A Pupil of Webern in the USSR: The Writings of Philip Herschkowitz (1906-1989)


Marina Lupishko 1


"Fest und Locker": The Second Viennese View of Form

In the musical world, there are not many cases when a figure, underrated and virtually unknown in his own time, has afterwards become a source of great influence. The name of Bach comes to mind first, followed by, perhaps, those of Schubert, Ives, and Webern. Today, at the close of the century, when we are trying to analyze causes and effects of the recent past, it is not always necessary to look too far back for an example.


A Chronology of Herschkowitz’s Life

The name of Philip Moiseevich Herschkowitz (1906-89) is still largely unknown, not only in the West but also in the former USSR, where he spent the most active half-century of his life. To people closely familiar with his views and writings, he stands out as one of the most interesting theorists of his time. To those who know Herschkowitz by only hearsay, he is "a pupil of Schoenberg" who curiously ended up in Russia, an ostracized and tragicomic figure. Ten years have passed since his death, but the research on Herschkowitz is just being started. In 1991 a collection of some 300 pages of his writings appeared in print in Moscow, followed by two more volumes in 1993. 2 Around that time, a short series of articles in Soviet and Western journals seemed to have started paving the way. 3 Few further steps have been made since then, the only notable exception is the recent Austrian publication of the fourth volume, containing works in both German and Russian languages. 4

Favin (Fabish) Herschkowitz (Herscovici) was born in the Romanian town of Yassy on 7 September 1906, to the family of a Jewish button merchant.5 At the age of twenty-one, he graduated from the Yassy conservatory and entered the Vienna Academy of Music, where his principal teacher was Josef Marx. From 1929 to 1931 Herschkowitz studied privately with Alban Berg; in 1932 he attended a summer course on conducting led by Hermann Scherchen. In that year he became a proofreader for Universal Edition, where Berg’s works were published under Herschkowitz’s observation. From February 1934 to February 1939 (5 years, 3 times a month except for the summers) he studied privately with Anton Webern. At the end, Webern gave Herschkowitz a handwritten diploma "which said that Herschkowitz, having followed a full course of instruction, has a right to teach composition and theory."6 With this diploma, Herschkowitz escaped from the Anschluss to Chernovtsy, a little Romanian-Ukrainian town which had been annexed to the USSR, and taught at a music college there until the beginning of the war. 7

The following five years Herschkowitz spent as an evacuee in Uzbekistan where he was made a member of the Union of Composers and given a position as Associate Professor in the Tashkent Institute of Arts. In August 1946 he arrived in Moscow. In 1949, when a campaign against "cosmopolitans" (i.e., Jews) had begun, he was expelled from the Union of Composers; in 1953, after Stalin’s death, he was accepted into Muzfond (a kind of trade-union for musicians) as a non-permanent member. As time passed by and serialism started breaking through the Iron Curtain, his role in underground Russian music-making became more and more distinct: "It was Herschkowitz who directly influenced young composers in a ‘pernicious, noxious and corrupting’ way by wanting to escape from the suffocating, although in many aspects comfortable, prison of ‘socialist realism.’" Among those "directly influenced" who had professional contacts with Herschkowitz, Smirnov names Edison Denisov, Alfred Schnittke, Sofia Gubaidulina and fifteen others.8 This was done mostly through private lessons (Herschkowitz’s primary source of income) and partly through lecture series in the Leningrad, Kiev, and Erevan conservatories during the 1960s.

"Beginning from the sixties, he came to realize his mission and quit the ridiculous attempts to adapt at the cost of losing himself."9 That was the time when Herschkowitz started writing his theoretical works, only two of which would be published in the 1970s, by the Estonian Tartu University Scholarly Notes.10 At around the same time, he produced a series of musical compositions ("Three Pieces" for piano, "Four Pieces" for cello and piano, a "Cantata" for voice and chamber ensemble to poems of Rilke, Lorca and others), which, Dmitri Smirnov claims, have never been performed publicly.11

It all led to feeling deprived and deserted. The long "period of stagnation" replaced the short Khrushchev thaw. Despite a circle of close friends, Herschkowitz found no recognition in the musical circles of Moscow. In 1979 he made an attempt to emigrate to Israel – a thoughtless step which cost him the expulsion from Muzfond and a loss of many "friends." After perestroika, a possibility finally came: an invitation from the Alban Berg Stiftung to help in the preparation of Berg’s works for publication. In December 1987, with his wife Lena, Herschkowitz left for Vienna, the city of his youth, where he died after brain-tumor surgery in 1989.


Herschkowitz and His Teachers

The literary style of Herschkowitz’s Russian writings is close to the style of Schoenberg’s works written originally in English. The amazing fluency in a foreign language mastered in adulthood – Russian in the case of Herschkowitz, English in the case of Schoenberg – links them together although they never met in person.12 Moreover, it is very unlikely that Herschkowitz had actually read any of Schoenberg’s books except Harmonielehre.13 The logical succession of thought, the use of metaphors, the aphoristic brightness of style – all these are strong points of both Herschkowitz and Schoenberg. At the same time, a certain dryness in presenting main ideas in both authors is combined with excessive self-references when secondary ideas are discussed. Despite all this, the Russian language of Herschkowitz reads easily and at places is even captivating.

The role of Herschkowitz can be seen as threefold. First, considering the particular environment in which he lived, his main merit becomes that of a missionary. A musical outsider in a communist country, Herschkowitz was introducing the freedom to study the "forbidden" philosophy of Schoenberg’s circle to his pupils who lacked this knowledge. Second, being aware of the fact that neither Schoenberg nor Webern left any completed works on form, Herschkowitz felt a need to systematize the information received from them. He declaimed against the popular opposition "composer-theorist":

It is accurate to think that great masters like Bach, Beethoven or Wagner were as great theorists as composers. Undoubtedly, they were aware of what they were doing and, therefore, realized profoundly what had been done before them. This is exactly ‘theoretical’ work, though unformulated and thus left unknown to anyone except themselves. If the theoretical ideas of Schoenberg and Webern have received their (oral and partially written) formulation, it was only because they had to earn their bread by giving composition lessons.14

And lastly, having gone farther than his teachers, Herschkowitz created what he called "the material concept of musical form," in which the most minute detail becomes an integral part of the whole. The further separation of "firm" and "loose" structures, the idea of "supercycles" in Beethoven and Mahler, the concept of bi-functionality and bi-formality, the genealogy of homophonic forms – this is only an incomplete listing of his innovations, summed up by his most devoted pupils, Smirnov and Gofman.15

The Inherited Ideas: Schoenberg, Berg, Webern

The question arises: to what degree was Herschkowitz original? Except for instances of adding something to or openly rejecting a Schoenberg-Webern thought, he mentions himself very rarely, as if constantly speaking on behalf of his teachers. In the preface to his article "Webern and His Theory of Form," Herschkowitz states in parentheses:

It is appropriate to say here that I am not able to establish which ideas belong to Webern and which belong to Schoenberg. I choose, quite at random, sometimes one name, sometimes the other. As a matter of fact, one can choose either one, because the ideas of both masters have joined together, having created one single whole. 16

With this in mind, any attempt to identify the source of any reference of Herschkowitz might seem impossible. However, several such attempts have already been successful. Such an establishing of authorship would help to show how these ideas evolved historically and would become a fitting tribute to each master’s theoretical legacy, oral and written. The materials used to clarify sources of Herschkowitz’s references to his teachers are listed below. First and foremost, it is The Path to the New Music,17 a sixty-page translation of the sixteen popular lectures given by Webern in 1932-33. The two textbooks written by Schoenberg in the United States, Fundamentals of Musical Composition18 and Structural Functions of Harmony,19 have clarified some of Herschkowitz’s terminology. In addition, the two recently published manuscripts of Schoenberg gave an insight into the so-called "unified concept of music theory" (the task Herschkowitz also occupied himself with). The earlier one, on coherence (ar. 1917),20 was meant to present a theory that would unify the separate disciplines of counterpoint, instrumentation, form, and harmony. The concept of coherence was later reformulated as the concept of the musical idea (1934-36); the volume with this title was intended to present the four separate disciplines consistently as a theory of composition.21


Berg’s Influence

In the beginning of "Webern and His Theory of Form," Herschkowitz pays a tribute to his teacher Berg:

Berg surprised me very much by saying, ‘A successfully done musical work hides lots of great things the composer did not think about.’ Many times I have been asked by my students, ‘This place in Beethoven you are showing us – was it done consciously?’ My answers were, ‘That is a question of psychology, not music’; or ‘I can not tell the ratio of conscious and subconscious parts of Beethoven.’ Those seemed right to me. But the most correct answer is that of Berg. 22

As an illustration, Herschkowitz discusses a structural link in the first movement of Beethoven’s Third Symphony, Op. 55. There is a g’’ repeated six times in the first violin in mm. 7-8 in the beginning of the exposition and, curiously enough, a V6/5 tutti chord repeated six times in mm. 128-131 of the end of the exposition. To Herschkowitz this link, along with many others, represents a "reflection of the central conscious creative idea of the piece."

The most remarkable of what I heard from Berg concerns Bach and Handel. Bach is Bach, Handel (to say it in Russian) is the most talented khalturshchik [hack-worker]. Also, there is a parallel correlation in our time: Mahler – Richard Strauss. . . Far from instantly, this thought became a part of my musical philosophy. Only after studies with Webern, it gave rise to my notion that the words ‘great masters’ are not an estimation but a technical term. I began to look at the music of great masters as not just of better quality but as completely different in its essence. . .

. . And, most importantly: I understood that all great masters comprise one single chain. 23

In this chain, after the hypercritical Herschkowitz dropped Brahms, Haydn and Berg, only seven remain: Bach, Mozart, Beethoven, Wagner, Mahler, Schoenberg, and Webern.

