1st Sonata in F minor, Op. 2/1 (1794-5)
The three sonatas that make up Beethoven’s Op. 2 were dedicated to Haydn, however they seem more as a tribute to Mozart. For evidence of this it would be enough to glance at the opening segment of the first of the sonatas:
This shape with its rising arpeggio is known as the ‘Mannheim rocket’ and it was one of Mozart’s favourite devices. The theme looks like a quotation from the Minuet of Mozart’s ‘Dissonant’ String Quartet in C major, K-465-III (1785), which incidentally was also dedicated to Haydn:
However the following example from the Finale of Mozart’s Fortieth Symphony in G minor K.550-IV (1788) shows an even more striking resemblance. Here the time signature, rhythm, tempo, accompaniment figuration, and articulation are the same:
But there is a great difference between these themes. If both of Mozart’s themes are based on a period – the most simple and primitive form of principal theme, Beethoven’s theme is constructed as a sentence – the most complex and developed type.
One more example from Mozart – the opening of his Twenty-fifth Symphony in G minor K.183 (173dB)' written at the age of 17. Here the resemblance is clearer still:
It is interesting to note that Beethoven had already used this idea before as the opening theme of his draft of the unfinished C minor Symphony (Hess 298) as well as in his Piano Quartets WoO 36.
Let us look at the opening phrase of Beethoven’s theme in more detail. Referring to the same example Schoenberg stated:
"The term phrase means, structurally, a unit approximating to what one could sing in a single breath."
We can either regard it as a complex motive, a motive-group, or ‘gestalt’ (as it was named after Schoenberg). It consists of separate elements that are later repeated and developed independently, forming the themes and the remaining musical content of the piece. This segment is divided into the right-hand motive of 10 notes (5 staccato crochets – dotted crotchet – semiquaver triplet – and staccato crotchet), and the motive of the accompaniment (3 crotchets). The latter can be compared to the amphibrach (~ ' ~), or even tribrach (~ ~ ~) poetic foot. However, the former is not so obvious. It is based on the iambus foot (~ '), but because it is so unified, it is difficult to identify the inner division of its elements and it can therefore be interpreted differently:
|~ ' | ~ ~ ~ ' | ~ ~ ~ '||(iambus + 2 fourth paeons)|
|~ ' ~ ~ | ~ ' | ~ ~ ~ '||(second paeon + iambus + fourth paeon)|
|~ ' ~ | ~ ~ ' | ~ ~ ~ '||(amphibrach + anapest + fourth paeon)|
|~ ~ ~ | ~ ~ ' | ~ ~ ~ '||(tribrach + anapest + fourth paeon)|
|~ ~ | ~ ~ | ~ ' | ~ ~ ~ '||(2 pyrrhics + iambus + fourth paeon) etc.|
The fourth paeon | ~ ~ ~ ' | with the fourth syllable stressed coincides with the ‘Fate motive’. ‘Thus Fate knocks at the door’ is Schindler’s famous pronouncement upon the basic motif of the Fifth Symphony Op. 67 (1808), but its authenticity is questionable. However, it is interesting to trace its conscious use in other compositions: for example the Eighteenth Sonata Op.31/3 (1801-2), the Twenty-third Sonata Op. 57 (1804-05) or the Thirty-second Sonata Op. 111 (1821-2). In this sonata it appears in its pure form as the motive of accompaniment in bb. 2-3.
Thematically, the right-hand motive and the left-hand accompaniment can be explained as the melodic and harmonic representations of the tonic triad. The right-hand motive is a fast run up the steps of an F minor broken chord, a compound sixth in range, followed by a return to the penultimate step that is embellished with a written-out turn (or gruppetto). The intervallic characteristics here almost completely coincide with all three given examples from Mozart: (V)+5+3+4+5+3–1–2–1+1 (in semitones).
During his lessons Herschkowitz used to speak frequently on the early Beethoven sonatas, as if their analysis would prove his statement that ‘the words ‘A Great Master’ are not an appraisal, but a theoretical definition.’ The way that these early sonatas structured gave him a reason to declare that Beethoven was a Great Master.
"Beethoven is Beethoven in his piano sonatas beginning from the first; whilst in all his other cycles, in no way is he Beethoven from the very beginning. I have a very specific litmus paper test for determining this."
This litmus paper test, of course, was the Schoenberg-Webern concept of ‘fixed’ and ‘floating’. The idea of defining these two opposite conditions of musical structure was developed by Herschkowitz to a great extent.
According to this concept a fixed structure, which is represented by the principal theme of any piece of music, has only three possible types of construction – a period, a sentence and a three-part song. They can be only created of elements that are identical in form, but opposed in harmony.
