 “I”6 )
*
V 38
(F 4
~ retrans.
109
40
43
45
E5)
( )
recap.
^3(F 4)
*
^1!
*
music theory spectrum 31 (2009)
110
5
^3 (F 4)
10
^2(E5)
*
*
*
* *
I
V 38
40
43
(F 4
~
retrans.
V
I)
45
E5)
^1!
( )
*
recap.
^3(F 4)
V 64
5 3
I
50
IV (V 42 “I”6 )
(A: I
55
^3 (F 5)
IV (V 42 “I”6)
^2(E5)
^1(D5)
V
VI
^3 (F 4)
IV (V 42 “I”6)
(I)
^2(E4)
^1(D4)
V
I
example 3(a). D: measures 1–12 and 38–59, annotated score
is supported by features that help to associate the octaveleap 1 (measures 47–50) with the final 1: the reappearance of the octave leap at the end of the first 3–2–1 progression (measure 54) and the general similarity between the two progressions.
Example 3(b) offers more systematic explanation of the structure. Graph (i) adapts for D major Schenker’s notation (1979, Fig. 21b) for the interrupted structure. A key feature of this idea is the subordinate relationship of the second branch to the final 1. Graph (ii) expresses the same idea with
bach’s inventions: figuration, register, structure, and the “clear way to develop inventions properly” In D, register and large-scale parallelism highlight the anticipation of ^1. Schenker's conception of Another notation for interruption (FC: Fig. 21b) similar conception ^3
^2 ( ^3 ^2) ^1 (ii)
(i)
5 43 47
^ ^ (iii) 3 2
5
ant. ^1!
( )( ) * *
antic.
7th
6th
recap.
24 35
39
* *
(iv)
7th
7th (reminder) recap. retrans.
N
6 5 4 3
I V VI V
5
*
*
9
12
19
24
43 47 51 54
33
35
I
V I
39
43
47
51
54
111
bach’s inventions: figuration, register, structure, and the “clear way to develop inventions properly”
111
In D, register and large-scale parallelism highlight the anticipation of ^1. Schenker's conception of Another notation for interruption (FC: Fig. 21b) similar conception ^3
^2 ( ^3 ^2) ^1 (ii)
(i)
5 43 47
^ ^ (iii) 3 2
5
ant. ^1!
( )( ) * *
antic.
7th
24 35
39
* *
(iv)
7th
6th
7th (reminder) recap. retrans.
N
recap.
6 5 4 3
I V VI V
5
*
9
12
19
24
33
I
V I
35
39
43
47
51
54
*
( ) ( ) * (v)
*
*
*
( ) * *
* *
*
(A: I V
IV “I 6 ”V
*
*
*
*
*
I
43 47 51 54
6 4
*
5 3
*
*
*
(b: V 42 I6 VII6(III6“I6”V) I)
I) V 5
6 5 VI 1
V 7 V
I
VI
(I) IV “I6 ” V I
example 3(b). Derivation of structure
a slightly different notation, adding an inner voice. A latent property of this inner voice is the anticipation of the final 1 at the outset of the second branch. While such an anticipation usually has no particular significance, register and design bring it to the fore in D. As a result, the anticipated 1 may be perceived as overriding the 3–2–1 motion in structural priority, as indicated in graphs (iii) and (iv) (with somewhat
different notations).12 Besides being supported by design and register, such a perception also yields aesthetic rewards. The octave-leap texture in measures 5–8 and 47–50, which in itself may appear strikingly unsophisticated for Bach, While it is controversial whether the conception of the second branch as subordinate to the first is cogent in all instances of the interrupted
12
music theory spectrum 31 (2009)
112
56
^3
38 38 I
( ^4 ^3) IN P
^2
^1
^3
IV 8 7
I
V
I
( ^4
^3)
^2
^1
^3
( ^4
^3)
^2
^1
V
I
*
IN
IN
P
IV (V 42 “I6”)
*
V
I
I
P
IV (V 42 “I6 ”)
example 3(c). Cadential formula with “I 6” between IV and V
turns out to be a vehicle in the subtle and witty poetics of two unexpected Urlinie events. Moreover, since both D5 and D4 appear as representatives of Urlinie 1 in this reading, the initial registral discrepancy is satisfactorily reconciled. The
as the bass of IV or II6. 4 initiates a passing motion 4–3–2 in hemiola rhythm, in which the passing 3 supports an apparent I6 and 2, harmonized by V, returns to its correct position in the upper voice.13 As the subsequent examples will testify
music theory spectrum 31 (2009)
112
56
^3
( ^4 ^3) IN P
^2
^1
^3
( ^4
^3)
^2
^1
38 38 P
IN
IV 8 7
I
V
I
I
IV (V 42 “I6”)
V
I
^3
( ^4
^3)
^2
^1
V
I
*
IN
P
*
IV (V 42 “I6 ”)
I
example 3(c). Cadential formula with “I 6” between IV and V
as the bass of IV or II6. 4 initiates a passing motion 4–3–2 in hemiola rhythm, in which the passing 3 supports an apparent I6 and 2, harmonized by V, returns to its correct position in the upper voice.13 As the subsequent examples will testify, such “I6” chords, whose bass tones represent passing upper voice 3s, appear frequently as intermediate elements between IV or II and V in Bach’s cadences. The awareness of their non-tonic function is essential for Bach analysis.14
turns out to be a vehicle in the subtle and witty poetics of two unexpected Urlinie events. Moreover, since both D5 and D4 appear as representatives of Urlinie 1 in this reading, the initial registral discrepancy is satisfactorily reconciled. The D5 fulfills the aspiration of the F 4–E5 motion towards the higher octave, whereas the D4 remains in touch with the original register. By contrast, if we based our interpretation on an ordinary interrupted structure, only D4 would represent the final 1. Graph (v) proceeds to the foreground reading. Among other things, it shows several more instances in which repetitions of the thematic figure suggest certain voice-leading connections (small asterisks). A noteworthy phenomenon, bearing on several subsequent analyses, is the transfer of such connections from the treble to the bass in cadences (measures 9–12, 21–24, 35–38, 51–54, 56–59). As illustrated in Example 3(c), this formula involves the motion from a local 3 to its incomplete neighbor 4 in the bass, which concurrently functions
For illustrating the general formula, Example 3(c) shows the opening chord as I, although, as evident from Example 3(b), graph (v), the chord in measure 56 may in its actual context be perceived as a parenthetical event between VI and IV. Characteristics of such progressions include a relatively emphatic IV (or II), a relatively weak “I6,” often approached through a local V 42, and a V –I cadence. Psychologically speaking, the expectations created by the emphatic subdominant are not satis fied by the weak V 42– “I6” progression but only by the strong V –I. As in Rothstein 2006 (268 ff .), such “I6” chords may be described as inverted cadential 64s, especially when their metric position is clearly strong in relation to the subsequent dominant. However, when the 63 occupies the second beat in a hemiola rhythm, as in the present case, the aptness of this description is somewhat more questionable. Incidentally, this kind of cadential formula is not limited to Baroque music; for a hemiolic example similar to Example 3(c), see Beethoven, Sonata in F Minor, op. 2 no. 1, second movement, measures 5–8.
13
14
structure it is interesting to note that the two Inventions that are analyzable as embodying variants of the interrupted structure show concrete features supporting such subordination. In a , the second branch is brief and starts from I 6; in D, the anticipated 1 overshadows the Kopfton’ s return.
bach’s inventions: figuration, register, structure, and the “clear way to develop inventions properly” 1
9
13
17
1
8
^5
( ) (i)
P
6
I
10
S (ii)
15
D S D
S
S
S
20
D P
( ) ( ) G
F
E
(etc.)
4 6 2
D
F
V
(B: II
(“I”) 65
V
4 I6 2
V
B
I 53 )
25
Cf. theme in B major
delayed tension
G
F
E
release D F
B
113
bach’s inventions: figuration, register, structure, and the “clear way to develop inventions properly” 1
9
13
17
1
8
10
^5
( ) (i)
(ii)
P
6
S
4 6 2
I
15
D S D
S
S
S
20
D
( ) ( ) G
F
P
E
(etc.)
D
F
V
(B: II
(“I”) 65
113
V
4 I6 2
B
I 53 )
V
25
Cf. theme in B major
delayed tension
G
F
release D F
E
B
example 4(a). E : first section (measures 1–20)
As for figuration, two rhythmic elements, syncopation and dactyls—hereafter S and D—help to identify units of structural significance. Following the pattern set by the theme, the S element signals the beginnings of such units and the D element signals their ends. Hence after the sequential two-bar SD units in measures 9–12, which lead the bass from E via D to the C in measure 13, the pattern is lengthened to four bars (SSSD) in measures 13–16, delaying the arrival at the goal B (Example 4[a], graph [ii]). The impact of figuration and register for structural perception becomes especially evident by considering the status of the B major chord at the downbeat of measure 15. This is precisely the moment at which the preceding two-bar rhythm would lead us to expect the E–D –C motion to reach its goal. However, the occurrence of this B within the lengthened SSSD pattern and its high registral position (above its immediate
: supreme lucidity—with a turn to obscurity
e
As illustrated in Example 4(a), the opening section of E (measures 1–20) offers especially lucid illustration of the structure-determining impacts of register and figuration. The outer-voice frameworks are clarified by extreme registral position. The top voice presents an ascending arpeggiation 1–3–5 (E5–G 5–B5), with a passing 4 (A 4) occurring in a lower register. The bass descends stepwise from I to V (E2–D 2–C 2–B1); B1—the only note below C2 in the Inventions—confirms the registral logic by its appearance at the very end of the section.15
That Bach wrote this B 1 even though this tone was not always readily available in the contemporary keyboard instruments may testify to the importance of registral logic for his musical thinking.
15
music theory spectrum 31 (2009)
114 25
Theme S
30
S
S
Digression D
D
D
D
35
“Main discourse” continues S D
S
D
S
D
Decisive breakaway D D
music theory spectrum 31 (2009)
114 25
30
Theme S
S
S
Digression D
D
D
D
35
“Main discourse” continues S D
S
D
S
Decisive breakaway D D
D
N
(to D in m. 41)
example 4(b). Measures 25–39, annotated score
surroundings) suf fice to dispel any effect of goal arrival. Rather, this B functions as harmonic support for the passing motion E5–D 5–C 5, which prolongs the C minor harmony (II in B major). Register and figuration also strongly pertain to the analysis of the second section (measures 21–42); see Example 4(b). In terms of key relationships, the G minor passage in measures 29–32 is a crucial event for preparing the establishment of III at the end of this section. However, key areas and prolongational spans do not necessarily or even usually coincide. In fact, instances in which a new key area and a
prolongational span begin concurrently (as in measure 5 of D, shown in Example 3) are rather exceptional. In modulation the new key ’s tonic frequently appears in a structurally subordinate position prior to its actual establishment, as exemplified by the above-discussed B major chord (or by the A minor chord of the first recapitulation gesture in a ) . In the present case, register and figuration, as well as the lack of preparation, suggest a relatively weak structural position for the first G minor chord (measure 29). Its lowest note, G 3, is a sixth above the preceding bass note B2, which enables the G minor triad to be perceived as emerging from 5–6 motion
bach’s inventions: figuration, register, structure, and the “clear way to develop inventions properly” 21
39
42
() (i)
21
36
38 39
42
P
25
30
35
S S SD D D D D
S
D
40
S
D
S
D
D D D
( ) ( )
B A (A ) G (ii)
(cf. m. 25)
21
115
(iii)
B
A A
G
N
N
B5 B5
6 6
example 4(c). Second section (measures 21–42), structural derivation
above B. An emphatic return to the registral vicinity of the B follows in measure 39 in which the C ortin
such relationships concern both the S element (B 5–A5; see circles) and the D element (F –E see b s), and also the
bach’s inventions: figuration, register, structure, and the “clear way to develop inventions properly” 21
39
42
21
38 39
42
21
25
30
35
S S SD D D D D
() (i)
36
S
D
115
40
S
D
S
D
D D D
( ) ( )
B A (A ) G (ii)
(iii)
B
A A
G
N
(cf. m. 25) P
N
B5 B5
6 6
example 4(c). Second section (measures 21–42), structural derivation
above B. An emphatic return to the registral vicinity of the B2 follows in measure 39, in which the C 3, supporting a Neapolitan sixth, is marked by the first halt in the left hand’s eighth-note motion since measure 29, by hemiola rhythm (measures 39–40), and by the ensuing cadential progression. These features suggest a bass-line connection between the initial B2 and this C 3, relegating the intervening G minor chords to a lower structural status. Considerations of right-hand figuration support and refine such a reading. As evident from Example 4(b), the first four measures of the G minor passage (measures 29–32) comprise dactyls only (DDDD), deviating from the prevalent norm of S beginnings for structurally significant units. After this passage, the S element is resumed, and three SD units follow (measures 33–38). Somewhat reminiscent of the first recapitulation gesture in a , this DDDD passage suggests a change in surface design but fails to establish it, whereas the upcoming Neapolitan sixth on C (measure 39) is marked by a more decisive abandonment of the S element. The digressive character of the DDDD passage is strengthened further by stepwise connections between the preceding theme statement in B major (measures 25–28) and the ensuing SD unit (measures 33–34). As we can see in Example 4(b),
such relationships concern both the S element (B 5–A5; see circles) and the D element (F 5–E5; see beams), and also the bass, in which the association between the bracketed figures in measures 25 and 33 supports the chromatic connection between B2 and B 3 despite the registral difference. Following the clues given by figuration leads to a reading in which the composing-out of the B major harmony continues after the DDDD digression up to the emphatic Neapolitan sixth; for systematic illustration, see Example 4(c). The leading upper-voice progression descends a fifth from F 5 to B4 and is consistently articulated by the D element. The higher stratum of notes, shown by circles in Example 4(b), has subsidiary significance for voice leading, but by echoing the chromatic head-motive B5–A 5–A 5–G 5 of the B major theme statement it strengthens the sense in which this statement extends its influence into the subsequent events despite the destabilization of the B major key.16
The G 5 in measure 35 resolves to the F 3 in measure 36, which stands for an inner-voice tone despite its low registral position. This low position enables this F 3 to associate registrally with the subsequent F 3 and G 3, highlighting the 5–6 motion in measures 36–38.
16
music theory spectrum 31 (2009)
116 43
^5
(i)
I
51
55
58
59
47
^5
50
55
( ) () ( ) 60
() ( ) ( ) ^4
II 6
^3 ^ ^ 2 1
V 64 53 I
(ii)
( ) ( )
^4
^3
^2 ^1
(V 42 “I6 ”)
I
Cf. theme
VI
II6
quasi V 64 53 I
delay
release
(iii)
D
^5
D
^4
S
D
S
D S
^3
S
From:
S
D
^2 ^1
^2
^1
music theory spectrum 31 (2009)
116 43
^5
(i)
I
51
55
58
59
47
^5
50
55
( ) () ( ) 60
() ( ) ( ) ^4
^3 ^ ^ 2 1
(ii)
( ) ( ) ^4
II 6
^3
(iii)
^2 ^1
D
^5
(V 42 “I6 ”)
V 64 53 I
I
VI
II6
quasi V 64 53 I
delay
Cf. theme
D
^4
S
D
S
D S
^3
S
S
D
^2 ^1
^2
^1
From:
release
II6
(V 42 “I6”) V
example 4(d). Third section (measures 43–62)
While the concluding section (measures 43–62) constitutes a formal recapitulation, it shows nothing of the lucid correlation between register and structure that characterizes the opening section. Through inverted counterpoint (partly at the twelfth), the strong-beat elements of the SD and SSSD units in measures 9–16 are shifted from the registral extremes to the middle register in the corresponding passage of measures 51–58. As illustrated in graph (iii) in Example 4(d), the highest tones do not form an Urlinie descent but neighbor motion around the 8 (E 5–F 5–E5–D 5–F 5). Figuration, however, proves once again its reliability as a key to structure. At the end of the last E major theme statement (measure 50), the D element is transferred from the right hand to the left hand, carrying along 5. In the subsequent passage (measures 51–58), the S and D elements remain in the left hand, which,
owing to these high-profile rhythms, may be heard as attracting the primary melodic attention.17 Figuration helps thus to direct the listener’s attention to the left-hand progression 5–(6–5)–4–3, in which the 4–3 motion is highlighted through the lengthened SSSD pattern (measures 55–58) and through the absence of right-hand activity at the decisive moment (measure 58–59 1). The 3, in turn, supports a “I6” whose function is similar to those discussed above in connection with the cadences of D. It is a passing tone in a 4–3–2 progression, in which 2 is implied by the
17 There is also a less evident way in which figuration supports the 5–6 connection in measures 50–51: the right-hand dactyls in measure 50 outline a syncopated B 4–G 4–E4 figure that corresponds to the lefthand C 4– A3–F 3 figure in measure 51.
bach’s inventions: figuration, register, structure, and the “clear way to develop inventions properly” 9
16
21 39
42
51
55 59
^5
( ) ( )
( ) ( ) recap.