"Webern and His Theory of Form" or Three Types of Main Theme

Form in the aesthetic sense represents for Herschkowitz the same thing it represented for Schoenberg, Berg and Webern – a living organism: "Webern used to say, a piece of music is not like a stick; it is more like a flexible arm or leg, it has joints. Loose parts serve as ‘joints,’ alternating with firm ‘bone’ parts."24 Form is by no means a given pattern: it is a coming-into-being as unique as a piece of music. What is constant though is the principle of form-making. Herschkowitz calls it "the principle of repetition" and attributes this idea to Schoenberg.25 Forms are put together by the similarities of bigger and smaller parts, the smallest of which is the motive. 26

Before an actual music analysis, Herschkowitz outlines the two instruments of his research: "exact" and "varied" repetition. He states that the distinction was originally made by Webern. 27 In discussing exact repetition, Herschkowitz attributes to Webern its division into "motivic" (the exact repetition of rhythm) and "thematic" (the exact repetition of pitches):

According to Webern, [the term] motive . . .can be applied to the duration of sound only. On the other hand, pitch belongs exclusively to theme. Motivic and thematic repetitions can coincide but always remain separate. Therefore, the exact repetition is no longer all-embracing and indivisible.28

The "exact" repetition of rhythm, regardless of note values, is therefore called "motivic," the "exact" pitch repetition – "thematic." Motivic repetitions also include augmentation and diminution (those are still considered "exact"), thematic – transposition, inversion and retrograde. The Scherzo of Beethoven’s Sonata Op. 2, No. 2 29 demonstrates motivic repetition: the rhythm of each motive is repeated. The transition theme of the first movement of Op. 2, No. 1 is an example of thematic repetition: the descending passage c—b flat—a flat—g, repeated three times in mm. 15-20, comes from m. 7 of the main theme, although the rhythm is changed.

Before going into the discussion of "varied," as compared to the exact, repetition, Herschkowitz relates the two types in Schoenberg’s fashion: both kinds are ultimately the same; on an abstract level, there is an exact repetition available in every varied one. Such a repetition can look as different as the main theme seems to be from a subordinate one, or, speaking in Herschkowitz’s terms, as "firm" is from "loose." But the "loose" is only a differently organized "firm." The last postulate is a keystone of Herschkowitz’s Formenlehre.

Whereas non-varied repetition represents something very concrete even when it deals with duration or pitch only, varied repetition is not concrete in most cases. Varied repetition, unlike non-varied, takes place at all levels of musical form. . . At a certain level, where the ‘repeated’ and the ‘repetition’ begin to have different structures, we face the possibility and the necessity to differentiate ‘firm’ from ’loose.’ 30



A firm structure, says Herschkowitz, is easy to find because it has only three types of manifestation, two are simple, one is compound. These three types are: "period," "eight-bar sentence," and "three-part song." "Period" is the first and the simplest type. Herschkowitz quotes Webern, who defined a period as "a structural phenomenon which consists of two phrases, identical or similar to each other, where each ends with a cadence." 31 The most typical period Herschkowitz finds in the theme of Mozart’s Sonata for piano K.331 (mm. 1-8). However, in musical "reality" such pure periods rarely occur: according to Schoenberg, "only a small percentage of all classical themes can be classified as periods." 32 The theme of the Largo appassionato of Beethoven’s Op. 2, No. 2 (mm. 1-8) can be called a period as well, though the phrases are less similar:

There are smaller note values in the second phrase in place of the bigger note values of the first phrase. . .The two half-notes (mm. 2-3) seem to be the ‘axis of symmetry’ of the first phrase, the four eighth-notes – of the second. 33

A period consists of only two phrases. Webern failed to explain why this number is compulsory. "I was persuaded by his mere eagerness," 34 admits Herschkowitz. Later, however, the explanation was found:

If we take into account that cadences are harmonic key points, we can reformulate the definition of period: . .period is a type of first theme which consists of two phrases identical in form and opposite in harmony. This identity and this opposition between phrases represents the essence of the period as a firm structure.35

At the end of the article "Webern and His Theory of Form," Herschkowitz justifies any deviation from his rule about the period, thus demonstrating his very characteristic approach to exceptions in general:

The cadences are not always harmonically opposite. We can find, as an exception which proves the rule, periods identical both formally and harmonically. However, it is not very important whether the exception proves the rule or not. Any such anomaly is an artistic problem for a great master, consciously or subconsciously, and the rest of the piece is the solution. Ultimately, anomaly proves the norm, although being only a particular type of the norm. 36


Eight-bar Sentence

The descriptions of "eight-bar sentence" and "three-part song" are found in the article "The Development of Form as a Whole, Development of the Main Theme." 37 "Sentence" is the accepted English translation of this structural phenomenon, called by Herschkowitz fraza in Russian, Satz in German. 38

The two distinctive features of a sentence are the absence of periodicity and the absence of an internal cadence. However, a certain trait of periodicity remains, for a sentence usually starts with a two-measure motive followed by its repetition, normally on the dominant. The rest of a sentence is put together by means of motivic development. Words like "fragmentation" (Schoenberg’s terms "reduction" or "condensation") and "liquidation" are used to describe this process. 39

This is how Herschkowitz applies Schoenberg’s terminology to the description of the beginning of Op. 2, No.1: "A two-bar motive, two-bar motive repeated, then fragmentation by one bar and liquidation" (mm. 1-8). 40 An analogous example is the first movement of Op. 2, No. 3: "2+2+1+1+ liquidation," though the fragmentation is repeated here (mm. 9-12). Such an "extended eight-bar sentence" is not a rare case in Beethoven. 41 Another example of a "sentence with repeated fragmentation" is found in the Rondo of the Sonata for piano ("Pathétique") Op. 13 (mm. 4-12). Here one also could observe a varied repetition of the principal two-measure motive (mm. 1-2, 2-4). Herschkowitz insists on calling this a sentence because 1) the underlying harmony of the first two-measure motive is clearly tonic, of the second – clearly dominant, and 2) there is a parallel between the half-note motives of each of the two-measure segments. "I discovered . . .that only the strong-bar motive is exactly repeated in a sentence! How it is done – only Beethoven knows!!!" 42 The "strong bar," out of the principal two, falls from the second half of m. 1 to the first half of m. 2. The rest of the "very prolonged sentence" features a "very simple" fragmentation of motives (1+1+ ½ + ½ + ½ ), repeated in mm. 8-12, and two closing two-bar segments with a perfect cadence at the end. Note, that the anacrusis has disappeared in the closing measures (mm. 12-17).

Three-part Song

The third type of firm structure is called a "three-part song." 43 Here is Herschkowitz’s definition:

Period and sentence are joined together to form the third type: three-part song. In a three-part song, the first part is a period or an eight-bar sentence, then comes the [four-bar] second part, then the third one: if the first one is a period, the third part is the repetition of the second phrase of the period. 44

Thus a typical design of a three-part song, according to Herschkowitz, is AA’BA’ or "rounded binary."

The essence of the three-part song can be found in a period which represents the theme of a minuet or a trio. The period repeats without any changes in order to declare its intrinsic aspiration to fill up the whole piece with its repetitions. . .The first exact repetition makes it easier to comprehend the second non-exact one. 45

In describing the middle section of a three-part song to his pupil Smirnov, Herschkowitz remarks, "Webern told me that it ‘stands on the dominant,’" and admits that he had not understood this expression for a long time, "though it must be understood – it’s important!" 46 A normative example from early Beethoven is the "Adagio" from the first Sonata for piano. The middle section (mm. 9-12) stands on the dominant. The remaining four measures (mm. 13-16) are a varied repetition of mm. 5-8 an octave higher. However, and this is important, the cadence in m. 14 is "motivically" the same as in m. 2, that is, the third part of this three-part song combines the features of both A and A’ phrases of the initial period.

Herschkowitz terms such a case "the synthesis of the two phrases." 47 Sometimes the synthesis is carried out by the extension of the third section, as in Mozart’s

"Andante grazioso" of K.331 (mm. 16-18) or the "Largo appassionato" of the second Sonata for piano of Beethoven. In the second phrase of the initial period of the "Largo appassionato" (mm. 5-8), there is no repetition of the accented second beat of m. 2 (see the above discussion of this "unconventional period"). The extension of the closing third section (mm. 13-19) has three statements of the original "sarabande" rhythmic pattern, each time with an added sf (mm. 14-16). The final cadence of this three-part song is borrowed from the ending of the second phrase, thus both phrases are "synthesized" here also (compare mm. 7-8 and 18-19).


"Fest und Locker": An Introduction

The idea of two different qualities of structure – fest and locker or "firm" and "loose," originated by Schoenberg and developed by Webern – did not have a big impact on their writings. From Herschkowitz we know that Webern stressed the importance of this division in his discussions with pupils. The only echo of these discussions is found in the postscript to The Path:

The contrast between firm and loose is a fundamental one. But the firmness of the first subject (presentation of the theme!) is different from that of the codetta. Even in Bach’s fugues this contrast can be seen in the episodes. Example: the six-part Ricercar from the "Musical Offering."48

In his investigations of "stable" and "loose" formations in The Musical Idea manuscript, Schoenberg went no farther than giving their definitions:

A statement is stably formed [=firm] when its smaller components do not have the tendency to move away from a perceptible center (for example, a harmonic one) but instead arrange themselves around it (concentric tendency). . . A connection is loose if the parts are capable of certain amount of independent motion (eccentric tendency?). 49

In Fundamentals of Music Composition, there is an extended description of the "loose" structure in conjunction with its most visible embodiment, the subordinate theme:

The lyric, or singable, character is the result of a loose construction . . .The ‘looseness’ consists in disregarding almost all features except the rhythmic ones, thus neglecting the profounder implications, and providing richness of content through the multiplications of themes. 50

The main achievement of the New Viennese School of thought is, according to Herschkowitz, this differentiation between "firm" and "loose" structures.51 The "loose" begins where the firm main theme, the embodiment of the tonic, ends. The following description is quoted from Herschkowitz’s article "About One Invention of J. S. Bach (On the Problem of the Origin of Sonata Form)":

The subordinate theme usually begins as if it belonged to one of main-theme types. But that is just the beginning: the continuation unfolds, in Webern’s words, along the line of ‘free fantasy.’ But that ‘freedom’ and that ‘fantasy’ are freedom and fantasy only because the continuation of the second theme ignores the elements of firm structure in the main theme. In the rest, there is no freedom at all: everything which follows is absolutely and definitely (though ‘occultly’) related to the main theme. Ignoring the logic of first-theme types, the second theme uses association of ideas as its motor force.52

What are "the elements of firm structure"? The regular number of measures, normally divisible by four, more or less periodic design, and the harmonic stability achieved by the tonic/dominant opposition of cadences (period, three-part song) or principal motives (sentence). As opposed to that, "loose" structures are characterized by greater length, irregular number of measures, modulation, more active motivic development, quicker harmonic rhythm and a concealed motivic relatedness to the firm main theme.

