Bach's inventions

101

101

Bach

Bach

’

’

s

s

Inve

Inve

ntion

ntion

s:

s:

Figur

Figur

ation,

ation,

Regis

Regis

ter

ter

,

,

Structur

Structur

e,

e,

and the “Clear Way to Develop Inventions Properly” 

and the “Clear Way to Develop Inventions Properly” 

olli väisälä

olli väisälä

Bach’

Bach’s 15 two-part Inventions are viewed from the Schenkerian perspes 15 two-part Inventions are viewed from the Schenkerian perspective,ctive,focusing on threefocusing on three

main topics:

main topics:(1) the significance of figuration (design) and register as structural determi(1) the significance of figuration (design) and register as structural determinants,nants,

(2) the enlargement of characteristic surface figures,

(2) the enlargement of characteristic surface figures,and (3) the significance of theand (3) the significance of the UrsatzUrsatzfor ac-for

ac-tual musical events.

tual musical events.It is argued that these three topics pertaiIt is argued that these three topics pertain crucially to the musical organizationn crucially to the musical organization

in the Inventions and also

in the Inventions and also offer significant viewpoints for the justification of offer significant viewpoints for the justification of Schenkerian analysisSchenkerian analysis

in Bach research.

in Bach research.

Keywo

Keywords:rds:BachBach,,InvenInventiontions,s,ScheSchenkerinkerian an analyanalysis,sis,figurafiguration,tion,regiregisterster,,enlaenlargemergementsnts

B

B

ach’s

ach’s

15

15

two-part inventions

two-part inventions

belong to the very 

belong to the very 

best known repertoire of W

best known repertoire of W

estern art music.

estern art music.

Written

Written

for pedag

for pedag

ogical purp

ogical purp

oses,

oses,

they still hol

they still hol

d a standard

d a standard

position in both keyboard and counterpoint pedagogy.

position in both keyboard and counterpoint pedagogy.

 They

 They

have

have

also

also

frequently

frequently

serve

serve

d

d

as

as

analyti

analyti

cal

cal

examples

examples

of 

of 

cont

cont

rap

rap

unta

unta

l dev

l dev

ices

ices

,

,

moti

moti

vic d

vic d

evel

evel

opme

opme

nt,

nt,

and f

and f

orm.

orm.

11

Several have doubtless also considered their harmony and

Several have doubtless also considered their harmony and

 voice

 voice

leading,

leading,

but

but

they

they

have

have

not

not

featured

featured

prominently

prominently

in

in

the most significan

the most significan

t Schenkerian lit

t Schenkerian lit

erature.

erature.

The presen

The presen

t

t

study aims to fill in this gap,

study aims to fill in this gap,

suggesting that the Inventions

suggesting that the Inventions

constitute an instructive corpus also for giving a “strong

constitute an instructive corpus also for giving a “strong

foretaste”

foretaste”

of the clar

of the clar

ity and imag

ity and imag

inativenes

inativenes

s of Bac

s of Bac

h’

h’

s

s

 voice-lead

 voice-lead

ing str

ing str

uctures.

uctures.

 Three

 Three

general

general

topics,

topics,

each

each

of

of

which

which

has

has

significance

significance

for

for

Bach’

Bach’

s music and

s music and

its analysis,

its analysis,

will be my focus

will be my focus

.

.

The first deals

The first deals

 with the role of figuration and

 with the role of figuration and

register as structural determi-

register as structural

determi-nants and as

nants and as

analytical criteria.

analytical criteria.

The second topic

The second topic

is Bach’

is Bach’

s

s

tendency to develop characteristic foreground figures by

tendency to develop characteristic foreground figures by

en-larging them as

larging them as

larger structural fram

larger structural fram

eworks.

eworks.

The third ad-

The third

ad-dresses the r

dresses the r

elationship between the

elationship between the

“axiomatic”

“axiomatic”

background

background

of Schen

of Schen

kerian a

kerian a

nalysis

nalysis

,

,

the

the

Urlinie 

Urlinie 

,

,

and the

and the

actua

actua

l mus

l mus

ical

ical

events.

events.

The first of these top

The first of these top

ics addresses the

ics addresses the

means 

means 

by which

by which

the composition expresses the multilevel structures that

the composition expresses the multilevel structures that

Schenkerian analysis seeks to el

Schenkerian analysis seeks to el

ucidate.

ucidate.

