Philipp
Herschkowitz:
On
an invention of Johann Sebastian Bach:
to
the problem of the genesis of Viennese classical sonata form[1]: Translated from
Russian by Dmitri Smirnov, text edited by Guy Stockton
see also:
Introduction
to Herschkowitz
Corrections
and Index
Herschkowitz:
On an invention of Johann Sebastian Bach (1967-70s)
Herschkowitz:
Three-part Invention in F minor (1967)
1. F minor
However, if we turn our attention to the order of interludes, if we establish the fact that after the appearance of all three interludes the second and the third appear again,
I1
I2 I3
I2'
I3'
we can see a more precise picture of the symmetry within the work. As it turns out, the two appearances of the second interlude divide the Invention into three similar segments:
the last two of which are identical, and the first differs from them by its interlude only.
Now, when the structure of the Invention begins to be visible, we can come nearer to the understanding of the transpositions of its theme:
|
T F minor T C minor T F minor |
T A-flat major T E-flat major T C minor |
T D-flat major T A-flat major T F minor |
T F minor |
The above table, showing the distribution of these transpositions into segments, clearly reveals that each of the three pairs of appearances of the theme at the beginning of each segment relate to each other as tonic and dominant:
1)F minor – C minor
2)A-flat major – E-flat major
3)D-flat major – A-flat major
At this stage of the research it is worth taking into consideration that: 1) In the first segment, unlike the other two, the third appearance of the theme harmonically coincides (F minor) with its first appearance; 2) The similarity of both of the last segments concerns not only their formal structure, but also their harmony – they represent a relation that is determined by an exact transposition.However, there is one difference: under the conditions of triple counterpoint, the voices in the third segment are placed in a different order compared to the second segment.
It is necessary to turn special attention to the harmonic similarity of the first and third appearances of the theme in the first segment.But we also need to turn special attention to the fact that at the beginning of the segment there is a double appearance of the theme, and at the end – a single appearance.This layout clearly resembles a correlation of the first and third parts in a three-part song[3], where the first part is a period (consisting of antecedent and consequent)[4], and the third part is the repetition of the antecedent or the consequent.In these conditions, an interlude placed between the double and single appearances of the theme, – between the “period” and the repetition of the “antecedent” or “consequent”,– finds itself in the position of the second part of a three-part song.
A
three-part song is one of the types of principal theme.Taking
into account the fact that the first segment of the Invention begins and
ends in the same key (the main key of the piece), we have every reason
to consider this whole segment, with all its
previously mentioned structural qualities, as the principal theme of this
work, which is not only and not simply an invention, but also something
else.
Of course, there is a big difference between this kind of “three-part song” and Beethoven’s three-part songs that constitute the principal themes in the slow movements of his sonata cycles.There we can find the highest stage of structural development of this type of principal theme, and here we are faced with its embryonic state.This state is characterised as such by the fact that a fragment of this three-part song theme (the antecedent of the period) has to be considered– in relation to the polyphonic writing of the piece – also as a theme.From one point of view the theme of the piece consists of eight bars, but from another, not less grounded, – it consists only of two bars. Behind polyphonic writing there is always a homophonic form, no matter how embryonic it is; and these are inseparably linked, like the soul of the piece with its body.This form – a sonata form as will later be shown – enlightens the invention.The essence of the succession of the epochs of Bach and the Viennese classics is hidden in the alloy of polyphonic and homophonic writing.Anton Webern considered polyphony as a manifestation of a musical idea in the sum of four voices and homophony as, occurring in the process of development, a concentration of a musical idea in one voice accompanied by the rest of the voices.On the basis of such a conception it is possible to imagine that this concentration was preceded and favoured by the origin of homophonic form in the entrails of polyphonic writing. This form was that new musical space, in which “the sum of four voices” as the main bearer of a musical idea soon had to be transformed into an accompanied principal voice.
In Bach’s archaic three-part song the antecedent and consequent of its first part – the first 2+2 bars – form a sequence and are therefore in contradiction with the essence of the period that they make.However, this sequence constitutes a tonic-dominant relation: i.e. the exact relation of functions that provides the harmonic opposition of antecedent and consequent, which is the main characteristic of a period.It is not out of place to note that it is possible to find periods in Beethoven’s music where antecedent and consequent form a sequence (the theme of the Scherzo from the Twelfth Sonata, Op.26-II, the theme of the Allegretto from the Fourteenth Sonata, Op.27/2-II).[5]But if these periods belonging to Beethoven coincide with sequences, in this case the sequence plays the role of a period.There the period is primary and the sequence is secondary, but here is the opposite.
