Well-Tempered Clavier Research Articles

Tempering the clavier: a corpus-based examination of Bach’s cognition of intonation in the Well-Tempered Clavier

While it is well known today that J.S. Bach’s The Well-Tempered Clavier (WTC) was not composed with equal temperament in mind, it is unknown exactly which, if any, well temperament Bach had intended for the work. While equal temperament produces 12 uniform intervals of each type, other systems of well temperament slightly stretch and compress the size of various fifths, resulting in alterations to other intervals. A number of competing hypotheses have been published as to which temperament Bach intended, or whether he intended a specific temperament at all. While we do not have a definitive historical answer as to Bach’s preference of temperament in this work, this paper applies corpus methodologies to compare these systems. This paper develops and utilises Detuning-Emphasis Correlation (DEC): the relationship between scale-degree pairs' deviation from just intonation and their frequency of use. Frequency of use is compared to a ‘baseline’ frequency, found by averaging a scale degree pair’s prevalence across the corpus. This paper analyses the 48 fugues of Bach’s WTC by computing DECs for selected well temperaments (Werckmeister III, Bach-Lehman, Niedhardt, Vallotti, and Young), aiming to find a significant negative DEC for some temperament. While no temperament was found to fit the WTC in this way, strong correlations between these well temperaments indicated that the work would highlight similar affects for the various keys regardless of which (non-equal) well temperament is used to realise this work.

Rachmaninoff’s Preludes as a Cyclic Work

For over 18 years during the period 1892 to 1910, Sergei Rachmaninoff composed thePrelude, Op. 3, No. 2; 10 Preludes, Op. 23; and 13 Preludes, Op. 32. The key organization of Rachmaninoff’s 24 Preludes seems random at first glance, not based on any systematic order, as are the sets of Johann Sebastian Bach’s The Well-Tempered Clavier and Frédéric Chopin’s 24 Preludes, Op. 28. However, they consist of all the different major and minor keys and are uniquely integrated by cyclic manipulation of tonal relationships and thematic ideas. While they share numerous features, such as the use of common tones/chords, stepwise motion, chromatic lines, intervallic motives, and a certain rhythmic pattern, they also present divergent elements, such as bold key changes, irregular inclusion of relative- and parallel-key relationship, and effective contrasts in various aspects in many of consecutive preludes. The set of Rachmaninoff’s 24 Preludes is organized in his own unique, original, and meaningful system and conceptual design, which the author believes is highly successful as an integral, cyclic composition.

N. A. Rimsky-Korsakov. Prelude and Fugue G major in the Composer’s Autograph

Among the music manuscripts from the collection of N. A. Rimsky-Korsakov, stored in the Manuscripts Department of the National Library of Russia, Stock 640, manuscript No. 344 is of particular interest. This source includes sketches and completed works, of which three fugues have not been published to date, with one exception of the Prelude in G major, first published in volume 49 (A) of the Complete Works of N. A. Rimsky-Korsakov. The materials in autograph No. 344 refer to the composer’s productive period — the mid-to late-summer of 1897. The compositions he was working on at that time (including the opera “Mozart and Salieri”, Quartet in G major and Trio in С minor) were specifically reflected in the content of the autograph. This article contains a description of the manuscript Stock 640, No. 344 and the polyphonic sketches and compositions included in it. An analysis of the materials included in the autograph allows us to conclude that the manuscript does not belong to the educational works of Rimsky-Korsakov, and the musical materials included in it correspond to different forms of musical composition and are compositional manuscripts, that is, manuscripts representing the process of writing music. The specificity of the work on fugues observed in No. 344 allows us to identify among the materials a unique complex for Rimsky-Korsakov’s autographs of several types of composition of polyphonic works: sketches (mostly related to pre‑compositional work on fugues), contrapuntal probes (a term by M. Monich), analytical notes of various types and compositional manuscripts of completed works. Analytical notes of the harmonic reduction of J. S. Bach’s cis minor prelude (vol. I of “The Well-Tempered Clavier” — BWV 849) and a schematic representation of the composition of the double fugue from Mozart’s Requiem (KV 626/2) serve as genre-style models of the unreleased cycle by N. A. Rimsky-Korsakov “Prelude and Fugue in G major”. These considerations build up the second part of the article. Analytical notes of the harmonic reduction of the cis minor prelude by J. S. Bach (vol. I of “The Well-Tempered Clavier”, BWV 849) and a schematic representation of the composition of the double fugue from Mozart’s Requiem (KV 626/2) serve as genre-style models of the unpublished Rimsky-Korsakov’s cycle “Prelude and Fugue in G Major”. The second part of the article is devoted to these materials.

