The research by professor O.N. Greenbaum

The research by the Doctor of Philology, professor of Saint-Petersburg State University Oleg Natanovich Greenbaum concerns the study of nature and matter of Russian classical verse. The question under investigation is the unity of form and contents of a poetic text, the treatment of which is impossible without the notion of 'rhythm' within the framework of the phenomenological trinity 'form-rhythm-contents' of a verse.

The nature and matter of the poetic text go back to its common essential aesthetic origin. It would seem that this question does not allow any alternative or polar opinions. However, the fundamental principles of poetic study have been a subject of much controversy for over 100 years. These heated debates possess at times somewhat destructive power for science. One can recall the vehement polemics of 10-20ies of the XXth century between A. Belyj and V.M. Zhirmunsky, the strongly different opinions of M.L. Gasparov and V.E. Holshevnikov on the question of the syllabic-tonic system of Russian verse (70-80ies), or the recent argument concerning the subject of "meter and meaning" between M.L. Gasparov and B.P. Goncharov.

The XXth century progress in mathematics, physics and other sciences could not but influence linguistics, putting forward the principle of morphological description and classification of linguistic phenomena. The rapid development of computer engineering based on the well-known principle of a binary calculation system caused structuralism to gain new energy; the scientific discussions of the 60-ies seemed to bring "artificial intellect" to life; the growing potential of intellectual computer programs (chess, for instance) created the illusion of formal methods having endless possibilities and efficiency in varied spheres of the humanities. The computer programmes designed to write (or, to be more precise, to calculate) verses were supposed to demonstrate the victory of logic over feelings. In short, the history of attempts to study the form of a phenomena without considering its contents can be regarded as a negative, but nevertheless valuable experience.

Our work is directly connected with the discussion of the nature of Russian classical verse, which has been going on for over 100 years and has triggered controversial opinions and points of view on both aesthetic and morphological trends and ideas concerning art, speech and text as a source of linguistic norm.

The change of the scientific paradigm is thought to be essential within the purpose of returning to the immanent, aesthetically significant nature of the poetic text, i.e. the transition to methodology, based on the fundamental principles of philosophic-phenomenological and aesthetic formal knowledge. The transition to this method has two major purposes: accumulating in a solid system the experience of the previous generations of poetry researchers belonging to both traditional and structural trends and acquiring a new instrument for practical study of the Russian verse matter.

The principle of artistic images self-limited development and the aesthetic formal method of the Russian classical verse study were formulated, developed and tested by O. Greenbaum in the book "The Harmony of Strophic Rhythm in Aesthetic Formal Measurement" (2000). In the book the following questions are treated:

  • fundamental philosophical and artistic categories (motion, rest, rhythm, form, contents, harmony, measure) in the aspect of their subsidiarity and correlation;
  • the applicability of "The Golden Section" law and Fibonacci dynamic series to the Russian classical verse;
  • the questions of correlation and use of the golden proportion and Fibonacci series for describing the processes underlying the formation of different strophe types, and also for assessing the degree of their stability and harmonicity, which started rhythmical-harmonical typology of the Russian classical verse strophe;
  • rhythmical-harmonical and rhythmical-syntactical characteristics of the Onegin strophe and the Russian classical sonnet and their correlation with the contents of the verse in the works by different authors.

The book mentioned was granted the diploma of the best scientific work at Saint-Petersburg State University Philological Contest. The author's interests centred around the study of rhythmics on the word level of the poetic text. The main conclusions are as follows:

Harmony is a conceivable substance of an aesthetic object, and measure is its material substance. Measure is thus a form of harmony and harmony is contents or aesthetically realised measure. Rhythm is a common and specific notion, being connected to the very essence of the creative work and perception of a work of art; rhythm is an aesthetically significant motion of poetic thought, organised according to the laws of harmony. Rhythm creates harmony and it is 'an aesthetically realised form' (B.V. Tomashevsky). Harmony cannot be measured, but it is possible to discover and investigate the structural principle underlying an aesthetic object which determines the very existence of the object. This principle is "The Golden Section" law or Divine proportion. In other words, the motion of a poetic thought is realised in rhythm, and rhythm makes harmony perceptible and organises the development of the poetic thought in a strophe according to the law of "the Golden Section."

