Inventions and symphonies were written for pedagogical purposes. Open lesson on the topic: “Work on the inventions of J.S. Bach

21.03.2019

15 two-part inventions and 15 three-part symphonies

In many works, Bach embodies his ideas in polyphonic forms of a mixed or free type. In this regard, a few words about inventions as pieces that are still playing important role in the piano, mainly instructive and pedagogical repertoire (F. Busoni was an ardent propagandist and an excellent interpreter of these compositions. Among the performers of the 20th century, we note the Canadian pianist Glenn Gould.).

Invention literally means fiction, invention, composition. This title actually refers only to fifteen pieces of a two-voice warehouse. As for the fifteen three-part pieces, Bach called them symphonies or fantasies. It is no coincidence that both of them coincide in number, keys, and artistically harmonious correlations of two- and three-part pieces. In the Köthen manuscript collection of 1723, the composer grouped them in pairs and, therefore, intended to be performed in this form. Bach's invention and symphony, presenting special genres, do not constitute, however, completely independent polyphonic forms. Some are fugues, others are canons. In addition to the diminutiveness of most of them and especially pronounced homophonic features, some are distinguished by two characteristic devices.

The first is an imitation with an octave answer. This is how the C-dur, D-dur, E-dur, a-moll, d-moll, g-moll, c-moll, f-moll inventions and c-moll, h-moll symphonies are written. In them, Bach, as it were, returns to his predecessors of the 17th century. Although the compositional structure of these pieces is extremely close to the fugue, the tonic-dominant antithesis as the initial impulse of development is absent here, and to the extent that this is no longer a Bach fugue in the exact sense of the word.

In some symphonies, directly close to the fugue, a technique is used that deviates the form in a different direction. The peculiarity lies in the fact that the theme initially does not appear in a purely monophonic texture: it is immediately accompanied by another more or less contrasting melody of an episodic nature.

In addition, each piece also has individual characteristics. Thus, the symphony in B-dur is richly saturated with close stretta passages of perfect plastic beauty. In the developmental middle of the e-moll symphony, a subtly expressive technique of the enharmonic deviation e-moll - g-moll - e-moll through a reduced seventh chord is used. Symphony f-moll (triple three-voice fugue) has at the same time the features of an old two-part sonata form. In the d-moll symphony, the theme is counterpointed in the bass by its generalized version. This technique is often found in other genres, as, for example, in the large choral prelude "Jesus Christus unser Heiland" on the theme of Hussite origin.

Thus, symphonies and inventions represent a series of different, including "free" or intermediate forms. It is known that when composing them, the composer set himself, among other things, also pedagogical tasks and strove to demonstrate to the student the polyphonic technique and techniques of coherent, melodious performance of melodic voices on a variety of compositional structures. And in small things you hear a great artist: inventions and symphonies are true masterpieces of Bach's polyphony.

K. Rosenshield

Collection output:

STYLISTIC ANALYSIS OF I.S. BACH AS A FORM OF WORK OF A HIGH SCHOOL STUDENT IN A SPECIAL PIANO CLASS

Kopylova Lyudmila Viktorovna

teacher

"Sunny children's art school",

Russian Federation, Tyumen region, Surgut

STYLISTIC ANALYSIS OF I.S. BACH'S INVENTIONS AS A FORM OF UPPER-FORM PUPIL'S WORK IN THE CLASSROOM OF SPECIAL PIANO

Ludmila Kopylova

teacher
of “Solar Children's Art School”,
Russia, Tyumen Region, Surgut

ANNOTATION

Specific difficulties in the execution of I.S. Bach, oblige a high school student - a pianist to have special knowledge and skills. The method considered in the article stylistic analysis, prepares the student for awareness of the execution of inventions, revealing the basic principles in articulation, dynamics, fingering, tempo.

ABSTRACT

Specific difficulties in playing I.S. Bach's inventions oblige an upper-form pupil - pianist to have special knowledge and skills. In the article the considered method of stylistic analysis prepares the pupil to realize playing of inventions revealing basic principles of articulation, dynamics, finger notation, and tempo.

Keywords: musical pedagogy; polyphonic music; stylistic analysis.

keywords: musical pedagogy; polyphonic music; stylistic analysis.