While each level de-

While each level

de-pends on the fundamental principles of harmony and voice

pends on the fundamental principles of harmony and voice

leading,

leading,

I will b

I will b

e emphasizing

e emphasizing

that the dete

that the dete

rmination of 

rmination of 

structural weight—which element belongs to which level—

structural weight—which element belongs to which level—

is largely based

is largely based

on quite

on quite

different factors,

different factors,

such as

such as

figuration

figuration

In this paper,

In this paper,I shall allude to Bach’I shall allude to Bach’s preamble to the Inventions ac-s preamble to the Inventions

ac-cording to the translati

cording to the translation of the Wiener Urtext Edition (ed.on of the Wiener Urtext Edition (ed.Erwin Ratz Erwin Ratz 

and Karl He

and Karl Heinz Füssl,inz Füssl,trans.trans.unknownunknown):):“A “A sincere sincere guide,guide,in whicin which loversh lovers

of keyboard mu

of keyboard music,sic,and particuand particularly those desirilarly those desiring to learn,ng to learn,are shown aare shown a

clear way not on

clear way not only (1) how to plly (1) how to play faultleay faultlessly in 2 parts,ssly in 2 parts,but also,but also,uponupon

further progress,

further progress,(2) how to treat three obbligato parts correctly and well;(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

and at the same time not only to be inspired with good inventions but to

develop them prope

develop them properly;rly;and most of all to achieve a cantabile manneand most of all to achieve a cantabile manner of r of 

playing and to gain a strong foretaste of composition.”

playing and to gain a strong foretaste of composition.”

I am indebted to Lauri Suurpää for his valuable comments on a

I am indebted to Lauri Suurpää for his valuable comments on a

draft of this article.

draft of this article.

1

1 See,See,for example,for example,Derr (1981) for dDerr (1981) for discussion on such iscussion on such aspects.aspects.

and register.

and register.

22

 _The

 _The

_second

_second

_and

_and

_third

_third

_topics

_topics

_identify

_identify

_two

_two

sources for the musical

sources for the musical

contents 

contents 

of

of

such

such

structures:

structures:

piece-spe-

piece-spe-cific figur

cific figur

es,

es,

on the one hand,

on the one hand,

and the genera

and the genera

l striving for the

l striving for the

Urlinie 

Urlinie 

descen

descen

t,

t,

on the other.

on the other.

 While

 While

none

none

of

of

these

these

topics

topics

is

is

by

by

any

any

means

means

original,

original,

a

a

specia

specia

l attent

l attent

ion to them is

ion to them is

,

,

I believ

I believ

e,

e,

highly be

highly be

neficia

neficia

l for

l for

our understanding both of Bach’s musical organization and

our understanding both of Bach’s musical organization and

of the value of Schenkerian analysis in its illumination.

of the value of Schenkerian analysis in its illumination.

 While

 While

several

several

analysts—Rothgeb

analysts—Rothgeb

(1971)

(1971)

and

and

Oster

Oster

(1961)

(1961)

being classic examples—have pointed out the impacts of

being classic examples—have pointed out the impacts of

fig-uration (or design) and register for structural clarification,

uration (or design) and register for structural clarification,

the significance of these factors seems not always to be fully 

the significance of these factors seems not always to be fully 

realized in analytical practice (as I have discussed in Väisälä

realized in analytical practice (as I have discussed in Väisälä

2008

2008

).

).

Motiv

Motiv

e enlargem

e enlargem

ents are

ents are

,

,

of course

of course

,

,

a familia

a familia

r topic in

r topic in

the Schenkerian

the Schenkerian

literature

literature

(see,

(see,

for

for

instance,

instance,

Burkhart 19

Burkhart 19

78),

78),

and my contribution in this respect is confined to

and my contribution in this respect is confined to

illuminat-ing its particular significance for the present repertoire.

ing its particular significance for the present repertoire.

 while

 while

the

the

examples of

examples of

section

section

1 ser

1 ser

ve pri

ve pri

marily

marily

to i

to i

llustrate

llustrate

the structure-determining significance of figuration and

the structure-determining significance of figuration and

register

register

,

,

I will also pay attention to the structures they help

I will also pay attention to the structures they help

to determin

to determin

e,

e,

including th

including th

e backgroun

e backgroun

d level.

d level.

Similar inte

Similar inte

r-

r-twinemen

twinemen

t of topics is evident in all the sections.

t of topics is evident in all the sections.