The method of rhythmical-harmonical precision includes two premises, which follow from general theoretical postulates. The principle of "The Golden Section" is considered not in its formal aspect, but as one of the basic factors for the self-development of poetic thought, and the measure of such self-development is not a line of poetic text, but a strophe. Rhythmical-harmonical precision (RHP) of a verse is determined by the ratio of its three constituents: the syllabic volume of the strophe S, the number of unstressed syllables in it B, and the number of stressed syllables (tonic volume of the strophe) T. The syllabic volume predetermines the unity of the strophe, and the number of stressed and unstressed syllables determines its rhythmical variation. This rule was sensed by many researchers, B.V. Tomashevsky, for example "The numbers must be perceived as quality. Some strict laws of speech rhythm were realised in Pushkin's poems to utmost perfection."

Applied to poetry, "the golden proportion" of rhythm allows us to compare the real rhythmical harmonical parameters of the text with the unit level of RHP t = 1, which was established as a result of the strophic rhythm analysis of the sample text of Russian poetry - Pushkin's novel "Eugene Onegin". Compositionally the rhythmical "Golden Section" is calculated according to three syllabo-tonic parameters of the verse, namely: the total number of syllables in the strophe S ("the whole"), the number of the unstressed syllables B ("the greater") and the number of the stressed syllables T ("the lesser"): t = 0,087 / ( S / B - B / T ), where the coefficient 0,087 correlates to the unit level of RHP t = 1. It should be mentioned that the method of searching for narration structural-semantic centres, introduced by E.K. Rosenov, is based on a different principle. Here it is a line of the poetic text which is used as a unit of calculation, and the structural harmony of the work is linked to the closeness of its parts sizes to the proportion of "the Golden Section", which is formally determined by dividing the total number of lines in the text into the coefficient of 'the Golden Section" a = 1,618.

The compositional-rhythmical "Golden Section" most brightly reveals itself in the novel "Eugene Onegin", and it is different in works by other poets. This means that a) "the Onegin strophe" as a structural-dynamic unity possesses the potential, realised in the historical motion of the genre, and the novel by Pushkin is a sample of such kind of works; b) different character of the poetic thought motion determines the appearance of different quantitative and qualitative values of "the golden proportion".

The study of the Russian classical sonnet allowed to make the conclusion that the Russian classical sonnet as a specific lyrical-philosophical poetic form reveals a different rhythmical (when compared with the "the Onegin strophe") and structural?tonic kind of "the Golden Section", which fully agrees with the philosophical credo of the sonnet and its three-piece structure. This kind of "the Golden Section" is based on the ratio of tonic volumes of quatrains and tercets; and the very measurement of the sonnet texts RHP on the basis of empirically established accent potential difference of quatrains and tercets, as well as the ultra-stability of the data received allow to view "the Golden Proportion" as an immanent structural-tonic factor of the Russian classical sonnet organisation.

Our data prove the well-known conclusions about the resemblance between the Onegin strophe and the Russian classical sonnet from a different point of view. Our data also support the idea that rhythmical-harmonical parameters of RHP have the power of a differential feature, capable of serving as one of the style defining parameters along with structural, rhyming and semantic characteristics.

The research following the book mentioned also contained a new theoretical postulate, linking together the questions of RHP of the poetic text and rhythmical perception of the verse. This postulate states the law, known in psycholinguistics as the law of Weber-Fehner, which is used for the transition from the rhythmical harmonical characteristics of the verse to psycho-physiological evaluation of its perception. The law of Weber-Fehner establishes the logarithmic dependence between the force of the external action and the intensity of human sensations caused by this action. By taking a logarithm of the dynamic values of RHP t in every nodal point of the verse, we get a O(t) ("rhythmical sensation"), which describes and characterises the process of rhythmical dynamical sensations when the text is being read. Thus the parameter O(t) allows us to consider the results obtained to be an indicator of psycho-physiological processes of verse perception. Having studied the behaviour of O(t) parameter in the works written with the Onegin strophe - those by Pushkin, Baratynskiy, Lermontov etc.- we came to the following interpretation of the character of the established dependencies: harmonical change of the external irritant force predetermines a uniform increase of the efforts, minimising the human attempts to perceive the poetic text. The principle of interaction, allowing readers to receive maximal effect at minimal resource consumption is called 'the maximum information principle' (K.B. Sokolov) or 'the information resonance principle' in art criticism and 'the resonance isomorphism principle' in the natural sciences (I.P. Shmelev). The mathematical formula of these principles is "the Golden Section" law. Thus, the circle of investigation is exclusive. If you take into account the epithets given by researches of Pushkin's poetry (A. Belyj, V.M. Zhirmunsky, B.V. Tomashevsky, V.V. Nabokov etc.). to his verse - "light", "airy", "divine", it turns out that there is not only a way of subjective, emotional assessment, but also a way of real physical evaluation of Pushkin's phenomenon.