Joining the world polyphonic music, the peak of which is the work of I.S. Bach, is an indispensable condition for the harmonious development of a musician of any specialty, including a pianist. Studying polyphonic works- I.S. Bach, one of the difficult sections music pedagogy. Achievements in the study of polyphony of the 17th-18th centuries by researchers, including domestic ones, are so significant for understanding the patterns of the composer's musical language that they cannot be ignored. Unfortunately, there is a noticeable gap between the research literature and the practice of teaching it in music schools. Valuable theoretical observations and generalizations remain forgotten. The study of I.S. Bach is conducted according to outdated editions and is reduced to a formal study of voice leading. Thus, the topic “Stylistic analysis of the inventions of J.S. Bach as a form of work of a high school student in a special piano class" is relevant, and its study is necessary. The novelty of this work is that we have adapted the experience of teachers-researchers, their methods of working on the polyphony of I.S. Bach, to his methodology, with a senior pianist. The purpose of the work is to substantiate the effectiveness of stylistic analysis, for the performance of inventions, by a senior pianist. The object of the research is the process of development of musical performance of a senior schoolboy-pianist. The subject of the research is the stylistic analysis of the work. The hypothesis of the study - we assume that the performance of inventions by a senior student will be conscious if a stylistic analysis of the work is used. Research objectives:

  • analyze the scientific and methodological literature on the research topic;
  • to identify the psychological and pedagogical features of senior schoolchildren-pianists;
  • to determine the main stylistic principles that influence the performance of inventions by a senior pianist.

In progress theoretical research methods were used: verbal explanation, comparison, generalization, stylistic analysis.

Artists, scientists, musicians, teachers, showed big interest to the stylistic analysis of clavier works by I.S. Bach. Book by I.A. Braudo - “On the study of clavier works by I.S. Bach in music school". Its author reveals pedagogical value clavier music, raises the question of various editions of works by I.S. Bach, talks about authentic compositions. The author also outlines the basic principles of performing polyphony by I.S. Bach - dynamics, articulation, tempo, fingering. I.A. Braudo offers and technical ways study of polyphony. Book - N.P. Kalinina “Clavier work of I.S. Bach in the piano class”, points to the overcoming of the existing stereotypes of the mechanical mastering of the works of J.S. Bach as part of the school curriculum. N.P. Kalinina explains how to achieve young pianists, thoughtful performance of polyphonic pieces. How to help students master a special type of sound production, teach them to hear and understand polyphonic presentation. In the book "Conversations about Bach" - I. Temchenko and A. Khitruk, the authors try to identify the range of problems that arise today for every performer, from a schoolchild to a concert musician. Article Kopchevsky N.I., to the collection "Little Preludes and Fugues", encourages teachers to study this material, considering it necessary for an initial acquaintance with the style of ancient works. His article, for the collection "Inventions", tells about the editors-researchers who contributed to the propaganda of I.S. Bach.

Interest in the work of I.S. Bach, appeared in dramatically changed cultural and historical conditions, during the development piano music and dominance in it romantic style. The works of I.S. Bach, were restored from drafts, manuscripts, three quarters of a century after his death. The first pedagogical edition of “I.S. Bach", became the editors - K. Czerny. She firmly established herself in the pedagogical repertoire, as she possessed pianistic virtues. Many generations of musicians have been brought up on this edition. The study of creativity I.S. Bach were engaged famous musicians and composers. Subsequently, they were forced to admit that K. Czerny's version gave the pianists a distorted portrait of the composer. Its shortcomings were that it reflected the performing features of the era of romanticism, in which K. Czerny lived. A new attitude to the work of I.S. Bach, marked by the desire to free him from stylistic inconsistencies and convey his true appearance, took shape only in the 19th century. So the editors - F. Busoni strive to show how much the widespread style of performance contradicts the true nature of the music of J.S. Bach. To do this, F. Busoni stylistically describes and explains the articulation, dynamics, fingering, tempo, form of the work, and deciphers the decorations. The polemical orientation of his thought leads to some exaggerations and causes some controversial places in his wording. F. Busoni does not consider his interpretation to be the only correct solution. He says that his understanding can serve as a good guide, which one who knows the other right way does not need. Since the publication of the inventions by I.S. Bach, edited by F. Busoni, a lot of time has passed. During this time it was released a large number of other editions, including the textually fundamental academic edition edited by L. Landshof. But it is unlikely that any edition could reach the level of F. Busoni's edition in terms of its instructive qualities - its pedagogical orientation, a vivid expression of a single ideological and aesthetic concept. At the time of F. Busoni, there was no scientific and textual edition of the inventions. L. Landshof's edition is based on the urtext, the author's text, by I.S. Bach. To the edition of F. Busoni, the “Appendix” was added, based on the urtext of the inventions. Discrepancies of a fundamental nature - incorrect notes, accidentals were noted, corrected, commented on in the "Appendix", and teachers can use them. Today, F. Busoni's version is relevant, it is taught in music schools. To teach a student to distinguish between the actual author's text and editorial additions to it is the task of a large educational value. This skill will help the student to become familiar with characteristic features originals written for the clavier and with the difference between these texts and piano works, to understand the essence of editorial work. In each individual case, the student will observe how the editor, based on reading the pure author's text, makes his specific performance conclusions.