Figuration

Figuration

and register will retain their significance as analytical

and register will retain their significance as analytical

crite-ria throughout the analyses,

ria throughout the analyses,

including those focus

including those focus

ing on fig-

ing on

fig-ure enlargements (which are not based on the desire to find

ure enlargements (which are not based on the desire to find

such enlargements

such enlargements

).

).

Finally

Finally

,

,

besides illuminatin

besides illuminatin

g Bach’s mu-

g Bach’s

mu-sical language

sical language

,

,

I will suggest that these topics also offer sig-

I will suggest that these topics also offer

sig-nificant arguments for defending the value of the

nificant arguments for defending the value of the

Schenkerian ap

Schenkerian ap

proach in

proach in

Bach r

Bach r

esearch.

esearch.

Such arguments

Such arguments

 will be outlined in secti

 will be outlined in secti

on 4.

on 4.

abbreviations and analytical symbols

abbreviations and analytical symbols

 The article

 The article

indentifies each Invention

indentifies each Invention

by key in

by key in

boldface:

boldface:

1

and register.

and register.

22

 _The

 _The

_second

_second

_and

_and

_third

_third

_topics

_topics

_identify

_identify

_two

_two

sources for the musical

sources for the musical

contents 

contents 

of

of

such

such

structures:

structures:

piece-spe-

piece-spe-cific figur

cific figur

es,

es,

on the one hand,

on the one hand,

and the genera

and the genera

l striving for the

l striving for the

Urlinie 

Urlinie 

descen

descen

t,

t,

on the other.

on the other.

 While

 While

none

none

of

of

these

these

topics

topics

is

is

by

by

any

any

means

means

original,

original,

a

a

specia

specia

l attent

l attent

ion to them is

ion to them is

,

,

I believ

I believ

e,

e,

highly be

highly be

neficia

neficia

l for

l for

our understanding both of Bach’s musical organization and

our understanding both of Bach’s musical organization and

of the value of Schenkerian analysis in its illumination.

of the value of Schenkerian analysis in its illumination.

 While

 While

several

several

analysts—Rothgeb

analysts—Rothgeb

(1971)

(1971)

and

and

Oster

Oster

(1961)

(1961)

being classic examples—have pointed out the impacts of

being classic examples—have pointed out the impacts of

fig-uration (or design) and register for structural clarification,

uration (or design) and register for structural clarification,

the significance of these factors seems not always to be fully 

the significance of these factors seems not always to be fully 

realized in analytical practice (as I have discussed in Väisälä

realized in analytical practice (as I have discussed in Väisälä

2008

2008

).

).

Motiv

Motiv

e enlargem

e enlargem

ents are

ents are

,

,

of course

of course

,

,

a familia

a familia

r topic in

r topic in

the Schenkerian

the Schenkerian

literature

literature

(see,

(see,

for

for

instance,

instance,

Burkhart 19

Burkhart 19

78),

78),

and my contribution in this respect is confined to

and my contribution in this respect is confined to

illuminat-ing its particular significance for the present repertoire.

ing its particular significance for the present repertoire.

Finally

Finally

,

,

while Schenkerian

while Schenkerian

analysts are

analysts are

always concerne

always concerne

d

d

 with

 with

the

the

relationsh

relationsh

ip

ip

between

between

the

the

Urlinie 

Urlinie 

and the actual

and the actual

music,

music,

the existing literature would

the existing literature would

seem to lack illumination

seem to lack illumination

of this topic based on systematic studies of well-defined but

of this topic based on systematic studies of well-defined but

sufficiently e

sufficiently e

xtensive corpus

xtensive corpus

es of basic re

es of basic re

pertoire.

pertoire.

The 15

The 15

Inventions provide an opportunity for outlining how such a

Inventions provide an opportunity for outlining how such a

study may be conducted.

study may be conducted.

I shall proceed by first discussing selected analytical

I shall proceed by first discussing selected analytical

ex-amples for illuminating the first two topics in sections 1 and

amples for illuminating the first two topics in sections 1 and

2.

2.

In sect

In sect

ion 3,

ion 3,

I shall t

I shall t

ake a mor

ake a mor

e compr

e compr

ehensive

ehensive

look at

look at

the thir

the thir

d topic

d topic

.

.