In the simplest examples of Beethoven’s periods – the first parts of three-part songs – the antecedent ends with a half-cadence (on the dominant) and the consequent with a perfect cadence (on the dominant or tonic).The third part, that ends in these examples with a perfect cadence on the tonic exclusively, is the repetition of the consequent of the first part even in those cases where the harmonic content of the perfect cadence of this consequent is not the tonic, but the dominant.The type of cadence, but not its harmonic content, determines what is repeated in the third part – antecedent or consequent.In this way, it seems that in the examined three-part song, the third part also repeats the consequent, because it is placed on the tonic but has the same perfect cadence as the consequent that is placed on the dominant. However, the antecedent that is placed on the tonic also ends with a perfect cadence, and the third part is principally identical to it.Therefore, the third part is in the first instance the repetition of the antecedent but not the consequent.This undoubtedly constitutes one more primitive feature of the given three-part song, together with the primitive features of its first part (the sequence and, in connection to this, – the identical perfect cadences of both antecedent and consequent).[6]
The second part (the first interlude) holds very little resemblance to the structure of Beethoven’s second parts.However, the main feature of a second part is present here: it dwells on the dominant.Here the dominant pedal is not as obvious as in the second part of the principal theme from Beethoven’s First Sonata, Op.2/1-II; it is not even as clear as the abstract (hidden) dominant pedal in the Largo appassionato of his Second Sonata, Op.2/2-II.But nevertheless, in the conditions of the embryonic state of this three-part song, the fact that the interlude (the second part) begins with the dominant triad (though minor) and ends with a real dominant means that we can’t treat this any different to a dwelling that is typical for a second part.
Whilst continuing to examine the structure of the piece, we could take into consideration the fact that the other two segments also consist of three parts, like the first.The first and third parts of all three segments are relatively identical to each other; however, together with this, the second parts of the second and third segments differ from the second part of the first segment.This difference between the first segment on the one hand, and the second and third segments on the other, is linked to one more difference: while the first segment(principal theme) begins and ends with the same principal key (F minor), each of the following two segments end in a different key to their beginning.
The second segment begins with a period in A flat major with the antecedent in the tonic and the consequent in the dominant, as in the initial period of the principal theme.The structure of the third part, like the principal theme, relates to either the antecedent or consequent (which are identical by their structure).However, and this is the main point, it differs from both of them by its harmony: it is in C minor — not in A flat major.[7] (See example 2)
Speaking on the second part of this segment we have to state that it is not the embryonic dwelling on the dominant, like in the three-part song (principal theme), but a complex sequence that provides the connection by modulating between the keys of the first and third parts.
The third segment is the precise repetition of the second segment transposed a perfect fifth down.So, the keys A flat major and C minor are replaced with the keys D flat major and F minor.
It is necessary to give an account on the importance of the harmonic difference between the first and second as well as between the second and third segments.If the first segment represents the principal theme, what do the two following segments represent?And there is another question: why do we not have a fourth segment that would be harmonically identical to the first, and serve as a recapitulation of the principal theme?
It would be more appropriate to answer the second question first: the last bars of the piece that follow the third segment, formally coincide with the third part of the principal theme and represent its shorter recapitulation.
Returning
to the first question it is necessary to mention that the second segment
is characterised by its harmony (A flat major is the parallel major key;
C minor is the minor dominant) like
the subordinate theme of the piece written monothematically.[8]However,
this “monothematicism” has another primitive feature here: it is not
only the thematic elements of the principal and subordinate themes that
are almost identical, but their structures also.
The
third segment, which is a precise copy of the subordinate theme transposed
a fifth down (and with a different order of voices relative to each other) represents
its recapitulation.It is
characterised as such by its third
part that is placed in
the main key after the
dominant on which the third part of the subordinate theme
was placed in the exposition.
So
it follows that this work has a mirror recapitulation: the principal and
subordinate themes appear here not as in the exposition, but in reverse
order.
Finally
it becomes clear that the examined monothematic piece with a shortened
mirror recapitulation represents a sonata form: the first appearance of
the second interlude functions as a transition,
and
its second appearance (between the second and third segment) – functions
as a development section.
* * *
Anton
Webern, who regarded Beethoven’s creative output as the highest point
of the development of musical form, promulgated the necessity of the analysis
of any musical composition written before or after Beethoven on the basis
of Beethoven’s formal principles.This
kind of research gives possibility, on the one hand, to retrace a primitive
state of these principles in the works of the masters of the pre-Beethoven
time, and on the other hand – to learn their modifications that have
been undertaken in the following processes of their development in the
works of the masters of the second half of the 19th century
and the first half of the 20th century.
The
basis of Webern’s teaching about form consists of the recognition of
two different states of musical structure (“fixed” and “floating”)
that oppose each other; the presence of both of them in a musical work,
i.e. the presence of their opposition, is its indisputable condition.The
highest level of musical form, which reveals itself within Beethoven’s
creative output, is apparent when “fixed” and “floating” are clearly
differentiated from one another.