The study of polyphonic works by I.S. Bach, a serious stage in high school. Senior student - age from 10-11 to 15 years. At this age, the main characteristics are fixed and develop. cognitive processes. Perception - is characterized by purposefulness, attention - by arbitrariness and stability, memory - by a logical character, thinking - differs more high level generalizations, acquires a theoretical and critical orientation. A teenager has an intellectual maturity. It is expressed in the desire to know something. The active and interested attitude of a student to polyphonic music depends entirely on the method of work of the teacher, on his ability to lead the student to a distinctly figurative perception of the basic elements of polyphonic music and a number of concepts inherent in it.

Works by I.S. Bach, indispensable material, for development musical thinking, for the education of initiative and independence of the student. To understand the polyphonic pieces of I.S. Bach, we need special knowledge, we need a rational system for their assimilation. Achieving this goal is based on a solid knowledge of the foundations of the theory of polyphony, the laws and properties of the composer's musical language, and the performing traditions of his era. Inventions I.S. Bach - two-part pieces. Invention in translation is an invention, an invention. It is a true school of voice leading. The basis of the work was the theme. In the theme, the composers of the 17th-18th centuries saw its development, transformation, variety of polyphonic and contrapuntal methods of development. Works of the ancient polyphonic style, built on the development of one artistic image, on multiple repetitions of the theme - this core, which contains the entire form of the play. The student's attention to the topic should be directed before the beginning of the analysis of the play. Analyzing the theme, the student determines its boundaries, its character, its rhythmic and interval side. The teacher, together with the student, must trace the development and transformation of the theme in each voice. The theme sounds in its basic form, it can sound in octave imitation, in circulation, in magnification. Such an analysis of the topic will convince the student that the whole invention is a dialogue of the interlocutors. The main method of working on a theme is to work at a slow pace in order to convey intonational expressiveness. This approach to the analysis of the topic changes the student's attitude to the invention. I.S. Bach uses various polyphonic devices in his pieces - double octave counterpoint, reversible counterpoint, sequential development. If we present counterpoints to a schoolboy as artistic techniques associated with the entire structure of the composer's polyphonic creativity, he will have the opportunity to concretize his knowledge in this area. So, for example, when two voices change places, such a polyphonic technique is called double counterpoint. When two voices present the same melodies, but in reverse, it is called reversible counterpoint. The more the student learns about different sides and properties of the polyphonic style, the more actively his consciousness will be included in the meaning of work on clavier works I.S. Bach. The counterposition is a melody that is uttered simultaneously with the theme. In other words, the opposition is the counterpoint to any introduction of a theme in a polyphonic work. The main method of work is in an ensemble with a teacher. Directing the student's attention to the relationship between theme and opposition. Long before the two voices join, the piece is performed in an ensemble with a teacher - first in sections, then in its entirety. Memorizing each voice by heart is obligatory, because work on polyphony is, first of all, work on a monophonic melodic line.