Howe

Howe

ver

ver

,

,

sinc

sinc

e a single In

e a single In

ven

ven

tion ma

tion ma

y

y

,

,

of 

of 

course,

course,

pertain to all th

pertain to all th

ree topics

ree topics

,

,

it would be im

it would be im

practical to

practical to

keep the topics stric

keep the topics stric

tly separate in the dis

tly separate in the dis

cussion.

cussion.

Hence,

Hence,

 while

 while

the

the

examples of

examples of

section

section

1 ser

1 ser

ve pri

ve pri

marily

marily

to i

to i

llustrate

llustrate

the structure-determining significance of figuration and

the structure-determining significance of figuration and

register

register

,

,

I will also pay attention to the structures they help

I will also pay attention to the structures they help

to determin

to determin

e,

e,

including th

including th

e backgroun

e backgroun

d level.

d level.

Similar inte

Similar inte

r-

r-twinemen

twinemen

t of topics is evident in all the sections.

t of topics is evident in all the sections.

Figuration

Figuration

and register will retain their significance as analytical

and register will retain their significance as analytical

crite-ria throughout the analyses,

ria throughout the analyses,

including those focus

including those focus

ing on fig-

ing on

fig-ure enlargements (which are not based on the desire to find

ure enlargements (which are not based on the desire to find

such enlargements

such enlargements

).

).

Finally

Finally

,

,

besides illuminatin

besides illuminatin

g Bach’s mu-

g Bach’s

mu-sical language

sical language

,

,

I will suggest that these topics also offer sig-

I will suggest that these topics also offer

sig-nificant arguments for defending the value of the

nificant arguments for defending the value of the

Schenkerian ap

Schenkerian ap

proach in

proach in

Bach r

Bach r

esearch.

esearch.

Such arguments

Such arguments

 will be outlined in secti

 will be outlined in secti

on 4.

on 4.

abbreviations and analytical symbols

abbreviations and analytical symbols

 The article

 The article

indentifies each Invention

indentifies each Invention

by key in

by key in

boldface:

boldface:

major keys are giv

major keys are giv

en in majuscu

en in majuscu

le;

le;

minor in minus

minor in minus

cule.

cule.

The

The

abbreviations are used both in the text and in the analytical

abbreviations are used both in the text and in the analytical

example

example

s.

s.

There are two symbols used for special purposes

There are two symbols used for special purposes

in the analytical examples:

in the analytical examples:

an asterisk denotes voice-

an asterisk denotes voice-

leading

leading

relations

relations

hips clarified by p

hips clarified by p

arallelism

arallelism

of figuration;

of figuration;

and an

and an

accent sign (

accent sign (

>>

) denotes special emphasis pertinent for struc-

) denotes special emphasis pertinent for

struc-tural hierarchy.

tural hierarchy.

contrapuntal design and form

contrapuntal design and form

 Although

 Although

I shall

I shall

concentrate on

concentrate on

the

the

voice-leading struc-

voice-leading

struc-ture rather than

ture rather than

contrapuntal design or

contrapuntal design or

form,

form,

some notions

some notions

concerning the latter two aspects will be necessary for my 

concerning the latter two aspects will be necessary for my 

discussion.

discussion.

Most Inventions fall

Most Inventions fall

into two basic types with re-

into two basic types with

re-spect to thematic style and the nature of the opening

spect to thematic style and the nature of the opening

imita-tion.

tion.

Inventions of

Inventions of

Type

Type

1 (

1 (

C

C

,

,

 D

 D

,

,

 d

 d

,

,

 e

 e

,

,

 G

 G

,

,

an

an

d

d

a 

a 

) open with a

) open with a

statement of a short theme figure in the right hand alone or

statement of a short theme figure in the right hand alone or

accompanied by a simple left-hand gesture to establish the

accompanied by a simple left-hand gesture to establish the

tonic.

tonic.

This statement is f

This statement is f

ollowed b

ollowed b

y imitation in the le

y imitation in the le

ft

ft

hand.

hand.