Herschkowitz illustrates these with the first movement of Beethoven’s Sonata for piano Op. 2, No. 1. The transition (mm. 9-20) already ignores the elements of the firm structure of the preceding sentence: a two-measure reminiscence of the main theme is not repeated – instead, we are immediately confronted with a fragmentation by one measure (mm. 11-14), followed by three descending closing passages leading to the dominant of Ab major. The fact that the subordinate theme is both a "motivic" (rhythmic) and "thematic" (inverted) repetition of the main theme is clear: according to Herschkowitz, sf is used to replace the strength of the triplet here. Having started as a sentence it soon "loosens" its contours: the repeated two-measure motive is followed by its incomplete repetition in m. 25, a long fragmentation (mm. 26-32) and an extremely extended liquidation (mm. 33-41).

In analyzing loose structures, Herschkowitz always stresses the importance of his postulate about the "association of ideas," i.e. motivic relatedness of the "loose" to the "firm." Sometimes the principal motive of a firm theme simply comes back slightly modified in a loose one. In the Andante of Mozart’s Sonata for piano K. 279, the principal c-c-c’’ motive is transformed into the triply diminished g’’ in the transitional m. 10, and then into the triply augmented g in the first three bars of the subordinate theme (mm. 11-13).

In the majority of cases, however, such motivic association remains obscured. For the purpose of dealing with such cases, Herschkowitz proposes a method, discovered by him and therefore modestly called "Herschkowitz’s law."53 It states that an element of the main theme often returns in a metrically displaced variant in the subordinate theme.54 The best example can be found in the "Adagio" of the Sonata for piano Op. 2 #3. The secondary theme’s syncopated soprano line (m. 19) "refers" to the main theme’s syncopated fragmentation started on the upbeat of m. 6 – to the point that both rhythms are utterly the same. The downbeats of the secondary theme belong to the bass, not the soprano line, thus providing proper spaces for the sixteenth-note rests in the soprano.

We now come to the "looseness" of the development section. Though "loose" does not have any particular formal models as "firm" does, Herschkowitz the analyst could not resist making another classification:

While the tonal meaning of the second theme is to be a ‘carrier’ of the dominant key, the transition and the development with their different type of looseness subsequently represent the pathway from tonic to dominant and from subdominant to tonic. . .The development often consists of sequences, just as the first transition in the exposition. Sequences destroy the gravitational power of the dominant and return its tonic to the position of the first step in the tonic key. ‘Sequences’ is what loose means in the development section. 55

The development section, according to Herschkowitz, is very often analogous to the middle section of a three-part song: a two-measure motive and its repetition, standing on the dominant. Accordingly, a typical development may often consist of two sections, each one with its own model of sequence, in subdominant and dominant keys consecutively. 56

The analytic system which consistently applies the two different types of structure ("firm" and "loose") as its tools is one of the main analytical achievements of Philip Herschkowitz. His teachers, who originated, used and taught these concepts, left very little evidence of it in their writings. Herschkowitz not only left a detailed account of the analyses made at his lessons with Berg and Webern, but also enlarged and systematized them by adding his own layer of "discoveries." The following list of Herschkowitz’s additions to these analyses can be drawn from the preceding discussions:

1. The axiom about a necessary harmonic opposition of cadences in a period.

2. "The rule of the eight-bar sentence": only a metrically strong bar undergoes

development in fragmentation.

3. The observation about a "synthesis of the two phrases" of the initial period in the last section of a three-part song.

4. "The law of Herschkowitz": an element of the main theme often returns in a metrically displaced variant in the subordinate theme of a sonata form.


"Tonal Sources of Schoenberg’s Dodecaphony"

The Formenlehre of Webern-Herschkowitz has Schoenberg’s Harmonielehre as its basis. Such terms and concepts as "firm" and "loose" can be related back to Schoenberg’s three postulates set forth in Harmonielehre and reformulated by Herschkowitz in "Tonal Sources of Schoenberg’s Dodecaphony":57 (1) the relativity of consonance and dissonance; (2) the short-lived nature of any sound system; (3) the hegemony of tonic, based on the antagonism between dominant and subdominant.

Schoenberg’s popular thesis about the "emancipation of dissonance" became a pre-condition for his idea of the relativity of the very opposition "consonance /dissonance." According to Herschkowitz’s statement, the difference between consonance and dissonance is "quantitative, not qualitative."58 This difference is determined by the amount of time necessary for a dissonance to assimilate into a "consonance."

From the ephemeral nature of dissonance, there follows the second postulate about the short-lived nature of any "sound system," one of its instances being the three-century-old tonal system that produced the still existent hierarchy of consonances and dissonances. The history of Western music has demonstrated how the old system of medieval modes gave birth to the major-minor system of today, and how the latter has absorbed the old system, acquiring some of its essential elements:

A new system reproduces the matter of an old system on a higher level. [Schoenberg’s idea was that] major and minor modes both represent two syntheses, one – of Ionian, Lydian and Mixolydian, the other – of Dorian, Phrygian and Aeolian. . . The appearance of the harmonic functions (in the modern sense of the word) was caused by this concentration.59

All four finals of the old church modes obtained new roles in the new major-minor tonality, in the capacity of its two dominants (g and e) and subdominants (f and d). 60

The structure of the tonal system is based on the hegemony of tonic over the rest of the scale degrees. Answering the question of how the tonic’s hegemony is accomplished, Herschkowitz says that it is "based on the balance between the antagonistic powers of dominant and subdominant and their regions." 61


The "Main Tonal Antagonism"

The balance between the two pillars of tonality, dominant and subdominant, can be represented partially by the formula S T D. However, "balance does not mean equality of strength: subdominant is not only stronger than dominant, it is even stronger than tonic and dominant taken together." 62 As a matter of fact, the dominant is related to the tonic in a more obvious way than tonic is to the subdominant: the fifth scale degree can be represented as the tonic’s second overtone, whereas the overtone origin of the subdominant is less clear if deduced from the tonic. It is much easier to reverse the overtone scale relationship between the tonic and the subdominant: the tonic is the subdominant’s second overtone; therefore, the subdominant has a much stronger downward pull against the tonic. 63

How, then, does the hegemony of the tonic, based on the balance of these two functions, become accomplished? Through the union of the tonic and the weakest partner of the antagonism: the dominant. The tonic helps the dominant to stand against the subdominant as an equal, and therefore to prevent the latter from impinging upon the tonic’s hegemony.64

Here in Herschkowitz’s speculations comes a moment when Schoenberg’s theory of harmony is postulated as a basis for a Webern-Herschkowitz theory of form. The role of Herschkowitz thus becomes to explain the mechanism of mutual dependency of these two disciplines:

This situation appears conspicuously in a musical form. Properly speaking, musical form reflects the balance of forces described here. . .Not without reason, in the Classical epoch, they used to say that a piece is out of C major, not in C major, as we should say today. This in is a heritage of Romanticism. It reflects the epoch in which form, having been stereotyped, was connected with harmony only conventionally, but not organically. On the contrary, the word out of concentrates the idea of form as tonality in action. . . .

Music, the most immaterial of all arts, becomes our full property provided that we have a material concept of musical form. Thus, we should not speak about the equality of powers in a key, but the equality of masses. The equality of masses, situated not in space but in time. . .→←.Musical form is musical time; outside this time harmony, as an exponent of a sound system, does not exist.65

The formula of the main tonal antagonism, S T D, when applied to the temporal process of a piece of music, is modified into a variant of TDST, with the tonic as a point of departure and arrival, at both ends of a musical form. In other words, the balance is inconceivable without at least the double appearance of the tonic. This double appearance is the actual realization of the hegemony of the tonic over the dominant and subdominant. The curious thing for Herschkowitz is that the tonic’s hegemony is "expressed quantitatively!"66 His concept of form becomes truly "material" if one takes into account this simple mechanical method by which the hegemony of the tonic is achieved not only through the union of tonic and dominant, but also by the very concrete doubling of the tonic’s "total mass."67

The next quotation from Herschkowitz explains why sonata form has been considered "superior" to other homophonic forms:

Sonata form is the most clear and obvious example of how this tonal balance is achieved in a musical form. The initial tonic presents itself in this form (as actually in all the others) in the main theme. It is followed by the secondary theme and closing theme in the dominant. The dominant is so much neutralized by the subdominant in the development section that in the recapitulation the final tonic is allowed to spread not only to the main theme but also to the secondary theme and closing.68

Thus, the traditional nineteenth-century view of sonata form as the "rivalry" of the two themes/keys in the exposition is transformed into an image of "collaboration" of the same themes/keys in the forthcoming "struggle" between tonic and subdominant in the development. The structural outlines of sonata form provoked another apt remark of Herschkowitz: the dominant is a "shield" against the subdominant. Since the modulation to the dominant key occurs much earlier – already by the secondary theme of the exposition – than a modulation to the subdominant, the role of the dominant becomes that of an ally:

The sound that initially proclaims itself tonic automatically provokes the aspiration of the subdominant to take its place and keep it permanently. This aspiration is the push which sets in motion the mechanism of ‘dominant/ subdominant’ antagonism. The ‘salvation’ of the tonic from this threatening perspective becomes feasible only by temporarily passing its role of center on to the dominant. 69

Such a "temporary exchange" of centers from tonic to dominant in the secondary themes of sonata form is necessary in order to prevent the "permanent exchange" of centers from tonic to subdominant in the first phase of the development section. "The proof of such an initiative of the tonic [to pass its role onto the dominant] is the presence of the transition that modulates into the dominant key." 70 On the other hand, the "exchange of centers" between tonic and subdominant could have happened without any transition, by mere juxtaposition of keys, since the tonic can easily function as the subdominant’s dominant.