The
principal theme in Beethoven’s music, as a rule, is built “fixed”;
the subordinate theme, transition and development section are built “floating”;
furthermore they are built “floating”in
varying ways.Later we will
see in particular that there are principal differences between the “floating”
of a subordinate theme and the “floating” of a development section.Concerning
the co-relation of “fixed” and “floating” in a musical work, it
is necessary to state that it is a
balancing co-relation: a less floating subordinate theme can
correspond to a less fixed principal theme.A
musical problem within a work can even stand the relationship of the two
themes on its head: the principal theme can have a floating structure and,
correspondingly, the subordinate theme can have a fixed structure.
Musical
composition represents a system of repetitions of
different categories and scales.The
repetition could reproduce the pattern that is repeated in whole or partly,
literally or modified.It could
be applied only to the pitch (ignoring note duration,) or vice versa (only
the duration of the notes without taking their pitch into account.)This
is repetition on the smallest scale, or better to say – on the lowest
level.At a higher level the principal
theme, that is a complex of repetitions, in turn, appears in the role of
a repeated pattern – only now, the repetition is very far from being
precise.
There
are particular types of
principal theme.One of them is a
three-part song, which is the type of principal theme that we are
examining in this particular piece.In
the basic examples of the types of principal theme the essence of their
fixed structure is revealed, in general, in
a simple or complex combination of formal similarity with a harmonic opposition
of their compound parts.
In
musical composition a floating element is conditioned by a fixed element.
While the fixed principal themes have their own types, there are no types
of floating subordinate themes in nature: the principal theme is fixed
by itself; but the subordinate theme is floating
in relation to the principal theme.
The
subordinate theme begins
as if it belongs to one of the types of principal theme.But
it only begins like this; the continuation of this beginning proceeds,
as Webern said, by way of a "free fantasy".This
"freedom" and this "fantasy" are "a free fantasy" only with respect to
the fact that the fixed elements that appear in its initial part are ignored
in the development of the subordinate theme.But
despite this there is no real "freedom" here at all, because everything
here is placed in a certain definite, though
mysterious, relation to the principal theme in this or that way.
The subordinate theme, avoiding the logic of the types of structure of
principal theme, uses an idea association
as an engine of its realization.In
other words,the motives and
the thematic elements of the principal theme (and sometimes of the transition),
appear in new co-relations that force them to fundamentally change their
appearance, sometimes making them unrecognizable.These
elements become the part of the structure that differs from the structure
of the principal theme, let us say, like the shadow differs from the subject
to which it belongs.The floating
subordinate theme reflects the fixed principal theme like a shadow, which
does not exist by itself, but is only a vague reflection of the real subject
that cast it.However, the subordinate
theme is only perceived as an especially new and contrasting phenomenon
because of the opposition of the floating structure to the fixed structure.In
connection with this, everything that has appeared in the principal theme
is changed, when it reappears in the subordinate theme, as if it has obtained
a different physical state.
Whilst
the essence and meaning of the subordinate theme is to be a bearer of the
subordinate key (as opposed to the principal theme, that bears the main
key), the transition and the development section, by their floating qualities
– that are different from the "floating" qualities of the subordinate
theme – correspondingly represent the way from the main key to the subordinate
key, and vice versa: from the subordinate key to the main key.The
latter deserves special attention.
It
is necessary to understand the structure of the development section not
only from the point of view of its function, but also of its scale. If
the subordinate theme represents the repetition of the principal theme,
the development section is the repetition of something that has a much
bigger scale: in sonata form (of which we are speaking here,) the recapitulation
is not the only repetition of the whole exposition, the development section
also fulfills this role.If the exposition,
that is characterized by an exchange of the main key with the subordinate
key, receives in the recapitulation its repetition in which the main key
is indivisibly predominant, this could only happen because of the presence
of another repetition of the exposition, where as the result of a struggle
with the returning main key, the subordinate key is suspended from the
position that it gained.In the development
section the fight of the two keys is reflected in the formal plan by the
highest level of ‘floating’, the scale of it defines its essence, which
fundamentally differs from the essence of the floating subordinate theme.
In
the development section all the motives and thematic elements are "developing".By
combination, they could be subjected to very far-reaching variation, and
as a result it is often a wrong impression created about the presence in
the development section of new elements that have nothing in common with
the exposition, or, in contrary, about the absence of the important elements
of the exposition. The development section is formulated with sequences;
moreover the sequenced segments themselves are very often composed of sequences.
The sequences organize the processes of annihilating the gravitating forces
of the tonic of the subordinate key and return this tonic to the position
of degree subjected to the main tonic, which obtains its hegemony again.
The
sequence is the essence of the "floating" within the development section.
The difference between the "floating" of the subordinate theme
and the "floating" of the development section is defined by the fact that
the subordinate theme resting on the subordinate key is static, while the
dynamism is the main feature of the development section that makes the
return journey from the subordinate key.The
tool of this "dynamic floating" within the development section is the sequence
with its labile structure, which is constantly in motion and resembles
quicksand, and for which, the repetition is the everlasting occasion for
the multiple and multi-faced modifications.