Statistical analysis of Bach’s Well-tempered Clavier

Bach’s Well-tempered Clavier is the greatest work of Bach keyboard music, it contains 48 preludes and fugue, it is one of Bach’s representative works of music creation. This paper firstly inputs MIDI data of Bach’s Welltempered Clavier, and then constructs the analysis model of Bach’s Well-tempered Clavier. The experimental results show that the envelope of the number of occurrences of each musical note is in the shape of a double hump, indicating that the statistical number of musical notes played by the right hand or the left hand should be in the shape of a single camel peak in the musical range.

The Reception of J. S. Bach’s Well-Tempered Clavier in the Manuscript of A. K. Glazunov (National Library of Russia, F. 187, No. 642)

The manuscript of A. K. Glazunov’s educational fugues (National Library of Russia, F. 187, N 642) is an important document refl ecting the creative ideas of the young composer at the fi nal stage of his musical education (summer 1881). Two elements of the manuscript stand out: rewriting a fragment of one of the fugues from J. S. Bach’s “WellTempered Clavier” and beginning to record the themes in all major and minor keys. Various forms of work – from composing themes to entire compositions — reveal Glazunov’s understanding of J. S. Bach’s “Well-Tempered Clavier” as a voluminous – both instructive and creative – source.

«Modification of ghosts»: conductors interpretations of Yevhen Stankovych’s Sinfonietta in 2017 and 2023

«Modification of ghosts»: conductors interpretations of Yevhen Stankovych’s Sinfonietta in 2017 and 2023

Controversy over Stretto in Bach’s Fugue

The secrets of composer skill, in particular the techniques of counterpoint and canon, attracted the attention of S. Taneyev from an early age. The composer’s short but succinct handwritten text, presented in the article, highlights one of the aspects of this interest associated with the search for a constructive basis – the original structure in the polyphonic works of J. S. Bach. Contrapuntal texture grows from these fragments, and they also serve as an impetus for the creation of a certain polyphonic form. The six-voice canon discovered by young Taneyev, which explains all the strettos in the fi rst fugue of the Well-Tempered Clavier, remained a relevant argument for mature Taneyev – a scientist and composer – in a professional dispute with S. Smolensky.

Rethinking WTC: a new interpretation of the Well-Tempered Clavier by J. S. Bach through the prism of the theory of Boleslav Javorsky

In this project I sought to get new insights into the interpretational process, to make a contribution to the renewal of methods of working with a musical text, to find a new way to communicate meaning found in music, to broaden the role of the pianist to a co-creative one, and to unfold a new facet of the understanding of the Well-Tempered Clavier by J.S. Bach. The initial inspiration for this project came from the theory of the Ukrainian-born musicologist Boleslaw Javorsky (1877-1942), the main sense of which can be formulated as: the main foundation of the Well-Tempered Clavier (WTC) is the protestant chorales, and that the WTC is an artistic interpretation of images and plots of the Bible. The use of metaphors, images and narrative is important as a way of working with music for many musicians. For me this way of thinking has always been the most important working method, along with the wide range of other elements within my individual working processes, which inform my artistic practice. I intended to go further and through the creative process during this project develop a new methodological approach in working with the music text. I call the process in search for meaning in preludes and fugues. I try in this project to tell the story of my personal understanding of this iconic piece, often called the pianist's Bible. The story presented is not merely a descriptive Bible story, but rather a personal reflection over our existence. My working process began with trying to find and understand the connection between words in the chorales as well as other vocal works of Bach, and the music text of WTC. When analysing the found connection, each prelude and fugue receives a concrete semantic meaning. I decided to place the pieces chronologically according to the meaning I found, so that the entire WTC becomes a unified coherent story, instead of a collection of 48 separate pieces. I did not attempt to imitate the way of performing that was common during Bach's time, but rather to use all the advantages of the keyboard instrument of our time and all the expressive means it offers to share my findings. By experimenting with interweaving the motives of vocal music with WTC's music texture, I wanted to make my understanding of the genesis of the piece audible, but also to embed my reflections into my playing. It also broadened the role of the pianist to a more co-creative one, which was the common practice in Bach's time, but in an entirely different way. In other words, my intention was to make my interpretation historically informed, but to be faithful to the spirit of the time, rather than to the letter of the time. The legendary Bach scholar Albert Schweitzer wrote about WTC: "What is gripping, is not the shape, or the structure of the pieces, but the worldview reflected in them". To make my understanding of this worldview audible to all listeners, and to invite them to immerse themselves into Bach’s spiritual universe (where the music's aim is the “recreation of the spirit”), is the overall goal of the project. Bach’s faith generated his music, and so I hope that this music can in turn generate faith, which we need in our current times more than ever.