"Both the period and the sentence represent something akin to parallel lines. The two clauses of the period – the antecedent and consequent – should be compared to finite parallel lines. However, what happens in the sentence resembles two unrestricted parallel lines, which, as they should do, meet in infinity. Like two rows of glimmering lights by night step by step approaching each other in the infinite perspective of a street until reaching a point of fusion, the paired appearance of the initial element within a sentence (like the first two lights on the opposite sides of the street) is repeated again and again, reducing gradually until approaching liquidation; the last point of which actually represents here the point of infinity. It is not insignificant that a rest and fermata are placed at the very end of the liquidation. The appearance of this fermata above the rest at the end of liquidation is rare, but is characteristic for the sentence because it represents a kind of vacuum that is generated by the preceding cadence. The fermata actually allows the rest to become a part of the cadence; this gives the cadence the essence of infinity, which this fermata symbolizes."
The presence of the fermata above the rest clearly indicates the end of the development. By increasing the rest as if by ‘ritardando’ the rest is shown to belong to the previous theme rather than to the following passage.
"‘Vacuum’, ‘exhausting’, ‘infinity’ – are the characteristic features of the principal theme that correspond – as we shall see later – to the level of the highest type of musical form – the sonata form."
The principal theme, which occupies the first eight bars of the First Sonata, is the most typical example of a sentence. Herschkowitz explained the construction of this particular sentence in my second lesson with him:
"In the first 4 bars, there is a motive and its repetition; this is followed by a reduction of this motive, and in the last two bars – ‘liquidation’ (dilution or dispersion of the motive). Webern discovered polyphony between the main voice and the accompaniment here, describing this as a canon. We could write a whole book about these two bars!!!"
A few years later when he asked me how this theme was constructed, I answered:
– This is ‘der Satz’.
– Of course, – he agreed, – why do we have to invent new definitions when we have the German term ‘der Satz’ <…> Here at the beginning we can see a repetition of two bars. Then only the second bar is repeated. Why?
– Because the first bar is the upbeat.
– Because the first bar is weak, and the second is strong, – Herschkowitz corrected me.
– In the 7th bar there is a reduction into half a bar. How can we see this?
– We can see this because of the rests in the left hand.
– Yes, because of the accompaniment. After this, dispersion takes place. Beethoven is a radioactive composer. Everything in his music is interconnected.
This next citation is from one of his essays dedicated to the First Sonata. Here Herschkowitz mentions additional details regarding harmony:
"This principal theme represents a typical example of the sentence […] it consists of two bars on the tonic and their repetition on the dominant. This is followed, by way of division, with only the second bar (on the tonic) and its repetition (on the dominant), and then with only the first half of the bar and its repetition, so greatly transformed that this simultaneously becomes the liquidation of the sentence."
It would come as no great surprise to learn that this was very similar to the way that Webern taught Herschkowitz and the way that Schoenberg taught Webern.
10th of June 1934 Schoenberg enters in his notebook the musical example of this theme with the following comment: ‘A sentence such as this is a good example of a stable formation [feste Formung].’ He explains that the second two bars are the dominant form of the first two bars (tonic form). Bars 4 and 5 with shortened ‘upbeats’ (meaning the ascending arpeggios of the fist and third bars) are virtually reduced repetitions of the first and second two bars respectively; and only last two bars ‘produce rhythmic and tonal digressions, which, however, use (half-)cadence as a means of retardation (or condensation).’
In his Fundamentals Schoenberg writes:
‘In many classical examples one finds a relationship between the first and second phrase similar to that of dux (tonic form) and comes (dominant form) in fugue. This kind of repetition, through its slightly contrasting formulation, provides variety in unity.’
Then Schoenberg examines the opening of the First Sonata:
"...the first phrase employs only I, and the second phrase only V."
The liquidation is generally supported by a shortening of the phrase. Thus in [the theme of the First Sonata] the two-measure phrases are reduced or condensed (in m. 5-6) to one measure…
Here Schoenberg provides an example with a detailed analysis of the motive work. He divides the opening two-bar phrase into three elements: a, b and c, and he divides the whole theme into four sections: tonic form (‘gestalt’), dominant form (‘second gestalt’), reduction with ‘climactic ascension’, and ‘melodic residues’. It is especially interesting to follow Schoenberg’s work; it holds the most thorough explanation of the melodic residues in the liquidation of the last two bars:
Of course, there are other writings that deal with the analysis of this theme. Donald Francis Tovey, for example, portrays it as follows:
Bars ¼ /1-8. – Eight-bar theme (A); 2+2 in sequence, followed by 1+1 sequence, rising 2-bar half-close on dominant. Pause. The theme contains two figures –
"and from its 4th bar the bass rises up the scale from E to C."