Very
often in the development section it is possible to distinguish two sections,
and each of them has, as a rule, its own "model" – that is sequenced
– and its sequential
repetitions.The border between
these sections latently represents the moment of the final breakaway with
the subordinate key together with the appearance of the first signs of
the restoration of the hegemony of the main tonic.
Returning
after this short summary of Webern’s concept of musical form[9]
to the research of Bach’s invention that possesses a sonata structure,
it is now possible to understand that the primitiveness of this structure
is stipulated by the low level of differentiation between the two elements
of musical construction – “fixed” and “floating” – that characterize
the given composition.While the
principal theme is not sufficiently “fixed”, the “floating” of
the subordinate theme is reached only indirectly – not by formal but
by harmonic means, which could not be the contrary
because of the so far reached likeness between the subordinate theme and
principal theme.And, of course,
the reason for this peculiar structural co-relation of the two themes,
and for the rudimentary character of the transition and development section,
is because all of the parts are conditioned by each other.
The
defect of the “fixed” element of the principal theme
(three-part song) is displaced, to a certain extent, in each of
its parts.
The
illusory nature of the fixed quality of the first part is defined by the
fact that both antecedent and consequent of the period constitute a sequence.It
is possible to name this sequence as a period only
in a metaphorical way; however, at the same time, in the conditions
of the birth of the new form, it possesses the ability to
perform the function of a period.
The
“fixed” element is undoubtedly lost also because of the fact that its
third part, being harmonically identical to the antecedent of its first
part is, as we have already stated,arather
definite repetition of the antecedent, but not of the consequent that concludes
the period.However, this gap in
the “fixed” element is bridged here to a certain extent by borrowing
the important characteristic features
of the consequent – despite the fact that it doesn’t represent
the repetition of it (or, it does represent
a repetition of the consequent, but
not in the first instance).Thiscreates a
synthesis of the antecedent and consequent of the initial period
(as in the third parts of Beethoven’s most exemplary three-part songs):
copying the harmonyof
the double-voiced antecedent (with the similar structure
of both antecedent and consequent), the third part takes the appearance
of the consequent that is characterized
by the triple-voicedtexture
and triple counterpoint.
And the second part, like the other two parts, favors by its own structure the striving of this three-part song (principal theme) for rather pretending to be a fixed construction, than for actually being a fixed construction.Normally, the size of the second part is much more often equal to that of the antecedent or consequent of the preceding period and, as a rule, it is divided into two halves, the second of which relates to the first as the repetition to the repeated.In this particular case the second part, consisting of two bars (i.e. corresponding to the indicated norm), represents not a bar and its repetition, but a completely different structure: while the first bar is divided into two different halves, the second bar is composed of two repetitions of the second half of the first bar.Nevertheless, the first half of the first bar has also not been deprived of a repetition – peculiar however, – because the second part as a whole is set out as a two-voiced canon, and therefore everything that appears in one voice is reproduced, i.e. repeated, by the second voice.It is worth taking into consideration the fact that all of the interludes (and only them) are composed here as canons.Another fact worth noting is that this first interlude, the only interlude without a repetition and the only one that is double-voiced and structurally asymmetrical, does not performthe function of a modulation – in opposition to the rest of the interludes.Thus, as previously stated, one could and should interpret its harmony as dwelling on the dominant of the principal key.Because the other two interludes (both of which appear twice, are composed of three voices and are clearly symmetrical in their inner repetitions) have modulatory functions, the opposite characteristic features of the first interlude, including its structural asymmetry, stress the fact of the absence of modulation contained within it.This shows the presence of the certain "fixed" qualities of the principal theme: the fixed principal theme – i.e. the principal theme that is not an exception as regards to the structure, does not modulate.
Nevertheless, the weakened “fixed” qualities of the principal theme of this work are conditioned in particular by this peculiar division of the second part together with the examined deviations of the other two parts from something that had to become their structural archetype in later years.Completing the study of the principal theme it is necessary to mention the fact that also in these later years, under the conditions of predominating homophony, the second parts of three-part songs often, in contrast to the other two parts, preserved an appearance of imitative polyphony (see for example the principal themes of the slow and final movements of Beethoven’s Second Sonata, Op. 2/2-II and IV).
The weakened “fixed” qualities of the principal theme correspond with the weakened “floating” qualities of the subordinate theme.Moreover, because of the fact that the structures of both the principal and subordinate themes represent in principle the same three-part song, it is possible to state that the weakened “fixed” element of one theme and the weakened “floating” element of the other are mutually determined.
The weakened “floating” (i.e. being on the edge of “fixed”) qualities of this subordinate theme are contained in the fact that it appears in the shape of a three-part song.However, here is only the framework of a three-part song in which the essence of it is absent.A “three-part song” where the first part is placed in one key and the third part in another is not a real three-part song.Its harmonic instability is the essence of its “floating” qualities, which conceal themselves behind the appearance of a fixed construction.