«Хорошо темперированный клавир» И. С. Баха: клавесин, клавикорд, орган, фортепиано

The article is devoted to the interpretation of "The Well-tempered Clavier" as one of the most popular works by I. S. Bach in the modern educational process. Subject of study: the influence of the harpsichord, clavichord, organ on the specifics of piano writing. As a methodology, an integrated approach is used, which allows making generalizations about Bach’s music, personifying individual means of instrumental expressiveness. Pedagogical and performing perspectives of problem statement are singled out. Two preludes and fugues from the first volume are used as material of study — Cis-dur and f-moll. Possible composer's preferences in choosing the necessary instrument are proved. For this purpose, original methods are proposed for optimizing the interpretation process. The obvious consistency of the requirements of performing practice of the past and the present is proved.

Appreciation of Form in Bach’s Well-Tempered Clavier

While previous research has raised doubts about the ability of listeners to perceive large-scale musical form, we hypothesize that untrained and unfamiliar listeners can, indeed, recognize structure when cognitive form judgments (coherence and predictability) are differentiated from enjoyment ratings (pleasantness, interest, and desire to hear again). In a between-groups experiment, listeners (n = 125) were randomly assigned to hear one of four versions of Bach’s Prelude in C minor from Book I of The Well-Tempered Clavier: 1) the original; 2) a mildly scrambled one in which two larger sections were switched; 3) a highly scrambled one; and 4) a randomized one. Significant differences were observed between versions in ratings of coherence and predictability, but not in ratings of pleasantness, interest, or desire to hear again. Individuals who had played the piece before could also explicitly identify structural intervention. It was assumed that relative incoherence would result in higher complexity and, thus, be reflected in longer retrospective duration estimates; however, estimates did not differ between stimuli. These results suggest that untrained listeners can evaluate global form, independently of their level of familiarity with a musical piece, while also suggesting that awareness of incoherence does not always correspond with decreased enjoyment.