^4
^3
^2 ^1
example 4(e). Overview
cadential dominant (measure 59, beat 3).18 The comparison of graph (ii) with the cadences in D (see especially Example 3[c]) illustrates how the harmonic structure of the conclud-
117
obscure form in which the 4–3 motion appears in the bass and the 2 is omitted altogether.20 Graphs (i)–(iii) in Example 4(d) elucidate the derivation of the structure from a more normal registral setting. The transformations leading from the “normal” setting to the actual music are unusually radical, which relates with the curious, only “minimally conclusive” musical effect of the conclusion. In particular, the final cadence (measure 59)—missing 7 as well as 2 and featuring a registrally high rhythmically weak dominant, B3— sounds deliberately understated.21 Example 4(e) graphs the overall structure, showing actual registers. It also sheds some light on the significance of the 8 (E5) that covers the Urlinie progression, indicating by a dotted tie its relationship with the prominent 8 of the opening. The obscurity of the Urlinie descent should not be confused with structural ambiguity. While the bass-line articulation of 4 and 3 and the omission of 2 makes this descent
bach’s inventions: figuration, register, structure, and the “clear way to develop inventions properly” 9
16
21 39
42
51
obscure form in which the 4–3 motion appears in the bass and the 2 is omitted altogether.20 Graphs (i)–(iii) in Example 4(d) elucidate the derivation of the structure from a more normal registral setting. The transformations leading from the “normal” setting to the actual music are unusually radical, which relates with the curious, only “minimally conclusive” musical effect of the conclusion. In particular, the final cadence (measure 59)—missing 7 as well as 2 and featuring a registrally high rhythmically weak dominant, B3— sounds deliberately understated.21 Example 4(e) graphs the overall structure, showing actual registers. It also sheds some light on the significance of the 8 (E5) that covers the Urlinie progression, indicating by a dotted tie its relationship with the prominent 8 of the opening. The obscurity of the Urlinie descent should not be confused with structural ambiguity. While the bass-line articulation of 4 and 3 and the omission of 2 makes this descent less prominent, it leads unambiguously from 5 to 1 and is, as far as I can see, the only plausible Urlinie candidate in this piece.
55 59
^5
( ) ( )
( ) ( ) ^4
recap.
^3
^2 ^1
example 4(e). Overview
cadential dominant (measure 59, beat 3).18 The comparison of graph (ii) with the cadences in D (see especially Example 3[c]) illustrates how the harmonic structure of the concluding section is modeled on the cadential pattern.19 These observations suggest that while the Kopfton 5 is established in the opening section by a lucid 1–3–5 highregister arpeggiation, the rest of the Urlinie takes the more 18
Despite the apparent similarity between the cadences to B major in measures 17–18 and to E major in measures 59–60, I have interpreted them differently. Whereas the bass D in measure 17 already represents the third of the upcoming I of B major, the bass G in measure 59 is a passing 3 between 4 and 2 (cf. Examples 4[a] and 4[d]). This difference in interpretation is supported by differences in design and register. Whereas measure 17 is marked by a clear-cut change in design, measures 58–59 are connected through a tie, which makes the latter sound as a continuation to the preceding events. The perceptually salient unfolding F 5– A4–G 4–E5 (measures 58–62) also discourages perceiving the “I6”, occurring in the midst of the F 5-A4 interval, as a real tonic. Finally, the prominence of the registrally isolated E2–D 2–C 2–B2 (+B1) bass line in the first section overshadows the local dominant in measure 17, but the final cadential dominant (m. 59) is not similarly overshadowed. Metrical relationships differ, however, from the cadences in D. The “I6.” in measure 59 of E is clearly strong in relation to the subsequent V, which makes it more justified to describe it as an “inverted cadential 64.”
19
***
By the above four examples, I have attempted to present a sample of ways in which figuration (or design) and register 20
21
For discussion of bass-line articulation of the Urlinie , see Wen 1999. As regards my notating the implicit 2 below the bass V in Example 4(d), graphs (ii) and (iii) (instead of showing 2 as returning to its normal upper-voice location), I have been partly motivated by visual simplicity. However, this notation also conveys the idea that the left hand attempts, as it were, to express both structural outer voices in one melodic line and one register, but the impossibility to do this for the V and 2 necessitates the omission of 2. In considering the aesthetic motivation behind such features, it may be noted that the weak Urlinie articulation and the concomitant lack of registral connections with preceding events enhance the character of the concluding section as a self-contained entity, reflecting the general tendency in this Invention towards sharp sectionalization.
music theory spectrum 31 (2009)
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relate with structure. The significance of figuration is evident both in determining small-scale structural units and in establishing large-scale connections. Registral proximity and extremity often also support such connections. However, voice-leading connections may also transfer from a register to another if this is clarified through other factors, such as figuration or dissonance treatment. Such transfers may have various compositional purposes. In E , for example, the registral drop in the initial 5–6–4–3 progression helps to clarify structural hierarchy by undermining this progression in relation to the eventual high-register Urlinie descent. However, registral transfers may also be employed for imparting a special character to the Urlinie progression, as exemplified in two different ways by D and E. Before turning to further examples for illustrating my second main topic, figure enlargement, it is worthwhile to point out some manifestations of this phenomenon in E.
117
5
^5? Arp. A4
D5
^3? F5
example 5(a). d : opening
51–59) relates analogously with the E major theme statement; in fact, the section in its entirety might be conceived as a kind of enlargement of the theme.
music theory spectrum 31 (2009)
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relate with structure. The significance of figuration is evident both in determining small-scale structural units and in establishing large-scale connections. Registral proximity and extremity often also support such connections. However, voice-leading connections may also transfer from a register to another if this is clarified through other factors, such as figuration or dissonance treatment. Such transfers may have various compositional purposes. In E , for example, the registral drop in the initial 5–6–4–3 progression helps to clarify structural hierarchy by undermining this progression in relation to the eventual high-register Urlinie descent. However, registral transfers may also be employed for imparting a special character to the Urlinie progression, as exemplified in two different ways by D and E. Before turning to further examples for illustrating my second main topic, figure enlargement, it is worthwhile to point out some manifestations of this phenomenon in E. One such feature has already been mentioned in reference to Examples 4(b) and 4(c): the B major theme statement is followed by a hidden repetition of its initial B5– A 5– A 5–G 5 figure. Moreover, as illustrated in Example 4(c), graph (i), the Neapolitan sixth in measure 39 enables the permutation of this chromatic figure (B– A –[A ]–G ) to form the top voice framework of the entire second section, whereas the counterpointing B–C –D bass line reproduces the beginning of the countersubject (measure 25). The vertical alignment in Example 4(a), graph (ii), illustrates how the subsequent figure of the B major theme statement, G 5–F 5–E5–D 5 (measure 26) is enlarged in anticipation in the first section. The relationship between the small and the large is reinforced by a delay –release pattern manifest in the rhythmic organization on both scales. The associational network is further strengthened by the surface occurrences of the G 5–F 5–E5–D 5 figure in measures 14–15 (summarizing the larger figure) and in measures 35–36 (marking the return to the B major harmony after the B– A – A –G enlargement). Finally, as shown in Example 4(d), graph (ii), the C 4–B3– A3–G 3 line in the concluding section (measures
5
^5? Arp. A4
example 5(a). d : opening
51–59) relates analogously with the E major theme statement; in fact, the section in its entirety might be conceived as a kind of enlargement of the theme. 2. figure enlargement
d: syncopation as a key to structure
The opening section of d (measures 1–18) offers a model example of a concentrated development of a musical idea by surface repetitions, culminating in the enlargement of the very same idea. Before entering this example, it should be acknowledged that Wayne Petty (2006), working independently, has recently presented an excellent discussion of figure enlargement in this section. The following description agrees essentially with Petty ’s, but I will attempt to contribute to our analytical understanding by relating this feature to larger structural perspectives. Moreover, my interpretation of the harmonic structure in the opening section differs substantially from Petty ’s. From the Schenkerian perspective, the opening of d poses the problem of identifying the Kopfton. As illustrated in Example 5(a), two plausible candidates appear: 5 (A4) of the opening theme figure and the higher 3 (F 5, measure 4) that
D5
^3? F5
bach’s inventions: figuration, register, structure, and the “clear way to develop inventions properly” 15
Implicit syncope . . .
~ ( )
. . . becomes explicit.
7
10
~
15
( ) ( ) ( ) () ~ ~ () A
A
B
B
A
G
A
F
(B
10
A
10
G
10
F)
10
10
P
G
F
119
bach’s inventions: figuration, register, structure, and the “clear way to develop inventions properly”
119
15
Implicit syncope . . .
~ ( )
~
. . . becomes explicit.
7
10
15
( ) ( ) ( ) () ~ A
A
B
B
A
G
A
F
(B
10
A
10
G
10
F)
10
P
10
G
~ ( )
quasi V 64
F: II
F
5 3
I
example 5(b). First section (measures 1–18)
closes the opening imitations and starts the ensuing sequence.22 3 seems at first to be supported by its higher register, but, as shown in Example 4(b), the sequential descent in measures 7–14 shifts the focus back to the vicinity of the original 5 by leading the top voice to the syncopated B 4 (measures 14–15). As a new surface rhythm, this syncopation helps to mark B , but it also creates a special association with the opening. As shown in Example 5(b), the theme
implies a syncope figure on B . Similarly implied syncopes saturate the music, but measures 14–15 become a special moment by turning the implicit into explicit at the original level. In the ensuing cadence to III (F major), the A–B connection is completed to form an enlargement of the theme figure’s top voice A–B – A–G–F as the framework of the entire section. The passing A is transferred to the bass of the F major 63 chord in measure 16, another example of a local “I6” whose bass fulfills such a passing function.23
22
According to Forte and Gilbert (1982, 264), the Kopfton finds its primary expression in the A 5 in measure 5. Despite the high register of this A5, measure 5 is, I would suggest, an unlikely location for such a decisive event because measure 7 is marked by a much stronger change in design and also because measure 5 is characterized by voice-leading tendencies that are only fulfilled in measure 7 (see Example 5[a]).
23
Features such as left-hand figuration ensure that this F major 63 is heard as part of the process leading to the III (m. 18), rather than already representing the III, as Petty (2006, Example 2) shows it. Another feature in my analysis that deviates from Petty ’s is the reading of a G bass as supporting the syncopated B . This reading relies on the expectations
music theory spectrum 31 (2009)
120 7
14
18
26 29
36
38
^5
^5
( ) ( ) ( ) ( 64
I
5 3)
III
V
44
47
^4
49
^3
^2 ^1
() ( )
(recap. gesture
N
“I”
7
V
VI 5 6 V 64 53 I
example 5(c). Overall sketch
The concentration of relationships in this example is
The A–B – A–G–F framework in the opening section points
music theory spectrum 31 (2009)
120 7
14
18
26 29
36
38
^5
44
47
^5
49
^4
^3
^2 ^1
( ) ( ) () ( ) ( ) ( 64
(recap. gesture
5 3)
N
I
III
V 7
“I”
V
VI 5 6 V 64 53 I
example 5(c). Overall sketch
The concentration of relationships in this example is characteristically Bachian. Not only is a figure enlarged, but the crucial detail in the enlargement—the syncopated B — also bears a special foreground relationship with the original figure. Moreover, additional features enhance the association between the small and the large. The sequential passage in measures 7–14 subtly sustains the memory of the B – A–G–F line in an inner voice.24 Furthermore, the sequential F 5–B 4 descent (measures 7–15) is anticipated at the start of the sequence (measures 7–8), as is the accompanying D3–G3 bass motion (see brackets in Example 5[b]).
The A–B – A–G–F framework in the opening section points to 5 as the melodic starting point or Kopfton. As illustrated by the overall sketch in Example 5(c), this suggestion is borne out by the subsequent events. The second section balances the opening A–G–F motion by approaching A from above (C–B– A, measures 18–38). References to the higher 3 (F 5) remain, however, an important element in the music. As shown in Example 5(d), an annotated score of the concluding events, the last of such references is made by the recapitulation gesture in measures 44–461. As observed above (Example 1[c]), this gesture does not yet represent the structural tonic return; its bass tone (“I”) functions within a larger bass-line descent that leads from the tonicized A minor to the C in measure 47, a goal underlined through the ensuing hemiolic cadential pattern. Despite its non-structural status, the recapitulation gesture functions as a reminder of the original F 5 and directs attention to the subsequent E5 and D5, which cover Urlinie tones 4 (G4) and 3 (F 4) at the upper sixth (measures 47–49). Most remarkably, the 4 is made stand out through another explicit syncope—the second one in the piece—confirming the key role of this rhythmic device for the structure of d.
created by the chain of parallel tenths at the downbeats of measures 7, 9, 11, 13. When the syncopated B arrives one eighth-note earlier than expected (measure 143), coinciding with a G, I find it easy to perceive the tenth G–B as continuation to this chain. According to Example 5(b), it is not obvious whether B , A, G, and F in measures 8, 10, 12, and 14 are related through voice-leading or function as incomplete neighbors (echappée tones) of preceding inner-voice tones. However, as indicated by Petty (2006), these tones may also be perceived as implicitly suspended in the subsequent measure and thus forming a voice-leading line.
24
bach’s inventions: figuration, register, structure, and the “clear way to develop inventions properly” 38
40
^5
V
45
(recap. gesture)
“I”
121
50
^4
^3
() syncope!
V 7 (= 75
VI5 6 4
^2
^1
() 6
“I6”
V 64 53
I
5) 3
example 5(d). Conclusion (measures 38–52)
The implicit G (8) is made explicit at the downbeat of
bach’s inventions: figuration, register, structure, and the “clear way to develop inventions properly” 38
40
45
^5
50
(recap. gesture)
^4
^3
^2
() syncope!
V 7
“I”
V
121
()
VI5
(= 75
6 4
^1
6
“I6”
V 64 53
I
5) 3
example 5(d). Conclusion (measures 38–52)
The implicit G5 (8) is made explicit at the downbeat of measure 5. As the melodic peak tone and as the endpoint of the opening imitations, it attracts a stronger focus than any preceding top-voice element. After the attainment of this G5, statements of the 8–7–6–5 progression appear at various levels, as indicated in Examples 6(b) and 6(c).The most remarkable of these statements spans most of the Invention (measures 1–20). The connection between this enlargement and the foreground progression in measures 3–4 is reinforced by similar harmonic support I–V –IV for the 8–7–6 top-voice
g : the expansive descending tetrachord g offers another fascinating example in which the determination of Kopfton links with figure enlargement and features an implied element turning explicit. The pertinent figure is the descending tetrachord G–F –E –D or 8–7–6–5. As illustrated in Examples 6(a) and 6(b), the tetrachord occurs first as a chromaticized form in the bass (measures 1–2), a typical passus duriusculus figure serving as the first countersubject (even though the concomitant 6–5 upper-voice motion is less typical).25 The second countersubject, given in the right hand of measures 3–4, with its conspicuous ascent to 7 (F 5), is more unusual. As indicated in Example 6(b), F 5 points to a preceding implicit G5 as its point of origin. Consequently, the 8–7–6–5 progression may be perceived as also residing implicitly in the second countersubject.
P
G
25
While the right-hand figure at the end of measure 1 may appear to express a seventh chord (V 65 ), there is no satisfactory resolution for the apparent seventh (C 5), which implies that it has a more unusual anticipatory function.
F
E
D
5 ) IV 6 5 V 8 7 6 5 4 3
I (V 61
5
implicit ^8 . . .
G . . . becomes explicit ^8 G
F ^7 D
( ) ( ) ( ) () ( ) Theme
G
G F Theme
F
E
E
( V )
IV7
F E
F
E
D
G F E
D
P
D
I
I
G
Cs. 2
Cs. 1
I
example 6(a). g : opening, underlying pattern
music theory spectrum 31 (2009)
122
VII 43 I6
( VII
example 6(b). The establishment of 8
III5
6
7
) II5 3
V
music theory spectrum 31 (2009)
122
5
implicit ^8 . . .