The
harmonic dualism that characterises the subordinate theme of this invention-sonata
occurs very often within Bach’s works written in minor keys.If
in later times, only one of the two keys (the dominant minor or the parallel
major) could be the bearer of the subordinate idea of a work, in Bach’s
music the subordinate idea, which had not yet emancipated from its embryonic
state, inevitably demanded, in its seeming awkwardness, that both of the
mentioned keys had to jointly serve as its bearer.
Of
course, in the conditions of the examined mono-thematic[10]
work, stipulated by the archaic aesthetic, the presence of
two subordinate keys that are opposed to
one main key represents the means of the principle opposition
of the subordinate and principal themes: i.e. the means of indirectly creating
a floating structure from one theme in relation to a fixed structure of
another.
However,
the presence of two keys in one theme also presupposes the presence of
a modulation that joins them together.And
inasmuch as one key occupies the first part and another – the third part
of the subordinate theme, the modulation, of course, is placed in the second
part.Therefore, the principal and
subordinate themes have different second parts because their functions
are different.
The
modulation is created here by means of a complex sequence: one-and-a-half
bars and their repetition (a fourth lower = a fifth higher) represent the
sequence themselves, where the half-bar is repeated twice (a second higher
and a second higher again).The second
part of the subordinate theme, like the second part of the principal theme,
is exposed as a two-voiced canon (however with the addition of the third
voice that seems to be “free” and “separate”).The
“follower” (answer) of the repetition (the second one-and-a-half bar)
is identical to the “leader” (subject)[11]
of the repeated (the first one-and-a-half bar):
The second part of the principal theme and the second part of the subordinate theme, despite their difference, are related to each other:
1)
In both of them the answer is placed a fifth lower than the subject
2) In both cases the answer follows the subject with the same time-interval: a crotchet later
3)
The unrepeatedmotive
of three quavers, which has appeared in both voices of the canon in the
second part of the principal theme, represents, in contrary, the only motive,
i.e. the only repeating element, in each of the two voices of the second
part of the subordinate theme, where it appears in both of the one-and-a-half
bar segments, and in them – three
times in each of the two voices:
![[Example 8]](image019.png){kind=link}
i.e.
exactly the same number of appearances of the motive that is repeated in
[the “subject” of][12]
the second part of the principal theme:
and
in one case it is a gradual descending repetition, and in the other –
graduallyascending.
Under
more careful examination it appears that the third voice[13]
of the second part of the subordinate theme is not “free”, however,
it is “separated”.By the duration
of its sounds (there are only crotchets throughout) it represents the reproduction
of the voice that descends through a chromatic scale in the first and third
parts of both principal and subordinate themes.However,
it is also of the same “bone and flesh” as the canon: by the abstraction
of the rests, we can state that the third voice is composed as a chain
of simple repetitions and of repetitions of the retrograde inversion form
of the augmented three quaver motive:
In
other words, there are good reasons to consider the second part of the
subordinate theme as a three-voiced canon. In
the conclusion of the examination of the subordinate theme, it is necessary
to stress once more that, as in the principal theme, where the consequent
of the initial period represents the dominant of the main key, but not
C minor as an independent key, the consequent of the first part of the
subordinate theme also does not represent E-flat major as an independent
key, but is subjected harmonically to the key of the antecedent (A-flat
major) as the bearer of its dominant.Only
the third part of the subordinate theme could and should claim harmonic
independence – it really is placed in C minor.Schoenberg’s
concept of harmony, and his teaching on artificial dominants in particular,
allow one to distinguish something that is a modulation from something
that is not: to distinguish extended tonality from something that lies
beyond it.On the basis of this
teaching it is easy to realise that here the subordinate theme is resting
on two different keys, one of which is represented by the tonic and dominant
(the first “part”) and the other – by the tonic only (the third “part”).A
third key is not present here. As
previously mentioned, in the mirror recapitulation of this piece, the subordinate
theme that precedes the principal theme is transposed a fifth lower in
relation to the exposition, without any modification.Therefore
its third part appears in the tonic F minor, and the first part in D-flat
major – the subdominant (or to be more precise, the subdominant of the
parallel key).So, this piece represents
the prototype of those works by Mozart (and Schubert), where the recapitulations
find themselves in the main key (in the tonic of the principal key) after
beginning in the subdominant (in the key of the subdominant). It
is now important to clarify why the recapitulation of the principal theme
is shortened.Consisting of two
bars[14]
that represent the tonic of the main key, the principal theme in the recapitulation
is identical to two of the
elements from the whole principal theme – its third part and the antecedent
of the initial period. However, the essence of the matter lies in the fact
that these two bars appear immediately after exactly the same bars (also
placed on the tonic) that represent the third part of the recapitulation
of the subordinate theme.Three times
– twice in the exposition (in the principal and subordinate themes) and
once in the recapitulation (in the subordinate theme) – the antecedent
and consequent, composing a period and appearing in different keys (F minor,
A-flat major and D-flat major) had the same co-relation: tonic and dominant.Only
here, when after the enclosing two bars of the recapitulation of the subordinate