Here Tovey gives no name to the form of the theme, speaking of ‘sequences instead of tonic-dominant forms and ‘figures’ instead of motives. The idea of reduction is not discussed, and liquidation is not even considered.
Vladimir Protopopov, a follower of the IMT-theory of Boris Asafiev that involves a ‘tripartite development of musical form’: initium (initial impulse) movere (progressing motion) and terminus (termination or conclusion), divides the theme into three parts that perform three different functions: initio-development-cadence:
Similarly there is no place for the idea of liquidation here – the last part of the theme is regarded as a united segment functioning as the termination of the progressing motion or simply, a cadence. This echoes the tradition accepted in Russia to consider the idea of this construction as a ‘division with closure’. In relation to this theme Kinderman notes:
In a foreshortening process phrases are divided into progressively smaller units; the effect is to drive the music forwards with a nervous intensity quite alien to the relaxed rococo elegance of the ancient regime.
He gives a detailed description of this process:
"The opening theme of op. 2 no. 1 juxtaposes two-bar phrases on tonic and dominant, using a version of the ‘Mannheim rocket’ figure with a rising staccato arpeggiation peaking first on A flat and then B flat in the treble, while staccato chords on the weaker beats in the left hand provide the accompaniment. The vitality of this theme is sustained from within, through constant re-examination of the ongoing musical discourse. Bar 5 is an intensification of bar 2, cutting the initial phrase to half its length; 6 similarly curtails the second phrase to a single bar. All the dynamic markings are structural: they emphasize the melodic peaks of the opening phrases as well as the isolation of those pitches through sforzandi, while the crescendo to fortissimo at the broken chord in bar 7 reinforces both the upper linear motion to the fifth degree, C, and the growing intensity of the process of rhythmic diminution. The last bars of the theme are also controlled by consistent foreshortening in the harmonic structure: the tonic chord in bar 7 is sustained for only a half-bar, whereas the shift from tonic to dominant in the last bar of the theme is compressed in successive beats. The very silence at the fermata after the turn-figure in this bar seems generated by the intensity of the drive toward concision, resulting in virtual liquidation of the basic thematic material. In this arresting theme the initial two-bar units are thus reduced to single bars, half-bars, and single beats before the music abruptly confronts that silence out of which it came into being."
All of these writings help us to understand a certain uniqueness contained within the teachings of Schoenberg-Webern-Herschkowitz. But of course it is possible to view the same things in different ways. In one of my recent articles I tried to make a comparison between rhythmic patterns and the characters of the Morse code, where short note durations are compared with dots, and long durations – with dashes. With this in mind, rhythm-patterns or motives can be defined as follows:
Using such definitions we can gain a clear picture of how a composer introduces, combines and develops rhythm-motives in his music, visibly demonstrating the rhythmic structure of a piece:
Studying the same Beethoven theme again and again we can find more and more fascinating details. Just by chance it occurred to me that in the right hand we have 10 notes in the opening motive followed by the shortened motive-forms of 9, 6 and 6 notes, and at the end, at last, when we reached the liquidation, it forms a phrase of the same 10 notes again that by their shape represent a sort of a retrograde form of the initial motive. Is this not amazing?
✶ ✶ ✶
Although the rest of this book will concern itself with mainly the principal theme of each sonata, I feel it is quite important at this point to deviate slightly and show the difference between a fixed principal theme and a floating subordinate theme. The function of a subordinate theme is to introduce a contrast, as well as to show and express a subordinate tonality as a new feature, but at the same time its subordinate nature manifests itself in the qualities of a derivative character, and in a wider view it is a kind of repetition of a principal theme.
Schoenberg enumerates the following features of the subordinate theme or group:
"1. Loose structure; 2. Spinning out (chain-like interconnection); 3. Evasion of definitive cadences; 4. Codettas or closing themes at the end of the group. He explains a loose (=floating) structure as a ‘direct and immediate repetition of segments, juxtaposition of contrasting segments, often with an overlap; little or no recurrence of earlier features within the section."
So, we can see that in some respects the floating structure of a subordinate theme supposes to be even more sophisticated than the fixed construction of a principal theme. But we have to be aware of the different levels of floating elements in a musical form: the subordinate theme as a rule is more floating than the principal theme but less floating than the transition or even less floating than the development section.
According to Herschkowitz, Webern stated:
"A subordinate theme begins in the same manner as a fixed principal theme, but at a certain moment it refuses to continue along the fixed line, changing its course into a free fantasy."
However ‘it is the sort of ‘free’ fantasy where nothing is occasional’ – as Herschkowitz once explained to me grabbing himself by the throat to show that there is no real ‘freedom’ at all. After completing his detailed analysis of the first movement of the First Sonata, Herschkowitz arrives at the following conclusion:
…by its own structure, the subordinate theme is drawn towards a sentence along the whole of its length; but at the same time, it consistently refuses to become a sentence.