The Three Stages of "Tonal Dodecaphony"

The second part of the article "Tonal Sources of Schoenberg’s Dodecaphony" discusses the "process of absorption" of the tonic by the subdominant that happened historically over the nineteenth century. As a result of this process, the development of functional tonality came to an end. The "disintegration" of the tonal system went through three stages, called by Herschkowitz "the stages of tonal dodecaphony": (1) the "artificial dominants"; (2) the minor subdominant and its region; (3) the "roving chords." It would be appropriate to discuss this theory only briefly here since it appears repeatedly in Schoenberg’s and Webern’s writings.71 The notion of "region," however, will clarify the matter when the music analysis is approached.

Here is Herschkowitz’s definition of "artificial dominant": "a dominant-seventh chord on any scale degree other than the fifth." 72 Any key can "borrow" the dominant-seventh chord of any closely related key. Thus, in C major, five "artificial dominants" are possible: on 1, 2, 3, 6, and 7 scale degrees, i.e., V7/IV, V7/V, V7/vi, V7/ii, and V7/iii. The thirds of these artificial dominants, together with the seventh of V7/IV, represent the five chromatic pitches complementary to the C-major scale. Artificial dominants in late Romanticism became "active participants of cadence, a strong means of its strengthening and enrichment." 73

F minor becomes related to C major when the equivocal relationship between tonic and subdominant in the overtone series comes into play. "The identity of the C-major tonic chord with the dominant chord of f minor determines the relationship of f minor to C major as subdominant minor (iv)."74 In C major, the subdominant minor’s closely related keys are c minor, Db major, E flat major, and A flat major; together they comprise the region of the subdominant minor. 75 There are other regions: of the dominant (iii, V and their dominants; vii7) and subdominant major (ii, IV and their dominants; vi). If one compares the "total mass" of the subdominant region to the "total mass" of the dominant region in this "expanded key," one sees that subdominant largely outweighs dominant in the second stage of the tonal dodecaphony. 76

The "roving chords," presented in abundance in Wagner, are the ones that include augmented or diminished intervals which allow them to become pivot chords for enharmonic modulation. The diminished seventh plays a special role here: its emergence became conceivable only after the flat submediant was added to the key at the second stage of the "tonal dodecaphony." At this stage, "the barrier separating dominant from subdominant disappears," 77 since roving chords, appearing on every scale degree, could be no longer related to any particular region:

The tonal balance is unthinkable without the relationship of the perfect fifth between tonic and dominant on one hand, and between subdominant and tonic on the other. The diminished fifth represents the only interval identical with its own inversion, and therefore identifies dominant with subdominant. 78

Tonality was "done for" because all chords gradually became roving. In these circumstances a tonic was no longer necessary, "for there was nothing consonant there any more." 79

Form in the Light of Harmony

The notion of structure as used by Herschkowitz differs considerably from the accepted analytical tool, "formal structure." "Substance" is the nearest possible synonym. "Firm" and "loose" substances consist of the same material, although their "chemical compositions" – motivic contents – are somewhat different. To continue the chemical analogy, their "electrical charges" are also quite opposite: the different types of the "loose" depend on whether they belong to either the dominant or subdominant pole of the main tonal antagonism.

Firm structure is always notable for its harmonic stability, owing to the two supporting points always present there, tonic and dominant. In a period the stability is achieved by the dominant-tonic balance between the two cadences. In an eight-bar sentence, the first two-measure motive typically repeats itself in the next two measures on the dominant.80 In a three-part song, it is the balance between the middle section, standing on the dominant, and the outer sections in the tonic. Not considering the final cadence of the theme, which could be either in the tonic or on (not in) the dominant, the main theme always exemplifies the main key: "The firm main theme, as for its structure, never modulates."81

Loose structure, on the other hand, is modulation personified. Herschkowitz explains: "Modulation as a phenomenon is characterized by a certain duality: by its mechanism it belongs to harmony, by its function it is a category of musical form."82 Therefore, modulation that does not perform important formal functions in a piece is not modulation as such: "Schoenberg rejected the idea of digression [short-term modulation]. There is only one modulation in a piece, rarely two."83 Modulation in a long-range sense – leaving the tonic and coming back to it – is accomplished in sonata form through the regions of dominant and subdominant keys successively. The possible number of all deviations from the tonic is reduced to only two if we apply Schoenberg’s concept of regions to each scale degree: in a major key, ii, IV and vi belong to the subdominant region; iii, V and vii – to the dominant region. "Schoenberg’s concept of harmony and his idea about artificial dominants in particular allow us to distinguish what modulation is from what it is not, to distinguish expanded tonality from what lies beyond it."84

As to the terminology used to describe firm structure, it suggest an analogy with syntax.85 Herschkowitz is trying to prevent us from its misuse: "Period is a type of main theme, and that’s all." 86 The periodic structure of Classical music is what distinguishes this music from that of the Baroque era. Predictably, in the Romantic music theory all eighteenth-century music became seen as consisting of periods of different lengths. However, such a non-discriminative view of period resulted in confusion even among the eighteenth-century theorists. 87

In light of the foregoing, the tendency to call the subordinate theme "an extended period" is not surprising.88 True, a subordinate theme can often be structured similarly to the main theme: it begins and ends in one key. The general mood of the theme, its lighter texture and its harmonic stability often lead to its misinterpretation as a more stable area of the exposition. However, "firm" is only the beginning: the continuation of the theme normally rejects periodic structure. Besides, the stability given to the subordinate key by the closing theme is necessary in terms of establishing the "temporary tonic." This upper-level stability is given by the closing theme to the whole main theme-subordinate theme complex, which makes the entire complex as firm as the main theme itself.89

Herschkowitz states that the "looseness" of the subordinate theme is somewhat relative: the transition and the development section are far looser, being harmonically unstable and consisting of sequences. The most commonly used comparison is that the subordinate theme is a "contrasting repetition" of the main theme:

You have probably been told that the secondary theme represents a contrast. But it is only a repetition! Webern told me how Schoenberg explained it; they smoked a lot at that time; Schoenberg used to take a matchbox and show: here is the main theme – then showed the other side of it – and here is the secondary theme! The main and the subordinate themes are the same, but seen from different angles.90

The "law of Herschkowitz" states that a motive of the main theme often returns in a metrically displaced form in the subordinate theme. The rest of the theme is put together by means of "free fantasy." This term was not invented by Webern or Schoenberg. Fantasia as a genre during the Classical era was characterized by improvisatory nature and structural freedom:

In sonata form, dance and fantasia complement each other; periods begin as dances but often move to the fantasia by means of digressions and extensions, to return to the dance at the beginning of the next period. . .Indeed, we can visualize the discursive sonata style of classic music as a play between two poles, (1) rigorously regular dance patterns and (2) totally free fantasia. These are worked together so deftly that neither controls the other.91

As for Herschkowitz, he would certainly disagree with the latter statement: 

The novelty of the subordinate theme is primarily the result of the fundamental difference between the structures of the two themes. Apart from its structure, the subordinate theme does not differ from the main theme, because all motivic and thematic elements of it are determined by the main theme and come from the main theme.92

The central issue for all of Herschkowitz’s musical theorizing is the link between harmony and form in general and in any particular piece of music. In a piece of music, harmony in the broadest sense "is the form’s building material": 93

Harmony and form are as inseparable from each other, as the pitch of a sound is from its duration. The sense of an individual sound is in its being a certain pitch. Nevertheless, of the two attributes of a sound, the primary one is not pitch but duration, for of the two attributes, the first is unthinkable apart from the second, i.e. is fully dependent on the second.94

In a broad sense, form is the instrument by which the tonic manifests its hegemony; "The loss and return of the hegemony of tonic is the only event making up the whole fabric of musical form, the only event taking place in musical time. The event itself is not a goal, but only a means of manifestation of the main tonal antagonism."95 The tonal sound system chooses musical form to reveal its most characteristic feature – relativity of tonal centers. The music analysis by Herschkowitz, as reviewed and restored in the subsequent chapter, is intended to demonstrate that in every tonal piece, no matter how large or small it is, form is "a means of the making of tonality."96


"The Anomaly Proves the Norm": Beethoven-Analysis by Herschkowitz

At the end of "Webern and His Theory of Form," Herschkowitz defends both himself and Webern against future attacks on the inflexibility of the theory when he speaks in favor of any possible deviation from it, as long as this deviation is explainable: "A firm main theme does not necessarily belong to one of the three types but inevitably reveals certain features which allow us to attribute it to one of the firm structure’s types."97 The analyses of Beethoven’s compositions discussed here will demonstrate how this attribution works in practice. The discussion of the first example is fully borrowed from the same article and is considerably abridged for the purpose of comprehensibility. The two more extended analyses, based on the analytical sketches from Herschkowitz’s book and Smirnov’s article "Geometr," are attempts to "restore" the thought process of Herschkowitz.


"Loose" and "Firm" in the Rondo Theme of Op. 14, No. 1

On first sight, the main theme of the Rondo of Sonata for piano Op. 14, No. 1 is completely devoid of periodicity (mm. 1-8). After the four-measure first phrase, there follows not the repetition of the four measures, but two identical two-measure closing gestures, separated by one octave.

The substitution of these two closing phrases for the second phrase is needed here because a ‘normal’ second phrase, following such an untraditional first phrase, would not have been able to perform its traditional harmonic function.

The first phrase is characterized by a highly unusual preponderance of dominant over all its harmony. . . The dominant has such a power and weight here that it would have been impossible to counterbalance it with only one perfect tonic cadence at the end [of the theme]. 98

Such permutation of harmony, says Herschkowitz, caused serious changes in the typical formal pattern of a period. Instead of being repeated exactly, the first phrase undergoes a radical motivic reformation in the second part of the "period." The signs of this "secondary identity" (sic!) of the two phrases are listed by Herschkowitz as follows:

1. The triplets of the bass of the first phrase correspond to the sixteenth-note passage found on the last two beats of mm. 5 and 7 of the second phrase:

a) Both the triplets and the sixteenth-notes are descending E-major scales.

b) The repetition of the sixteenth-note passage an octave lower corresponds to the almost two-octave range of the triplet passage.

c) Both the triplets and the sixteenth-notes are anacruses.99

2. The motives of the second phrase indirectly correspond to those of the first:

a) The only definite equivalence is that of the downbeats of mm. 4, 6, 8.

b) There are also three "hidden" correspondences. 100

It is not that the period lacks symmetry between the two phrases: the symmetry is permuted so much that the periodicity of the Rondo theme is called into question. The opening phrase of the period is structured in a way similar to that of a miniature sentence: the principal perfect-fourth motive (b-d#-e) is followed by its harmonically opposed varied repetition (e-e-f#-g-a) and ends with a fragmentation reduced to the multiple reiterations of a single pitch. As opposed to that, a much more "periodic" second phrase features two perfectly symmetrical sub-phrases.