theme the only two bars of the recapitulation of the principal theme appear,
the two sentences [the antecedent and consequent] both
placed on the tonic, though belonging to the different themes, follow
each other.The main tonic at the
end of the recapitulation of the subordinate theme, preceding the main
tonic of the beginning of the recapitulation of the principal theme, renders
the rest of the principal theme as needless and impossible.It
is possible to say that the tonic-consequent following the tonic-antecedent
is the dominant sublimated into the tonic.This
is the same dominant that always – three times – immediately followed
the tonic.The two appearances of
the tonic, one after the other, represent, in the given circumstances,
the legitimate and natural end of the piece. Of
course, it is very interesting that the “missing” – as if evaporated
– six (of the eight) bars of the recapitulation of the principal theme
are nevertheless, by their quantity, present
within the piece.However, it is
not six bars that are missing, but only four: the similarity of the remaining
two bars with two elements
from the whole principal theme not only permits, but demands that they
should be counted twice, and considered not as two, but four bars (the
more so because they appear and are perceived as the echo of the third
part of the recapitulation of the subordinate theme which precedes them).The
other four bars, really missing in the recapitulation, could be found (it
is necessary to repeat that here we are speaking only about the quantity,
but not about their formal and harmonic essence) in the second part of
the subordinate theme and its recapitulation (one bar in each of them)
and in the development section (two bars).In
other words, as the second part of the principal theme consists
of two bars, the other second parts consists
of three bars (of one-and-a-half bars and their repetition);
as the transition also consists of
two bars, the development section – the repetition of the
interlude that serves as a transition – consists
of four bars.The bars
concealed in the third interlude and its repetition, and also in the repetition
of the second interlude, have shortened the recapitulation of the principal
theme.This is not mechanical bookkeeping
however – it is organic.Such
quantitative structural compensations occur very often in the
music by all Great Masters (and by Beethoven first of all). It
is also necessary to note that the last bar of the piece stands apart from
the recapitulation of the principal theme.The
bar is wholly occupied with the final chord of the last cadence, which
strongly differs from all other multiple cadences by the fact that it is
the only concluding chord
– the only end – while each of the other similar chords also act simultaneously
as the beginning of the next segment of the composition.Final
chords of the cadences within each segment – we are speaking in particular
and especially about the antecedents and consequents of the first parts
and also about the third parts – are
placed outside their borders and therefore it occurs that the harmonic
formation and formal arrangement of each segment
do not coincide by their size: the first of them is longer
than the second.This is why every
“harmonic end” is a “formal beginning”.But
there is only one exception: the last bar.By
its form it means nothing.It is
a formal vacuum.(However, because
of its fermata [or pause], the last bar becomes equal to two bars, i.e.
the same duration as the main formal element of the work.)But
because of a lack of the necessity to be a beginning for any other repetition,
it can perfectly perform its harmonic function: it embodies not only the
end of the piece, but also the sum of all those points of rest that the
previous cadences could not actually perform because their closing chords
had to tear themselves between the functions of beginning and ending –
to unite in themselves the essence of the beginning and the essence of
the end.The presence of this sum
within the last chord is concretised by its duration that is doubled by
the fermata (the pause). In
the conclusion of the examination of the themes and their recapitulations
we can not leave without attention to the fact that the coinciding of the
end of the antecedent with the beginning of the consequent within the initial
period is also one of the features of a weakened “fixed” quality within
the principal theme. The
only things left to investigate are the transition and
the development section. They
are remarkable in two respects: firstly, because they are short; secondly,
because, despite the difference of their functions, they are built in the
same way and moreover – from the same motives.Both
of these qualities make the transposition and the development section primitive
when compared to the transition and development section of Viennese classical
sonata form.The transition is composed
here of one bar and its sequential repetition, and the repeated bar itself,
in turn, can be considered as a bar that can be broken down in two structurally
identical and sequential half-bars.[15]The
development section represents the doubling of the transition, and this
is not just a quantitative doubling: the two bars that represent a sequence
in the transition, here in the development section are sequenced
as a whole.The transition
and development section are sequenced at different intervals: the second
bar of the transition is placed a perfect
fourth higher than its first bar; the third and fourth bars
of the development section are placed
a major second lower than its first and second bars.Because
of the difference between the intervals of these two sequences, a very
close relation is created between the transition and development section:
if the first two bars of the development section are placed
a perfect fourth lower than the transition, the last two bars
appear a perfect fourth higher
than the transition.Therefore the
second bar of the first couple of bars of the development section
is identical to the first bar
of the transition, and the first
bar of the second couple of bars of the development section is identical
to the second bar of the
transition.It is easier to say,
the transition as a whole is identical by its pitch to the
middle – the second and third – bars of the development