The openings of the principal and subordinate themes in the First Sonata are very alike. They are both built of the same motives, a and b, with only a slight variation of motive b: the triplet of semiquavers within the second bar of the principal theme is simplified and replaced with just a single quaver stressed by sforzando in the second bar of the subordinate theme. Thematically they form a kind of false mirror, where an ascending movement though erroneously is reflected with a descending movement and vice versa:
The second step is also the same – the first two-bar statement is repeated. However in contrast to the principal theme, instead of the harmonic opposition i-V between the statement and its repetition, the statement is repeated harmonically precisely, partly because the statement itself already contains such an opposition. Another distinction is the dominant pedal point, which the opening of the subordinate theme dwells upon. This is one of the characteristic features of a floating type of construction:
The reduction of the statement into one bar follows, but here motive a is used instead of motive b as in the principal theme. This separate bar is not repeated as in the true sentence of the principal theme, and this is another typical feature of floating construction. Instead, a new half-bar pattern c is introduced, which appears three times making a division into half-bars. Here we can observe the beginning of the segment that Webern called ‘an element of free fantasy’. But we have to understand that this free fantasy is not completely free, and the new element is not absolutely new – its origin can be easily traced. For example, its rhythmic pattern of three quavers can be originated from the semiquaver triplet of the principal theme that is ‘missing’ in the subordinate theme; but here it is three times augmented. Thematically it repeats the fragments of the melodic shape of the second and fourth bars within the principal theme, beginning from their upbeats (f – a-flat –g and g – b-flat –a-flat). This segment is juxtaposed, developed and then partly repeated.
Its development takes a backward step: pattern c is extended instead of being shortened and this appears three times, creating one-bar divisions. This is followed by another backward step – pattern ‘c’ returns to its half bar state and now appears five times:
In this respect the following comment by Herschkowitz is rather remarkable:
"The essence of the floating very often lies in the backward steps that are quite frequently repeated."
Hence, floating constructions differ from the straight-lined and successive fixed constructions by breaking the chain of consistency and deviating from a simple logical developmental process by disregarding certain expectable steps or making backward steps with their repetition that can be regarded as unnecessary.
After such irregular reduction and division our floating sentence or more precisely ‘quasi-sentence’ reaches the point of its liquidation. The liquidation is performed mainly in the melodic voice of the right hand while in the left hand we can observe one-bar and then half-bar divisions. This forms a separate 4-bar segment that is juxtaposed and then repeated:
The subordinate theme concludes with a passage of seven closing bars (or codetta) formed by two cadencial bars (oII7–I6/4–V7–I) that are repeated precisely and then repeated again with a written out ritardando. By this the exposition comes to its end.
✶ ✶ ✶
The four movements of the First Sonata are constructed as a sonata form, a small rondo, a minuet with trio, and a sonata-rondo. They contain eleven themes: four of them are principal themes (1, 4, 6 & 8), six more function as subordinate themes and one as a closing theme. However we have to bear in mind that the themes that appear as the ‘trio’ of a minuet, scherzo or rondo (here 7 & 11) are normally structured as principal themes, but function as subordinate. The mentioned themes represent a complete diversity of theme-structures: among them there are two sentences (1 & 8), three 3-part songs with a period (4, 7 & 11), one 3-part song with a sentence (6), four quasi-sentences (2, 3, 5 & 9) and one quasi-period (10). They have a complex motive and thematic relationship that we can not discuss here in detail – this would require another substantial book. However it is easy to demonstrate here the tonal interconnections of all the themes. The scheme below shows their entire tonal network that is created with astonishing logic, consistency, and strong ideas of symmetry:
- See: Rosen, p. 123, Cooper, pp. 23-24.
- Fundamentals, pp. 3-5.
- From ‘Webern and his teaching’, On Music, vol. I, p. 62.
- From a letter dated 8th April 1988, See also: Geometer, p. 186.
- On Music, vol. I, p. 49.
- Geometer, p.34.
- Geometer, pp.95-98. See also pp. 193-197.
- On Music, vol. II, pp. 59-60.
- Musical Idea, pp. 178-9.
- Fundamentals, pp. 21-22.
- Tovey, p.11.
- Protopopov, p. 7-9.
- Kinderman, p. 30.
- Music and the Morse code.
- Fundamentals, p. 204.
- Webern on Musical Form, p. 163.
- This is fully described in Geometer, pp. 95-99.
- On Music, vol. II, pp.61-63.
- On Music, vol. I, p.97.
- Harding defines them differently: I – sonata form, II – modified sonata form, III – menuetto and trio or ternary form, IV – sonata form. Harding, p. 2.
- Refer also to the Thematic Catalogue at the end of the book.