G . . . becomes explicit ^8 G
F ^7 D
( ) ( ) ( ) () ( ) Theme
G
Cs. 2
G F Theme
Cs. 1
G
F
E
E
IV7
( V )
E
D
G F E
D
P
D
I
F E
F
VII 43 I6
I
( VII
III5
6
7
) II5 3
V
example 6(b). The establishment of 8
stretch in each case. At the end of the piece a 5–4–3–2–1 line follows, completing an octave descent, a rare specimen of the 8-Urlinie .26
of the opening F – A–(F)–C motion in a higher octave, whereas the descending scalar passages participate in the enlargement of the descending F –E–D–C motion.27 With one exception, the highest note in each surface statement takes part in these enlargements. This exception is the G5 in measure 8, whose status as subordinate embellishment (neighboring tone) is clarified through dissonance treatment. A crucial event for triggering the F –E–D–C descent is the reharmonization of F by the V 7 of C major in measure 7, which forces F to resolve to E, and this resolution occurs only after the G5, at the second beat of measure 8. (Apart from the change of harmony, this point is marked by the first change in the canonic technique.) A third element of figuration appears in measures 4–6 in a sequence of descending thirds. Adding to the remarkable density of interlevel connections, this pattern of descending
: the ascending arpeggiation and stepwise descent
f
Example 7(a) illustrates the precision in which figuration and register elucidate figure enlargement in the opening section of F . Two basic elements of figuration appear at the outset: the ascending arpeggiation in eighth-notes and the scalar descent involving sixteenths. As shown by beams above and below the stave, the initial figure in each element is enlarged through occurrences of that very element. The repetitions of the ascending arpeggiation figure articulate an enlargement 26
Schenkerians disagree on how rare 8-Urlinien are in Bach. In V äisälä 2008, I argue that several pieces for which Schenker and his followers have suggested 8-line readings are more meaningfully interpreted as embodying 5-Urlinien.
Forte and Gilbert’s analysis (1982, 206–07) shows the F –E–D–C line but not the F – A–C arpeggiation. (They indicate the 5 as established already in measure 5 by the metrically weak C 6.)
27
bach’s inventions: figuration, register, structure, and the “clear way to develop inventions properly” 7
G ^8
9
11
14
15
17
F ^7
E ^6
( ) ~ ( ) (rchg.-over)
Th.
Cs. 1 Th.
(d: I
I
(V 5
Cs. 2
8
IV V 6 4
7 5 3
I)
(c: IV
P
6
20
22
D ^5
^4
) IV 8
example 6(c). Overall sketch
23
^3 ^2
^1
( ) Th. Cs. 1
VII 65 I) 6
123
(“I6”)
7
V 64
(IV 6
6 5 )
5 3
I
bach’s inventions: figuration, register, structure, and the “clear way to develop inventions properly” 7
G ^8
9
11
14
15
17
F ^7
E ^6
( ) ~ ( ) (rchg.-over)
Th.
Cs. 1 Th.
Cs. 2
8
(d: I
7 5 3
IV V 6 4
5
I
P
(V
I)
6
(c: IV
20
22
D ^5
^4
23
^3 ^2
) IV 8
^1
( ) Th. Cs. 1
VII 65 I) 6
123
(“I6”)
7
V 64
(IV 6
6 5 )
5 3
I
example 6(c). Overall sketch
thirds, A5–F 5–D5–B4, is also enlarged over the course of the first section, as indicated by circles in Example 7(a). Example 7(b) clarifies the structural position of these elements. Reminiscent of the opening section of E, the top voice presents a high-register arpeggiation towards the Kopfton, 1–3–5 (F 5– A5–C6), which is elaborated by a passing 4 in a lower register (B4). As the notation in Example 7(b) makes evident, the F – A–C arpeggiation is doubled at a lower octave, and the passing B connects registrally with these doublings.28 The descending fourth (F 4–E5–D5–C5) represents an inner voice. The large descending-third pattern (A5–F 5–D5–B4), which brings about the transfer from the high 3 to the low 4, is formed by the combination of these voices.
Example 7(c) sketches the overall structure. After the tonicized dominant (measure 12), I43 (measure 25) effects a fleeting return to the tonic and directs the focus to the subsequent subdominant (measure 26).29 This subdominant is highlighted in the formal design by initiating a kind of recapitulation, based on the lower-fifth transposition of measures 4–12. Through this transposition, the F 5–E5–D5–C5 progression of the opening section becomes B 4– A4–G4–F 4, which, in the absence of the ascending arpeggiation, assumes top-voice status and takes care of the Urlinie descent.
28
The I43 is emphasized by its bass’s extreme low register (C2). The I43 does not occur as a surface harmony, but the reading aligns the strong bass C2 at the beginning of measure 25 with the upper voices of the functionally crucial I 7 (V of IV) at the end of the measure. Comparable 43 chords formed by the combination of non-simultaneous bass and upper voices appear in my readings of the Prelude in C Minor from WTC II (Example 8, measure 25), E (Example 17, measure 22), and A (Example 18, measure 17).
29
Such octave doublings of structural frameworks occur frequently in the Inventions. Compare, for instance, the opening section of E (Example 4[a]) and the B –C– A -G framework in E (most clearly shown in Example 17), which also involves the expression of a passing tone (B , measure 22) in the lower octave.
music theory spectrum 31 (2009)
124 F *
5
A *
10
(F)
C *
FA(F)C
F E D
FEDC
(summary)
F
E (C: V 43
6 5
D
C
I)
example 7(a). F : opening section, figure enlargement 3
7
9
12
14
5
10
^5
^5
P
P
music theory spectrum 31 (2009)
124 F *
5
A *
10
(F)
C *
FA(F)C
F E D
FEDC
(summary)
F
E (C: V 43
6 5
D
C
I)
example 7(a). F : opening section, figure enlargement 3
7
9
12
14
5
10
^5
^5
P
P
P
I5
6
II V
6 ( 6 II 4 3
I5
C: II 6
6 V 5
)
7
6
I
II
V
example 7(b). Opening section, structure 4
12
25
29
^5
31
4
^4 ^3 ^ 2
(V) I 43 IV 5
6
11
12
^5
^1
I
8
20
25
29
31
^4 ^3 ^ 2
^1
VI
I5
6
II
V
I 43 IV 5
6
V I
example 7(c). Overview
bach’s inventions: figuration, register, structure, and the “clear way to develop inventions properly”
French Suite VI, Allemande, opening
I8
12 25
I8
(V ) 7 IV 5
4
F, overall structure
26
(“I”)
29
6
V
I
31
(V ) 7 IV 5
(“I”)
6
V
I
125
as an applied dominant to IV, and a 4–3–2 motion above the prolonged IV; the prolongation of the IV also takes a similar form in both cases (IV –V 65–“I”–II6).31 Such correspondences between small- and large-scale structures are not without interest even when they involve separate and unrelated works. Pedagogically speaking, small-scale correspondents, in which structural relationships are readily perceptible, may be helpful in making large-scale structures more accessible. Moreover, clear foreground occurrences of a structural framework confirm its position among the composer’s resources, buttressing the notion that the framework may also have guided large-scale organization. A largely similar overall structure is to be found in the Prelude in E Major from The Well-Tempered Clavier I . Just as in F , the initial 1–3–5 arpeggiation is highlighted through occurrences of an arpeggiating surface figure, and thus represents figure enlargement.32 Another common feature with F
bach’s inventions: figuration, register, structure, and the “clear way to develop inventions properly”
French Suite VI, Allemande, opening
I8
12 25
I8
3
Prelude in E (WTC I ), overall structure
(V ) 7 IV 5
4
F, overall structure
26
29
as an applied dominant to IV, and a 4–3–2 motion above the prolonged IV; the prolongation of the IV also takes a similar form in both cases (IV –V 65–“I”–II6).31 Such correspondences between small- and large-scale structures are not without interest even when they involve separate and unrelated works. Pedagogically speaking, small-scale correspondents, in which structural relationships are readily perceptible, may be helpful in making large-scale structures more accessible. Moreover, clear foreground occurrences of a structural framework confirm its position among the composer’s resources, buttressing the notion that the framework may also have guided large-scale organization. A largely similar overall structure is to be found in the Prelude in E Major from The Well-Tempered Clavier I . Just as in F , the initial 1–3–5 arpeggiation is highlighted through occurrences of an arpeggiating surface figure, and thus represents figure enlargement.32 Another common feature with F is a concluding section starting from IV and based on a lower-fifth transposition of the opening section. However, telling differences between the two pieces become evident in the prolongation of the IV. In the Prelude, a IV –IV 7 frame work supports Urlinie tones 4 and 3(!), the latter being prepared by an extraordinary VI. This level shows the first glimpse of the extreme character difference between robust diatonicism and delicate chromaticism that separates the Invention and the Prelude despite their structural convergences.33
6
(“I”)
V
I
31
(V ) 7 IV 5
(“I”)
8 14 15
21
6
V
I
I8
(V ) 7 IV 5
( IV 5 ) IV 7 V
125
I
example 7(d). Points of comparison
b: the diminished fourth as a source of bass-line drama
To gain additional perspective on such str ucture, let us briefl y look at some related examples, illustrated in Example 7(d). The opening phrase of the Allemande from French Suite VI provides an interesting small-scale correspondent.30 Just like F , this phrase presents a 1–3–5 arpeggiation accompanied by I–V, a fleeting return to the tonic 30
While the preceding examples of figure enlargement mostly focus on upper-voice events, bass-line figures may 31 32 33
For Schenker’s analysis of this phrase, see Schenker 1979, Fig. 109, d1.
Another example of such a prolongation of IV occurs in measures 234–24 in a (Example 1[a]). Alegant and McLean (2001) also discuss this enlargement. For a more detailed analysis of this Prelude, see V äisälä 2008.
music theory spectrum 31 (2009)
126 a) Opening
b) Overall sketch 5
9
14 17 18
19
^5
A
G
F
E
C F E D C (smooth, scalar progression: laconic expression)
G
I IV VII6 I
(A G F E )
C I
26
^4
= G
23
III
5
6 5 1
28
^3
^2 ^1
A
G F E
F
E D C
IV
example 8. Bach, Prelude in C Minor from The Well-Tempered Clavier II
V 43 I IV 7 V
I
music theory spectrum 31 (2009)
126 a) Opening
b) Overall sketch 5
9
14 17 18
19
^5
G
A
G
F
E
C F E D C (smooth, scalar progression: laconic expression)
G
I IV VII6 I
26
^4
(A G F E )
I
III
6 5 1
^3
A
G F E
F
E D C
C 5
28
^2 ^1
=
23
V 43 I IV 7 V
IV
I
example 8. Bach, Prelude in C Minor from The Well-Tempered Clavier II
also be enlarged, and such enlargements may have significant expressive consequences. A particularly dramatic example of bass-line enlargement is b, in which a figure with a diminished fourth, D– A –B, occurs both as a foreground characteristic and in the structural framework. For illustrating the expressive implications of different bass lines, a point of comparison is offered by the Prelude in C minor from The Well-Tempered Clavier II ; see Example 8. A common feature in the large-scale structures of b and this Prelude is that a heavily tonicized III does not lead to a strong root-position V, as is most often the case. However, the Prelude is characterized by smooth, conjunct bass motion and by the concomitant laconic expression on both the small and the large scale, whereas the diminished fourth imparts a sense of violent dramaticism to b.34
Examples 9(a)–(c) survey details featuring the D– A –B figure. As shown in Example 9(a), it is introduced by the opening bass line (whose figured form becomes the countersubject); A substitutes for C as a connective between D and B. While C does appear at the beginning of measure 2, the parallelism of right-hand figuration brings out the D– A –B framework rather than D–C –B.35 Example 9(a) also shows how another important source of expressivity, the chromatic A – A relationship, is subtly introduced at the joint of the first two thematic statements. The implicit A of the half-cadence V leads to the explicit A of the tonicized V.
34
Apart from bass-line features, Example 8 shows two enlargements of the opening G– A –G–F –E upper-voice figure, the larger of which has been previously presented in Wintle 1986, Example 10. However, my analysis differs in several respects from Wintle’s. A consquential detail
is the F-minor chord in measure 17, which Wintle reads as beginning the prolongation of IV but which I see as subordinate to the motion from III to the emphatic V of IV in measure 18, whose top-voice G5 corroborates the significance of the G 4–G5 coupling and also the Kopfton status of 5 (Wintle reads 3 as Kopfton). This parallelism also supports reading the I 6 chords in measure 1 as connected, whereas Schenker (1996, 35, Fig. 3) indicates the latter I 6 as a passing chord. (Schenker’s Figure is internally inconsistent, however, since some of its graphs show the I 6 chords as connected.)
35
bach’s inventions: figuration, register, structure, and the “clear way to develop inventions properly”
I
*
*
D
D
6
~ (A )
*
B
V 65
I
A II
A
Underlying scalar model
Dim. 4th heightens dramaticism and expressivity
DA B IV 6
127
( )() ( ) *
*
V
example 9(a). b: opening
Examples 9(b) and 9(c) show two returns to the tonic, both of which have the character of abrupt dramatic turns.
the opening thematic statements, implants the D– A –B figure into a dominant prolongation (V – ). The diminished
bach’s inventions: figuration, register, structure, and the “clear way to develop inventions properly”
I
*
*
D
D
6
~ (A )
A
*
B
V 65
I
A II
Underlying scalar model
Dim. 4th heightens dramaticism and expressivity
DA B IV 6
127
( )() ( ) *
*
V
example 9(a). b: opening
Examples 9(b) and 9(c) show two returns to the tonic, both of which have the character of abrupt dramatic turns. They also share common features of pitch relationships. The first return (measures 7–8, Example 9[b]), occurring after
7
~
A
D
A
( )
A
B
A
6
V
!
the opening thematic statements, implants the D– A –B figure into a dominant prolongation (V – ). The diminished fourth is given a pungent character by the way it serves to “resolve” the seventh between D4 and C 5 (brought about by a bold use of counterpoint at the twelfth). The A – A relationship features as a cross relation between the outer voices (see dotted arrow). The second return (Example 9[c]) is the main return in the large-scale form and coincides with a pair of recapitulatory thematic statements. Just as in the first return, a tonicized V (measure 17) precedes the D– A –B bass figure— which now occurs on two scales—producing the outer-voice A – A cross relation. The interpretation of prolongational relationships is, however, much more complicated for the second return. One might again consider reading the D bass (measure 18) as subordinate to dominant prolongation, spanning from the V in measure 17 to the V 65 at the end of measure 20. However, the D bass is now too strongly marked by emphasis, design, and register for being relegated to such a subordinate role. Design connects this D bass with the other framing point of the pair of recapitulatory statements, the B bass of the eventual root-position tonic (measure 21), suggesting that the D represents the tonic triad in an anticipatory fashion.
I
example 9(b). First tonic return
music theory spectrum 31 (2009)
128
( ) 17
Theme
Cs.
20
DA
Theme
Cs.
D
A B
D
A
B
(i)
6 4
4 3
E
D
A B
4 2
E
6
6 5
D
A
B
B
music theory spectrum 31 (2009)
128
17
20
Theme
Cs.
DA
B
^2
^1
Theme
Cs.