The skills of the correct division of the melody - articulation, were given great importance in the era of I.S. Bach. Articulation is one of the main expressive means in the ancient music of I.S. Bach. Articulation - important way organizing motifs, phrases and thereby revealing the nature, building the form of a fragment or a whole work. Braudo, advises: “An attempt to establish some kind of dominant stroke in clavier playing is pedagogically inappropriate. The art of strokes develops not on the development of individual techniques, but on the comparison of stroke manners. The study of articulation is better to start with the study of two-voice works, in which each voice is assigned its own articulation coloring, when shorter notes are played legato, longer ones non-legato or staccato. Inter-motive articulation - is used to separate one motive from another, that is, to take a caesura - breathing. The most obvious kind is a pause. Students need to be introduced to different ways designations by intermotive articulation - two vertical lines, the end of a league, a staccato sign on a note before a caesura. Schoolchildren-pianists need to master inter-motive articulation, without which the stylistically correct performance of I.S. Bach is impossible. The main thing is to convey the relief convexity of motives, their distinct pronunciation and their separation from each other. It is necessary to teach the schoolboy pianist to distinguish between the main types of motives. In this case, one should use the information that the student receives in the classes of solfeggio and music theory. He must distinguish between iambic and choreic motifs. iambic motives - go from weak time to strong time are often referred to as outliers. Choreic motifs - enter on a strong beat, end on a weak beat. The main method of work is to learn each motive separately, and then play everything in a row at a slow tempo, using the following technique: sing the first sound of each motive more deeply and significantly, and soften the last sound by prematurely removing the finger from the key.

Fingering in clavier works early music has a range of specific features. Right choice fingers, an important condition for competent, expressive performance of polyphony. The performing tradition of the era of I.S. Bach, when articulation was the main means of expression, fingering was subordinate to it, aimed at revealing the convexity and distinctness of motive formations. Previously, clavier players used three middle fingers of approximately the same length and strength, which ensured the achievement of sound and rhythmic evenness, an important statute of early music. Introduction by I.S. Bach of the first finger, did not affect the principle of shifting the fingers - a long finger through a short finger 3-4-3. The sliding of a finger from a black key to a white key has also been preserved. F. Busoni, was the first to revive the fingering principles that correspond to the identification of the motive structure and the clear pronunciation of motives. The restored method of F. Busoni, is the most effective in our time, for the implementation of evenness of sound. The method of mastering is to teach the student to read and learn the fingering.

A sense of proportion in relation to all dynamic changes in any work by I.S. Bach is a quality without which it is impossible to artistically and stylishly convey his music. The dynamics in clavier works is terrace-like, this term came into use thanks to F. Busoni. The basis was the instruments for which the works were written. The concept of clavier combines instruments - spinet, clavichord and harpsichord. Each tool has its own specifics. The modern piano is an instrument that makes it possible to perform works of various styles on it. When we talk about the use of piano expressiveness in the performance of clavier music, we do not mean an attempt to imitate the sonority of ancient instruments on the piano, but to find in the process of playing those dynamic techniques that are necessary for correct performance. The difficulty that we encountered in the work on the clavier works by I.S. Bach, lies in the fact that they were not written for the piano I. Braudo formulated an important difference in the means of dynamic expressiveness, highlighting two of its varieties - instrumental and melodic. Thanks to instrumental dynamics, it is possible to match voices as well as sections musical form. So in two-voice plays, I. Braudo assumed the use of two voices by different instruments. To this end, it offers different dynamic tones for the upper and lower voices. By melodic dynamics is meant the identification of intonational relief with the help of dynamic means. The main functions of melodic dynamics: revealing covert polyphony, revealing a motivic structure, revealing a question-answer structure, dynamic detection of imitations. In inventions, each voice is independent, has its own dynamic development, in order to emphasize the independence of each voice more clearly. Therefore, the climaxes in the voices do not coincide, such climaxes are called private, which is typical for the polyphony of I.S. Bach. The cadences at the end of the movements are performed energetically and sonorously. Each new part begins with a dynamic nuance - piano, with a subsequent increase in sonority based on motives. The overall climax of the piece sounds bright and expressive. Our task is to help the student draw up a dynamic plan that reflects an understanding of the form of the work, the features of voice leading.

The choice of tempo in the music of I.S. Bach, depends on the choice of articulation. With a change in the articulatory technique, not only the sound, but also the tempo appearance can become completely different. Tempo is secondary to articulation and largely follows from it. What a student acquires when working at a slow pace - an understanding of music - is the most essential. And it is important to teach him that it is the understanding of music that he considers his main achievement, something that should remain and gain a foothold in all future work. By achieving a faster pace, he should consider the circumstance less significant and accessible only if the main thing is not violated - the quality of performance. Meaningfulness and melodiousness - that's what is the key to the stylish performance of J.S. Bach.

