Bach’s “Fours”

Kira I. Yuzhak


The grouping of plays of the same type is of concern to both their authors and researchers. For the former, this is already reflected in the titles of works, and for the latter, it leads to a multifaceted search for the hidden mechanisms of composers’ thinking.

Thus, the various ways in which Bach united groups of his works were revealed by A. Milka in the article “Bach’s “sixes”” (1999). In Bach’s major cyclic opuses, another “measure” attracts attention: the quadruple , noticeable especially since it is formed by canons (“The Art of Fugue”) or duets permeated with canonical work (III Keyboard Exercise).

But when it comes to canons , we remember that in Bach they are often grouped in groups of ten or/and four: “The canonical variations on the Christmas song Vom Himmel ö da komm ich her ” BWV 769 contains four contrapuntal canons (variations I– IV) and four thematic (V variation); “Musical Offering”—ten canons: six contrapuntal and four thematic; “Various Canons on the First Eight Bass Notes of the Previous Aria” (i.e. the theme of the Goldberg Variations) - 14 canons written in groups of four, six and four canons.

In fact, the grouping of four affects not only the canons in Bach, and this is natural: let’s not forget how many four-movement suites and sonatas he wrote. So it is not surprising that the four orchestral suites created in different years are numbered by V. Schmieder as a specific four .

Therefore, one should carefully study not only how Bach organizes the quadruples of his works, but also how, under the pressure of circumstances, he himself violates the intended plan (which, as is known, took place when engraving the “Musical Offering” and “The Art of Fugue”).

But even if we focus on the already studied sixes and fours, the question arises: what factors provide diversity in them and hold the whole together? A. Milka showed this on the structure of sixes; In the proposed work, an attempt is made to analyze Bach's quadruples in this aspect . The internal organization of the “quartet” depends on the context in which it is immersed: in a contrasting environment it is configured to demonstrate the diversity of its components, while in a similar environment it is organized according to the order of its main technical characteristics. The functional and semantic load of the “fours” depends on how they are presented in a large cycle: together or scattered. In the first case, the differences between the “quartet” and the surrounding plays come to the fore; in the second, it strengthens the structure of the whole in which it is built from the inside.

Keywords: J. S.Bach; canon; Clavier Übung; Die Kunst der Fuge, BWV 1080; Musicalisches Opfer, BWV 1079; Einige Canonische Verænderungen, BWV 769; Aria mit Verschiedenen Verænderungen (Goldberg-Variationen), BWV 988

For citation: Yuzhak K. I. Bach’s “Fours” [Electronic source]. In: Sovremennye problemy muzykoznaniya / Contemporary Musicology, 2022, no. 1, pp. 39–77. (In Russ.) DOI: 10.56620/2587-9731-2022-1-039-077


Gerver L.L. Smena pravila po khodu kanona [Change of Rule in the Course of the Canon]. In: Problemy i metody izucheniya starinnoj muzyki: sb. statej po materialam mezhdunar. konf. 4–5 dekabrya 2014 goda [Problems and Methods of Studying Early Music: Sat. Articles on the Materials of the International. Conf. December 4–5, 2014] / Sankt Peterburgskaya gos. konservatoria im. N. A. Rimskogo-Korsakova. Saint-Petersburg: Skifiya-print [Scythia-print], 2019. Pp. 40–52.

Dolzhanskij A.N. Puti razvitiya teorii E.N. Korchinskogo [Ways of development of the theory of E.N. Korchinsky]. In: Aleksandr Naumovich Dolzhanskij. Sbornik statej k 100-letiyu so dnya rozhdeniya / predislovie i kommentarii k stat’jam K.I. Yuzhak [Alexander Naumovich Dolzhansky. Collection of Articles for the 100th Anniversary of the Birth / Preface and Comments on the Articles by K.I. Yuzhak]. Saint-Petersburg: Sudarynya, 2008. Pp. 160–182.

Ivanova K.N. “Gol’dberg-Variatsii” I.S. Bakha (BWV 988): kanony dlya ispolneniya i kanony dlya ukrasheniya [“Goldberg Variations” by J.S. Bach (BWV 988): Canons for Performance and Canons for Decoration]. In: Universitetskij nauchnyj zhurnal. No. 33 (filologicheskie i istoricheskie nauki, arheologiya i iskusstvovedenie) [University Scientific Journal. 2017. No. 33 (Philological and Historical Sciences, Archeology and Art History)]. Saint-Petersburg, 2017. Pp. 107–117.

Kyuregyan T.S., Moskva Yu.V., Kholopov Yu.N. Grigorianskij khoral: ucheb. posobie [Gregorian Chant: Textbook]. Moscow: Moskovskaya gos. Konservatoria [Moscow State Conservatory], 2008.

Milka A.P. Berlinskij avtograf kak tcikl [Berlin Autograph as a Cycle]. In: Vtorye Bakhovskie chteniya: Iskusstvo fugi: materialy nauch. konf. 29–30 marta 1993 / Sankt-Peterburgskaya gos. konservatoriya; sost. A.P. Milka, nauch. red. K.I. Yuzhak [Second Bach Readings: The Art of the Fugue: materials of scientific. conf. March 29–30, 1993 / comp. A.P. Milka; scientific ed. K.I. Yuzhak.]. Saint-Petersburg, 1993. Pp. 50–75.