D D
(i)
A
( )
E
D
A B
E
(ii)
4 2
V 42
4 2
6 4
4 3
A B
D
B
^4
^3
()
A
8
7 5 )=V 65 3
V( 64
V
B
6 5
6
I6
( )
I
example 9(c). Second tonic return (recapitulation) and conclusion
While the D bass of measure 18 seems thus to represent the tonic, it is not preceded by anything that would normally prepare a structural tonic return: no dominant with a raised leading tone appears. Such preparation follows only after the D bass through the D– A –B figures. The small-scale
D2– A 3–B3 figure (measure 18) dramatically transforms the chord on D, which momentarily sounds like a D major chord, into I6. The V 56 of the larger D2– A 2–B2 figure in turn prepares for the root-position tonic. The unusual temporal order—a representative of I preceding the preparation for
bach’s inventions: figuration, register, structure, and the “clear way to develop inventions properly”
I—suggests an unusual reading based on temporal displacements, as illustrated in graphs (i) and (ii) in Example 9(c). As shown by slanted lines in graph (i), the A 3 and B3 of the small-scale D2– A 3–B3 figure may be perceived as belated inner voices, which “should” have coincided with E2 and D2, respectively, so as to create a normal approach to the I6 from V 24. But these E2 and D2 may in turn be understood as anticipatory upper voices in relation to the A 2 and B2 of the eventual V 65–I motion, as indicated in graph (ii). Through this reading, it is possible to account both for the connection between the D and B basses as representatives of the tonic and for the intervening A as part of the dominant that prepares for this tonic. The pattern of nested temporal displacements is supplemented by the combination of two thematic statements in inverted counterpoint: the E and D of the former statement are liable to be perceived as bearing an anticipatory relationship with the A and B of the latter (graph [i]).36
129
17–18) speaks to the significance of such a pattern as a compositional resource, suggesting that a related pattern may also underlie the tonic return as a whole. Example 9(d) depicts the overall structure. The large-scale bass line in measures 1–21, B–D–(A)– A –B (I–III– VII–V 65–I), combines two central sources of expressivity, the D– A –B figure and the chromatic A – A relationship. The A major harmony in measure 14 sounds first just as a dominant answer to the preceding D major statement but then unexpectedly begins the process that leads to the tonic return with temporal displacements. The unexpected character of the tonic return is also evident in durational proportions. The first section lasts 11 measures and the second section (from the cadence to D to the recapitulation) only 6, whereas in most Inventions the second section is about as long or somewhat longer than the first. Perceiving a voice-leading relationship between the VII in measure 14 and the V 65 that eventually leads to the
bach’s inventions: figuration, register, structure, and the “clear way to develop inventions properly”
I—suggests an unusual reading based on temporal displacements, as illustrated in graphs (i) and (ii) in Example 9(c). As shown by slanted lines in graph (i), the A 3 and B3 of the small-scale D2– A 3–B3 figure may be perceived as belated inner voices, which “should” have coincided with E2 and D2, respectively, so as to create a normal approach to the I6 from V 24. But these E2 and D2 may in turn be understood as anticipatory upper voices in relation to the A 2 and B2 of the eventual V 65–I motion, as indicated in graph (ii). Through this reading, it is possible to account both for the connection between the D and B basses as representatives of the tonic and for the intervening A as part of the dominant that prepares for this tonic. The pattern of nested temporal displacements is supplemented by the combination of two thematic statements in inverted counterpoint: the E and D of the former statement are liable to be perceived as bearing an anticipatory relationship with the A and B of the latter (graph [i]).36 The events in b provide another indication of Bach’s imaginative and nuanced art of retransition and recapitulation. In this case—in contrast to a and d—there is no recapitulation gesture subordinate to dominant prolongation, but the dominant and tonic areas show a temporal overlap. While my reading of temporal relationships is exceptionally complex, it seems to me that the complexity is required by the exceptional nature of the events leading to the unexpected tonic return. Moreover, the multilevel occurrence of the displacement pattern also offers certain kind of support for the reading. The readily perceptible small-scale displacement (measures
17–18) speaks to the significance of such a pattern as a compositional resource, suggesting that a related pattern may also underlie the tonic return as a whole. Example 9(d) depicts the overall structure. The large-scale bass line in measures 1–21, B–D–(A)– A –B (I–III– VII–V 65–I), combines two central sources of expressivity, the D– A –B figure and the chromatic A – A relationship. The A major harmony in measure 14 sounds first just as a dominant answer to the preceding D major statement but then unexpectedly begins the process that leads to the tonic return with temporal displacements. The unexpected character of the tonic return is also evident in durational proportions. The first section lasts 11 measures and the second section (from the cadence to D to the recapitulation) only 6, whereas in most Inventions the second section is about as long or somewhat longer than the first. Perceiving a voice-leading relationship between the VII in measure 14 and the V 65 that eventually leads to the root-position I (measure 21) is supported by the return of a similar registral setting, as evident in Example 9(d). As regards the Urlinie , the temporal-displacement figures involve the consecutive presentation of the 4–3 motion in several registers. The 3 ascends from the low D2 to higher octaves until reaching the D5 of the obligatory register in the final cadence, as indicated by circles in Example 9(d).The last occurrence of the D– A –B figure forms the top voice of this cadence, A substituting for C as Urlinie 2 in a fitting conclusion to this Invention.
129
: figure enlargements overshadowing urlinie descent
c
36
The parentheses in Example 9(c) indicate that the anticipatory E –D motion in the large-scale displacement figure and in the latter of the small-scale figures could be removed without affecting the structure, since this motion also occurs in its due place above the A –B bass motion (these unfolding figures represent the type shown in Schenker 1979, Fig. 43d4). By contrast, the belated A and B in the first of the small-scale figures cannot be removed and are indicated in their “corrected” location in graph (ii).
As the final example in this section, I shall present some observations of figure enlargement in the first, and perhaps best known, of the Inventions. Whereas the preceding examples have concentrated on figures introduced at the very beginning—in the theme or the countersubject—the overall design of C is crucially affected by enlargements whose point
music theory spectrum 31 (2009)
130 ^5
^4
( )
(i)
recap.
D A
3
5
7
10
12 14
A
17
18
^3
^2 ^1
() ( )
B
21
^5
^4
^3
^2 ^1
() ( ) () (ii)
^4
recap. ^3
^4 ^3
D A B
music theory spectrum 31 (2009)
130 ^5
^4
( )
(i)
3
5
7
10
A
12 14
17
^2 ^1
() ( )
recap.
D A
^3
B
18
21
^5
^4
^3
^2 ^1
() ( ) () (ii)
^4
recap. ^3
D A B
^4 ^3
D A B
(D: IV 5 I
V
I
5
6 5 V 6
VII
I
V)
III VII
= V V 42 I6 5
6
V 65
I
V I
example 9(d). Overall sketch
of origin is the inversion figure appearing after the opening imitations. As illustrated in Example 10(a), the inversion figure beginning with A5 (measure 3), is taken up at its original level after the cadence to A minor (measure 15). This restatement triggers enlargements of the characteristic A–F –E framework at three structural levels and in three registers, as indicated by letter names in Example 10(b).37
3
15
IN
() ( ) = A F E
6 5
~
A5 without harmonic support
37
One might question whether the original inversion figure (measure 3) is actually based on the A–F –E framework since the A might also be interpreted as a neighbor to the immediately following G. However, I
VI offers harmonic support for A5
example 10(a). C : Introduction and resumption of the inversion fi gure starting from A 5
bach’s inventions: figuration, register, structure, and the “clear way to develop inventions properly” 7
^3
15
^2 ^1 C B C
21
( ) () ( ) ( ) A F
A
A
E
I VI IV V I (C–B–C reproduces the original counterpoint of m. 1)
F E
chr. P
A I
V
VI
F
131
22
() A
F E
E (I6 )
IV “I6 ” V
I
example 10(b). Overall structure and fi gure enlargement
For illuminating the artistic motivation behind such
illustrated in Example 10(b), the 2 occurs in an octave below
bach’s inventions: figuration, register, structure, and the “clear way to develop inventions properly” 7
^3
^2 ^1 C B C
( ) A F
E
I VI IV V I (C–B–C reproduces the original counterpoint of m. 1)
15
( ) () ( ) A
A
chr. P
21
F E
A I
V
VI
F
131
22
() A
F E
E (I6 )
IV “I6 ” V
I
example 10(b). Overall structure and fi gure enlargement
illustrated in Example 10(b), the 2 occurs in an octave below the obligatory register. Moreover, the structural top voice is covered not only by the A4–F 4–E4 inner-voice figure but also by a C5–B4–C5 neighboring figure in the highest voice.38 The latter figure also represents figure enlargement, as it reproduces the original counterpoint of the theme (measure 1, latter half). The Ursatz is further weakened by the brevity of the structural dominant, which appears at the last possible moment, one quarter before the final tonic.
For illuminating the artistic motivation behind such events, it should be observed that the original statement of the inversion figure is strongly marked by both design and register (A5 being the highest tone in the music until measure 14). Such prominence, I would suggest, creates a compelling impulse for the composer to develop this idea, but an immediate development through enlargement is made impossible by the lack of harmonic support for A5 above the tonic harmony (Example 10[a]). Only the cadence to A minor (measure 15) provides the long-awaited opportunity for the artistic impulse to flourish. The concentration on figure enlargements towards the conclusion of this Invention is so strong that it almost entirely overshadows the articulation of the Urlinie descent. As
***
The above examples have illustrated that the significance of the Urlinie for actual musical events is widely variable. In 38
find it more appropriate to read this G as a passing tone in accordance with the original statement of the theme figure (in which the corresponding D is clearly a passing note). Such a reading also agrees with what is typical in similar figures in Bach: when an accented sixteenthnote is followed by a leap and three stepwise moving sixteenths, the second of these stepwise sixteenths is usually a passing tone.
Larson (1983) suggests that the V of the first cadence (measure 7) starts a dominant prolongation extending all the way to the final cadential V; in this case the Urlinie 2 would be articulated in the obligatory register (D5). However, the large-scale design, characterized by the pervasive parallelism between the first two sections (measures 1–7 and 7–15) and by a clearly contrasting concluding section (measures 15–22), clarifies that the V in measure 7 is subordinate to a I –V –VI progression.
music theory spectrum 31 (2009)
132
some Inventions, such as E or D (Examples 2 and 3), the impulse to articulate the Urlinie descent, or to give it some special character, appears as a central source of musical content. At the other end of spectrum, C bears little or no trace of such an impulse. The next section is devoted to closer and more comprehensive discussion of this crucial topic.
Second, I shall examine whether the initial determination of governing top-voice tone is reflected in the remaining events so as to manifest special compositional attention to elements that form a stepwise descent from this governing tone to the tonic. 5 or 3? a comparison between d and e
3. structural perspectives: the predictive power of the urlinie
My emphasis on figuration and register as analytical criteria involves an aspect of empirical orientation in analysis. In section 1, I focused explicitly on the support offered to Schenkerian readings by concrete compositional features such as figuration (design) and use of register. This relates with my discussion in V äisälä 2008, in which I attempt to show how the consideration of four types of analytical
For an introductory example that illustrates what may be understood by the predictive power of the Urlinie , let us return to the structure of d and compare it with that of e. As explained in the analysis of d, both a lower 5 (A4) and a higher 3 (F 5) appear as significant focal points in this Invention, but the former takes precedence and assumes Kopfton status. Decisive for Kopfton establishment is the fact that the conclusion of the first section establishes a strong linear connection with the 5 rather than the 3, through the
music theory spectrum 31 (2009)
132
some Inventions, such as E or D (Examples 2 and 3), the impulse to articulate the Urlinie descent, or to give it some special character, appears as a central source of musical content. At the other end of spectrum, C bears little or no trace of such an impulse. The next section is devoted to closer and more comprehensive discussion of this crucial topic.
Second, I shall examine whether the initial determination of governing top-voice tone is reflected in the remaining events so as to manifest special compositional attention to elements that form a stepwise descent from this governing tone to the tonic. 5 or 3? a comparison between d and e
3. structural perspectives: the predictive power of the urlinie
For an introductory example that illustrates what may be understood by the predictive power of the Urlinie , let us return to the structure of d and compare it with that of e. As explained in the analysis of d, both a lower 5 (A4) and a higher 3 (F 5) appear as significant focal points in this Invention, but the former takes precedence and assumes Kopfton status. Decisive for Kopfton establishment is the fact that the conclusion of the first section establishes a strong linear connection with the 5 rather than the 3, through the enlarged A–B – A–G–F figure. As illustrated in Example 11, a lower 5 (B4) and a higher 3 (G5) also occur as focal points in e, an Invention whose harmonic structure is strikingly similar to that of d. However, the 5 and 3 assume the reverse order of structural importance in these two Inventions. A convenient way to compare their structures is offered by a three-voice model that superimposes a 3-line over a 5-line, shown as graph (i) for each case.39 In both d and e, the Invention theme starts with the lower 5, whereas the higher 3 is marked as the endpoint of the opening imitations and as the starting point for the ensuing sequence. The motions towards this 3 are somewhat different in the two Inventions, since the 5 and 3 are connected through arpeggiation (A4–D5–F 5) in d, whereas a 1–2–3 Anstieg above the original 5 is discernible in e.40
My emphasis on figuration and register as analytical criteria involves an aspect of empirical orientation in analysis. In section 1, I focused explicitly on the support offered to Schenkerian readings by concrete compositional features such as figuration (design) and use of register. This relates with my discussion in V äisälä 2008, in which I attempt to show how the consideration of four types of analytical criteria—in addition to design and register, these include meter and rhetorical/gestural emphasis—helps to clarify the emergence of Schenkerian structures (multilevel patterns of harmony and voice leading) in several Bach examples. Such observations evoke the crucial epistemic question about the explanatory power of Schenkerian concepts. In principle, one could approach this question empirically by assessing the extent to which these concepts are supported by compositional features such as those listed above. While a comprehensive treatment of this question goes beyond the scope of the present article, I shall focus on one aspect of it, concerning the background top-voice paradigm, the Urlinie . According to this paradigm, the overall top-voice structure consists of the choice of one of the tonic triad’s tones as a governing element (Kopfton) and of a stepwise descent from this tone to the tonic. I will examine whether this paradigm has predictive power for concrete compositional features in the corpus of the 15 Inventions. This examination involves two parts. First, I shall outline criteria for determining the governing top-voice tone during the opening events in each Invention.
39 40
This model is similar to one of Neumeyer’s (1987) “three-part Ursatz” models. The 1–2–3 ascent is somewhat shaded by the appearance of a high 5 (B5) in measure 2, which is also present in the two subsequent
bach’s inventions: figuration, register, structure, and the “clear way to develop inventions properly” A shared three-voice model
18
38
47
cf. theme
(not present)
(ii)
^3
[ ][ ]
^5 8) (5 5) (8 (5 5)
I
III
(5 5)
(i)
[ ]
[
][ ]
V 8 7 VI V I
^3
^5 8) (5 5) (8 (5 5)
[ ]
^5!
3
e
29
(i)
d
7
(5 5)
7
11
13
15
20
22
^3!
( )( ) ( ) ( ) ( ) ( )
(ii)
cf. theme
(not present)
5
6
133
bach’s inventions: figuration, register, structure, and the “clear way to develop inventions properly” A shared three-voice model
18
38
47
cf. theme
(not present)
(ii)
^3
[ ][ ]
^5 8) (5 5) (8 (5 5)
I
III
(5 5)
(i)
I
III
[ ]
[
][ ]
V 8 7 VI V I
^3
^5 8) (5 5) (8 (5 5)
[ ]
^5!
3
e
29
(i)
d
7
133
(5 5)
V 8 7 VI V I
7
^3!
( )( ) ( ) ( )
(ii)
(not present)
5
6
11
13
15
20
22
( ) ( ) cf. theme
example 11. Comparison between d and e
While the 1–2–3 motion already hints at the reinforcement of the 3 at the expense of the 5 in e, more decisive confirmation for Kopfton determination is given by the subsequent linear connections. In d, as already observed, such connections link with the opening 5 (A4–B4– A4–G4–F 4), but the tones that “should” follow the high 3 (E5 and F 5) fail to occur. Conversely in e, the corresponding higher strand of voice-leading (G 5–F 5–G5) is featured as the explicit
measures. However, the 1–2–3 motion is emphasized by the gestures leading to the strong beats of measures 2 and 3, and the primacy of 3 is further confirmed by the strong-beat parallel tenths in measures 3–5.