Ferruccio Busoni and His Legacy by Erinn E. Knyt

Reviewed by: Ferruccio Busoni and His Legacy by Erinn E. Knyt Jonathan Kregor Ferruccio Busoni and His Legacy. By Erinn E. Knyt. Bloomington, IN: Indiana University Press, 2017. [xii, 372 p. ISBN 9780253026286 (hardback), $85; ISBN 9780253026842 (paperback), $38; ISBN 9780253026897 (e-book), price varies.] Illustrations, music examples, tables. Ferruccio Busoni's activities as critic, pianist, and composer are usually characterized as products of their time, bringing about no lasting impact. Yet as Erinn Knyt argues throughout Ferruccio Busoni and His Legacy, his presence was [End Page 549] profoundly felt in the twentieth century and continues well into the twenty-first. Specifically, she identifies various manifestations of Busoni's "aesthetic ideals" (p. 5) in the activities and output of selected students that Busoni mentored or inspired, including Jean Sibelius, Edgard Varèse, Louis Gruenberg, Otto Luening, and Philipp Jarnach. Many of these students became musical pioneers in their own right, whether in exploring "how technology and new instruments could expand musical possibilities, how sonority could become an integral material of music," or "how stylistic heterogeneity could be used to break away from traditional forms" (p. 8). Chapter 1, "Unconventional Maestro," focuses on Busoni's general pedagogical approach, which on the surface does not seem to have been unique. It was, however, strikingly conservative. Johann Sebastian Bach provided his students with countless solutions to age-old questions of form, counterpoint, and thematic cohesion, with book 2 of Das wohltemperierte Klavier (The Well-Tempered Clavier) serving as the closest thing to a one-stop composition manual that Busoni would ever allow. Instead of Richard Wagner, Richard Strauss, or Gustav Mahler, it was Wolfgang Amadeus Mozart who guided Busoni's advice on orchestration. Busoni's abandoned orchestration treatise from around 1905 emphasizes Mozartian principles of spacing, voice leading, and "diverse instrumental timbres and colors" (p. 16) as do the exercises in orchestral transcription using Mozart's concertos that Busoni regularly assigned to his pupils. Indeed, Austro-Italian models dominated Busoni's examples of dramatic forms, musical characterization, stylistic cohesion, and even subject matter, with Mozart also serving as the source of an operatic tradition that ran through Vincenzo Bellini, Gaetano Donizetti, and Giuseppe Verdi. On the other hand, a strongly Germanic line of philosophers from Johann Wolfgang von Goethe to Friedrich Nietzsche shaped Busoni's aesthetics, which in turn attracted him to various contemporary movements, such as Jugendstil and futurism, while developing his own ideas that jelled in his Entwurf einer neuen Ästhetik der Tonkunst ([Sketch of a New Aesthetic of Music] Leipzig: Insel, 1907). Knyt is keen to point out that, despite its title, the Entwurf is not about breaking with the past. Rather, it reflects Busoni's pedagogy of "embrac[ing] the stylistic characteristics of all the compositions [a student admires] and to combine them, reflecting the multiplicity of musics in the sounding universe" (p. 24). Syncretism, however, does not a system make, and Knyt rightly notes the unpredictability and even contradictions of Busoni's pedagogical statements. Improvisation was a recommended compositional stimulus, but so was having a clear vision for the work. Students were inspired to seek out the unknown, yet Busoni cautioned against prioritizing originality. Serendipitous human experience could form the characteristic marrow of a work, just as much as the calculated lines and angles of centuries old architectural masterpieces. Knyt's comparisons of the teaching styles of Arnold Schoenberg and Nadia Boulanger at the close of chapter 1 hammer home just how distinctive Busoni's was for its day. In the next four chapters, Knyt examines how selected students put Busoni's esoteric prescriptions into practice. Sibelius, although never an official student, benefited enormously from Busoni's counsel for almost thirty-five years. According to Knyt, the breadth of their relationship has made it difficult for scholars to treat it comprehensively. She seeks to remedy that situation in chapter 2, "Janus-Faced Modernism," by arguing Busoni [End Page 550] "stimulated Sibelius's imagination and was a catalyst for his experimentation with sound, color, and structure. He helped Sibelius discover a distinctive style that was an alternative to both the avant-garde and the conservative trends of the day. At the same time, he promoted his music across Europe...

Semantic space of “Well-Tempered Clavier” of J. S. Bach as a basis of the performing concept

The relevance of the article is due to the issue of formation in a modern multicultural space of the new image of the executor — the carrier of new senses and cultural memory, as well as need for creative comprehension of the world treasury of musical art in the artistic realities of modernity and research on the specifics of its modern performing versions.
 The purpose of the article is to outline the determinants and the specifics of the semantic space of “Well-Tempered Clavier” of J. S. Bach as conceptual basis of the performing concept.
 The methodology of the article is based on the principles of a comparative approach, which enables the use of research tools for cultural studies and musicology, in particular historical, historical-contextual, genre, hermeneutical and semiological methods and approaches.
 The results. The article outlines the following factors of conceptual polyphony of “Well-Tempered Clavier” as accumulation and artist experience of reflection and protecting the world in symbolic forms, the significance of the synthesis of arts and the unity of emotion, image and symbol on the parameters of baroque aesthetics, the connection of “Well-Tempered Clavier” with the creativity of the artist, resonance of symbolic forms with axiological structures of historical and cultural epochs. The article substantiates the significance in pluralistic symbolic field of the works: semantics of tonality and tempo, which acts as a construction of performing chronotope; sacred melos with perceptually fixed semantics, means of embodiment of which is citing, representation as complementary unity, allusion-variable reproduction; numeric symbolism; rhetorical figures, sound treatment — visualization of the musical process; fixed in the context of European art semantics — in particular “mirror in the mirror” (on micro — and macro levels of the of the music text organization); the genre “ambivalence”, which determines the superposition of different variants of “genre’s memory” and enables the creation of an artistic-reflective arch between the era of Baroque and postmodernism, designated be the leveling of the genre.
 The scientific topicality of the article is due to the clarification and systematization of representations regarding the specifics of the semantic field of “Well-Tempered Clavier” of J. S. Bach and the positioning of conceptual polyphony of the work as the basis of performing concepts and text.
 The practical significance of article is determined by a direct possibility of applying research results in the performing practice.
 Conclusion. Performance of “Well-Tempered Clavier” of J. S. Bach on the basis of the interiorization of symbolic forms is a guarantee of its performing “reading” as an embodiment of the process of being human in a cross-cultural dialogue, deploying self-reflection in the space of a representation of postmodernism paradigm as a multidimensional cultural message, in which the axiological experience of humanity is concentrated and the eternal problems of its spiritual being are actualized.