It should be noted that in some initial assumptions, the methodology for studying a polyphonic work is the same for all instructive collections by I.S. Bach. Art by I.S. Bach is normative. It grew up on the basis of stable traditions and a strict system of laws and regulations. To perform the works of I.S. Bach, you need to know the stylistic features of writing. Thus, we substantiated the influence of stylistic analysis on the performance, in this case, of inventions. Only through an analytical study of the main regularities of the composer's style, one can comprehend the performing instructions of the composer himself. All the efforts of the teacher should be aimed at this.

Bibliography:

  1. Braudo I.A. On the study of Bach's clavier compositions at a music school. - St. Petersburg: "Reindeer", 1994. - 76 p.
  2. Kalinina NP. clavier music Bach in the piano class. - M.: Publishing house "Classics-21", 2006. - 144 p.
  3. Kopchevsky N.I. Selected articles. - M., 1966. - 25 p.
  4. Obukhova L.F. Age-related psychology. Tutorial. - M.: Pedagogical Society of Russia, 2000. - 443 p.
  5. Temchenko I.E., Khitruk A.F. Conversations about Bach. - M.: Publishing house "Classics -21", 2010. - 150 p.

An invention is an invention. Latin, Russian, English, Italian, French and a host of other languages ​​give an absolutely unambiguous translation of this word - "invention". But this can be said about any work of art born of the imagination of its author.

What does invention mean in music

In relation, the special ingenuity, the sparkling of the composer's insight in finding the most diverse options for developing and interweaving themes and voices are emphasized here.

According to tradition, an invention is a play that has very specific characteristics. First of all, we are talking about a polyphonic work, that is, about polyphony. Moreover, this is usually piano work. But monophonic melodies are usually not played on the piano, so everything that is written for the piano can be called polyphony?

No. In most polyphonic works, textured voices are unequal. There is a clearly recognizable melody, and there are voices that accompany it. They are of secondary importance and are usually called "accompaniment", or "accompaniment".

The main feature of polyphonic writing

The peculiarity of polyphony lies primarily in the fact that it does not have accompanying textural lines. All voices are melody, all major and equal. Keeping track of the expressive intonation and articulation of each of them is a difficult task for the performer.

That is why the genre of polyphony at all stages of music education (and almost at all competitions) is an obligatory part of the musician's program.

The same can be said about the composer's task - it is difficult to create a polyphonic work, it requires a lot of ingenuity.

Depending on the way the material is presented, such plays may have various titles: fugue, canon, imitation, two- or three-part invention, and so on.

Among the works of this genre classic version is a fugue, and the invention can be seen as educational material to prepare for its proper implementation.

30 Inventions by Johann Sebastian Bach

It was for this purpose that the greatest of the 17th century, Johann Sebastian Bach, created his immortal two-voice inventions in the amount of 15 and the same number for three voices, calling the latter symphonies.

In the preface to his inventions, Bach wrote that in this manual he showed how to manage not only with two, but, in the process of improvement, with three obligate (independent) voices, while simultaneously learning " good inventions and their proper development. Two main tasks are singled out: "to achieve a melodious manner of playing and at the same time acquire a taste for composition."

The incomprehensible greatness of Bach lies in the fact that, wanting to write simple exercises for the disciples, he created creations that have survived the centuries, have not lost the power of spiritual influence on man today.

The value of polyphonic pieces for the development of taste

Bach's inventions were written for the clavichord, since it was only on this instrument that it was really possible to "achieve a melodious manner" of playing rich in shades of sound. However, the modern piano makes this goal more fully realized.

Perhaps the composer did not even suspect to what extent his desire to instill a taste for composition would be fulfilled.

The modern musician, often with less knowledge of compositional technique than was the case in Bach's time, has a much greater understanding of the difference between true and false in the art of music.

Anyone who in childhood studied (even mechanically) at least 1-2 Bach's inventions will never be able to erase the concept of correct voice leading from memory. In every piece of music he will intuitively look for independently developing melodic lines and perceive their absence as a disadvantage.

Invention is a piece of music that has set the standard for defining authenticity in art.

Outstanding Invention Interpreter

Speaking of inventions, it would be unfair not to mention the name of the legendary Canadian pianist Glenn Gould. It so happened that it was Bach's inventions that played leading role in his birth as a performer, and this happened precisely in Russia.