134
top-voice framework of the opening section, but the lower 5 finds only implicit continuation. The comparison also yields additional illustration for Bach’s tendency towards figure enlargement (see brackets in Example 11). The enlargement of the A–B – A–G–F figure in d has already been discussed, but the G–F –G framework in e also reflects a detail in the opening thematic figure. While the figure starts from 5, 3 is activated through the G–F –G neighboring figure, hinting at its upcoming significance. The opening sections of d and e point thus to 5 and 3, respectively, as governing top-voice tones. In each case, such an initial bias finds correspondence in the remaining events, which privilege the elements of either the 5-line or the 3line according to the initial choice. In d, the higher 3-line
music theory spectrum 31 (2009)
materializes only sporadically, but e focuses strongly on 2 of this line, elaborating it by an octave progression F 5–F 4 (measures 15–19) and by the extended passing motion 2–1–7, with each tone explicitly present (in contrast to d, in which the high 7 is omitted).41 Another noteworthy difference concerns the treatment of 4 in the lower 5-line. Reflecting its status as an Urlinie tone, 4 in d is brought out by the prominent syncopated rhythm and by the subsequent hemiolic cadential progression (Example 5[d]). By contrast, the inner-voice 4 in e (measure 20) is not marked by equally outstanding means.42
survey of kopfton establishment
The comparison between d and e illustrates how the initial establishment of the governing top-voice tone correlates with the subsequent emphasis on elements forming a de-
and 8 in one (g ). I argue that in all cases there are clearly identifiable factors through which the Kopfton is established as the governing top-voice tone during the initial events (approximately within the opening section). Most of the pertinent factors are evident in the above comparison of d and e. Temporal and registral location are two basic factors. Of the plausible tonic-triad members, the first and the highest are the privileged candidates for the governing top-voice tone. If these criteria conflict with each other—a lower tonic-chord tone is followed by a higher one—two additional considerations pertain to the choice between them. The first of them concerns the events leading to the appearance of the higher tone. If it is attained through a clearly goal-oriented progression (such as an Anstieg ), or otherwise heard as realizing pre-existing tendencies, this will support the impression of its governing position. The second consideration concerns subsequent
music theory spectrum 31 (2009)
134
materializes only sporadically, but e focuses strongly on 2 of this line, elaborating it by an octave progression F 5–F 4 (measures 15–19) and by the extended passing motion 2–1–7, with each tone explicitly present (in contrast to d, in which the high 7 is omitted).41 Another noteworthy difference concerns the treatment of 4 in the lower 5-line. Reflecting its status as an Urlinie tone, 4 in d is brought out by the prominent syncopated rhythm and by the subsequent hemiolic cadential progression (Example 5[d]). By contrast, the inner-voice 4 in e (measure 20) is not marked by equally outstanding means.42
and 8 in one (g ). I argue that in all cases there are clearly identifiable factors through which the Kopfton is established as the governing top-voice tone during the initial events (approximately within the opening section). Most of the pertinent factors are evident in the above comparison of d and e. Temporal and registral location are two basic factors. Of the plausible tonic-triad members, the first and the highest are the privileged candidates for the governing top-voice tone. If these criteria conflict with each other—a lower tonic-chord tone is followed by a higher one—two additional considerations pertain to the choice between them. The first of them concerns the events leading to the appearance of the higher tone. If it is attained through a clearly goal-oriented progression (such as an Anstieg ), or otherwise heard as realizing pre-existing tendencies, this will support the impression of its governing position. The second consideration concerns subsequent events.43 If these events elaborate the higher tone or form voice-leading connections with it, this will corroborate its governing status. If, on the other hand, the higher tone is quickly abandoned in favor of prominent voice-leading connections with the lower tone—as in d—the higher tone will be perceived just as a temporary digression from the governing lower voice-leading strand. While these principles do not amount to rigorous rules for the determination of the governing top-voice tone—but rather represent “preference rules,” to cite Lerdahl and Jackendoff ’s (1983) notion—they offer suf ficient grounds for the illumination of this aspect in the present corpus. Let us start our survey from the majority of the Inventions with 5 as Kopfton. Example 12 presents an overview of the most significant upper-voice events in the opening sections of
survey of kopfton establishment
The comparison between d and e illustrates how the initial establishment of the governing top-voice tone correlates with the subsequent emphasis on elements forming a descent from that tone to the 1. To the extent that such correlation is generally evident, we may speak of the predictive power of the Urlinie for musical events. For testing such predictive power in the present corpus, it is first necessary to take a look at the ways of Kopfton establishment in the 15 Inventions. In my analyses, 5 serves as the Kopfton in ten Inventions (d, E, E , F , f , G, A , a , B , b ); 3 appears in four (C, c, D, e);
41
42
The articulation of the concluding 1 in the lower register has significant expressive consequences in e but is clearly insuf ficient for canceling the structural priority of the 3-line. While the three-voice model is useful for illustrating the relationship between d and e, the present comparison does not support identifying it as a “three-part Ursatz” with two Urlinien of equal status, since one or the other upper voice is clearly predominant. In d, the tones in the higher 3-line are, strictly speaking, transferred inner-voice tones. Such transference is concretized at the opening of d, in which scale degree 3 is transferred first from F 4 to F 3 and thence to F 5 (Example 5[a]).
43
To avoid circular logic, Urlinie events must naturally be excluded from considerations of Kopfton establishment, since we are concerned with the correlation between these two aspects.
bach’s inventions: figuration, register, structure, and the “clear way to develop inventions properly” opening imitations
d
E
E
F
f
sequence and other modulatory events 7
9
9
4
9
( )
beginning of second section (or the arrival at the tonic of the second key)
18
12
17 21
12 14
17
135
these Inventions, vertically aligning corresponding phases of formal design.44 In f , B , and b, there is no conflict between the temporal and registral criteria. 5 appears at the outset and the subsequent events show either no ascent to higher tonic-chord tones (B ), or an ascent to another 5 (f and b).45 In E , E, F , A , and a , the conflict between temporal and registral criteria is resolved in favor of the latter: the top voice proceeds from an initial 8 (=1) or 3 to a higher 5, which assumes Kopfton status. What may be identified as the most archetypal goal-oriented motions are those having 1 as their point of departure: the Anstieg 1 –2–3– 4–5 in A and the arpeggiations 1–3–5 in E and F .46 The “open-position” arpeggiation 3–8–5 (G4–E 5–B 5) in E is less archetypal, but the greater registral supremacy of the 5 at least partially compensates for what is perhaps lost in goal-orientedness. In a , finally, the effect of 5 is strongly influenced
bach’s inventions: figuration, register, structure, and the “clear way to develop inventions properly” opening imitations
sequence and other modulatory events
E
E
9
12
9
17 21
4
G
5
A
3
a
17
9
14
9
44
8
b
The formal design of B deviates from the most common pattern in which opening imitations are followed by se quential and other kind of modulatory material. In B , a sequential passage appears immediately after the first thematic statement (measures 4–5) leading to the second statement. Example 12 shows all these events (measures 1–8) under the rubric “opening imitations.” At the surface, these cases are not completely straightforward. In B , the priority of F 5 is not immediately obvious in the figuration of measure 1, but is clarified by the subsequent small-scale connections (F –E –D in measures 1–4); measures 6–9 further accentuate the F 5. In b, the F 4 occurs as the center of voice-leading activity in measures 1 –3 despite the higher B4, and the primary status of 5 is corroborated by the appearance of F 5 in measure 5. The octave ascents in b and f differ from each other in that the higher register is primary (obligatory) in b and the lower in f , as clarified by subsequent connections. The priority of motions ascending from 1 to the Kopfton is evident in Schenker 1979, §§120–6.
6
6
B
12 14
9
f
18
4
F
these Inventions, vertically aligning corresponding phases of formal design.44 In f , B , and b, there is no conflict between the temporal and registral criteria. 5 appears at the outset and the subsequent events show either no ascent to higher tonic-chord tones (B ), or an ascent to another 5 (f and b).45 In E , E, F , A , and a , the conflict between temporal and registral criteria is resolved in favor of the latter: the top voice proceeds from an initial 8 (=1) or 3 to a higher 5, which assumes Kopfton status. What may be identified as the most archetypal goal-oriented motions are those having 1 as their point of departure: the Anstieg 1 –2–3– 4–5 in A and the arpeggiations 1–3–5 in E and F .46 The “open-position” arpeggiation 3–8–5 (G4–E 5–B 5) in E is less archetypal, but the greater registral supremacy of the 5 at least partially compensates for what is perhaps lost in goal-orientedness. In a , finally, the effect of 5 is strongly influenced by another kind of preparation. While the upper-voice framework at the very beginning is 1–2–3 (as implied by meter and by contrapuntal relationships with the bass), 5 is
beginning of second section (or the arrival at the tonic of the second key)
( ) 7
d
45
12
example 12. Establishment of 5 46
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featured as the registral frame (E 4–E5) of the right-hand material, and its more decisive appearance in measure 3 is thus heard as realizing a pre-existing tendency. In all these examples, the high 5 is supported by its function as the point of departure for subsequent voice-leading motions (for E and F , see Examples 4[c], 4[e], and 7[c]). In particular, in the two Inventions in which the approach to the 5 is less archetypal, E and a , 5 is confirmed by elaboration through a neighboring 6. In d and G, the conflict between temporal and registral criteria is resolved in favor of the former. The 5 at the outset is followed by a higher tonic-chord member (3 or 8), but the latter is approached in a less than maximally goal-oriented way. In both cases, the subsequent descent to a prominent neighboring 6 confirms the governing status of 5.47 Similar considerations apply to Kopfton determination in the remaining fi ve Inventions. In c and D, the 3 appears at
135
(see Example 6[b] above). Moreover, the preceding events in this Invention do not show a clear focus on any other of the tonic-triad tones to compete with the 8.49 requirements for the 4 and 3 in a 5-urlinie
Having taken a look at Kopfton establishment in the 15 Inventions, let us proceed to examining the articulation of the remaining Urlinie tones. In considering the requirements for the satisfactory articulation of an Urlinie degree, it is important to allow for both harmonic support and explicit emphasis. Roughly speaking, the weaker harmonic support there is for an Urlinie degree, the more necessary it is to bring it out through special features of design, register, duration, or other kind of emphasis, in order for it to be experienced as a major structural element.50 Consider the dissonant Urlinie 4 in d, the syncopated G in measures 46 47, which represents a
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featured as the registral frame (E 4–E5) of the right-hand material, and its more decisive appearance in measure 3 is thus heard as realizing a pre-existing tendency. In all these examples, the high 5 is supported by its function as the point of departure for subsequent voice-leading motions (for E and F , see Examples 4[c], 4[e], and 7[c]). In particular, in the two Inventions in which the approach to the 5 is less archetypal, E and a , 5 is confirmed by elaboration through a neighboring 6. In d and G, the conflict between temporal and registral criteria is resolved in favor of the former. The 5 at the outset is followed by a higher tonic-chord member (3 or 8), but the latter is approached in a less than maximally goal-oriented way. In both cases, the subsequent descent to a prominent neighboring 6 confirms the governing status of 5.47 Similar considerations apply to Kopfton determination in the remaining fi ve Inventions. In c and D, the 3 appears at the outset and is not overridden by any subsequent ascent to other tonic-triad members.48 C and e show a 1–2–3 Anstieg towards the Kopfton, which is also confirmed by subsequent linear connections (see Examples 10[b] and 11). In g , the Kopfton 8 (measure 5) is not approached through an especially clear goal-oriented progression, but it is supported by registral supremacy, by the realization of the preceding implicit 8, and by the subsequent small-scale 8–7–6–5 motions
(see Example 6[b] above). Moreover, the preceding events in this Invention do not show a clear focus on any other of the tonic-triad tones to compete with the 8.49 requirements for the 4 and 3 in a 5-urlinie
Having taken a look at Kopfton establishment in the 15 Inventions, let us proceed to examining the articulation of the remaining Urlinie tones. In considering the requirements for the satisfactory articulation of an Urlinie degree, it is important to allow for both harmonic support and explicit emphasis. Roughly speaking, the weaker harmonic support there is for an Urlinie degree, the more necessary it is to bring it out through special features of design, register, duration, or other kind of emphasis, in order for it to be experienced as a major structural element.50 Consider the dissonant Urlinie 4 in d, the syncopated G in measures 46–47, which represents a passing seventh in a prolonged V 8–7–VI progression (Example 5[c]–[d]). Not any kind of passing seventh would be equally satisfactory as an Urlinie 4 ; the syncope and the hemiolic cadential progression are essential for making this 4 stand out. By contrast, Urlinie 2 , always supported by the 49 50
47
48
Neumeyer and Tepping (1992, 72–74) read the Urlinie from 8 in G, because “[o]nly from 8 (g′′) does subsequent voice leading follow [. . .],” which, of course, neglects the 5–6 connection. 6 and the accompanying IV are strongly underlined as the starting point of an extensive sequential descent in parallel tenths (measures 4 –10); cf. Example 14(e). In D, the initial 3 (F 4) is followed by an ascending motion, but this leads to 2 (E 5) in a way that con firms rather than challenges the governing position of the 3 (Example 3[a]). In c, the large-scale ascent from 3 to 5 (Example 14[g]) is not clearly goal-oriented in character, and the high 5 (G5, measure 13) is abandoned as soon as it is attained.
An ascending arpeggiation D 4–B 4–G5 is discernible as formed by explicit tones in measures 1–5 of g . While the notion of harmonic support and emphasis (or prominence) as complementary analytical criteria is, I believe, a principle tacitly observed by most mainstream Schenkerians, not all theorists agree on it. This is evident, for example, in David Beach’s (1990) and Joel Lester’s (1992) discussion of the opening of Mozart ’s Sonata in G Major, K. 283. Lester, advocating a 3-line reading, reproaches Beach’s 5-line reading, in which a cadential 64 supports 3, for arguing “from prominence to background status” (202). In my view, however, a conception of structural weight as partly dependent on prominence is strongly preferable, since—as the present discussion will make evident —this greatly enhances the predictive and descriptive power of Schenkerian theory for actual compositional features.
bach’s inventions: figuration, register, structure, and the “clear way to develop inventions properly”
structural V, is much less dependent on explicit emphasis— or even existence. The experiential weight of the all-important harmonic event will substitute for a weak or lacking articulation of the Urlinie tone, as exemplified by E and C (Examples 4[d]–[e] and 10[b]).51 Since the 5–4–3 stretch of the 5-Urlinie is unsupported at the background level, explicit emphasis pertains to the satisfactory articulation of this stretch in general. Moreover, since this stretch is the element that distinguishes the 5-Urlinie from the 3-Urlinie , it offers an optimal testing ground for the predictive power of the Urlinie . While it is dif ficult to define exactly what counts as suf ficient emphasis for an Urlinie degree, the predictive power of the Urlinie for this stretch may be assessed by comparing cases in which either 5 or 3 is initially established as the governing top-voice tone.52 Both 5-Urlinie and 3-Urlinie structures may involve 4–3 motions leading to 2–1, but only in the former are such mo-
137
Before surveying the Inventions from this point of view, some observations on middleground harmonies are necessary for refining our notions of the ways in which the requirement of explicit emphasis for Urlinie degrees 4 and 3 depends on harmonic support. Example 13 illustrates the harmonization of these Urlinie degrees in the ten 5-Urlinie Inventions, transposing the structures to C major or minor. In most cases (Example 13[a]–[b]), the primary harmony supporting the 4 is V 7 in root form or inversion, although the 4 is often prepared by a consonance. The requirement of explicit emphasis is indispensable for such dissonant 4s but less so for the subsequent consonant 3s. If the dissonant 4 attracts suf ficient attention, the expectation of its resolution will also guarantee attention to the 3. In d, for example, the 3 is rather unmarked (Example 5[d]). If, on the other hand, the 4 receives consonant support through a I–VII–III progression (Example 13[c]) or through a pre-dominant IV or II6 (Example 13[d]),
bach’s inventions: figuration, register, structure, and the “clear way to develop inventions properly”
51
52
53
137
structural V, is much less dependent on explicit emphasis— or even existence. The experiential weight of the all-important harmonic event will substitute for a weak or lacking articulation of the Urlinie tone, as exemplified by E and C (Examples 4[d]–[e] and 10[b]).51 Since the 5–4–3 stretch of the 5-Urlinie is unsupported at the background level, explicit emphasis pertains to the satisfactory articulation of this stretch in general. Moreover, since this stretch is the element that distinguishes the 5-Urlinie from the 3-Urlinie , it offers an optimal testing ground for the predictive power of the Urlinie . While it is dif ficult to define exactly what counts as suf ficient emphasis for an Urlinie degree, the predictive power of the Urlinie for this stretch may be assessed by comparing cases in which either 5 or 3 is initially established as the governing top-voice tone.52 Both 5-Urlinie and 3-Urlinie structures may involve 4–3 motions leading to 2–1, but only in the former are such motions an integral part of the fundamental structure. In 3Urlinie structures, the role of 4 is subsidiary; it may function as a complete or incomplete neighbor of 3 or as an inner voice passing tone, as in e (Example 11).53 To the extent that such 4–3 motions tend to be more consistently present and more strongly articulated in pieces in which 5 is initially established as governing, this testifies to the predictive power of the Urlinie .