It should be pointed out that the comparative data on RHP parameters and rhythm flow, as well as the sentence length do not characterise Pushkin's, Lermontov's, Baratynskiy's or others verse, but only bring into correlation a single type of poetic art - the Onegin strophe. On the other side, Pushkin's novel is the top of Russian poetic perfection. In our opinion this text should be a reference not only for qualitative but also for quantitative comparison. Our data - the results of accurately documented measurement procedures - permit us to speak of Pushkin's connections with Lermontov and Baratynskiy. Firstly, these facts allow us to evaluate qualitative-quantitative characteristics of the poets' skill. Secondly, one can count on receiving new knowledge, based on the idea of unity of the fundamental natural laws. We believe that the words of Marcus Aurelius "all the world is subordinate to the unified law" reflect not only the antique world perception but also the scientific paradigm of the new millennium.

In the architectonics of a verse the essential manifestation of the universal law of the artistic form is realised, the dynamic principle of "the Golden Section" being the aesthetic-formal expression of it. The RHP method allows describing the processes of poetic creative work from the point of view of their natural, harmonical origin. However, it is especially important in science that the comprehension of such processes is inseparable from the researcher's ability to perceive the artistic world in the context of unified natural evolution laws and of man as a part of this nature. This method, using the facts available and discovering the new phenomena enables scientists to answer numerous current questions of art criticism. The common methodological concept gives a possibility to integrate the efforts of researchers in different fields of knowledge, connected with the study of nature and matter of the creative work.

The psycho-physiological research by professor V.B. Slezin is of special interest to us. The fourth functional brain condition discovered by him has been named "slow vigil" and is characterised by the slowest "delta-rhythm" of brain action current (2-3 Hz). Until today there have been known three brain conditions (vigil, fast sleep (REM) and slow sleep) and two types of rhythm - alfa (8-12 Hz) and beta-rhythm (13-30 Hz). Two facts deserve mentioning in connection with this: firstly, the fact that delta-rhythm, present at the brain of an adult only during the period of slow sleep, appears when rhythmically organised prayer texts are being read. Secondly, this rhythm leads to the destruction of pathological bonds present in the human body, i.e. reading prayers heals literally, not figuratively. But most important is the fact that reading rhythmically organised texts influences the psycho-physiological condition of the human organism and that this rhythmical influence can be actually measured by means of physical devices. That means that the lightness and flow of the rhythmical verse is not only a qualitative, perceptible, subjective characteristic, but a measurable, objective value, reflecting real psycho?physiological processes of human activity.

According to G.J. Vinokur, Pushkin thought in strophes in his novel, and poetic thought shapes a single strophe in accordance with the law of harmonical self-development. Therefore, the ingeniously structured (G.A. Shengeli) the Onegin strophe cannot submit to any other rules but harmonical ones.

So, the three basic parameters of the syllabo-tonic verse S, B and T can be calculated for the most versatile poetic structures. In this case the researcher has a possibility to evaluate both theoretical qualitative-quantitative characteristics of numerous poetic forms and the degree of their harmonical realisation in concrete texts.

One more yet uninvestigated area is the study of rhythmics development dynamics on the word level from beginning to end of the verse, from its first line up to the last one. The parameters S, B and T are measured step by step for the constantly increasing volume of the poetic text, and the values of RHP t represent rhythmical-dynamical evaluations of the poetic thought self-development processes (or the reader's perception of this process, to be more precise.)