Applying the "firm" and "loose" concepts to Herschkowitz’s analysis of the Rondo theme enables us to see a certain "reversal" of formal functions between the two phrases. The movement starts out piano on an upbeat, conventionally implying a weak stress on the first of the two slurred pitches. Owing to this, the disposition of metrical accents seems somewhat unclear until the strong arrival of the downbeat of m. 4. This, along with other ways in which the main idea is presented here (e.g., the sequential motion of the bass and the ascending impetuous flight of the melody), suggests a certain "looseness" in the structure of the first phrase. The emphasis – agogic, tonic, and metric – on the dominant substantiates this idea. The "looseness" is counterbalanced by two cadential formulas on tonic, i.e. by the "firmest" possible second phrase. It is as if the first "loose" four measures, in order not to go any higher in the soprano and lower in the bass, were "anchored" by two full tonic cadences instead of one.

As Herschkowitz insisted, the "loose" always depends upon the "firm." This Rondo theme reveals the opposite: the firm second phrase not only comes after, but is also caused by the loose structure of the opening. Such an irregularity, however, is considered to prove, rather than break, the rules, by being fully explainable through them: "It was my exceptionally important task to demonstrate that any formal deviation is based ultimately on the same principles that make up the basis of a corresponding norm."101

 The "Inverted" Main Tonal Antagonism (MTA) in the First Movement of Op. 132 

The first movement of the String Quartet Op. 132 of Beethoven reveals very strange harmonic and formal traits: it has two recapitulations: the first is a perfect fifth higher than the exposition (i.e., in the dominant), the second (less exact than the first one!) – is in the tonic. (...)

In order to understand why there are two recapitulations in this movement of the quartet, one should pay attention to the subordinate theme first, and after that – to the main theme and all the rest.

The subordinate theme of this movement is in F major, i.e. in VI. Many of the formal problems posed and solved by Beethoven [in his other works] are variants of this one problem: [As a matter of fact,] the subordinate theme in VI represents here not dominant but subdominant.

Second phrase – B.

At the first recapitulation – C.

A second theme in the subdominant can be counterbalanced only by a recapitulationthat changes the harmonic position not only of the subordinate theme but also of the main theme. From this, the need for a second recapitulation follows, which restores everything to rights. The paradox here lies in the fact that the subdominant has protected the tonic from the dominant !102

This is the outline of the analysis presented by Herschkowitz in the less than a page long Part II of the article "Beethoven’s Paradoxes," but the analysis itself is missing.103 Let us expand on it by applying the "firm/loose" opposition and the principles of the MTA. This movement not only has a peculiar key-scheme of the exposition but other curiosities, of which the extreme contrast within and between themes and the very brief development section are mentioned most frequently.

Exposition         Development         Recapitulation I         Recapitulation II

Introduction I 1-8     Intro I 75-79                 #9; Intro II 119-120                #9; Intro I 193-194

Intro II 9-11             #9; Sect. I 79-91                #9; M.T. 121-131                   #9; M.T. 195-214

Main theme 11-22    Sect. II 92-102             #9; Trans. 131-159                #9; Trans. 215-223

Transition 22-48      Intro I 103-106              #9; S.T. 159-177                   #9; S.T. 224-232

Sub. theme 48-62    Retrans. 107-118          Closing 177-188               M.T. 233-253

Closing 62-74          #9; Trans. 188-192                                                   #9; Coda 254-264

Table 1: Beethoven’s Op. 132, first movement: a suggested key/section scheme.

Herschkowitz’s theory of the MTA and the concepts of "firm" and "loose" are helpful in affirming that the unusual key of the secondary theme is closely linked to its period-like structure and the sense of relaxation it brings. According to the theory, subdominant is generally stronger than tonic because tonic alone, without help from its own dominant, could easily be taken for the subdominant’s dominant. The sense of relaxation is owing to precisely this relationship between tonic and subdominant: some amount of energy is always needed to rise into the dominant (say, a transition), whereas "falling into the subdominant" is normally perceived as something natural for a tonic. The sense of relaxation is also due to the "firmer" structure of the secondary theme: it could be perceived as "being in the tonic," whereas the "looser" main theme (in a minor – the region of the dominant of F major) could be "substituted postfactum" for the actual secondary theme of this most peculiar sonata form.104 The reversal of functional roles between the main and the secondary theme provides an interesting case of temporal discontinuity not uncommon in late Beethoven: "the future," as it were, comes here before "the present."

As to the two-recapitulation phenomenon, it is directly related, as Herschkowitz points out, to the key-relationship of the two themes of the exposition. The short development section falls into two subsections, in successively "more" dominant keys (according to Herschkowitz’s scheme of a typical development). While the prevalent key of the first section is g minor (iv/iv), the second moves to the dominant of e minor and ends abruptly on the ff intrusion of the Assai sostenuto "motto"105 as the retransition begins p. The striking harmonic idiosyncrasy of the piece is that the dominant key has not occurred anywhere in the movement up to this point; instead, almost everything before the retransition had a strong subdominant feeling (m. 28ff). According to Herschkowitz’s "material" concept of musical form, in order to restore the tonal balance, the proportion of dominant has to equal the subdominant’s "mass"; thus, in the first recapitulation, both the main and secondary themes are placed in dominant keys (e minor and C major).

As to the brevity of the development, the section’s functional role – to modulate to the subdominant – has already been taken over by an exposition that employed a subdominant key area for the secondary themes; thus it ceases to be of full value here. The first recapitulation, taking over the role of the subordinate theme in the exposition thus acquires, as it were, an additional role of the second – rightful – exposition (note the omitted repeat of the exposition in this sonata form). The return to the tonic, clockwise on the circle of fifths, takes place in the development section with a feverish speed, zigzagging through the dominant and subdominant keys of g, C and a (mm. 75-102).

In comparison to the first, the second recapitulation is considerably varied. The return of the main theme after the subordinate theme in the second recapitulation is puzzling unless one recalls the role-reversal of the two themes in the exposition. It is provocative to assume that the composer wanted everything to fall into place here, since the secondary theme not only confirms the tonic more profoundly but also is followed (for the first and last time) by the main theme’s modest appearance. The traditional "present-future" temporality is thus restored. 106

The peculiarity of this Quartet movement is best explainable in Herschkowitz’s terms: it is the disposition of the Main Tonal Antagonism that is inverted. The typical formula for a Classical sonata form, T DST, is overthrown by Beethoven into its opposite, TSDT, with the subdominant region in the secondary theme, and the dominant region in the first of two recapitulations. This method also helps explain why the main and secondary themes are perceived as somewhat out of place: the tonic key of the main theme, being identified by our ear with the subdominant’s dominant, naturally and effortlessly "slips" into a subdominant key, which causes the prolonged dominant of the first recapitulation.


The "Waldstein" Sonata, Op. 53: The Symmetry of the Cycle

The first movement of this sonata has been already discussed by Herschkowitz as another example of a curious "loose/firm" construction of the exposition.107 Now let us examine the same work for the oddity of the cycle’s construction. Here the short second movement, called "Introduzione," functions in fact as a slow introduction to the final Rondo. The Rondo, in turn, does not fully resemble a typical sonata-rondo finale of Beethoven. It is worth quoting Herschkowitz as to what else besides the unusual title plays a role in linking the last two movements together: "The problem is that there is no subdominant in the first movement and the finale. How can one compose without the subdominant? But it still exists! Have a look at the middle movement. It is not even a movement; it is an introduction: ‘Introduzione’. It is absolutely brilliant."108 This rather mysterious statement is only partially elucidated by the preceding discussion with Dmitri Smirnov. The discussion of the finale that took place on November 9, 1983 provides yet another puzzle (Herschkowitz starts):

-- It is the last Rondo of all Beethoven sonatas (if we exclude the 27th). What is going on here in the main theme? Where does it end?

-- In m. 63. Besides, it’s divided evenly in half in m. 31.

-- Oh! Why bother with this? What form is [the main theme in]? -- Perhaps a period?

-- No, it’s a three-part song. The period here consists of eight measures, then the second part begins: it is very long. The third part begins in m. 32, then the second and third parts are repeated. What does the theme lack?

-- The subdominant.

-- Right. It means that the tonality is not fully established here: it hangs in the air, it soars. As if it was not a water-melon but the skin of a water-melon! In m. 63 the closing theme begins in place of the transition, then a minor is brought in immediately: the first subordinate theme. The second subordinate is in c minor. Then comes the development section. There is no subordinate key here, i.e. no subordinate theme. There is absolutely nothing in here! [I can only guess] how long a coda should be to balance it all.109

Exposition                 Development                 Recapitulation

Main Theme #9; 1-62            Section I 219-250                 Main Theme 314-344

Transition #9; 62-70              Section II 251-286                Transition 344-378

Second Theme I 70-86    Retransition 287-312             Retransition 378-402

Closing 86-98                                                             Coda #9; 403-543

Retransition 98-113

M. T. 114-175

S.T. II 175-218

Table 2:. Beethoven’s Op. 53, Rondo: a suggested key/section scheme.

The overall formal design of the main theme resembles a five-part rondo: ABA’B’A". What follows (mm. 62-70) is a transition to the secondary theme but this transition, interestingly enough, does not modulate into the secondary key of a minor. Instead, it confirms the tonic in the manner of a closing section. As a typical closing, it is represented by an extended perfect cadence (mm. 64-66) which includes IV6/4, the first appearance of the subdominant since the very beginning. As Herschkowitz points out, the main theme consists entirely of alternations between dominant and tonic, occasionally colored by an appearance of c minor in place of C major as another resolution of the dominant seventh-chord (mm. 15, 19, 45, 49 etc.).