Before surveying the Inventions from this point of view, some observations on middleground harmonies are necessary for refining our notions of the ways in which the requirement of explicit emphasis for Urlinie degrees 4 and 3 depends on harmonic support. Example 13 illustrates the harmonization of these Urlinie degrees in the ten 5-Urlinie Inventions, transposing the structures to C major or minor. In most cases (Example 13[a]–[b]), the primary harmony supporting the 4 is V 7 in root form or inversion, although the 4 is often prepared by a consonance. The requirement of explicit emphasis is indispensable for such dissonant 4s but less so for the subsequent consonant 3s. If the dissonant 4 attracts suf ficient attention, the expectation of its resolution will also guarantee attention to the 3. In d, for example, the 3 is rather unmarked (Example 5[d]). If, on the other hand, the 4 receives consonant support through a I–VII–III progression (Example 13[c]) or through a pre-dominant IV or II6 (Example 13[d]), the requirement of explicit emphasis is somewhat weaker for the 4. In the latter case, in particular, the salient 4 in the bass may substitute for top-voice emphasis.54 On the other hand, the 3, which in such cases is basically a passing tone above the IV, must be brought out by some special means. In both 5-Urlinie Inventions based on this harmonic pattern (E and F ), such means include the local harmonization of the 4–3 motion by chords that mimic the V 7–I motion.
While the conclusion in each of these Inventions is characterized by the weakness of the structural V (the cadential dominant), this V is still an indispensable part of the overall syntax. The issue of what constitutes a satisfactory Urlinie 4 may also be illuminated by a couple of e xamples that I find as unsatisfactory in this respect. Forte and Gilbert (1982, Ex. 213) locate the 4 in d in measure 45, and Neumeyer (1982) locates the 4 in a in measure 20. In neither case are there any special compositional features to distinguish these 4s from ordinary foreground passing notes. Another possibility is an unfolding in which 3–5 is answered by 4–3–2. For an example of such a structure, one might consider the Prelude in B Major from The Well-Tempered Clavier I .
the expression of the 4: comparisons of b , e , a, f , g, b, and c
In the most common structural type of 5-Urlinie Inventions (Example 13[a]), 4 occurs as a dominant seventh and is resolved to the 3 on the tonic. The six Inventions that 54
6 frequently substitutes for 4 as a top-voice tone above IV or II 6, help-
ing to avoid unwanted outer-voice octaves. For small-scale examples, see the auxiliary cadence at the end of a (measure 234, Example 1[a] and Example 1[d]) and the cadences in D (Example 3).
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(a) ^5– ^4–^3 harmonized by I–V 7–I with different inversions
f
7
A G
4 3
E
(b) ^5–^4–^3 harmonized by V 8 7–VI
B
b
d
I II6
V I
( ) ( ) I II6(V 42 “I6 ”)V I
a
4 6 3
4 6 3
8 7
6 5
(d) ^4– ^3–^2 harmonized by IV –V or II–V E
(c) ^5–^4–^3 harmonized by I–VII–III
F
I IV 5 6 V I
I IV 5 (V 65 “I”) 6 V I
Harmonic support for 5-Urlinien
I V
I
I
III V I
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(a) ^5– ^4–^3 harmonized by I–V 7–I with different inversions
f
A G
E
7
B
b
(c) ^5–^4–^3 harmonized by I–VII–III
d
a
4 6 3
4 3
(b) ^5–^4–^3 harmonized by V 8 7–VI
8 7
4 6 3
I V
6 5
I
I
III V I
(d) ^4– ^3–^2 harmonized by IV –V or II–V E
I II6
F
( ) ( )
I II6(V 42 “I6 ”)V I
V I
I IV 5 6 V I
I IV 5 (V 65 “I”) 6 V I
example 13. Harmonic support for 5-Urlinien
represent this structural type (B , E , A , f , G , b ) also share the formal characteristic of closing with a short recapitulation. Example 14 presents an overview of the structures in these Inventions, adding a 3-line case of a similar formal type, c, for comparison. For a starting point for structural comparisons, the reader may review my analysis of E , as shown in Example 2 above. In this Invention, the span from the opening to the recapitulation already expresses a 5–4–3 top-voice progression (with an embellishing 6), whose decisiveness is, however, undermined by a registral drop towards the 3. As indicated in Example 14(a)–(d), B , A , and f show a similar preliminary 5–4–3 descent (with or without an embellishing 6) characterized by a registral drop, which in f takes the form of a transfer to the bass. In these four Inventions, the Urlinie descent only occurs in the recapitulation after a return to the obligatory register. However, B (Example 14[a]) deviates from E , A , and f by restating 5 at the beginning of the
recapitulation, which simplifies Urlinie expression by making the 5–4 connection readily evident for short-span hearing. In E , A , and f (Example 14[b]–[d]), there is no such restatement, and Urlinie 4 relates directly with the initial 5.55 The need to clarify such a relationship, and to prevent the impression of the 4 as a neighbor of 3 gives additional reason to reinforce the 4 at the expense of the preceding 3. In E , A , and f , 4 is marked by an emphatic return to the obligatory register, which also brings about the expressive culmination in these Inventions. In f , the most emphatic articulation of 4 actually occurs one octave above the obligatory register (B 5), a feature whose expressive implications will be taken up presently. In both E and f , the registral drop of top-voice that undermines the initial 5–4–3 progression and the subsequent
55
In f , the 5 (C5) is restated at the beginning of the recapitulation (measure 29), but the listener’s attention is directed to the 4–3 dissonance resolution that transfers to the bass.
bach’s inventions: figuration, register, structure, and the “clear way to develop inventions properly” 6
a)
B
12
^5
( ^4)
b)
( ^3) ^5 ^4
^3 ^2 ^1
^5
23
( ^4)
recap.
^ ^ line is (A preliminary ^5–4–3 completed at the beginning of the recap. ^ The lower register of 3 clarifies the preliminary (non-Urlinie) status of ^ ^ ^ this 5–4–3 line. A restatement of the 5^ and Urlinie descent in the obligatory register follow in the recap.)
31
( ^3)
^4
^3 ^2
^1
recap.
Basic pattern:
recap.
12
E
17
recap.
(Similar, but without the restatement ^ of 5. The return to the obligatory register by an emphasized 4^ creates an effect of fulfillment.)
139
bach’s inventions: figuration, register, structure, and the “clear way to develop inventions properly” 6
a)
17
^5
( ^4)
b)
^5
( ^3)
recap.
^ ^ line is (A preliminary ^5–4–3 completed at the beginning of the recap. ^ The lower register of 3 clarifies the preliminary (non-Urlinie) status of ^ ^ ^ this 5–4–3 line. A restatement of the 5^ and Urlinie descent in the obligatory register follow in the recap.)
^3 ^2
^1
recap.
^5
( ^3)
^4 ^3
^2 ^1
recap.
14
17
29
( ^4)
( ^3)
recap.
(Similar, but without the restatement ^ of 5. The return to the obligatory register by an emphasized 4^ creates an effect of fulfillment.)
recap.
recap.
(Ditto.)
^4 ^3 ^2 ^1
f
18
( ^4)
^5
d)
^4
Basic pattern:
31
( ^4)
A
23
9
c)
^3 ^2 ^1
recap.
12
E
( ^3) ^5 ^4
B
12
recap.
(Otherwise similar, but the return to the obligatory register, one octave ^ lower than the emphasized 4, creates a tragic effect.)
example 14. Structural comparison between B , E , A , f , G , b , and c
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140 4
10
14 18
^5
^4!
27
29
( ^5 ^4 ) ^3
^2 ^1
() G
e)
recap.
Basic pattern:
recap.
^ ^ ^ line leading to the (The 5–4–3 recapitulation assumes Urlinie status owing to special emphasis and registral circumstances. The 3^ in this line is one octave higher than the obligatory register, creating an effect of extra joyousness.)
^5
b
f)
( )
recap.
( ) recap.
^ ^
139
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140 4
10
14 18
^4!
^5
27
29
( ^5 ^4 ) ^3
Basic pattern:
^2 ^1
() G
e)
recap.
recap.
^ ^ ^ line leading to the (The 5–4–3 recapitulation assumes Urlinie status owing to special emphasis and registral circumstances. The 3^ in this line is one octave higher than the obligatory register, creating an effect of extra joyousness.)
^5
( )
( )
b
f)
recap.
recap.
11
13
22
^ ^ Urlinie motion anticipated (The 4–3 in the bass through a temporaldisplacement figure.)
23
( ) N
c
g)
recap.
(A 3-Urlinie structure with a ^ neighboring 4 leading to the recap.)
recap.
example 14. [continued ]
rise to highlight the Urlinie 4 are accompanied by analogous registral features in the bass: a withdrawal from and a return to the low register. In f , the tonic at the beginning of the recapitulation is further weakened by its 63 position (with the
transferred 3 in its bass), whereas the subsequent Urlinie 4 is underlined by a quick descent to the low C 2, features brought about by the modification of the countersubject. Such registral events are not evident in the bass line of A,
bach’s inventions: figuration, register, structure, and the “clear way to develop inventions properly”
but the emphasis on the Urlinie 4 is all the stronger, involving, among other things, a restatement of the 4–3 motion in the bass through the kind of temporal-displacement figure that was encountered in the above analysis of b. In all these Inventions ( A , E , and f ), the recapitulation shows significant modifications of the theme or the countersubject or the general setting, with the effect of emphasizing Urlinie 4 —suggesting that Bach’s compositional procedures were influenced by the striving for a clear Urlinie progression. In B , structural clarification does not call for equally extreme emphasis on the 4 owing to the restatement of the 5. Nevertheless, even in this case the theme is recomposed so as to considerably reinforce the emphasis on the 4.56 Special compositional attention to the Urlinie 4 is also evident in G (Example 14[e]), but this relates with the formal scheme in a way that contrasts with all the preceding examples. Once again, a 5–4–3 progression (with an embellishing
141
figure in b enables an unusual both/and solution to this structural problem. The relatively prominent neighboring 4 in the 3-Urlinie structure of c (Example 14[g]) offers a relevant point of comparison for Urlinie 4 s. Since this neighboring 4 leads to 3 at the beginning of the recapitulation, the formal position of 4 is comparable to that of the Urlinie 4 in G. However, despite the relative prominence of this neighboring 4, it is not marked by anything equally outstanding as the trills that highlight the Urlinie 4 in G; hence this comparison supports the predictive power of the Urlinie . To supplement these structural considerations, it is worth while to present some notes on the expressive significance of the 4–3 motion. This motion is especially laden with expression in E , A , and f , in which it coincides with the reestablishment of the obligatory register. In E and A , in which the obligatory register is the highest in use (for scale degrees 5, 4,
bach’s inventions: figuration, register, structure, and the “clear way to develop inventions properly”
but the emphasis on the Urlinie 4 is all the stronger, involving, among other things, a restatement of the 4–3 motion in the bass through the kind of temporal-displacement figure that was encountered in the above analysis of b. In all these Inventions ( A , E , and f ), the recapitulation shows significant modifications of the theme or the countersubject or the general setting, with the effect of emphasizing Urlinie 4 —suggesting that Bach’s compositional procedures were influenced by the striving for a clear Urlinie progression. In B , structural clarification does not call for equally extreme emphasis on the 4 owing to the restatement of the 5. Nevertheless, even in this case the theme is recomposed so as to considerably reinforce the emphasis on the 4.56 Special compositional attention to the Urlinie 4 is also evident in G (Example 14[e]), but this relates with the formal scheme in a way that contrasts with all the preceding examples. Once again, a 5–4–3 progression (with an embellishing 6) leads to the recapitulation. However, now the 3 that closes this progression is not undermined by a registral drop, but rather reinforced by a temporary rise to a higher register (B5). The preceding 4 is underlined by the unique textural element of the trill, which appears in both hands, concretizing the transference of the 4 to the bass (measures 20–24). Owing to these features of design and register, the initial 5–4–3 motion assumes a much more emphatic and decisive character than in the preceding examples and becomes part of the Urlinie proper. The most extraordinary way of presenting and reinforcing the 4–3 Urlinie motion is evident in b, as analyzed above (Example 14[f]; cf. Example 9[c]–[d]). Whereas the preceding cases involve features that clarify the occurrence of this motion either within the recapitulation (Example 14[a]–[d]) or leading to it (Example 14[e]), the temporal-displacement
figure in b enables an unusual both/and solution to this structural problem. The relatively prominent neighboring 4 in the 3-Urlinie structure of c (Example 14[g]) offers a relevant point of comparison for Urlinie 4 s. Since this neighboring 4 leads to 3 at the beginning of the recapitulation, the formal position of 4 is comparable to that of the Urlinie 4 in G. However, despite the relative prominence of this neighboring 4, it is not marked by anything equally outstanding as the trills that highlight the Urlinie 4 in G; hence this comparison supports the predictive power of the Urlinie . To supplement these structural considerations, it is worth while to present some notes on the expressive significance of the 4–3 motion. This motion is especially laden with expression in E , A , and f , in which it coincides with the reestablishment of the obligatory register. In E and A , in which the obligatory register is the highest in use (for scale degrees 5, 4, and 3), the 4–3 motion in this register creates a sense of victorious fulfillment.The expressive effect is quite different in f , which is characterized by the unfulfilled striving towards the octave above the obligatory register. Example 15(a) illustrates how such a striving is manifest in the preceding events. In the theme, the diminished fifth E5–B 5 occurs prominently one octave higher than the surrounding voice-leading events (Example 15[a], measure 3).These high-register notes trigger a large ascending arpeggiation C5–F 5– A 5–C6 (measure 1–14), harmonized by a most expressive chromaticized 5-65 motion (see Example 15[b] for reduction). However, neither these nor any other high-register elements are able to establish the higher register structurally, since a return to the lower octave follows in each case. The high 4 (B 5) of the recapitulation represents the last desperate manifestation of the highregister striving, as it were, after which the 4–3 motion creates a tragic effect of resignation by effecting the return to the lower obligatory register.57
56
The left hand presents the original theme, whereas the right hand follows in a free stretto. 4 (E 5) is featured in several ways in measures 173–192.
57
In G, on the other hand, the temporary visit above the obligatory register for underlining 3 (B5) creates the effect of unexpected joyousness
music theory spectrum 31 (2009)
142
~ !
I5
IN
N
141
5
( )
music theory spectrum 31 (2009)
142
~ !
5
IN
( )
N
I5
~ ( ) ~
10
15
P
N
P
( 53 64
6 5 1
5) 3
4 2
II
V 6
example 15(a). f : opening section (measures 1– 17)
bach’s inventions: figuration, register, structure, and the “clear way to develop inventions properly” 5
9
14
17
25
29
143
31
^5
^4 ^3 ^2 ^1
() ( ) *
*
recap.
I5
6 5 1
II
4 6 2 V
7 4 2
I6
V 7
I
V I
example 15(b). Overall sketch
The Prelude in E minor from The Well-Tempered Clavier I and the Prelude in C minor from The Well-Tempered Clavier II
In this case, the striving towards higher register—evident in the couplings of 5 4 and 3 (G –G F –F E –E )—eventu-
bach’s inventions: figuration, register, structure, and the “clear way to develop inventions properly” 5
9
14
17
25
29
143
31
^5
^4 ^3 ^2 ^1
() ( ) *
*
recap.
6 5 1
I5
II
4 6 2 V
7 4 2
I6
V 7
I
V I
example 15(b). Overall sketch
The Prelude in E minor from The Well-Tempered Clavier I and the Prelude in C minor from The Well-Tempered Clavier II offer interesting related examples that illustrate a relationship between register and expression. As evident from Example 16, the E minor Prelude has many points of contact with f . The tragically unfulfilled striving towards the higher register is evident both at the opening (Example 16[a]), which closely resembles that of f , and in the large-scale structure (Example 16[b]). The expression of Urlinie 5 and 4 involves elaborate coupling (B 4–B 5, A 5– A 4), which is followed by the closing return to the low obligatory register.58 The C minor Prelude, as graphed in Example 8(b) above, offers a contrasting example.
In this case, the striving towards higher register—evident in the couplings of 5, 4, and 3 (G4–G5, F 5–F 4, E 4–E 5)—eventually leads to the presentation of the final Urlinie degrees in the higher octave (D5–C5), imparting a sense of defiance to the conclusion of this Prelude, in deviation from the resigned endings of f and the E minor Prelude.59 Examples 17–18 depict the structures of E and A in more detail. They also offer additional illustration of enlargements of bass lines and harmonic patterns. While the
58
59
(Example 14[e]). The different expressive effects of high-register elements in f and G relate with the difference in stability between scale degrees 4 and 3. In f the unstable 4 (on V 7) resolves to a lower stable 3, whereas in G the stable 3 is articulated in the high register. My analysis of this Prelude deviates in several respects from that presented by Wen (1999, Example 11). The most significant difference is that Wen shows 1 occurring already in measure 29, which I find as premature given the weight of the subsequent harmonic events.