It was this method that we used while analysing both the common characteristic of the rhythmic development and contents of the 5th chapter of Onegin and the 11 strophes of Tatyana's Dream, considering the strophes of the Dream within the framework of the common poetic context of the 5th chapter.

The first results of rhythmical-dynamical analysis of Tatyana's Dream (Ch. 5, strophes 11-21) were presented to the public at the International Scientific Conference "Pushkin and Andersen. Philosophy, Poetics and the History of Literary Fairy-Tale" in Pushkinskie Gory, Russia, July 29 - August 2, 2002. Our paper "Tatyana's Dream: Rhythmical-Dynamics of Tragic Fairy-tale Metamorphosis" (in press) included the first version of the rhythmical-dynamical model of Tatyana's Dream, which was received with great interest by the scientific society.

Numerous researchers of Pushkin's work pointed out that Tatyana's Dream takes a special place in the plot dynamics of the novel. Structurally the strophes of Tatyana's Dream (Ch. 5, strophes 11-21) form the geometrical centre of the narration, symmetrically placed in respect to the beginning and the end of the novel. This location, however, is arguable, as it depends on whether the text of "Onegin's Voyage" is taken into consideration as well as the omitted strophes of the novel and some other fragments. Prof. V.M. Markovich's point of view seems more accurate as he treats Chapter 5 as the original "symmetry axis in the construction of the novel". Nevertheless even in this light the static approach does not allow to reveal the deep immanent qualitative aspects of the narration dynamics and novel architectonics, connected with the principle of harmonical self-development of its plot-line.

The part of the narration connected with the strophes of Tatyana's Dream is introduced into the text of the poetic novel as a special multi-semiotic sign. There is a possibility, in our opinion, to apply a notion of meta-metaphor as a meta?linguistic construction of the narrative metaphoric images to this fragment of the novel. Tatyana's Dream, contains a fairy-tale plot with folklore-mythological images, real characters of the novel (Olga, Lenskiy, Onegin), and has a tragic end, which all permit us to perceive the dream as such a metametaphor. But most of all, Tatyana's Dream is a Rubicon, including the metaphorically presented past of the heroine and the prophecy of future events.

Our research and the rhythmical-dynamical model of Tatyna's Dream do not only support the significance of this text fragment, but also allow to disclose the following: harmony is simultaneously a rhythmical and emotionally rich phenomenon, and, secondly, disharmonical rhythmical sensations precede the catastrophic denouement of Tatyana's Dream. This conclusion enables us to trace the point in the Dream where the fairy-tale plot turns into Tragedy. The rhythmical dynamical panorama of emotional instability of the narration testifies that the beginning of the 21st strophe is only the climax of the tragic plot development. The tragedy already begins in the 17th strophe, when "darling" Onegin appears in the Dream accompanied by wild animals and fable monsters as their master. The developments and the rhythmics of Pushkin's verse demonstrate the transition from a more or less smooth flow to the more and more expressive and tense narration. The behaviour of the curve on the sector between the 17th and 25th strophes changes dramatically. The oscillation amplitude of O(t) values at this point increases, and its fading starts only beginning with the 24th strophe, in the description of Tatyana's name day celebration. The 17th strophe is not only the harmonical centre of the dynamic plot development but it is also a dynamic counter-point of rhythmical sensations - on the borderline between the 17th and 18th strophes the smooth flow of the narration turns into a process full of emotional tension, stress and shock.

It is this character of the curve - quite smooth in the beginning and more and more saw-tooth shaped further with dramatic differences of RHP level that corresponds to the extreme emotional tension in the second part of Tatyana's Dream. This correlation of rhythm and meaning indicate their real unity and the possibility of measurement of such integral rhythm-meaning.

Thus the RHP method as an instrument for word level rhythmics study of the poetic text naturally developed into a device for study of the artistic images self-development in Pushkin's novel or for study of rhythmical-dynamics of the plot-line of "Eugene Onegin".