Similarly, static harmonic motion is an important feature of the first subordinate theme that arrives by means of juxtaposition of the two relative keys, C major and a minor. The melody of the theme, as in the third part of the main theme, is laid out in octaves.110 Similarly simple is the harmonic layout: mostly tonic-dominant alternations. The dominant is emphasized by sf, in order for E to be kept in mind for eight measures (mm. 71-78). The "real" closing theme firmly establishes a minor, with the ff and sf emphasis on the dominant and tonic alternation. The short retransition to the main theme does not modulate: it again simply juxtaposes a minor with C major (mm. 98-101 and 102-105). The main theme comes back unabridged, followed, without a transition, by the second subordinate theme in c minor. This theme brings in some harmonic acceleration by "wandering around" various degrees of the subdominant minor: c minor, f minor, Ab major (note the octave layout of the melody throughout the entire theme). The dominant-tonic emphasis is nevertheless reestablished beginning from m. 197.

At this point one may conclude that (1) the 176-measure exposition is characterized by the enormous preponderance of dominant over subdominant; (2) all the three themes (the main and the first and second subordinate) have periodic structures, octave delineation of melody, solid dominant-tonic framework – i.e., they are firm; (3) there are no modulations: change of key or mode takes place by simple juxtaposition.

The development adds Db major to the palette of the subdominant-minor colors of the second subordinate theme (mm. 229-240). The dominant retransition leads to the "recapitulation" of the second ABA of the main theme that keeps and prolongs the "transition" from mm. 62-70 as if it were indeed its own closing theme. The long bravura closing (m. 386ff) is in fact a retransition to the two further appearances of the main theme in the prestissimo coda. Thus, the entire movement becomes completely dominated by the main theme, which establishes the rondo idea properly.

If one counts all chords that carry out local dominant function in this movement, one will come up with a number hardly smaller than one hundred. As opposed to that, the total number of the local appearances of a subdominant major chord is only about a dozen (mm. 63-64, 67-68, 78-80, 82-84, 102-104, 257, 345-346, 349-350, 353-354, 428-30 etc.). The incomparable difference between the dominant and subdominant "masses" in the Rondo led Herschkowitz to characterize the origin of the F-major Introduzione as a compensation for the lack of the subdominant in the last movement of the sonata. This does not explain, however, the following confession made by Herschkowitz at his next meeting with Smirnov (December 30, 1983):

-- Do you remember my saying this is a rondo-sonata? I was mistaken then: this is a sonata [form]. I told you that the first subordinate theme was in a minor, the second in c minor. But it is the same theme, only here. . . Here we have a written-out repeat [of the exposition]. But the repeat is varied!111

Paradoxically, a pianistic innovation – the use of the long-held damper pedal that Beethoven insisted on in the main theme of the Rondo112 – provides us with a clue as to why Herschkowitz calls this movement a "sonata form with a written-out repeat." As Denis Matthew pointed out,

This theme, which cost Beethoven much pain in the making . . ., is anchored to a deep pedal-note. It is important to keep this note sounding, even on a modern piano and at the risk of blurring the harmonies: the whole point of the passage is its mistiness, and full daylight does not arrive until the first fortissimo, which may have given the sonata its earlier nickname, ‘L’Aurore’.113

The long pedal holds the two opposites, tonic and dominant, tightly together, both preventing the affirming victory of either one and imparting the atmosphere of "rarefied mountain air" (Eric Blom) on the Rondo theme. 114

In any major key, three cadences from the dominant-seventh are traditionally possible: V-I, V-vi and V-i, i.e. the dominant seventh-chord on G can be resolved into a C-major, a-minor or c-minor triad. The fact that the two subdominant themes are not preceded by a modulation signifies that they play an even more modest role here. Instead of providing the MTA by indulging in the keys of dominant and subdominant, the two "subordinate" themes of this Rondo seem to be nothing else than two equally possible resolutions of the all-prevalent dominant in the main theme.

Actually, it is quite doubtful whether we deal here with a sonata or rondo-sonata form. The overall design is ABAC(dev)A+coda; i.e. neither of the two subordinate themes appears in the main key in the recapitulation; instead, the prolonged "transition" takes over the functional role of the subordinate theme there. However, establishing the correct form is secondary to establishing the correct key scheme. The role of the brief Introduzione thus grows into a more functionally important one. Speaking in the terms of Herschkowitz, it provides the main proportion of subdominant not only for the last two movements but also for the entire cycle.

The "Adagio molto" differs in the following three aspects from the ensuing Rondo movement: (1) Distant harmonies appear by means of enharmonic pivot chords, not by juxtaposition (consider the tritones in mm. 1, 3, 5, 6); (2) Sequences play an important role in the relationship of the two-measure motives (mm. 1-6); (3) The tripartite ABA form of the Introduzione includes a "firmer" middle section ("the theme," mm. 9-16) in between the two "looser" outer sections.

All these features speak for establishing a movement-level opposition of "firm" and "loose" structures in the cyclic work. The reason for calling the entire Introduzione "loose" is verified by its being a functionally important section of the Rondo, written separately. As a loose section, it is the embodiment of the subdominant key area. The provisional departure from the main key into the subdominant in the second movement is needed here in order to clarify the key of the future movement and thus the entire sonata. However, the looseness of the entire movement as a part of the cycle does not necessarily makes the Adagio loose at all levels. The firm B section stands out in the middle with its sentence-like structure: a two-measure motive is paired with its dominant repetition (mm. 9-13), followed by fragmentation and liquidation (mm. 14-16). The temporary tonic F is not obscured by the surrounding ambiguities: two perfect cadences (mm. 8-9 and 16-17) conclude both sections A and B. In both cases (a link with the Rondo’s key scheme?), the cadence is preceded by a deceptive resolution of V7 into vi.

The "loose-firm-loose" structure of the Adagio places the key of subdominant at the very heart of the entire sonata cycle, creating a remarkable symmetry. As Charles Rosen has pointed out, the sonata’s first movement is also characterized by an emphasis on tonic-dominant relationship from the very start:

In each phrase of the themes, every second chord is a dominant seventh. . .The dominant seventh is the plainest, the most neutral of dissonances; its relentless alternation in scale progression with pure triads invests this movement with its particular sonority and invades every phrase. 115

The first movement makes use of both c-minor and a-minor harmonies as early as the main theme (mm. 9-13, 20-21 respectively). F major does not appear until the beginning of the development section (mm. 86-91), which explores the region of subdominant minor keys, "correspondingly" to the second subordinate theme of the Rondo (mm. 97-111). "New keys, however, may unlock familiar doors, and when c minor is reached in this context [of the development] the significance is realized – its dominant can resolve equally well into the home key of C major [m. 136ff]."116 Alternating between F major and f minor takes place in the closing theme in the recapitulation (m. 235ff), directly preceding the coda, which presents the main theme in Db major – "symmetrically" to the development of the Rondo (m. 249ff).

The three analyses presented here are just three of numerous ways in which "firm" and "loose" can interact at all levels of a piece of music, including micro- (between phrases of a theme), infra- (between themes in a movement) and macrolevels (between movements in a cyclic work). As has been demonstrated, the attribution of any structural element to either "firm" or "loose" structure depends significantly on where this element belongs in the MTA. In addition, the length and the degree of firm and loose of any formal unit belonging to one side of the MTA can determine the length and the degree of firm and loose in the corresponding structural element on the other side of it (as, for example, the exposition and the two recapitulations in Op. 132). Furthermore, the harmonic and structural status of a primary element may determine the key and structure of not only the following secondary elements (as in Op. 14, No. 1, and Op. 132) but the preceding ones as well (as in Op. 53). Such "abnormalities" function according to the same principles as the norm because Beethoven does not cease to be a tonal composer even in his boldest and most puzzling works. Thus, tonal harmony appears to be the guarantor of comprehensibility of any unconventional key-scheme or formal design of the period: "In every piece of music, harmony has a different future, a different mode of realization; and form is not a cliché but a ‘realiser’ of the harmonic future of the work, pre-determined by its main theme." 117

Lengthy analysis, often required to relate such irregularities to the theoretical postulates of Herschkowitz, may reveal certain weak spots but does not disprove the theory itself. According to it, ways in which "firm" and "loose" can be combined are many; the road to tonic is only one. Herschkowitz "obeyed" the rules imposed by his teachers not because he was unable to substantiate them (in fact, we saw the opposite) or was too faithful to question their reliability. These rules were not a product of unrelated abstract philosophizing; they came as a result of thorough study of the early Beethoven by Schoenberg, Berg, and Webern. Beethoven’s path was to "disobey" the rules imposed by his teachers. However, this disobedience was, in its own way, keeping to the path. By keeping to the path laid out by his own teachers, Philip Herschkowitz was able to explain much of what had remained unexplained before him.


1 mlupishko@utoronto.ca

2 Filip Gershkovich, O Muzyke: Stat’i, Zametki, Pis’ma, Vospominaniya (On music: articles, notes, letters, reminiscences), ed. L. Gofman and A. Vustin (Moscow: Sovetski kompozitor, 1991). The existence and content of volumes two and three was unknown to the author of the present publication in 1997, when this paper was being written. "Gershkovich," a Russian transliteration, is used here in the footnotes to refer to the Russian-language materials on or by Herschkowitz. See also: Detlef Gojowy, "Gershkovich, Filip," The New Grove Dictionary of Music and Musicians, ed. Stanley Sadie (London: Macmillan, 1980), 7: 301-302.

3 Dmitri Smirnov, "A Visitor from an Unknown Planet: Music in the Eyes of Filipp Herschkowitz," Tempo 173 (June 1990): 34-38; also in the same volume: "Herschkowitz Encountered," Tempo 173 (June 1990): 39-43; and Dmitri Smirnov, "Geometr Zvukovykh Kristallov," Sovetskaya Muzyka 3 (March 1990): 74-81, and 4 (April 1990): 84-93. See also, Dmitri Smirnov, "Iz ‘Knigi o Gershkoviche,’" Moskovski Muzykoved 1 (1990): 112-138. The first English translation, two and a half pages long, from Herschkowitz’s book was published in 1994: Ghuzal Badamshina, tr., "Filipp Herschkowitz: Mahler and Memories of War," Tempo 190 (September 1994): 23-25.