Exploring Changes in the Emotional Classification of Music between Eras

ABSTRACT Prior work has noted changes in musical cue use between the Classical and Romantic periods. Here we complement and extend musicological findings by blending score-based analyses with perceptual evaluations to provide new insight into this important issue. Participants listened to excerpts from either Bach’s The Well-Tempered Clavier or Chopin’s 24 Preludes – historically important sets drawn from distinct musical eras, with 12 major and 12 minor key pieces each. Participants selected one of five categories for each piece, adapted from previous musical analyses exploring historical changes in music’s cues. Combining participant classifications with score-extracted cues offers a useful way to complement and extend previous work exploring changes in the function of mode across musical eras based only on notational information. In doing so, we find evidence that changing associations of cues in the Romantic era influence judgments of affective meaning. This study provides a useful step toward bridging the divide between traditional approaches to musicology, music theory, and music perception by combining perceptual evaluations with cues extracted from musical scores to shed light on changes in musical emotion across eras.

«ХОРОШО ТЕМПЕРИРОВАННЫЙ КЛАВИР» И.С. БАХА: СМЫСЛОВЫЕ ОСНОВЫ ЦЕЛОГО

The article focuses on a number of musical "hints" about the content and semantic guidelines contained in the "Well-tempered Clavier" by J.S. Bach. The fact that most of his works do not have programs or verbal references and titles was pointed out. The religious subtext of the content of the musical unity is emphasized. The rows of accordance of semantic and musical series are given.

Концепція циклізації прелюдій Ф. Шопена та їх взаємозв’язки із циклом «Добре темперований клавір» Й. С. Баха

The purpose of the article is to disclose the unique features of a cycle of Preludes by F. Chopin and to define their internal interconnection with a polyphonic cycle “The well-tempered clavier” by J.S. Bach. The methodology of the work is complex; it lies in the combination of the basics of musicological, artistic, historical and cultural research; it is based on the positions of the intonational approach of Asafiev’s school and his successors. The scientific novelty of the research is defined by its analytical approach, concentrated on revealing Bach’s and romantic principles of cyclization that lets us determine in Preludes of F. Chopin different edges of an image, which are difficult to see while their consideration out of the context of the cycle formation as a whole. Conclusion. In Preludes op. 28 F. Chopin clearly made succession of chromatic 24 keys, with respect to the above-mentioned cycle of J.S. Bach. The structural and semantic interconnection of the prelude-fugue is suggested not only by the character of the idea, that is by something lying out of the “subject” of the work. Orientation on Bach’s cycle is “programmed” in the First Prelude and can be traced throughout all 24 plays. However, by establishing an obvious sign of resemblance, F. Chopin also differentiated the method of Bach’s baroque and logic of romantic aspiration to Beauty, to space immensity of the image. Beauty and spaciousness of overhead sense from the times of the ancient rhetoric were symbolized by the fifth intervalics: the fifth circle determined core interval construction of Preludes by F. Chopin, keeping separate from the mechanic movement of a step progression in the chromatic scale in the works of J.S. Bach. In connection with the underlined intonational junction of the major thematic “joints” of the work, denoted by the symbolism of “bachianism” and genre interconnections, the abovementioned Preludes by F. Chopin are considered as authorial composed cycle. Its essentials are “through” lines of semantic and intonational development, which are embedded in a musical work by its artistic nature and the stylistic setting of romantic aesthetics, organically “interwoven” with the pre-symbolic indicators of the contemporary art of “Pre-Raphaelites”.