In May 1957, a then-unknown young pianist from Canada arrived in Moscow. This was his first tour. Two- and three-part Bach's inventions - that's all that was included in concert program. A ticket to the hall of the conservatory cost 1 ruble, there were about 30 people in the audience.

After the start of the concert, only a few minutes passed - and it became clear to the audience that they were present at the birth of a miracle. People took turns leaving the hall to call to inform their friends about what was happening.

The second part began with a delay of 40 minutes - the audience filled the hall. After Moscow there was a concert in Leningrad, where a part of the Moscow audience went for Gould.

After these concerts, the Canadian pianist continued to tour in Europe, where he was already expected as new star the halls were packed. Until today, Gould's interpretation of inventions is considered an unsurpassed example.

Invention is not exceptional feature such a polyphonic form was used before him. Among those who write inventions today, one can name the names of S. A. Gubaidulin, R. K. Shchedrin, B. I. Tishchenko. With all the talent of their music, it still cannot compete with the "original source". These are phenomena of different scales.

It is customary to begin the study of Bach with simple pieces from the second Notebook Anna Magdalena Bach (1725), then two-part inventions, then three-part sinfonias (three-part inventions, as they are commonly called), then the so-called "French suites" (perhaps also "English suites") and, finally, the preludes and fugues "Good tempered clavier. During Bach's lifetime, neither the invention nor the sinfonia were published. Bach intended the inventions for teaching the performance of polyphonic works on the clavier - two, and then three-part. At the same time, he considered the acquisition of a melodious manner of performance by the student as the most important task. In addition, Bach considered the inventions as a guide to composition. They were supposed to serve as models for analysis and contribute to the development of composing technique in the field of polyphony. Like other works by Bach, the inventions are almost completely devoid of authorial indications as to the nature of the performance. Therefore, when working on them, the issue of editions becomes especially important. The teacher should study the main editions of the collection and use everything of value that they contain.

The most widespread in our pedagogical practice are the editions of the inventions of Busoni, Czerny and Goldenweiser. A. B. Goldenweiser set himself the task, first of all, to give the author's text verified according to the original source. This was important because in Czerny's widespread version there are a number of textual inaccuracies, up to incorrect notes. The editor writes out the fingerings in detail and gives a transcript of the decorations. It indicates the nature of performance only in in general terms, therefore, when working with a student, there is a need for additions in relation to dynamics and phrasing. Editorial Czerny must be recognized as imperfect. In addition to the inaccuracy of its text, a number of works, especially serious in nature and significant in content, are not revealed in depth enough in it (three-part inventions f-moll, a-moll). Czerny often "shrinks" the dynamic plan, as a result of which the form of the composition is indistinctly outlined. The abundance of dynamic "forks" gives excessive "undulation" to the phrasing; almost invariably found at the end of piano and diminuendo works - even in inventions energetic character- "smooth" Bach's style. The phrasing is often indicated in an excessively sketchy way, and it has to be supplemented. At the same time, it would be wrong to completely cross out Cherny's editorial. It also has a lot of persuasiveness. What attracts in this edition is the desire to reveal the melodious possibilities of the instrument and thereby embody the author's instructions given by him in the title of the collection. Editorial Busoni much more detailed, thorough and artistically meaningful than Czerny's edition. Without limiting himself to a detailed indication of the shades of performance and fingering, Busoni, with verbal explanations and in footnotes, reveals the nature of the work. Compared to Czerny, Busoni's interpretation is distinguished by greater masculinity, energy, and breadth of dynamics. In this sense, it is often closer to our ideas about Bach's style. However, the wording of Busoni does not always seem convincing. In his desire to reveal the courageous beginning in the composer's work, Busoni sometimes loses his sense of proportion. Sometimes he exaggerates the meaning of non legato. It is impossible not to reproach Busoni for the fact that, when editing inventions, he omits Bach's designations for melismas and writes decorations with notes directly in the text. This deprives the student of the opportunity to get acquainted with the principles of deciphering the ornament and introduces features of dogmatism into the editorial office: one has to be guided only by the prescribed method of execution. Meanwhile, it is precisely the area of ​​ornamentation that allows for especially great freedom, and one interpretation of even a prominent specialist is often not at all the only possible and best one in a particular case.



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