4 Philip Herschkowitz, Über Musik (viertes Buch), ed. Lena Herschkowitz and Klaus Linder (Wien: Mechitaristen Druckei, 1997). See also, Yuri Kholopov, "Philip Gershkovich’s Search for the Lost Essence of Music," Underground Music from the Former USSR, ed. V. Tsenova, tr. P. Kohanovskaya (Amsterdam: Harwood Academic, 1997): 21-35. Also, Klaus Linder, "Philip Herschkowitz," Schüler der Wiener Schule: Ein Programmbuch des Wiener Konzerthauses im Rahmen der HÖRGÄNGE 1995: 80-85.

5 The data are taken from two sources: Smirnov’s Tempo 1990 article and Herschkowitz’s life chronology compiled by Leonid Gofman: O Muzyke, 11.

6 Smirnov, "A Visitor," 34.

7 As Leonid Gofman puts it (O Muzyke, 6): "Destiny was as kind to Herschkowitz’s hanging-by-a-thread life as it was merciless to the untimely deceased Berg and Webern. In Austria, such a thread was his Romanian passport, which served as a safe-conduct, preventing a foreign citizen from being sent to a gas chamber. In one year, the Molotov-Ribbentrop pact gave Herschkowitz a sudden chance to get over to Chernovtsy, which then seemed a safer place. The beginning of the war with the USSR drove him across the country farther and farther East."

8 Smirnov, "A Visitor," 35. Says Victor Suslin in the same issue: "His influence on new Russian music was immense ... because it was thanks to him that a number of Moscow composers received, as it were, a thread which led back directly to Webern, to Schoenberg, and to Berg." 39.

9 Gofman (intr. to O Muzyke), 7.

10 Filip Gershkovich, "About One Invention of J. S. Bach," and "Tonal Sources of Schoenberg’s Dodecaphony," Tartu Scholarly Notes. Studies in Semiotics 6, no. 308 (Tartu, 1973): 344-379.

See also, Filipp Herschkowitz, "Some Thoughts on Lulu," International Alban Berg Society Newsletter 7 (Fall 1978): 11.

11 Herschkowitz’s Four Songs to Poems of P. Celan are listed among vocal chamber works by Prokofiev, Berg, and Stravinsky in a program to a concert given by Lydia Davydova (soprano) and Edison Denisov (piano) in 1966: see Yuri Kholopov and Valeria Tsenova, Edison Denisov (Moscow: Sovetski kompozitor, 1993), insert.

12 So far there is no evidence of it, at least.

13 There is a single reference to this book, in the beginning of the essay "Webern and His Theory of Form": O Muzyke, 60.

14 O Muzyke, 158 (footnote).

15 See Gofman, 8. See also Smirnov, "Geometr," 90.

16 O Muzyke, 63.

17 Anton Webern, The Path to the New Music, ed. Willi Reich (Bryn Mawr, Pa: Theodore Presser Company, in assoc. with Universal Edition, 1963).

18 Arnold Schoenberg, Fundamentals of Musical Composition, ed. Gerald Strang (New York: St. Martin’s Press, 1967).

19 Arnold Schoenberg, Structural Functions of Harmony, ed. Leonard Stein (New York: W.W. Norton & Company, Inc., 1969).

20 Arnold Schoenberg, Coherence, Counterpoint, Instrumentation, Instruction on Form, ed. and intr. Severine Neff, tr. Ch. M. Cross and S. Neff (Lincoln and London: University of Nebraska Press, 1994).

21 Arnold Schoenberg, The Musical Idea and Logic, Technique and Art of Its Presentation, ed. and tr. Patricia Carpenter and Severine Neff (New York: Columbia University Press, 1994).

22 O Muzyke, 61.

23 Ibid.

24 O Muzyke, 63. Cf. Schoenberg: "The form of a composition is achieved because (1) the body exists, and because (2) the members exercise different functions and are created for these functions." (The Musical Idea, 44). The concepts "firm" ("bones") and "loose" ("joints") will be examined in every detail below.

25 "Coherence is based on repetitions." (Schoenberg, Coherence, 9.)

26 O Muzyke, 64. Cf. Schoenberg: "Since the motive turns out to be the smallest part (smallest common denominator) of a piece of music, in general the presence of this smallest part in every larger part may guarantee that comprehensibility will be achieved." (Coherence, 26).

27 O Muzyke, 64.

28 Ibid.

29 All musical examples are taken from Beethoven’s piano sonatas, unless otherwise specified.

30 O Muzyke, 65-66. No description of motivic and thematic types of repetition is found in Webern’s book. In Schoenberg: "A motive can be repeated in the following ways: 1. Exactly: 1) a) starting from the same tone; b) starting from a different tone (transposition); c) with identical intervals; d) with almost the same intervals; e) with changed intervals (dur, moll). 2) a) in the same rhythm; b) in augmentation; c) in diminution; d) in altered rhythm (ornaments etc.). 2. Not exactly ..." (Coherence, 37. Italics added.).

31 O Muzyke, 68.

32 Schoenberg, Fundamentals, 25. Schoenberg uses the term "practice form" throughout this book to indicate a "formal model" (an abstracted "norm") of a period.

33 Smirnov, "Geometr," 76.

34 O Muzyke, 68.

35 Ibid. For Schoenberg, this opposition is not a necessary pre-condition for a normative period, although he agrees that "in a great majority of cases the antecedent ends on V, usually approached through a half or full cadence." (Fundamentals, 25).

36 O Muzyke, 71.

37 O Muzyke, 45-60.

38 Satz, the product of German terminology derived from grammar and rhetoric, dates back to H. C. Koch (1749-1816). The idiom "eight-bar sentence" is used by Webern’s translator: "Unlike the period, this isn’t a four-bar structure¼but one of only two bars, immediately repeated" (The Path, 27). Schoenberg: "An immediate repetition [of the two bars] is a simple solution, and is characteristic of the sentence structure" (Fundamentals, 21).

39 "Liquidation consists in gradually eliminating characteristic features, until only uncharacteristic ones remain, which no longer demand a continuation ¼Reduction may be accomplished by merely omitting a part of the model. Condensation implies compressing the content of the model, whereby even the order of the features may be somewhat changed." (Fundamentals, 58-9).

40 Smirnov, "Geometr," 77.

41 Cf: "It is characteristic of a sentence to contain, in certain conditions, a repeated fragmentation." Leonid Gofman, "Glavnaya Tema Pervoi Chasti Pyatoi Fortepiannoi Sonaty Betkhovena" (The main theme of the first movement of the Fifth Piano Sonata by Beethoven), Muzykal’naya Akademia 3 (March 1994): 23-25. Among the examples, he lists the main themes of the Violin Sonata Op. 23 and the object of his analysis, the main theme of the Piano Sonata Op. 10, No. 1.

42 Smirnov, "Geometr," 78. See also Op. 2, No. 1 where fragmentation is carried out by means of repetition of the second ("strong") bar of the principal two-bar motive.

43 This term was first proposed by A. B. Marx (1795-1866) who tried to reduce all existing formal models to "two fundamental patterns: AB and ABA, subsumed in German terminology under the single term Liedform¼in its ‘two-part’ (zweiteiliges) and ‘three-part’ (dreiteiliges) form." (Ian D. Bent, "Analysis," The New Grove 1: 374).

44 Smirnov, "Geometr," 78.

45 O Muzyke, 49. Both Schoenberg and Webern recognize period and eight-bar sentence as two structures that normally articulate "a complete musical idea or theme" (Schoenberg, Fundamentals, 20). Three-part song does not appear in this group but is treated as a next (higher) level of formal organization (Fundamentals, ch. XIII). Erwin Ratz includes three-part song in his classification of the "firm" and uses the expression "standing on the dominant": see William E. Caplin, "The ‘Expanded Cadential Progression’: a Category for the Analysis of Classical Form," Journal of Musicological Research 7/2-3 (1987): 215-57; 216. See also, Erwin Ratz, Einführung in die musikalische Formenlehre, 3rd enl. ed. (Vienna: Universal Edition, 1973).

46 Smirnov, "Geometr," 78.

47 Smirnov, "Geometr," 79.

48 Webern, The Path, 58.

49 Schoenberg, The Musical Idea, 118.

50 Schoenberg, Fundamentals, 184. See also Ibid, 204.

51 The word "structure" in this particular case refers not only to the outer (formal) but also to the inner (motivic, textural) organization of a theme. The word "theme" is used in Schoenberg’s sense to designate of course, the entire harmonic-melodic complex, not a mere melody or tune.

52 O Muzyke, 199.

53 Smirnov, "Geometr," 87.

54 Note that for Herschkowitz this is "motivic" repetition in the sense that Webern imposed on his students, i.e. repetition of rhythm regardless of exact pitches.

55 O Muzyke, 199. Cf: "As for the looser organization of the subordinate theme, [Ratz] discusses two ways in which this can be achieved: through a modulating tonal structure and through a chain-like succession of phrases." (Caplin, "Expanded Cadential," 216).

56 Cf. Ratz’s "first and second parts of a standard elaboration," with the third part being "the pedal point on the dominant." Erwin Ratz, "Analysis and Hermeneutics, and Their Significance for the Interpretation of Beethoven," tr. Mary Whittall, Music Analysis 3:3 (October 1984): 243-254; 245. See the development of the "Waldstein" Sonata: the first section (mm. 88-111) is led sequentially through different degrees of the subdominant (F major, g minor, c minor, f minor, bb minor etc.), whereas the second section (mm. 112-156), with a different sequential pattern, is mainly (m. 126ff) dominant preparation of the recapitulation.

57 O Muzyke, 13-45.

58 O Muzyke, 14.

59 O Muzyke, 17.

60 The Ionian and Aeolian modes introduced in the fifteenth century added two "new tonics," c and a. Webern, in The Path to the New Music, explains that the major and minor modes became prevalent because the tonic-dominant relationship was the most evident in them: "The need for a cadence was what led to the preference for these two modes, the need for the leading-note that was missing in the other modes." (28).

61 O Muzyke, 18.

62 Ibid.

63 The "strength of the subdominant" (the ability to move away from the tonic) has nothing to do with the way we perceive, for example, the plagal cadence (IV-I), a weaker one, as compared to the more decisive perfect cadence (V-I). For Schoenberg and Herschkowitz, the subdominant represents a centrifugal force within a tonality: it provokes the move away from the home key counterclockwise on the circle of fifths.

