Three-part
Invention in F minor (No.9)[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)
What does it mean – to analyse Bach proceeding from Beethoven?What would be the outcome if one should not consider Beethoven at all?One can see a run of a theme, another run, followed by many others; one interlude and then more.But how does one know how to group them, and how to recognise the completely different functions contained in each of the completely different runsof the one and the same theme.
It was once noted that ‘if God did not exist, it would be necessary to invent him’.[2]Bismarck even said that ‘if Austro-Hungary did not exist, it would be necessary to create it’.And I will say: if in a (certain) composition one can not see the subordinate theme, it does not mean that it is absent there; it may signify that the function of the subordinate theme is executed by some of the repetitions of the principal theme.And this is what we have in the three-part Invention in F minor by J. S. Bach.[3]
If we are guided by harmony we have to see that the principal theme is a three-part song: a four-bar period, a two-bar second part, a consequent (or rather an antecedent) as the third part.Of course, we would not expect that Bach could operate with the terms “fixed” and “floating”[4]on Beethoven’s level.And let us remember (something that has been noticed by others), that usually in Bach’s compositions written in minor keys there are two subordinate keys, that appear together: the parallel major and dominant (minor) keys.
And then we will see, that the principal theme itself, also with three parts (but arranged differently), appears as its own subordinate theme.After the two-bar interlude, that represents a “transition” (this is the second interlude; the first appeared as the second part of the three-part song of the principal theme; of course, it is necessary to analyse it like this – to define the function of the interlude, but not just giving to it a certificate that it is an “interlude” for handing in at the conservatoire or police-office), there is the beginning of the“subordinate theme” (the inverted commas could be avoided here).As a matter of fact, it is a repetition of the principal theme, but with two distinctions: 1) the harmonic relations are quite different 2) the second part is not the same at all.
Concerning the harmonic relations: the first part, as in the principal theme, is a “period”; the third part, as in the principal theme, – is the “consequent”.However, while the first and the third parts of the principal theme were placed in one and the same key (mostly in F minor), here the period is placed in A-flat major and the consequent that forms the third part – in C minor.We do not have to consider the E-flat of the consequent of the first part as an independent key; this is only the dominant of A-flat major that occupies the whole consequent.The “period” by Bach – it’s not for nothing that we place this word into inverted commas – is still in that ante diluvian[5](in the geological meaning of the word)[6] state, where antecedent and consequent can represent a sequence.However it is only by Beethoven that we are persuaded that this is a period: there are two similar periods in his piano sonatas: one in the Scherzo of his “Moonlight Sonata” (or Fourteenth Sonata quasi una Fantasia), Op.27/2-II, and another – in another Scherzo (I do not remember which in particular).[7]This means that the first and third parts together occupy both of the subordinate keys that were discussed earlier.
The
major difference between the constructions of the principal and subordinate
themes concerns their “second parts”.Firstly,
the difference is in their duration.In
the principal theme it is composed of
two bars, in the subordinate it contains
three bars (one-and-a-half bars and their sequential repetition).Additionally,
the material of the second part of the subordinate theme is completely
different from the material of the second part of the principal theme:
in opposition to the principal theme, (where the material of the second
part is basically dissimilar to the material of the first part), the subordinate theme
(where the modulation from one subordinate key to another occurs)
contains the motives of the first part which are developed.And
by this we have encountered one sensational and astonishing truth of music
history that sums up the opposition (that, as it seems to me, was unnoticed
before) between Bach and Mozart into one common feature (that has also
remained unnoticed): Beethoven’s “dividing line”[8]
between the two main kinds of “floating” (of the
development section and subordinate theme) is still absent in the
“floating” constructions in the music of both of them.
Of course, Mozart was already directed on the way to Beethoven, however he was still not very near to the target: a huge number of his development sections have very clear features of subordinate themes.The best example is the development section of the Fifth Piano Sonata in G major K.283/I, where the introductory part of the development section that, incidentally, represents new material, occupies most of the space within the development section.
The opposition between Bach and Mozart here is contained in the fact that [in Bach’s music] there are no development sections that include the subordinate themes within them, but, on the contrary, the “subordinate themes” include in themselves the obvious elements of the development sections.
Is it only like this here, in this prelude?I do not know, let us see.But what we already know is that: the road to the emergence of Beethoven, – who (like God of the Old Testament in one of the seven days of creation divided the firmament from the waters) divided with an extreme clarity in the world of “floating” the essence and notion of the subordinate theme and development section, – leads us through two stages.The first is Bach’s stage, where a “subordinate theme” (certainly in inverted commas) could not survive without interlude-like elements of a development section.The second is Mozart’s stage, where a development section (real, with no inverted commas), on the contrary, still could not manage without a (newly brought to light) subordinate theme.But it is necessary to note that between these two stages the ultimate transition of the musical hegemony from polyphony to homophony had already taken place.
In connection to this it is now necessary to briefly mention three aspects:
1.
The absence of the “dividing line”
that we were talking about in Bach’s music is much deeper than
in the music of Mozart: here we are speaking about the absence
of the “dividing line” between
the principal and subordinate
themes, i.e. not only between two kinds of “floating”, but more
than that – between “fixed” and “floating”.It
is possible to say with no risk that Bach
had an ability to create a subordinate theme by its essence and at the
same time he, Bach, had no idea about a subordinate theme.And
by this we approach the second aspect that is necessary to mention.