Inventions of

Inventions of

Type

Type

2 (

2 (

E

E





,

,

 E

 E

,

,

 f 

 f 

,

,

 A 

 A 

,

,

 B

 B





,

,

an

an

d

d

 b

 b

) open with

) open with

a longer theme comb

a longer theme comb

ined with a countersubjec

ined with a countersubjec

t,

t,

followed by 

followed by 

2

2 I discuss this in greater length in Väisälä 2008,I discuss this in greater length in Väisälä 2008,in which I identify fourin which I identify four

significant structural determinants that are logically independent of the

significant structural determinants that are logically independent of the

norms of

norms of harmony and harmony and voice-leading:voice-leading: design (including design (including figuration),figuration),

register

register,,metermeter,,and rhetand rhetorical/gestural orical/gestural devices.devices.All these All these factors pfactors pertainertain

to the present analyses,

to the present analyses,even though the greateeven though the greatest explicit attention isst explicit attention is

paid to the first two.

paid to the first two.

bac

bac

h’

h’

s inve

s inve

ntio

ntio

ns:

ns:

figu

figu

ra

ra

tio

tio

n,

n,

reg

reg

iste

iste

r,

r,

str

str

uct

uct

ur

ur

e,

e,

and th

and th

e “

e “

cle

cle

ar w

ar w

ay t

ay t

o dev

o dev

elo

elo

p inv

p inv

ent

ent

ion

ion

s pro

s pro

per

per

ly”

ly”

103

103

another statement with inverted voices.

another statement with inverted voices.

33

 _{A special variant of} 

 _{A special variant of} 

 Typ

 Typ

e

e

2

2

is

is

g 

g 

,

,

in which two counter

in which two counter

subje

subje

cts alter

cts alter

nate in the-

nate in

the-matic statements.

matic statements.

The rem

The rem

aining Inventions,

aining Inventions,

 c

 c

and

and

F 

F 

,

,

op

op

en

en

 with

 with

canons,

canons,

but,

but,

on

on

the

the

basis

basis

of

of

the

the

right-hand

right-hand

material

material

preceding the left-hand entrance,

preceding the left-hand entrance,

 F 

 F 

comes closer to Type 1

comes closer to Type 1

and

and

c

c

to T

to T

ype 2 (despite

ype 2 (despite

its one-voice opening).

its one-voice opening).

 A

 A

central

central

formal

formal

consideration

consideration

concerns

concerns

recapitulation.

recapitulation.

Most Typ

Most Typ

e 1

e 1

Inventions (

Inventions (

C

C

,

,

 d

 d

,

,

 e

 e

,

,

an

an

d

d

a 

a 

) lack an unequivocal

) lack an unequivocal

recapitulation,

recapitulation,

if we defin

if we defin

e this as

e this as

requiring the concurr

requiring the concurr

ent

ent

return of the structural tonic and of the theme at the original

return of the structural tonic and of the theme at the original

level.

level.

Howeve

Howeve

r

r

,

,

 d

 d

and

and

a 

a 

contain salient “recapitulation ges-

contain salient “recapitulation

ges-tures,”

tures,”

theme statements at the

theme statements at the

original level but prior to

original level but prior to

the

the

structural tonic return.

structural tonic return.

44

_{Most Type 2 Inventions (}

_{Most Type 2 Inventions (}

_E

_E





_,

_,

 _f 

 _f 

_,

_,

 _A 

 _A 

_,

_,

 _B

 _B





_,

_,

and

and

 b

 b

),

),

alo

alo

ng w

ng w

ith

ith

G

G

and

and

c

c

,

,

close wit

close wit

h a short une

h a short une

quivo

quivo

cal

cal

recapi

recapi

tulation

tulation

:

:

a tonic return ma

a tonic return ma

rked by a themati

rked by a themati

c state-

c

state-ment or two in the original key.

ment or two in the original key.

55

_{Such statements often in-}

_{Such statements often}

in- volve

 volve

adaptations

adaptations

with

with

crucial

crucial

structural

structural

significance;

significance;

hence

hence

Each invention subdivides according to thematic and key 

Each invention subdivides according to thematic and key 

design.

design.

Sections are usually

Sections are usually

(but not always)

(but not always)

concluded by a

concluded by a

cadence and opened by a thematic statement in a key that

cadence and opened by a thematic statement in a key that

differs from that in the beginning of the preceding section.

differs from that in the beginning of the preceding section.

In middleground readings,

In middleground readings,

measure lines are

measure lines are

employed to in-

employed to

in-dicate sectional

dicate sectional

borders.

borders.

Another significant

Another significant

kind of

kind of

formal

formal

entity is the retransition,

entity is the retransition,

by which I mean

by which I mean

any passage l

any passage l

ead-

ead-ing from the last strongly tonicized

ing from the last strongly tonicized

non-tonic scale degree to

non-tonic scale degree to

the tonic return.

the tonic return.