Bach’s Musical Universe: The Composer and His Work by Christoph Wolff

Reviewed by: Bach’s Musical Universe: The Composer and His Work by Christoph Wolff Zoltán Szabó (bio) Christoph Wolff. Bach’s Musical Universe: The Composer and His Work (New York: W. W. Norton & Company, 2020). 432 pp. Christoph Wolff’s pivotal research in Bach scholarship, spanning over many decades, hardly needs extensive introduction. The list of his influential publications extends from articles in academic journals, through editorial work in several annual volumes of the Bach-Jahrbuch, to his role of revising and expanding the fundamental scholarly source The New Bach Reader (1998). He is also the author of two sizable tomes on this topic, Bach: Essays on His Life and Music (1991), a collection of thirty-two articles on specific aspects of the composer’s life and works, and the comprehensive biography Johann Sebastian Bach: The Learned Musician (2000). His latest book, Bach’s Musical Universe (2020), broadens the scope of scholarly knowledge offered in his previous two books even further, while connecting with them in such an organic manner that it almost makes one wonder: why did we not miss the last part of this scholarly triptych before? Indeed, the author’s meticulously detailed work on Bach research is best appreciated with all three volumes at hand. Regular cross-referencing among them is needed, as numerous footnotes in this book refer the reader to the findings in the other two. The look and touch of a new book can add to the positive experience of using it, and there is almost no disappointment here. The feel of the book is pleasant, it is well bound, it stays open easily, and the font is large enough to read it without straining the eyes (sadly, this is not always the case with academic publications). Unfortunately, though, at least in my copy, there seems to be a color run on the cover page, printed in yellow and white letters, where within the white line of “The Composer and His Work,” the last three letters of the word “composer” are inexplicably yellow. The structure of the book is clear, as it arrives to its focus from two different directions. With evident respect, in chapter 1, Wolff presents and later relies on Carl Philipp Emanuel Bach’s summary catalogue of his father’s compositions, compiled shortly after Johann Sebastian’s death in 1750 and significantly amended in 1774. Concurrently, from a different approach, the author draws attention to those compositions that are “matching pieces of a certain kind or genre” (21). These have an “opus character” or represent an “opus collection”—a reference to the grouped instrumental compositions of [End Page 98] Corelli, Vivaldi, and others—indicating that Bach prepared these compositions with remarkable care. The Italian composers followed the traditions of collecting compositions in multiples of three, the “holy number,” representing the Father, the Son, and the Holy Spirit. Bach did compose a number of cycles in groups of six, for example the toccatas, suites, and partitas for keyboard, but often had other organizational means in mind, such as all the major and minor keys, as in the twice twenty-four movements of the Well-Tempered Clavier. Wolff’s examination of the unifying concepts of these thematically defined works is as valuable as his distinction between what constitutes an opus collection of instrumental works versus choral works. The two approaches should not necessarily lead to the investigation of the same Bach compositions, but, fascinatingly, they almost completely coincide—or perhaps, that is not a coincidence? It is also worth considering that another Bach scholar, Ruth Tatlow, following the lead of her own, very different investigation of proportional parallelisms, also focuses on almost exactly the same set of compositions.1 Intriguingly, some masterworks, such as the four orchestral suites, the sonatas for viola da gamba or traverso flute, and the motets, are missing from both scholars’ list of analyzed compositions, although the reason for this is not necessarily that they would not pass the opus-style benchmark. Bach’s Musical Universe is divided into eight chapters, with a prologue and an epilogue, scrutinizing the composer’s opus collections in roughly chronological order. Wolff’s selection of Bach compositions with an opus character...

A “Proto-Theme” in Some of J. S. Bach’s Fugal Works

This article focuses on a pattern of harmony and voice leading that appears, elaborated, in several fugue expositions (and generically related passages) by J. S. Bach. I contextualize this pattern in examples of “schematic” Baroque fugal writing and suggest that for Bach it functions as a sort of “proto-theme,” with respect to which certain expositions stand as “variations.” These expositions eschew normative I–V–I progressions ofStufenand thus offer a challenge to William Renwick’s exhaustive methodology for fugue analysis. Bach’s variations may respond motivically and energetically to a sense of retrogression implicit the proto-theme, as I demonstrate with an analysis of the Fugue in A minor from Book II ofThe Well-Tempered Clavier, BWV 889.