While most of the present examples enable a clear and unequivocal determination of the obligatory register, some cases are less straightforward in this respect, since they show Kopfton establishment and Urlinie completion occurring in different registers. Whereas the Prelude in C Minor (Example 8[b]) and D (Example 3) are characterized by the top-voice’s fulfilled upward aspiration, F (Example 7[c]) and E (Example 4[e]) highlight Kopfton establishment by a registral position higher than that of the rest of the Urlinie . It is not always clear whether such cases are better described by identifying either the beginning or the end of the Urlinie as being in disagreement with the obligatory register or by adopting a more flexible conception of obligatory register.
music theory spectrum 31 (2009)
144 a) Opening
3 2 IN
b) Overall sketch 7
^5
11
13
16
19
20
22
26
29
32
^4
36
37
^3 ^2 ^1
( )
music theory spectrum 31 (2009)
144 a) Opening
3 2 IN
b) Overall sketch 7
11
13
16
19
20
22
26
29
32
^5
36
^4
( ) ( ) P
I5
6 5
II V
I7
IV 5
6 V
IV 6
37
^3 ^2 ^1
(VII7
“I”) V 64 53 I
example 16. Bach, Prelude in E Minor from The Well-Tempered Clavier I
the 5–4–3 stretch in general
structures are largely similar, the accompaniment of the large-scale 5–(6)–4–3 motion shows differences that reflect those in the opening surface progressions (Examples 17[b]–[c] and 18[b]–[c]). E is characterized on both scales by the calm and steady 5–6 5–6 motion on the neighboring figure E –F –E (this figure is also evident in several other details). A , by contrast, features more dynamic falling thirds.60
The analyses of d, B , E , A , f , G, and b show that in each case in which Urlinie 4 appears as a dominant seventh, it is marked by some special features of design and/or register. We have seen that such features are less necessary for the articulation of the subsequent 3 because it attracts the listener’s attention through dissonance treatment.61 Of the remaining
60
A falling-thirds pattern is also discernible in measures 1–2 of E (E 5–C5– A 4–F 4), but this is only a detail in the I-II connection.
If the 4–3 resolution is complicated by registral transfers, as in G (Example 14[e]), there is more reason to bring out the 3.
61
bach’s inventions: figuration, register, structure, and the “clear way to develop inventions properly” 1
5
^5
a)
6
I
reduction
9
12
()
16
20
23
( ^4
IN
N
7 6 ( )
27
P
6 4 3
6 4 3
^3 )
( ) ( )
7
12
II
23
ech. (+ ant.)
^4
^3
^2
^1
recap.
P
N
VI
31
V 43 I
27
VII6 I6
II6 V I
Cf. opening
( )
ech. (+ ant.)
145
bach’s inventions: figuration, register, structure, and the “clear way to develop inventions properly” 1
5
9
12
16
20
23
27
^5
() IN
a)
6 4 3
7 6 ( )
6
I
7
12
5
6
( ^4
^4
^3 )
( ) ( ) 23
^2
^1
recap.
P
V 43 I
II
^3
N
VII6 I6
27
II6 V I
Cf. opening
( ) ( )
ech. (+ ant.)
c)
6
5
6
N
II
ech. (+ ant.)
*
*
I5 6 II VII6 I
6
VII I (or V 43)
example 17.
62
31
5 6 5 6
5
I
6 4 3
VI
reduction
b)
P
N
145
E : sketches
5-Urlinie Inventions, a already presents the 4–3 Urlinie motion within the opening section, underlining it by the VII–III cadence (Example 1[d]).62 In E and F , fi nally, the 4 is underlined by a pre-dominant II 6 or IV harmony
(Examples 4[e] and 7[c]), which in the case of F is strongly marked by the formal design. In E, Urlinie 4 and 3 occur in the bass but the rhythmic circumstances—the higher prominence of the left-hand rhythms and the right hand ’s
The interpretation of the details in approaching the III in a is by no means straightforward. As shown in Example 1(d), I read measure 5 as 6–6 suspensions above A and G, prolonging the II of C major. The D 5– 4 4 that resolves the first suspension represents Urlinie 4. While no 64 chords occur at the surface, this reading is supported by the strength of
the metrically supported bass line C –B– A–G–F in measures 3–6 and by the right hand ’s suspension–resolution pattern that follows the model of measure 4. Moreover, a 65––64 pattern is not uncommon in the prolongation of II in Bach; for a simple example, see Fugue in C Major from The Well-Tempered Clavier II, measures 40– 41.
music theory spectrum 31 (2009)
146 5
9
a)
I
b)
16
18
^5
^5
12
() ( )
( ^4
IN
( ) (5
6)
VI
IV
V 43
^3 )
20
^4
^3
^2 ^1
IN
^4 ^3
recap.
I
II7 V43
P
I V 42 I6 IV 6 “I6 ” V 64 53 I
( )( ) ( ) ( ) ( ) ()() ( ) () Cf. opening
)
music theory spectrum 31 (2009)
146 5
9
18
I
( ^4
IN
(5
b)
16
() ( ) ( ) ^5
a)
12
^5
6)
VI
IV
V 43
^3 )
20
^4
^3
^2 ^1
IN
^4 ^3
recap.
I
II7 V43
P
I V 42 I6 IV 6 “I6 ” V 64 53 I
( )( ) ( ) ( ) ( ) ()() ( ) () ( ) Cf. opening
c)
I
VI
IV
V43
falling 3rds
I
falling 3rds
example 18. A : sketches
immobility at the moment of the 4–3 motion (measures 58–59 1)—are optimal for bringing them out. In F , the Urlinie stretch 4–2–3–1 is effected by the unvaried transposition of the initial 8–7–6–5 progression and is similarly brought out by register and design (cf. Example 7[a]).63 These observations suggest that in the ten Inventions in which the 5 is initially established as the governing top-voice tone satisfactory Urlinie 4 and 3 also occur. By 63
To be precise, the emphasis on Urlinie 4 is actually somewhat weaker than on the opening 1 (=8), since measures 1–3 are left out from the transposed recapitulation.
comparison, those Inventions in which the 3 is initially established as governing (C, c, D, e) lack occurrences of 4 and 3 that would qualify as equally satisfactory Urlinie tones, if they occurred after an initial 5. Two pertinent comparisons have already been presented: the inner-voice 4 in e and the neighboring 4 in c are less strongly marked than the Urlinie 4s in d and G, respectively (Examples 11 and 14, [e] and [g]). Another pertinent comparison may be made between the 4–3–2 progression in the final cadence of D, in which the 4 is an incomplete neighbor of 3 (Example 3[a], measures 57–58), and the 4–3–2 Urlinie stretch in E (Example 4[d]). While these progressions are based on a similar voice-leading
bach’s inventions: figuration, register, structure, and the “clear way to develop inventions properly”
pattern, rhythmic features bring out the 4 and 3 in E in a way for which there is no counterpart in D. In C, finally, the somewhat similar 4–3–2 progression is even more weakly articulated (measure 213–4; Example 10[b]). On the basis of these comparisons, the present corpus testifies unequivocally to the predictive power of the Urlinie for the 5–4–3 stretch.64 the 2
Since Urlinie 2 may be weakly articulated or implicit, it holds less predictive power for actual musical events than do the 4 and 3 of the 5-Urlinie . Consequently, the 3-Urlinie holds less predictive power than does the 5-Urlinie . There are, however, two meaningful senses in which we can speak of the predictive power of the 2 and which justify its use as an analytical concept. The first is statistical: of the fifteen Inventions, twelve present the 2 explicitly in the highest
147
the role of the 8: kopfton or cover tone?
In g , the sole Invention in which 8 is initially established as the governing top-voice tone, a clearly articulated 8Urlinie follows.This one example thus would seem to suggest that the 8-Urlinie has predictive power similar to that of the 5-Urlinie . However, whereas the ten 5-Urlinie and the four 3-Urlinie Inventions form reasonably large samples for suggesting more general conclusions, one 8-Urlinie Invention is, of course, quite inadequate in this respect. In fact, a look at Bach’s works outside the present corpus reveals that there is a fairly common structural type contradicting such predictive power. In this structural type, a prominent 8 occurs at the outset and is never superseded by other tonic-chord members under the criteria outlined above; however, instead of beginning a convincing Urlinie descent, the 8 functions in a neighboring motion that covers registrally the actual Urlinie .65
bach’s inventions: figuration, register, structure, and the “clear way to develop inventions properly”
pattern, rhythmic features bring out the 4 and 3 in E in a way for which there is no counterpart in D. In C, finally, the somewhat similar 4–3–2 progression is even more weakly articulated (measure 213–4; Example 10[b]). On the basis of these comparisons, the present corpus testifies unequivocally to the predictive power of the Urlinie for the 5–4–3 stretch.64
the role of the 8: kopfton or cover tone?
In g , the sole Invention in which 8 is initially established as the governing top-voice tone, a clearly articulated 8Urlinie follows.This one example thus would seem to suggest that the 8-Urlinie has predictive power similar to that of the 5-Urlinie . However, whereas the ten 5-Urlinie and the four 3-Urlinie Inventions form reasonably large samples for suggesting more general conclusions, one 8-Urlinie Invention is, of course, quite inadequate in this respect. In fact, a look at Bach’s works outside the present corpus reveals that there is a fairly common structural type contradicting such predictive power. In this structural type, a prominent 8 occurs at the outset and is never superseded by other tonic-chord members under the criteria outlined above; however, instead of beginning a convincing Urlinie descent, the 8 functions in a neighboring motion that covers registrally the actual Urlinie .65 As shown in Example 19, the Prelude in F Major from The Well-Tempered Clavier I exemplifies such a structure. The 8–7–8 neighboring figure covers each degree of the 3–2–1 Urlinie (Example 19[b]). Kopfton 3 is never established above the initial 8 (F 5) through a goal-oriented progression or in an otherwise prepared way. Instead, the Prelude is characterized by a descending pattern, F –D–B – A, which proceeds from 8 to 3 both at the opening (Example 19[a]) and on the large scale (Example 19[b], graph [ii])—our final example of figure enlargement. 3 is raised to a higher register at the end of the large-scale pattern (A5, measure 16), but this registral event has the character of unprepared extra emphasis and is thus not comparable to the goal-oriented Kopfton establishment in Inventions such as C or E (Example 19[c]).66 Nevertheless,
the 2
Since Urlinie 2 may be weakly articulated or implicit, it holds less predictive power for actual musical events than do the 4 and 3 of the 5-Urlinie . Consequently, the 3-Urlinie holds less predictive power than does the 5-Urlinie . There are, however, two meaningful senses in which we can speak of the predictive power of the 2 and which justify its use as an analytical concept. The first is statistical: of the fifteen Inventions, twelve present the 2 explicitly in the highest voice (and obligatory register). The second is experiential: the cases in which 2 is implicit—exceptions from the rule— will have special experiential effects, as demonstrated by the “understated” cadence in E (Example 4[d]), by the rhetorical effect of the substitution of D– A –B for D–C –B in b (Example 9[c]–[d]), and—at least arguably —by the less than maximal conclusiveness of the ending in C. When the structural dominant arrives early, the elaboration of 2 may become a significant source of musical content, which is more typical for 3-lines than for 5-lines. In the Inventions, extensive elaboration of 2 occurs in two of the four 3-Urlinie pieces (D and e; Examples 3 and 11) but in only one of the ten 5-Urlinie pieces (a ; Example 1). Such examples testify to the significance of 2 as a compositional resource, even though the extent to which this resource is exploited is greatly variable.
64
65 66
From a more general viewpoint, the occasional occurrence of strongly articulated 4–3 motions in 3-Urlinie pieces does not, of course, negate the predictive power of the Urlinie , as long as such motions occur more consistently when the 5 is initially established as governing.
Schachter (1994) discusses one example showing this kind of covering 8. On the other hand, the progression in measures 123–163 of the Prelude is very similar to that in measures 20 –29 in G (Example 14[e]). In both cases, a voice exchange within II is underlined by trills, and, after a V 42, another voice exchange within I raises the 3 to a higher register.
music theory spectrum 31 (2009)
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18
~ ^3
^3
^2
^1
N
^3
F
D
B
^3
A
^2
^1
example 19(a). Bach, Prelude in F Major from The Well-Tempered Clavier I: beginning and ending F
D
B
A
147
music theory spectrum 31 (2009)
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18
~ ^3
^3
^2
^1
N
^3
F
D
B
A
^3
^2
^1
example 19(a). Bach, Prelude in F Major from The Well-Tempered Clavier I: beginning and ending F
(i)
(ii)
N
^3
^2
D
B
^3
^1
6
5
6
N
5
8
11
12
14
16
18
F
IN ^2 ^1
N
A ^3
5
(iii)
D
(F D B )
B
A
N
I5
6
II
V 42 I6
5 3
IV V I
example 19(b). Overall structure
cases such as the F major Prelude offer some additional perspective for the weak Urlinie articulation in these two Inventions. All three pieces show different manifestations of a covering 8 at the beginning and at the conclusion, even though the intervening events show a determined ascent to the Kopfton in C and E. The F major Prelude exemplifies Ursatz articulation at its weakest not only because of the covering 8–7–8 motion but also because of the extreme rhythmic weakness of the structural dominant (Example 19[a], measure 18, sixth eighth-note). The experiential effect of such weakness is readily evident: it is as if this Prelude hastened to make just some kind of minimally adequate ending so as to be ready for entering the Fugue. Examples such as this Prelude suggest one aspect of qualification for the principles of Kopfton determination as discussed above. 8 is not quite on an equal footing with other tonic-triad members as a Kopfton candidate. Even when it is favored by both the temporal and the registral criterion, it may function as a cover tone rather than the Kopfton; the awareness of such an option would appear significant for Bach analysis.
bach’s inventions: figuration, register, structure, and the “clear way to develop inventions properly”
Prelude in F Major
C
149
E
( ) ( )
example 19(c). Comparison with C and E
4. on the justification of schenkerian analysis
In addition to illuminating Bach’s voice-leading structures and the means of their expression, the topics of the present paper involves viewpoints that help defend the value of Schenkerian analysis for Bach research, and I shall close this paper by summing up such viewpoints. As an example of
As expressed by the title of his essay, Dreyfus sees Schenkerian analysis as representing “figments of imagination” conditioned by an “organicist” ideology, instead of describing any aspect pertinent to Bach’s composition. Terming his agenda as “intentionalism,” Dreyfus (1996, 171) observes that there is no historical evidence that Bach or his contemporaries intentionally arranged his music according to the
bach’s inventions: figuration, register, structure, and the “clear way to develop inventions properly”
Prelude in F Major
C
149
E
( ) ( )
example 19(c). Comparison with C and E
4. on the justification of schenkerian analysis
In addition to illuminating Bach’s voice-leading structures and the means of their expression, the topics of the present paper involves viewpoints that help defend the value of Schenkerian analysis for Bach research, and I shall close this paper by summing up such viewpoints. As an example of a writing that expresses misgivings about Schenkerian analysis in relation to Bach, we may cite Laurence Dreyfus’s essay “Figments of the Organicist’s Imagination” (Dreyfus 1996, Chapter 6 [169–88]). While Dreyfus’s discussion is based on a single analysis by Schenker, that of Bach’s Fugue in C minor from The Well-Tempered Clavier I (Schenker 1996, Chapter 3 [31–54]), he makes it evident that he intends his criticism as generally pertinent to the Schenkerian movement.67 Hence, while it would be out of place to discuss Schenker’s analysis of the C minor Fugue here, it is possible to suggest some ideas about how to encounter criticism such as Dreyfus’s— which is largely representative of antiSchenkerian arguments in general—by referring to the present analyses. 67 This is made evident, for example, by the following statement: “It might well seem curious to pay special attention to an Austrian music theorist writing some seventy years ago if it were not for the fact that Heinrich Schenker’s ideas have gained a remarkable and unprecedented foothold in the world of Anglo-American musical analysis. ” (Dreyfus 1996, 170.)