1.

1.

figuration and

figuration and

register as structur

register as structur

al

al

determinants

determinants

a 

a 

:

:

retransitional v

retransitional v





–

–





prolongation clarified

prolongation clarified

by uniform figura

by uniform figura

tion,

tion,

with a “f

with a “f

ailed”

ailed”

recapitulation gesture as a digression

recapitulation gesture as a digression

and register.

and register.

22

 _The

 _The

_second

_second

_and

_and

_third

_third

_topics

_topics

_identify

_identify

_two

_two

sources for the musical

sources for the musical

contents 

contents 

of

of

such

such

structures:

structures:

piece-spe-

piece-spe-cific figur

cific figur

es,

es,

on the one hand,

on the one hand,

and the genera

and the genera

l striving for the

l striving for the

Urlinie 

Urlinie 

descen

descen

t,

t,

on the other.

on the other.

 While

 While

none

none

of

of

these

these

topics

topics

is

is

by

by

any

any

means

means

original,

original,

a

a

specia

specia

l attent

l attent

ion to them is

ion to them is

,

,

I believ

I believ

e,

e,

highly be

highly be

neficia

neficia

l for

l for

our understanding both of Bach’s musical organization and

our understanding both of Bach’s musical organization and

of the value of Schenkerian analysis in its illumination.

of the value of Schenkerian analysis in its illumination.

 While

 While

several

several

analysts—Rothgeb

analysts—Rothgeb

(1971)

(1971)

and

and

Oster

Oster

(1961)

(1961)

being classic examples—have pointed out the impacts of

being classic examples—have pointed out the impacts of

fig-uration (or design) and register for structural clarification,

uration (or design) and register for structural clarification,

the significance of these factors seems not always to be fully 

the significance of these factors seems not always to be fully 

realized in analytical practice (as I have discussed in Väisälä

realized in analytical practice (as I have discussed in Väisälä

2008

2008

).

).

Motiv

Motiv

e enlargem

e enlargem

ents are

ents are

,

,

of course

of course

,

,

a familia

a familia

r topic in

r topic in

the Schenkerian

the Schenkerian

literature

literature

(see,

(see,

for

for

instance,

instance,

Burkhart 19

Burkhart 19

78),

78),

and my contribution in this respect is confined to

and my contribution in this respect is confined to

illuminat-ing its particular significance for the present repertoire.

ing its particular significance for the present repertoire.

Finally

Finally

,

,

while Schenkerian

while Schenkerian

analysts are

analysts are

always concerne

always concerne

d

d

 with

 with

the

the

relationsh

relationsh

ip

ip

between

between

the

the

Urlinie 

Urlinie 

and the actual

and the actual

music,

music,

the existing literature would

the existing literature would

seem to lack illumination

seem to lack illumination

of this topic based on systematic studies of well-defined but

of this topic based on systematic studies of well-defined but

sufficiently e

sufficiently e

xtensive corpus

xtensive corpus

es of basic re

es of basic re

pertoire.

pertoire.

The 15

The 15

Inventions provide an opportunity for outlining how such a

Inventions provide an opportunity for outlining how such a

study may be conducted.

study may be conducted.

I shall proceed by first discussing selected analytical

I shall proceed by first discussing selected analytical

ex-amples for illuminating the first two topics in sections 1 and

amples for illuminating the first two topics in sections 1 and

2.

2.

In sect

In sect

ion 3,

ion 3,

I shall t

I shall t

ake a mor

ake a mor

e compr

e compr

ehensive

ehensive

look at

look at

the thir

the thir

d topic

d topic

.

.

Howe

Howe

ver

ver

,

,

sinc

sinc

e a single In

e a single In

ven

ven

tion ma

tion ma

y

y

,

,

of 

of 

course,

course,

pertain to all th

pertain to all th

ree topics

ree topics

,

,

it would be im

it would be im

practical to

practical to

keep the topics stric

keep the topics stric

tly separate in the dis

tly separate in the dis

cussion.

cussion.

Hence,

Hence,

 while

 while

the

the

examples of

examples of

section

section

1 ser

1 ser

ve pri

ve pri

marily

marily

to i

to i

llustrate

llustrate

the structure-determining significance of figuration and

the structure-determining significance of figuration and

register

register

,

,

I will also pay attention to the structures they help

I will also pay attention to the structures they help

to determin

to determin

e,

e,

including th

including th

e backgroun

e backgroun

d level.

d level.