Polyphonic Setting of Endings in Fugues from “The Well-Tempered Clavier” by Johann Sebastian Bach

Relevance of the study is determined by outstanding role of J. S. Bach’s clavier fugues in professional musical education.Main objective of the study is to identify and systematize some techniques of braking and stopping at the final stage of form building in Bach's clavier fugues.Scientific novelty of the research arises from the study of musical material that had not previously attracted the attention of researchers. Also the problems connected with the final stage of fugue form building have not attracted sufficient attention.Methodology of the research. The methodological basis of the research is the idea that the text of a musical work implements a variety of communicative functions in relation to the reader / listener. In particular, it gives “signals” about the beginning of a certain stage of form building. To comprehend such “signals”, the method of complex — melodic, harmonic and polyphonic — analysis of musical works is used, as well as certain provisions of the musical rhetoric of the 18th century.Findings and conclusions. Among the texture shaping techniques that give “signals” about the fugue ending, we highlighted the techniques of texture compaction with the help of additional voices: weighting obligate voices with added notes, delay (“sticking”) of obligate voices, their splitting and the inclusion of new voices carrying a noticeable melodic (thematic) load. The variety in the use of these few techniques leads to the fact that among the fifteen considered examples no two are alike.We believe that attention to such techniques of texture organization and their communicative functions helps to choose adequate performing means and contributes to a more distinct articulation of the musical fabric.The use of such techniques is inseparable from form building and is strongly connected both with thematic (polyphonic) work and with harmonic design. Considering these connections we distinguish three types of Bach's clavier fugues completion: free endings (similar to rhetorical conclusio), codes and additions.The article also describes a method of thematic work, for which the name “resulting counterpoint” is suggested.

Cadence in Fugue: Modes of Closure in J. S. Bach's Well-tempered Clavier

In the traditional theory of fugue, the issue of cadence is normally relegated to a minor role, with only cursory attention given to how cadences articulate various modes of closure within a fugue. This article offers new perspectives on cadential practice in fugue based on a comprehensive examination of J. S. Bach's Well-tempered Clavier. Using some fundamental concepts of tonal cadence in general, including a strict delimitation of its harmonic content, a consideration of its formal scope of closure, and a set of cadential deviations, I investigate how cadence operates both to articulate formal boundaries and to realize potentialities for cadence that may not have a clear formal role. The study relies extensively on a distinction between subject-ending cadences (of limited formal scope) and independent cadences (not associated with the end of the subject)—the latter, more than the former, being responsible for major points of formal closure. I explain why a fugue's exposition rarely ends with a cadence and consider those exceptional cases where the end of the fugue brings a subject-ending cadence. The article concludes with analyses of cadential practice in three complete fugues (in D major, E♭ major, and G♯ minor, all from book I of the WTC).

Tonality Tunes the Statistical Characteristics in Music: Computational Approaches on Statistical Learning.

Statistical learning is a learning mechanism based on transition probability in sequences such as music and language. Recent computational and neurophysiological studies suggest that the statistical learning contributes to production, action, and musical creativity as well as prediction and perception. The present study investigated how statistical structure interacts with tonalities in music based on various-order statistical models. To verify this in all 24 major and minor keys, the transition probabilities of the sequences containing the highest pitches in Bach's Well-Tempered Clavier, which is a collection of two series (No. 1 and No. 2) of preludes and fugues in all of the 24 major and minor keys, were calculated based on nth-order Markov models. The transition probabilities of each sequence were compared among tonalities (major and minor), two series (No. 1 and No. 2), and music types (prelude and fugue). The differences in statistical characteristics between major and minor keys were detected in lower- but not higher-order models. The results also showed that statistical knowledge in music might be modulated by tonalities and composition periods. Furthermore, the principal component analysis detected the shared components of related keys, suggesting that the tonalities modulate statistical characteristics in music. The present study may suggest that there are at least two types of statistical knowledge in music that are interdependent on and independent of tonality, respectively.