2. A
subordinate theme – is the outcome and important dimension of the homophony
that had already reached a certain high level of its development.
3.
In relation to this it is worth noting
that Bach is the Schoenberg of his
own time.Both discovered new worlds
of harmony whilst remaining in the captivity of the old forms that could
scarcely be compared with the enormous innovation that these two Prometheuses
made as their property.
The
point is that three elements of music: harmony, writing[9]
and form, develop unevenly.Harmony is
the pioneer of this development; form follows
in last place.
The attainment of all the elements reaching the same level is the most rare phenomenon in the history of music.In live (not ancient) music, there is only one such point – the point that is marked by Beethoven.Beethoven finished on the shore of homophony what Bach began on the shore of polyphony.And from Beethoven to Johann Sebastian Schoenberg – everything carried on again, like it was in some – unfamiliar to me – ancient music.
But let us to continue and complete the analysis of this chromatic crucifixion (in Bach’s music, when the key of F minor or some intensive chromatics appear, it immediately becomes clear that there is talk about Golgotha or some neighbouring kibbutz.
After the end of the exposition the four-bar “development section” leads us to the mirror recapitulation (the material and polyphonic structure of the “development section” is the same as in the “transition”).
And the question arises: is all of my construction not artificial?Even the fact that the “development section” is so short – is this not a reason to doubt my analysis?
No.Because I have strong proof: all nine (or ten) bars of the “subordinate theme” are sequenced precisely, without the smallest change in the tonal relations; this is what the recapitulation demands.
If one looks at things with no principles (without the orientation to the principles of a certain form), we can’t avoid asking ourselves: where does the key of D-flat major from and what the hell is it doing at the beginning of the recapitulation of the “subordinate theme”?
Let
us remember that in the “exposition” the “subordinate theme” is
directed from A-flat major to
C minor, i.e. from the parallel major key to the key of the
(minor) dominant.These are two keys
that are able to serve as the bearers of the subordinate theme, and Bach
used them both together.It is clear,
that the most important thing is that the end of the subordinate theme,
which in the exposition was in C
minor, should now be placed into
F minor – the principal key.And
if the whole subordinate theme is repeated exactly a fourth higher in relation
to the exposition, this means that the recapitulation begins in the sphere
of the subdominant (where the key of D-flat major belongs to) as it appeared
in a much later time not only in
the music of Mozart, but also of Schubert.
The principal theme appears afterwards, in place of the coda.And this we find often, very often, in the music of Mozart.Here at the end, the principal theme appears not as a three-part song, but shortened.This is quite normal: in this sonata (we can avoid the inverted commas) it is not only the principal theme in the exposition that consist of three parts, but both appearances of the subordinate theme also.The point is not in the fact that one more three-part appearance would be too much, it is that the disappearance of the three-part structure in the principal theme at the end of the recapitulation signifies the solution of all the problems.Jesus Christ breathed his last upon the Cross…But let us return from mathematical poetry to poetic mathematics: the fifth and sixth bars from the end– the last two bars of the “subordinate theme – are simultaneouslythe same bars that could compose the antecedent of the period, the consequent of which is represented by what we would have to name the recapitulation of the principal theme.
And subsequently – this alone exemplifies the solution of the problem – this is the first time it has appeared, not as a period-sequence as in the earlier three times, but at last the period where the antecedent and consequent are the same, and they both are placed on the tonic.
For the conclusion I have to touch, and touch twice, on my musically- programmatic statement mentioned before.
1. Bach could not reject the program just because he was a great innovator.Like Theseus,[10] who entered the Labyrinth, needed the string of Ariadne,[11] every innovator in music needs in some compass that gives to him a possibility to move in the unfamiliar forest or unknown sea.A text, for example, as in Schoenberg’s Erwartung,[12] often could serve as such a compass.For Bach a program replaced a text.
2. What is a program?To answer this question it is necessary to ask first – what is music?Music – is a language, but this is a language so universal, that its “words” do not limited with precise and restricted notions.Music is the language that keeps the link with the languages of the animals, in where the notions, certainly, are not differentiated.Of course, like in any music, here it is possible to replace the incident at Golgotha with something else.But why should we have to replace this?Moreover, it is not we who are in need of this program, but God.
And if we have already begun to play this “game of billiards with the imagination”, let us continue.
The three voices of the triple counterpoint in the basic two-bar unit represent: the first, chromatic, in crotchets – the cross;[13] the second, diatonic, in semiquavers – the divine essence of Christ; the third, containing smaller durations – the human essence of Christ.The middle fragment of the subordinate theme, which has a development-like character, represents the crowds under the cross, which contain friends and enemies.
The principal theme depicts the formation of a man – the Son of God.The subordinate theme is the whole complex of Christ’ Passions.The principal theme at the end – this has already been specified.[14]
At the very end I want to pay attention to the fact that the last period, how it is tonally revealed to us, is the beginning and the end of the principal theme: it is – the antecedent [of a period] within a three-part song and the third part of the theme!So, this is quite a sublimated period.
Dying, Christ is raised into the sky.
7.-17.
/X. 67.
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)
HOME3: FRIENDS / INDEX1 / TEXTS / GALLERY / CDS / MUSIC / PERFORMANCES / ELENA / DMITRI / PHILIP / ALISSA / HOME1 / HOME2 / HOME3