section; one of which belongs to its repeated, so called “model” (or
“pattern”) and another – to the sequential repetition of the latter. In
other words, the development section is the same as the transition to which
two bars have been attached – one before it and one after.By
the addition of these two bars the function of the transition has been
transformed – taking into account the harmonic qualities of the subordinate
theme and its recapitulation – into its opposing function.This
defines the meaning of the symmetrical presence of the whole transition
in the development section.And at
this point it would be appropriate to state that everything that we perceive
as the musical power of expression, as
musical character, is in the end the emanation of structural relations,
and the co-relation of the transition and development section in this work
can serve as an example of this. The
mechanisms of the transition and development section could be better observed
if one pays attention to the co-relation of their half-bars: not only is
thesecond
bar of the transition placed a fourth higher (fifth lower) in relation
to the first bar, but
the second half of the first bar is placed at the same interval in relation
to its first half. The
noted distance between two halves of the first bar is kept the same in
the second bar, but the first half of the second bar and the second half
of the first bar are identical by their pitch. This
relationship is kept between any two
adjoining bars of the development section.And
exactly in this way, if proceeding from F minor (by the transition), two steps
by fourths (during the course of two bars),
one will reach the dominant of A-flat major.Likewise,
if one proceeds from C minor (by the development section), four steps
by fourths (during the course of four bars)
one will reach the dominant of D-flat major. The
common character of the motives and structures of the transition and the
development section is conditioned by the “monothematicism” of the
piece: if the transition is a reflection of the principal theme and the
development section is the reflection of the exposition as a whole, then
it is quite logical for them to be homogeneous.This
is because the principal theme represents the complete structural prototype
of the subordinate theme (the second of the two main components of the
exposition) and contains all of its motives and thematic elements.This
common character of the transition and thedevelopment
section is really a primitive feature of this sonata form, however it is
conditioned as such by the more fundamental primitive features of it.[16] Every
half-bar of the transition and the development section consists of three
motives placed vertically: 1)
Two crochets ascending chromatically,
borrowed from the voice in the first and third parts of the principal and
subordinate themes, which consists of crochets descending chromatically.(In
both half-bars this motive is placed in its pure unmodified form
only at the beginnings of the transition and the development section; in
the first half of the
second bar of the transition and in the
last three bars of the development section it is modified). 2)
Figuration borrowed from the conclusion of the row of three appearances
of the three–quaver–motive within the first and third parts of the
principal and subordinate themes: 3)
The motive of three quavers. The
texture of the transition and development section, like the texture of
the second part of the subordinate theme and its recapitulation, represents
a canon of two voices with the addition of a third voice that is separated
from the canon.But if in the noted
second parts the canon is created from the three–quaver motive, here,
in the transition and development section, this motive, in contrary, makes
up the separated voice.On the other
hand, the crotchets that make up the separated voice in the second parts
here serve as one of the two motive elements of the canon. In
this connection it is necessary to make two more precise definitions: 1)
The two motive elements that compose the two voices of the canon of the
transition and development section are as follows: In
one voice they appear in one order, and in the second voice they appear
in the reverse order: Hence,
it follows that each of these two voices plays the role of the “leader”
and “follower” (or the subject and answer) simultaneously: 2)
In the exposition as well as in the recapitulation the first and third
parts of the principal and subordinate themes are written with real triple
counterpoint.However, the triple
counterpoint of the second part of the subordinate theme (in
the exposition and recapitulation), transition and development section is
only potential: two voices
here have the relations of active double counterpoint,
i.e. each of the repeated patterns and the repetitions appear
not only in one and the same voice; but the third [reclining] voice
concentrates in itself the repeated elements together with the repetitions
despite the fact that it is quite able to enter into the relations of triple
counterpoint with the other two voices.It
is the “reclining” voice.However,
it is a “reclining” voice that is not “separated”, but is the one
of the two voices of the canon: the
other “voice” of which is really distributed between the other
two voices that
become partners in the double counterpoint of the “separated voice”,
which is also split up into two voices: One
can see that it has become necessary to distinguish between the voice (without
inverted commas) and the “voice”.In
this, one more duality is reflected (together with the main duality of
the piece: an invention that is also a sonata) – the duality that originated
by these “reclining” voices: if they were absent, there would be no
reason to speak about the canons!But
in speaking about the canons it is necessary to speak about their “voices”!And
it is also necessary to speak about the voices (in the different meaning
of the word) – because these canons are conditioned by the
potentially triple, but actively
double counterpoint. These
“reclining” voices appear as follows: the lower voice in the transition,
the middle voice in the development section, and the bottom voice again
in the second part of the subordinate theme and its recapitulation.They