Similar inte

Similar inte

r-

r-twinemen

twinemen

t of topics is evident in all the sections.

t of topics is evident in all the sections.

Figuration

Figuration

and register will retain their significance as analytical

and register will retain their significance as analytical

crite-ria throughout the analyses,

ria throughout the analyses,

including those focus

including those focus

ing on fig-

ing on

fig-ure enlargements (which are not based on the desire to find

ure enlargements (which are not based on the desire to find

such enlargements

such enlargements

).

).

Finally

Finally

,

,

besides illuminatin

besides illuminatin

g Bach’s mu-

g Bach’s

mu-sical language

sical language

,

,

I will suggest that these topics also offer sig-

I will suggest that these topics also offer

sig-nificant arguments for defending the value of the

nificant arguments for defending the value of the

Schenkerian ap

Schenkerian ap

proach in

proach in

Bach r

Bach r

esearch.

esearch.

Such arguments

Such arguments

 will be outlined in secti

 will be outlined in secti

on 4.

on 4.

abbreviations and analytical symbols

abbreviations and analytical symbols

 The article

 The article

indentifies each Invention

indentifies each Invention

by key in

by key in

boldface:

boldface:

major keys are giv

major keys are giv

en in majuscu

en in majuscu

le;

le;

minor in minus

minor in minus

cule.

cule.

The

The

abbreviations are used both in the text and in the analytical

abbreviations are used both in the text and in the analytical

example

example

s.

s.

There are two symbols used for special purposes

There are two symbols used for special purposes

in the analytical examples:

in the analytical examples:

an asterisk denotes voice-

an asterisk denotes voice-

leading

leading

relations

relations

hips clarified by p

hips clarified by p

arallelism

arallelism

of figuration;

of figuration;

and an

and an

accent sign (

accent sign (

>>

) denotes special emphasis pertinent for struc-

) denotes special emphasis pertinent for

struc-tural hierarchy.

tural hierarchy.

contrapuntal design and form

contrapuntal design and form

 Although

 Although

I shall

I shall

concentrate on

concentrate on

the

the

voice-leading struc-

voice-leading

struc-ture rather than

ture rather than

contrapuntal design or

contrapuntal design or

form,

form,

some notions

some notions

concerning the latter two aspects will be necessary for my 

concerning the latter two aspects will be necessary for my 

discussion.

discussion.

Most Inventions fall

Most Inventions fall

into two basic types with re-

into two basic types with

re-spect to thematic style and the nature of the opening

spect to thematic style and the nature of the opening

imita-tion.

tion.

Inventions of

Inventions of

Type

Type

1 (

1 (

C

C

,

,

 D

 D

,

,

 d

 d

,

,

 e

 e

,

,

 G

 G

,

,

an

an

d

d

a 

a 

) open with a

) open with a

statement of a short theme figure in the right hand alone or

statement of a short theme figure in the right hand alone or

accompanied by a simple left-hand gesture to establish the

accompanied by a simple left-hand gesture to establish the

tonic.

tonic.

This statement is f

This statement is f

ollowed b

ollowed b

y imitation in the le

y imitation in the le

ft

ft

hand.

hand.

Inventions of

Inventions of

Type

Type

2 (

2 (

E

E





,

,

 E

 E

,

,

 f 

 f 

,

,

 A 

 A 

,

,

 B

 B





,

,

an

an

d

d

 b

 b

) open with

) open with

a longer theme comb

a longer theme comb

ined with a countersubjec

ined with a countersubjec

t,

t,

followed by 

followed by 

1

1

0

0

2

2

m

m

u

u

s

s

i

i

c

c

t

t

h

h

e

e

o

o

r

r

y

y

s

s

p

p

e

e

c

c

t

t

r

r

u

u

m

m

3

3

1

1

(

(

2009

2009

)

)

2

2 I discuss this in greater length in Väisälä 2008,I discuss this in greater length in Väisälä 2008,in which I identify fourin which I identify four

significant structural determinants that are logically independent of the

significant structural determinants that are logically independent of the

norms of

norms of harmony and harmony and voice-leading:voice-leading: design (including design (including figuration),figuration),

register

register,,metermeter,,and rhetand rhetorical/gestural orical/gestural devices.devices.All these All these factors pfactors pertainertain

to the present analyses,

to the present analyses,even though the greateeven though the greatest explicit attention isst explicit attention is

paid to the first two.

paid to the first two.

bac

bac

h’

h’

s inve

s inve

ntio

ntio

ns:

ns:

figu

figu

ra

ra

tio

tio

n,

n,

reg

reg

iste

iste

r,

r,

str

str

uct

uct

ur

ur

e,

e,

and th

and th

e “

e “

cle

cle

ar w

ar w

ay t

ay t

o dev

o dev

elo

elo

p inv

p inv

ent

ent

ion

ion

s pro

s pro

per

per

ly”

ly”

103

103

another statement with inverted voices.

another statement with inverted voices.