The first results obtained display the unconditional unity of the rhythmics and contents of Pushkin's verse. Rhythm being an object of scientific interest presents itself as a unified "rhythm-meaning" (A. Belyj). But we believe that rhythm-contents receive their shape in the verse as a measure of their own limited self-development.

The adequate behaviour of the RHP parameter demonstrates in the best way possible not only the most significant formal property of the Divine proportion - its ultra-sensitive precision which fully corresponds to the aesthetic-philosophic understanding of the strophe as a measure of poetic thought self-development - but also indicates the inner immanent nature of correlation and the integrity of the phenomena under investigation.

So, the natural law of the Divine proportion, which reveals itself in the highest forms of artistic creations, appears in a new, rhythmical-dynamic form of the aesthetic law. "The Golden Section" law, known from the times of the Ancient Egypt, is one of the most intriguing mathematical laws. Having been formulated by the great Leonardo, it appears in the natural and humanitarian scientific investigations more and more often.

This law is not compulsory, and it is not the only one determining artistic impression. Nevertheless it remains as a law directly connected with aesthetic, artistic effect. It is this law that immediately influences the impression of integrity and beauty. Pushkin, being sensitive to beauty, first of all instinctively guessed the moments of "the Golden Section" in the development of his narration with amazingly mathematically precise intuition. Secondly, he established the proportional sizes of the parts in respect to the whole and thirdly, he emphasised the climax point of increasing expectation tension, compositionally setting the main ideas of the narration in places noticeable for immediate sensual perception.

List of Publications:

  1. Greenbaum O.N., Martynenko G.Y. The Russian Sonnet and "the Golden Proportion" of Rhythm" - SPb.: SPb State University Press, 1999.- 20 p.
  2. Greenbaum O.N. The Harmony of the Strophic Rhythm in the Aesthetic-Formal Measurement (Based on "the Onegin Strophe" and the Russian Sonnet) - SPb.: SPb State University Press, 2000.- 160 p.
  3. Greenbaum O.N. Aesthetic-Formal Verse Study: Methodology. Axiomatics. Results. Hypothesises. - SPb.: SPb State University Press, 2001.- 40 p.
  4. Greenbaum O.N. "The Onegin Strophe" as a Phenomenon of the Russian Versification// Materials of the conference, dedicated to the 110th anniversary of acad. B.M. Zhirmunsky's Birth. - SPb, 2001. P.299-309.
  5. Greenbaum O.N. The Harmony of Rhythm and Poetic Communication// Materials Of the 30th Scientific Method Conference of Teachers and Post-Graduate Students. Issue 11, Part 2.- SPb.: SPb State University Press, 2001. P.3-15.
  6. Greenbaum O.N. The Line, the Strophe and the Verse as a Rhythmical System// Materials Of the 31st Scientific Method Conference of Teachers and Post-Graduate Students. Issue 4, Part 2 - SPb.: SPb State University Press, 2002. P.12-28.
  7. Greenbaum O.N. Poetic Text and the Phenomenology of Rhtythm. //The World of the Russian Word.- Spb.: Zlatoust, 2002. # 3. P.47-52.
  8. Greenbaum O.N. The Harmony of Rhythm in the Poem by A.A. Fet "Шопот, робкое дыханье..." // Language and Speech. Volume.4. SPb.: SPb State University Press, 2002. P.23-28.
  9. Greenbaum O.N. Comparative Analysis of "the Onegin Strophe" of Pushkin and Baratynsky // RESPECTUS PHILOLOGICUS, mokslo darbai, 2002, Nr.1 (6). - Vilniaus Universitetas, 2002. S.72-92.
  10. Greenbaum O.N. The Harmony of the Strophic Rhythm in the Aesthetic-Formal Measurement (Measurement (Based on "the Onegin Strophe" by A.S. Pushkin) //The Ontology of the Verse.: Dedicated to the 90th Anniversary of V.E. Holshevnikov. - SPb.: SPb State University Press, 2000. P.170-195.
  11. Greenbaum O.N. "Wonderful" Tatyana's Dream as a Metamorphosis of the Pushkin's Novel// Cognitive Communication // Papers of the 4th International Scientific Conference.- Simferopol, 2002. p.97-99.