appear in every part of the piece where a “floating” structure is present.Therefore,
these voices are a sort of “trade mark” for the “floating” structure
here. The
common textural features of the transition and development section, along
with the second parts of the subordinate theme and its recapitulation,
have a profound meaning.In this
composition it has become possible to distinguish between the rudiments
of “fixed” and “floating” musical constructions.However,
they are only the rudiments.In
their mature state in the music of Beethoven, these structural dissimilarities
are more differentiated.In Beethoven
there is not only “fixed” that is opposed to “floating”, but there
are also two types of “floating” that oppose each other: the “floating”
that reveals itself in subordinate themes, and the “floating” that
becomes apparent in development sections.It
may seem that such a kind of opposition is completely absent in the examined
invention-sonata: here the subordinate theme is constructed by way of combining
the elements borrowed from the principal theme (the first and third parts),
and additionally, the second part is built on the basis of the principles
that form the construction of the development section. At this stage in
the development of musical form, the sequence (the tool of the development
section) is the only means of constructing the “floating” structure.As
such, it even intrudes on the principal theme, preventing it from obtaining
a
really fixed structure.Hence, the
antecedent and consequent of the first part of the principal theme represent
some likeness to a sequence.It is
only the third part, consisting of only one sentence[17]
and participating decisively in the creation of the contour of a three-part
song, that indirectly defines the meaning and function of the sentences
of the first part as components (the antecedent and consequent) of a
period – the “fixed” formal phenomena. And
nevertheless, despite the fact that the sequence is present here throughout
the whole piece and represents the main structural element of the transition
and development section as well as of the second part of the subordinate
theme and its recapitulation, there is a very essential distinction between
the former and the latter.This distinction
is contained in the fact that, in contrast to the normal canons of the
second parts, the canons of the transition and development section are
ambivalent: as previously noted, each of their voices plays
the role of the “leader” and “follower” (subject and answer) simultaneously.This
distinction reflects the essence of the difference between the two harmonic
categories.Firstly, in the transition
and development section, which are characterised by ambivalent canons,
the fundamental modulations of the piece take
place (one that connects the principal theme with the subordinate theme
and the other that joins the exposition as a whole with the recapitulation
as a whole).[18]And
secondly, in the second parts of the narrow frames of the subordinate theme
and its recapitulation, that are characterised with normal canons, the
inner modulationsoccur, which link the two keys that relate to each
other like two sides of the same coin.The
two “harmonic categories”, embodied in a formal context by the canons
of different kinds, already represent at this early stage the phenomena
that at a later time had to create an opposition, on a far greater scale
of harmonic and formal differentiation, between the static “floating”
of a subordinate theme and the dynamic “floating” of a development
section.However, the rudiments of
this dynamism are accented here by the fact that the development section
is similar to the only interlude where – in just one of the voices (the
“reclining” voice) – one of the motives is
transformed during its repetitions (the importance of change
due to variation within a development section has already been discussed). Perhaps,
it is necessary to stress something that needs no explanation: the perfection
of a piece of art does not depend on the time that it was created – i.e.
at an earlier or later moment within the development of art.However,
the character of this perfection
is defined by this moment.Under
the conditions of the invention its organics are only provided
by the primitiveness of the sonata.This
is the organics of the intermediate phenomena of musical fauna, the phenomena
that is as transitional as, in the world of animals, a species like the
duck-bill (or platypus) that belongs to the mammals, but propagates by
eggs like a bird.Only by the primitiveness
of its structure can a sonata be identified as an invention, giving to
the latter that distinctive ambiguity, that vast increase in richness and
depth. Bach’s
Three-part
Invention in F Minor is not his only composition in “Viennese”
sonata form.There are more.However,
in this connection it is really amazing that this is not the only work
where Bach manages to combine sonata form with triple counterpoint.A
thought inevitably comes to mind: Bach, being aware of the importance of
the innovation that he was creating, decided to unite this innovation with
something ancient, but having no less importance, and this was able to
serve as a catalyst for the introduction of the new musical phenomena into
the creative practice, which was still unable to seriously change its own
essence.The ancient law of triple
counterpoint stands as an exclamation mark to the new law of sonata form.Perhaps,
it is permissible to say, that here the sonata
has appeared from triple counterpoint, like Aphrodite appeared
from the sea.This maybe the truth
or some likeness of the truth, that permits one – to a certain extent
– to express admiration for the Greatest Master, whose work(if
to speak about the assimilation of his music by the following generations),
represent a map, on which there are still more blank spots than on the
map of Africa in the 19th century.We
must recognise, however, that Bach’s blank spots will never be completely
understood.And that is only because
the greatness of a Great Master is endless. But one of the main targets,
or in general, the foremost aim of musical science, is still attainable:
to find every possible way of enlarging our perspective on the correlation
of the closest past of musical art with a past that is more remote.
