Bach's inventions
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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.
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music theory spectrum 31 (2009)
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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music theory spectrum 31 (2009)
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
music theory spectrum 31 (2009)
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”
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.
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
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
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
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
6
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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
103
20
*
retransition figure resumed
“I” 6
2nd recap. gesture theme figure extended
*
104
music theory spectrum 31 (2009)
*
retransition begins
*
15
*
*
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
*
*
“I” IV 7 V
18
*
6 5
105
1st recap gesture
^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
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
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
*
*
()
22
*
* 1st recap gesture
6 5
V
18
“I” IV 7 V
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 retransi8 tional V – prolongation. 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 a as “failed” is not meant to belittle its significance for the retransitional events. While figuration and register support perceiv-
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 im-
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
^5
^4
38
44
46 47 48
^5
d
( ) ( )
V “I” V 7 V
38
^5
^4
V 8 (“I”) 7
^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
9
13
14
18
retrans.
1st retrans. recap. figure gesture resumed
^3
22
^2
23
107
25
2nd recap. gesture
^1
( ) () () ( ) ( ) * * * *
I
6 V 5
*
I)
(e: II
4 3
III
V
I)
V
^3 ^ 2
* *
6 4 6 4 6 6 6 6 6 2 5 2 5 4 5 4 5
(C: II 64
^5 ^ 4
6
(“I”
*
5 7 3 ) IV V
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 struc whose second branch is weakened by its
the uniformity of figuration is interrupted by a temporary digression.
bach’s inventions: figuration, register, structure, and the “clear way to develop inventions properly” 3
6
^5
9
^4
14
18
retrans.
1st retrans. recap. figure gesture resumed
^3
6 4 6 4 6 6 6 6 6 2 5 2 5 4 5 4 5
(C: II 64
13
6 V 5
I
22
^2
23
107
25
2nd recap. gesture
^1
( ) () () ( ) ( ) * * * *
4 3
(e: II
V
III
^3 ^ 2
* *
*
I)
^5 ^ 4
*
I)
(“I”6
V
5 7 3 ) IV V
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
^3
^2
^1
~ (extension of theme)
P
VII6 (or V 43 )
I6
II 6 V I
example 2. E : register, figuration, and structure
: parallelism of figuration and register
e
motions. Of these high-register tones, C6 occurs within a countersubject statement but A is marked by the freer em-
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
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 non-
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 shown by the large asterisks, as the D5 is featured by the reappearance of the octave-leap texture that originally established the E
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
* *
*
*
V 38
~
retrans.
V
I)
V 64
(A: I
40
43
(F 4
( )
recap.
^3(F 4)
5 3
I
IV (V 42 “I”6 )
45
E5)
109
^1!
*
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