33

 _{A special variant of} 

 _{A special variant of} 

 Typ

 Typ

e

e

2

2

is

is

g 

g 

,

,

in which two counter

in which two counter

subje

subje

cts alter

cts alter

nate in the-

nate in

the-matic statements.

matic statements.

The rem

The rem

aining Inventions,

aining Inventions,

 c

 c

and

and

F 

F 

,

,

op

op

en

en

 with

 with

canons,

canons,

but,

but,

on

on

the

the

basis

basis

of

of

the

the

right-hand

right-hand

material

material

preceding the left-hand entrance,

preceding the left-hand entrance,

 F 

 F 

comes closer to Type 1

comes closer to Type 1

and

and

c

c

to T

to T

ype 2 (despite

ype 2 (despite

its one-voice opening).

its one-voice opening).

 A

 A

central

central

formal

formal

consideration

consideration

concerns

concerns

recapitulation.

recapitulation.

Most Typ

Most Typ

e 1

e 1

Inventions (

Inventions (

C

C

,

,

 d

 d

,

,

 e

 e

,

,

an

an

d

d

a 

a 

) lack an unequivocal

) lack an unequivocal

recapitulation,

recapitulation,

if we defin

if we defin

e this as

e this as

requiring the concurr

requiring the concurr

ent

ent

return of the structural tonic and of the theme at the original

return of the structural tonic and of the theme at the original

level.

level.

Howeve

Howeve

r

r

,

,

 d

 d

and

and

a 

a 

contain salient “recapitulation ges-

contain salient “recapitulation

ges-tures,”

tures,”

theme statements at the

theme statements at the

original level but prior to

original level but prior to

the

the

structural tonic return.

structural tonic return.

44

_{Most Type 2 Inventions (}

_{Most Type 2 Inventions (}

_E

_E





_,

_,

 _f 

 _f 

_,

_,

 _A 

 _A 

_,

_,

 _B

 _B





_,

_,

and

and

 b

 b

),

),

alo

alo

ng w

ng w

ith

ith

G

G

and

and

c

c

,

,

close wit

close wit

h a short une

h a short une

quivo

quivo

cal

cal

recapi

recapi

tulation

tulation

:

:

a tonic return ma

a tonic return ma

rked by a themati

rked by a themati

c state-

c

state-ment or two in the original key.

ment or two in the original key.

55

_{Such statements often in-}

_{Such statements often}

in- volve

 volve

adaptations

adaptations

with

with

crucial

crucial

structural

structural

significance;

significance;

hence

hence

Each invention subdivides according to thematic and key 

Each invention subdivides according to thematic and key 

design.

design.

Sections are usually

Sections are usually

(but not always)

(but not always)

concluded by a

concluded by a

cadence and opened by a thematic statement in a key that

cadence and opened by a thematic statement in a key that

differs from that in the beginning of the preceding section.

differs from that in the beginning of the preceding section.

In middleground readings,

In middleground readings,

measure lines are

measure lines are

employed to in-

employed to

in-dicate sectional

dicate sectional

borders.

borders.

Another significant

Another significant

kind of

kind of

formal

formal

entity is the retransition,

entity is the retransition,

by which I mean

by which I mean

any passage l

any passage l

ead-

ead-ing from the last strongly tonicized

ing from the last strongly tonicized

non-tonic scale degree to

non-tonic scale degree to

the tonic return.

the tonic return.

1.

1.

figuration and

figuration and

register as structur

register as structur

al

al

determinants

determinants

a 

a 

:

:

retransitional v

retransitional v





–

–





prolongation clarified

prolongation clarified

by uniform figura

by uniform figura

tion,

tion,

with a “f

with a “f

ailed”

ailed”

recapitulation gesture as a digression

recapitulation gesture as a digression