64 O Muzyke, 18. See the editors’ preface to The Musical Idea: "[Schoenberg] explains the basic I-IV-V-I cadence¼in terms of conflicting forces: a statement, challenge, contradiction and conformation. The statement of the IV after a I not only functions in the tonic but also has the potential to act as a challenger, to become of tonic on its own. The introduction of V¼, however, contradicts any power play of IV and instead confirms the tonic." (62). The influence of Hugo Riemann’s functional theory with its Hegelian premise of "thesis-antithesis-synthesis" on Schoenberg is covered in: David W. Bernstein, "Schoenberg Contra Riemann: Stufen, Regions, Verwandtschaft, and the Theory of Tonal Function," Theoria 6 (1992): 23-53. The role Riemann’s ideas played in Herschkowitz’s musical upbringing is still to be established.

65 O Muzyke, 18-19. Cf. Adorno: "‘material theory of form in music’ [materiale Formenlehre der Musik]: that is, the concrete categories like statement ..., continuation ..., contrast ..., and however such categories may otherwise be labeled." Theodor W. Adorno, "On the Problem of Musical Analysis," Music Analysis 1:2 (1982): 169-187; 185. Both Herschkowitz and Adorno were Berg’s students.

66 O Muzyke, 19. Exclamation in original.

67 A discussion of Herschkowitz’s use of analogies from physics, mathematics, astronomy, geometry etc. could make up a separate chapter in this study.

68 Ibid.

69 O Muzyke, 21.

70 O Muzyke, 20.

71 See chapter VI, VII, and VIII of Webern’s The Path, 27-41; and Arnold Schoenberg, Theory of Harmony (Harmonielehre), tr. Robert D. W. Adams (New York: Philosophical Library, Inc., 1948), 123ff, 175ff, 192ff. See also: Structural Functions of Harmony, 15-29, 44-56.

72 O Muzyke, 24. "Artificial dominant" is the term Schoenberg uses in Structural Functions. In his Theory of Harmony, "secondary dominants" are viewed to arise from accidentals in church modes (Theory of Harmony, 123).

73 O Muzyke, 24. Cf. Webern: "dominants were produced on each degree of the scale – so-called ‘inter-dominants.’ ¼From there one ranged ever farther abroad, until the new accidentals came to predominate, ¼as one tried to end in an ever more complex way, at the cadence." (The Path, 29).

74 O Muzyke, 29. Schoenberg relates this process to the similarly equivocal resolution of the dominant into both major and parallel-minor tonic triads: Theory of Harmony, 171.

75 Cf. Schoenberg: "It is important to remember the derivation of these chords: from the region of the minor sub-dominant. They stand therefore in sharpest contrast to the secondary dominants, which belong mainly to the region of the dominant ..." (Theory of Harmony, 175).

76 See the chart of the regions in major in Structural Functions, 20.

77 O Muzyke, 35. According to Webern, the third stage of the destruction of tonality also took place in cadences: "The very end of a piece – the "cadence" – came to contain a number of chords that by their nature couldn’t be clearly related to one single key. Wandering, ambiguous chords appeared." (The Path, 28).

78 O Muzyke, 40.

79 Webern, The Path, 39.

80 William Caplin, who extensively explored the essence and interconnections of the first two types of firm structure, does not stress the harmonic opposition of the two-measure motive and its repetition in a sentence: "The first phrase, a presentation, opens with a two-measure basic idea. This idea is then immediately repeated in a way that prolongs the initial tonic harmony of the theme and thereby deprives the phrase of cadential closure." William E. Caplin, "Hybrid Themes: Toward a Refinement in the Classification of Classical Theme Types," Beethoven Forum 3 (1994): 151-165; 153.

81 O Muzyke, 202.

82 O Muzyke, 20.

83 Smirnov, "Geometr," 75.

84 O Muzyke, 204.

85 "The period was the most important concept adapted by music from traditional rhetoric." Leonard G. Ratner, Classic Music: Expression, Form, and Style (New York: Schirmer Books, 1980), 33.

86 O Muzyke, 68.

87 See Ratner, Classic Music, 34.

88 H. C. Koch was among the first who acknowledged the expanded form of a subordinate theme and listed the techniques of the expansion: Leonard G. Ratner, "Eighteenth-century Theories of Musical Period Structure," Musical Quarterly 42 (1956), 451.

89 The ways in which "firm" and "loose" interact on higher levels of musical form will be examined in chapter II.

90 Smirnov, "Geometr," 76.

91 Ratner, Classic Music, 233.

92 O Muzyke, 159.

93 Gofman (intr. to O Muzyke), 7.

94 O Muzyke, 140.

95 O Muzyke, 20.

96 Gofman (intr. to O Muzyke), 7.

97 O Muzyke, 72.

98 Ibid.

99 O Muzyke, 72-3. The purposefulness and impetuosity with which the first phrase achieves the dominant seventh-chord in m. 4 makes it, as it were, an upbeat to the two closing gestures: "It is beyond doubt that the anacrusis-like nature of the first phrase and the preponderance of dominant in it determine each other." (Ibid). The sixteenth-note passage is a rhythmic diminution of the triplet passage: there are sixteen quarter-notes in the first phrase and sixteen sixteenth-notes in the second. Moreover, the triplet "anacrusis" in the bass part is counterbalanced by the sixteenth-note anacruses placed in the top voice.

100 Ibid. The absence of multiple repetitions of a single pitch in mm. 5-9 makes it possible to imagine eliminating eight quarter-notes (two E’s and six A’s) from the first phrase in order to focus on the motives. The dotted-note motive in the first half of m. 2 comes twice diminished on the last beat of m. 5 on the same pitches (f#, g#). Correspondingly, the head motive (upbeat plus half-note), shortened by one quarter from the front, comes back on the downbeat of m. 5, bringing along sf accentuation of the second beat of the measure.

101 O Muzyke, 75.

102 O Muzyke, 163. The letters B and C refer successively to the Bb major of the second phrase of the subordinate theme (m. 53) and the C-major key of the same theme in the first recapitulation.

103 O Muzyke, 162-164. Such excerpts of lesser or greater length make up much of the volume O Muzyke. Unfortunately, the book contains a very small number of finished articles – which probably means that Herschkowitz never completed the preparation of his works for publication.

104 In the course of the present study, a confirmation of this hypothesis was found in Herschkowitz: "When a Beethovenian subordinate theme is in a subdominant key, the main theme modulates and becomes ‘loose,’ as, for example, in the L’Aurore ["Waldstein"] or the second movement of [Op. 10, No. 3]." (Smirnov, "Geometr," 85-86). In the first movement of the "Waldstein" sonata, however, the secondary theme is in the mediant major (III), a dominant even stronger than V. There is something in the main theme which helps understand the unusual key of the second theme: IV/IV in m. 5. Such a far-reaching subdominant (normally an attribute of the development) in the first theme needs a strong dominant counterpart and a "firmer" formal organization of the second. In the Largo e mesto of Op. 10, No. 3 briefly discussed above in connection with the Rondo of the same cycle, the "subordinate theme" is in the relative major), and is articulated with a double-bar (m. 30) to separate it from the preceding "main theme" which modulates into the dominant key in the third section of its "vague three-part song structure" (mm. 17-29). Herschkowitz insists on calling the entire form a small rondo, not a sonata ("Geometr," 80).

105 See the discussion of how the "motto" formula g#-a-f-e underlies the entire motivic material of not only this movement but also the first movement of Op. 130 and the "Grosse Fugue," Op. 133, in: Daniel K.L. Chua, The ‘Galitzin’ Quartets of Beethoven, Opp. 127, 132, 130 (Princeton: Princeton University Press, 1995), 54-106, 201-244.

106 See the discussion of this phenomenon in: David B. Greene, Temporal Processes in Beethoven’s Music (New York: Gordon and Breach, 1982) and Sylvia Imeson, "The Time Gives It Proof": Paradox in the Late Music of Beethoven (New York: Peter Lang Publishing, Inc., 1996).

107 See my footnote 102.

108 Smirnov, "Geometr," 89. The date of this meeting is December 30, 1983. Here we are again possibly dealing with a misquotation: the development section of the first movement of Op. 53 is almost entirely subdominant and even is referred to as a "typical development" by Herschkowitz on the same page (see my footnote 55).

109 Smirnov, "Geometr," 88.

110 See Herschkowitz’s discussion of the first movement of Mozart’s Piano Sonata K. 576: "What do we see in the subordinate theme of the first movement? A canon with an eighth-note interval. In the development, there is a similar canon – with a one-measure, then a half-measure interval. And what do we see in the recapitulation? A ‘zero’ canon, the same one as in the beginning of the exposition. The subordinate theme here means – ‘broken down’ octaves. It suggests that Mozart puts octaves in connection with the main key – this is why there are no octaves in Schoenberg!" (Smirnov, "Geometr," 90).

111 Smirnov, "Geometr," 89.

112 See Kenneth Drake, The Beethoven Sonatas and the Creative Experience (Bloomington & Indianapolis: Indiana University Press, 1994): "Beethoven’s pedal indications in the Rondo have been explained as the result of the lesser sonority of his piano, the presence of a split damper pedal, and the composer’s deafness. Czerny comments, however, that¼ ‘the effect of the Rondo is entirely calculated upon the use of the pedal, which, it is evident, is intrinsic here to the music.’" (153).

113 Denis Matthews, Beethoven Piano Sonatas (Seattle: University of Washington Press, 1967), 35.

Cf. Drake: "Through Beethoven’s pedal the whole achieves a floating effect, particularly since one must play as lightly as possible¼ Most important, the blurring of tonic and dominant stacks the melody notes and harmonies on top of each other, so that the music stands still. In fact, the great advantage of the short, improvisatory Introduzione over the F-major Andante [favori WoO 57] is that the piece thereby moves from a state of tranquility to one of immobility." (153).

114 According to Herschkowitz’s teaching, harmonic motion which includes only the dominant-tonic relationship is somewhat ambiguous; to establish the tonic firmly, the subdominant is needed to balance the dominant.

115 Charles Rosen, The Classical Style: Haydn, Mozart, Beethoven (N.Y.: W.W. Norton & Company, Inc., 1972), 397. Rosen illustrates his statements with the following mm.: 1-13, 35-38, 50-51, 74-78.

116 Matthews, 35.

117 O Muzyke, 164.

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