As expressed by the title of his essay, Dreyfus sees Schenkerian analysis as representing “figments of imagination” conditioned by an “organicist” ideology, instead of describing any aspect pertinent to Bach’s composition. Terming his agenda as “intentionalism,” Dreyfus (1996, 171) observes that there is no historical evidence that Bach or his contemporaries intentionally arranged his music according to the concepts on which Schenker based his analyses. Nor can Schenker’s analyses provide such evidence, since they are based on the “method of ‘seek and ye shall find’” (181). This expression invokes the charge of circular reasoning that has often been made against Schenkerianism, namely, that Schenker’s demonstration of the prolongational structures’ adherence to the norms of harmony and voice leading is based on searching for elements that fit such norms. Starting from the last of these issues, I would suggest that the most ef ficient way to counter the charge—and danger— of circularity is to recognize the significance of analytical criteria such as figuration (design), register, meter and gestural/ rhetoric emphasis, the first two of which comprised my first main topic. Since these criteria involve compositional features that are logically independent of the norms of harmony and voice leading, they enable us to justify a Schenkerian reading in a clearly non-circular way. Going back to my first example, the V –V prolongation in measures 14–22 of a is supported by the cooperation of unified figuration with the use of register, which brings out the E2–G 2– A2–D 2 bass unfolding. Moreover, the dominant
music theory spectrum 31 (2009)
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prolongation accompanies a B5–B4 top-voice motion (with passing B 5 substituting for B5), which associates with the most salient high-register feature in the previous events, the coupling C5–C6 at the beginning of the second section (mm. 6–9), thus supporting the larger connection from 3 to 2. Hence my interpretation of both the dominant prolongation and its position in the larger context does not rely on “figments of imagination,” “organicist” ideology, or circular reasoning, but on prominent compositional features. The hypothesis that prolongational patterns pertained to Bach’s composition helps to explain the emergence of such features; abandoning the study of such patterns—i.e., Schenkerian analysis— would risk losing an important aspect of the way in which Bach shaped his music. a is, of course, no isolated example in the above analyses. Similar justification is characteristic of them, as has been made explicit in a number of cases (and is implicit in others). More comprehensive
familiar to him. Since Bach undoubtedly was capable of applying such principles without conscious effort for surface patterns, it is not unrealistic to assume that his creation of larger patterns may have utilized a similar capability. My second main topic, figure enlargement, also has certain implications for the question about the compositional significance of multilevel organization for Bach. If Bach’s music shows a tendency to develop surface figures by enlarging them into large-scale patterns, this points to the compositional significance of the latter. To be sure, we should be cautious in assessing the significance of figure enlargements, since apparent enlargements might also arise as chance products, especially when involving common-place figures such as filled-in intervals. However, several features reinforce the connections between the small-scale originals and their enlargements in the above examples, making it unlikely that they would occur by chance. First, an enlarge-
music theory spectrum 31 (2009)
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prolongation accompanies a B5–B4 top-voice motion (with passing B 5 substituting for B5), which associates with the most salient high-register feature in the previous events, the coupling C5–C6 at the beginning of the second section (mm. 6–9), thus supporting the larger connection from 3 to 2. Hence my interpretation of both the dominant prolongation and its position in the larger context does not rely on “figments of imagination,” “organicist” ideology, or circular reasoning, but on prominent compositional features. The hypothesis that prolongational patterns pertained to Bach’s composition helps to explain the emergence of such features; abandoning the study of such patterns—i.e., Schenkerian analysis— would risk losing an important aspect of the way in which Bach shaped his music. a is, of course, no isolated example in the above analyses. Similar justification is characteristic of them, as has been made explicit in a number of cases (and is implicit in others). More comprehensive examinations of the extent to which Schenkerian analysis can be justified through non-circular analytical criteria—and how strongly such criteria are manifest in the existing Schenkerian literature—cannot be undertaken here, but this issue would seem a promising area of future studies with crucial epistemic implications for Schenkerian research. While I will not speculate on Bach’s intentions, I would note that I find the question of intentionality less crucial to the cogency of analytical concepts than does Dreyfus, since there is no reason to assume that composers’ conscious intentions cover all significant aspects of their work. For a point of comparison, one may consider the role of syntax in language. Competent speakers of a language do not, as a rule, intend to use a certain kind of syntax, yet syntax is crucial for the way in which they shape their sentences. Analogously, prolongational patterning may be crucial for the way in which a composer shapes his music regardless of the extent of intentionality involved. As regards Bach, the plausibility of this hypothesis is enhanced by the fact that the relationships in prolongational organization rely on basic principles of harmony and voice leading that were intimately
familiar to him. Since Bach undoubtedly was capable of applying such principles without conscious effort for surface patterns, it is not unrealistic to assume that his creation of larger patterns may have utilized a similar capability. My second main topic, figure enlargement, also has certain implications for the question about the compositional significance of multilevel organization for Bach. If Bach’s music shows a tendency to develop surface figures by enlarging them into large-scale patterns, this points to the compositional significance of the latter. To be sure, we should be cautious in assessing the significance of figure enlargements, since apparent enlargements might also arise as chance products, especially when involving common-place figures such as filled-in intervals. However, several features reinforce the connections between the small-scale originals and their enlargements in the above examples, making it unlikely that they would occur by chance. First, an enlargement is often triggered by a prominent surface repetition, or several repetitions, of the small-scale figure (see especially the analyses of d, F , and C). Second, the connection between the small and the large is often reinforced by other factors, such as harmonic support; in g , for example, the enlargement of the 8–7–6–5 descent (G5–F 5–E 5–D5), which itself might be regarded as commonplace, also involves the less usual I–(V )–IV harmonic support for the 8–7–6 (occurring both in measures 3–4 and on the larger scale in measures 1–15; see Example 6). In addition, comparisons between largely comparable structures, such as d and e (Example 11) or E and A (Examples 17–18), show deviations that accurately reflect the differences in the initial surface material. My third main topic, Urlinie articulation, relates, of course, directly with the justification of Schenkerianism. By surveying the ways of Kopfton establishment and the articulation of subsequent Urlinie degrees, I have attempted to show that there is empirical support for the compositional significance of this Schenkerian background concept, concerning especially the 5–4–3 stretch of the 5-Urlinie .
bach’s inventions: figuration, register, structure, and the “clear way to develop inventions properly”
To what extent these results are generalizable to Bach’s enormous output is a question that cannot be addressed in this paper. Suf fice it to say that if the Inventions testify to the structure-determining roles of figuration and register, to the multilevel presentation of musical ideas, and to the significance of the Urlinie (especially the 5-Urlinie ) as pertaining integrally to Bach’s compositional faculties, such faculties are certainly exploited outside the present corpus. It is, however, not impossible that the Inventions show exceptional clarity in some aspects of structural articulation because of Bach’s outspoken pedagogical intent to show a “clear way [. . .] not only to be inspired with good inventions but to develop them properly.” There is, of course, no reason to assume that Bach consciously conceived of structural levels in a way resembling Schenker’s theoretical formulations. However, if I am right in suggesting that all the evidence points to the pertinence of such levels for Bach’s way of composing, it is
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g : 6 A : 12, 13,14, 18 a : 1(a), (b), (d), 12, 13 B : 12,13,14 b: 9, 12, 13, 14
works cited
Adrian, Jack. 1985. “ J. S. Bach’s Invention in A Minor: A Re-View.” In Theory Only 8.7:15–27. Alegant, Brian, and Donald McLean. 2001. “On the Nature of Enlargement.” Journal of Music Theory 45.1:31–71. Beach, David. 1990. “ The Cadential Six-Four as Support for Scale-Degree Three of the Fundamental Line.” Journal of Music Theory 34.1:81–89. Burkhart, Charles. 1978. “Schenker’s ‘Motivic Parallelisms’.” Journal of Music Theory 22.2:145–75.
bach’s inventions: figuration, register, structure, and the “clear way to develop inventions properly”
To what extent these results are generalizable to Bach’s enormous output is a question that cannot be addressed in this paper. Suf fice it to say that if the Inventions testify to the structure-determining roles of figuration and register, to the multilevel presentation of musical ideas, and to the significance of the Urlinie (especially the 5-Urlinie ) as pertaining integrally to Bach’s compositional faculties, such faculties are certainly exploited outside the present corpus. It is, however, not impossible that the Inventions show exceptional clarity in some aspects of structural articulation because of Bach’s outspoken pedagogical intent to show a “clear way [. . .] not only to be inspired with good inventions but to develop them properly.” There is, of course, no reason to assume that Bach consciously conceived of structural levels in a way resembling Schenker’s theoretical formulations. However, if I am right in suggesting that all the evidence points to the pertinence of such levels for Bach’s way of composing, it is conceivable that his quest for exemplary clarity may also have affected the ways in which foreground ideas, or “inventions,” are reflected and developed by middleground patterns. In any case, whatever Bach might have consciously intended as constituting the “proper development of inventions,” the organization in his music enables us to understand this phrase in a much less superficial sense than what is often realized. appendix: a list of examples treating each invention C: 10, 19 c: 14 D: 3 d: 1(c), 5, 11, 12,13 E : 2, 12, 13, 14, 17 E:4,12,19 e: 1(c), 11 F : 7,12,13 f : 12, 13, 14,15 G: 12,13, 14
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g : 6 A : 12, 13,14, 18 a : 1(a), (b), (d), 12, 13 B : 12,13,14 b: 9, 12, 13, 14
works cited
Adrian, Jack. 1985. “ J. S. Bach’s Invention in A Minor: A Re-View.” In Theory Only 8.7:15–27. Alegant, Brian, and Donald McLean. 2001. “On the Nature of Enlargement.” Journal of Music Theory 45.1:31–71. Beach, David. 1990. “ The Cadential Six-Four as Support for Scale-Degree Three of the Fundamental Line.” Journal of Music Theory 34.1:81–89. Burkhart, Charles. 1978. “Schenker’s ‘Motivic Parallelisms’.” Journal of Music Theory 22.2:145–75. Derr, Ellwood. 1981. “ The Two-Part Inventions: Bach’s Composers’ Vademecum.” Music Theory Spectrum 3:26–48. Dreyfus, Laurence. 1996. Bach and the Patterns of Invention. Cambridge MA: Harvard University Press. Forte, Allen, and Steven E. Gilbert. 1982. Introduction to Schenkerian Analysis . New York: Norton. Larson, Steve. 1983. “On Analysis and Performance: The Contribution of Durational Reduction to the Performance of J. S. Bach’s Two-Part Invention in C Major.” In Theory Only 7.1:31–45. Lerdahl, Fred, and Ray Jackendoff. 1983. A Generative Theory of Tonal Music . Cambridge MA: MIT Press. Lester, Joel. 1992. “Reply to David Beach.” Journal of Music Theory 36.1:199–206. Neumeyer, David. 1981. “ The Two Versions of J.S. Bach’s A-minor Invention, BWV 784.” Indiana Theory Review 4.2:69–99. ———. 1987. “ The Three-Part Ursatz.” In Theory Only 10.1–2:3–29. Neumeyer, David, and Susan Tepping 1992. A Guide to Schenkerian Analysis . Englewood Cliffs: Prentice Hall.
music theory spectrum 31 (2009)
Oster, Ernst. 1961. “Register and the Large-Scale Connection.” Journal of Music Theory 5.1:54–71. Reprinted in Readings in Schenker Analysis and Other Approaches , ed. Maury Yeston, 54–71. New Haven: Yale University Press, 1977. Petty, Wayne. 2006. “ Thoughts on Schenker’s Treatment of Diminution and Repetition in Part III of Free Composition, and its Implications for Analysis.” In Structure and Meaning in Tonal Music: Festschrift in Honor of Carl Schachter , ed. L. Poundie Burstein and David Gagné, 73–78. Hillsdale NY: Pendagron Press. Rothgeb, John. 1971. “Design as a Key to Structure in Tonal Music.” Journal of Music Theory 15.1–2:230–53. Reprinted in Readings in Schenker Analysis and Other Approaches , ed. Maury Yeston, 72–93. New Haven: Yale University Press, 1977. Rothstein, William. 2006. “ Transformation of Cadential
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Music Theory Spectrum, Vol. 31, Issue 1, pp. 101–152, ISSN 0195-6167, electronic ISSN 1533-8339. © 2009 by The Society for Music Theory. All rights reserved. Please direct all requests for permission to photocopy or reproduce article content through the University of California Press’s Rights and Permissions website, at http://www. ucpressjournals.com/reprintinfo.asp. DOI: 10.1525/mts.2009.31.1.101
music theory spectrum 31 (2009)
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Oster, Ernst. 1961. “Register and the Large-Scale Connection.” Journal of Music Theory 5.1:54–71. Reprinted in Readings in Schenker Analysis and Other Approaches , ed. Maury Yeston, 54–71. New Haven: Yale University Press, 1977. Petty, Wayne. 2006. “ Thoughts on Schenker’s Treatment of Diminution and Repetition in Part III of Free Composition, and its Implications for Analysis.” In Structure and Meaning in Tonal Music: Festschrift in Honor of Carl Schachter , ed. L. Poundie Burstein and David Gagné, 73–78. Hillsdale NY: Pendagron Press. Rothgeb, John. 1971. “Design as a Key to Structure in Tonal Music.” Journal of Music Theory 15.1–2:230–53. Reprinted in Readings in Schenker Analysis and Other Approaches , ed. Maury Yeston, 72–93. New Haven: Yale University Press, 1977. Rothstein, William. 2006. “ Transformation of Cadential Formulae in the Music of Corelli and His Successors.” In Essays from the Third International Schenker Symposium, ed. Allen Cadwallader, 245–78. Hildesheim: Olms. Schachter, Carl. 1994. “ The Prelude from Bach’s Suite No. 4 for Violoncello Solo: The Submerged Urlinie.” Current Musicology 56:54–71. Schenker, Heinrich. 1979. Free Composition. Trans. Ernst Oster. New York: Schirmer Books. ———. 1996. The Masterwork in Music , Vol. 2. Ed. William Drabkin. Trans. John Rothgeb, Ian Bent, and Hedi Siegel. Cambridge: Cambridge University Press. Travis, Roy. 1976. “ J. S. Bach, Invention No. 13 in A Minor: Reduction and Graph.” In Theory Only 2.8:29–33. V äisälä, Olli. 2008.“ Analyzing Bach—and How Bach Actually Wrote.” The Journal of Schenkerian Studies 3:159–210. Wen, Eric. 1999. “Bass-line articulation of the Urlinie .” In Schenker Studies 2, ed. Carl Schachter and Hedi Siegel, 276–97. Cambridge: Cambridge University Press. Wintle, Christopher. 1986. “‘Skins and Bones’: The C Minor Prelude from J. S. Bach’s Well-Tempered Clavier, Book 2.” Music Analysis 5.1:85–96.
Music Theory Spectrum, Vol. 31, Issue 1, pp. 101–152, ISSN 0195-6167, electronic ISSN 1533-8339. © 2009 by The Society for Music Theory. All rights reserved. Please direct all requests for permission to photocopy or reproduce article content through the University of California Press’s Rights and Permissions website, at http://www. ucpressjournals.com/reprintinfo.asp. DOI: 10.1525/mts.2009.31.1.101
is Associate Professor of Music Theory at Ithaca College. His research interests include Brahms, Music Theory Pedagogy, Disabilities Studies, and Interwar Japanese Music. david pacun
C ontributors teaches in the Department of Music of BarIlan University, Israel. eytan agmon
matt baileyshea
is Assistant Professor at the University of
Rochester. fernando benadon
is Assistant Professor of Music at
American University. is Associate Professor of Music at the University of North Carolina-Greensboro. guy capuzzo
richard domek
is Professor of Music at the University of
is Senior Assistant of Music Theory at the Sibelius Academy, Helsinki. olli väisälä
is Associate Professor of Music Theory at Ithaca College. His research interests include Brahms, Music Theory Pedagogy, Disabilities Studies, and Interwar Japanese Music. david pacun
C ontributors
is Senior Assistant of Music Theory at the Sibelius Academy, Helsinki. olli väisälä
teaches in the Department of Music of BarIlan University, Israel. eytan agmon
matt baileyshea
is Assistant Professor at the University of
Rochester. fernando benadon
is Assistant Professor of Music at
American University. is Associate Professor of Music at the University of North Carolina-Greensboro. guy capuzzo
richard domek
is Professor of Music at the University of
Kentucky. is currently Associate Professor at Emory University in Atlanta, GA. Her research focuses on the analysis of postwar art music through the perspectives of cultural studies, semiotics, and East Asian aesthetics. Her recent publications include “Gesture and Calligraphy in the Late Works by Chou Wen-chung” in Contemporary Music Review 26.5–6 (2007) and The Music of Louis Andriessen (Cambridge University Press, 2006).
yayoi uno everet t
is Assistant Professor at the CollegeConservatory of Music, University of Cincinnati. c. catherine losada
is the Florence Levy Kay Fellow in Ethnomusicology at Brandeis University wayne marshall
timothy r. mckinney is Associate Professor of Music Theory at Baylor University.
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