Milka A.P. Bakhovskie “shestyorki” (Printsipy organizatcii bakhovskikh sbornikov v kontekste osobennostej Barokko) [Bach's “Sixes” (Principles of Organization of Bach's Collections in the Context of the Features of the Baroque)]. In: Muzykal’naya kommunikatsiya: [Musical communication: coll. scientific tr.]. Saint-Petersburg: Rossijskij Institut Istorii Iskusstv [Russian Institute of Art History], 1996. Pp. 220–238. (Problemata Musicologica-8).

Milka A.P. “Muzykal’noe prinoshenie” I. S. Bakha: K rekonstruktsii i interpretatsii [“Musical Offering” by J.S. Bach: Toward Reconstruction and Interpretation]. Moscow: Muzyka [Music], 1999.

Milka A.P.“Iskusstvo fugi” I. S. Bakha: K rekonstruktsii i interpretatsii [“The Art of the Fugue” by J. S. Bach: Toward Reconstruction and Interpretation]. Saint-Petersburg: Kompozitor [Composer], 2009.

Milka A.P. Otnositel’no zagolovka odnogo iz kanonov I. S. Bakha [Concerning the Title of One of the Canons of J. S. Bach]. In: W prostranstve smyslov: Tekst i intertekst: sb. statej [In the Space of Meanings: Text and Intertext: Collection of Articles]. Petrozavodsk: Verso, 2016. Pp. 262–271.

Milka A.P., Yuzhak K.I. Stretta vs kanon [Stretta vs Canon]. In: Opera musicologica. 2020. V. 12. No. 5 (S). Pp. 40–62. DOI: 10.261156/OM.2020.12.5.003.

Skrebkov S.S. Polifonicheskij analiz [Polyphonic Analysis]. Moscow: Muzgiz [Music State Publishing House], 1940.

[Zukkerman V.A.]. Glava VII. Masshtabno-tematicheskie struktury [Chapter VII. Scale-Thematic structures]. In: Mazel’ L.A., Zukkerman V.A. Analiz muzykal’nykh proizvedenij: Elementy muzyki i metodika analiza malykh form: ucheb. spetskursa dlya muzyk. vuzov [Analysis of Musical Works: Elements of Music and Methods of Analysis of Small Forms: Special Course Textbook for Music Universities]. Moscow: Muzyka [Music], 1967.

Yuzhak K.I. Nekotorye osobennosti stroeniya fugi I. S. Bakha: Stretta v dvukh tomakh “Khorosho temperirovannogo klavira” [Some Structural Features of J.S. Bach's Fugue: Stretta in the Fugues of The Well-Tempered Clavier]. Moscow: Muzyka [Music], 1965.

Yuzhak K.I. Duety iz Clavier Übung III: edinstvo v mnogoobrazii [Duets from Clavier Übung III: Unity in Diversity]. In: Opera Musicologica. 2009. No. 1. Pp. 83–100.

Yuzhak K.I. Ob odnoj osobennosti Chetyryokh uvertyur BWV 1066–1069 I. S. Bakha [On one Feature of the Four Overtures BWV 1066–1069 J.S. Bach]. In: Tekst khudozhestvennyj: Smysl i struktura. K 100-letiyu so dnya rozhdeniya Yu.G. Kona: sb. nauch. statej. / Petrozav. gos. konservatoriya im. A.K. Glazunova; Kaf. teorii muz. i kompozitsii; nauch. red.: E.G. Okuneva, I.V. Koposova, N.P. Khil’ko [Artistic Text: Meaning and Structure. To the 100th Anniversary of the Birth of Yu.G. Kon: Sat. scientific Art. / Ministry of Culture of the Russian Federation, Petrozavodsk State A.K. Glazunov Conservatory, Department of Theory of Music and Composition; scientific ed.: E.G. Okuneva, I.V. Koposova, N.P. Khilko]. Petrozavodsk: VPPrint, 2021. Pp. 176–196.

Yankus A.I. “Gol’dberg-Variatsii”: dve gruppy kanonov (BWV 988, BWV 1087) [“Goldberg Variations”: two groups of canons (BWV 988, BWV 1087)]. In: Contemporary Musicology. 2022. No. 1. Pp. 78–104.

Evangelisches Kirchengesangbuch. 47. Aufl. Hamburg: Friedrich Vittig Verlag, 1957.

[Marpurg F. W.]. Abhandlung von der Fuge nach den Grundsätzen und Exempeln der besten deutschen und ausländischen Meister... Nebst LXII. Kupfertafeln. Berlin: A. Haude und J.G. Spener, 1753.

[Walther J.G.] Musicaliasches Lexicon oder Musicalische Bibliothec... Leipzig: Wolffgang Deer, 1732.

Wolff Chr. Vorwort. In: J.S. Bach. Vierzehn Kanons über die ersten acht Fundamentalnoten der Aria aus den „Goldberg-Variationen“ BWV 1087.3. Aufl. Leipzig : Deutscher Verlag für Musik 8004, [1987]. S. 3–4.

Wolff Chr. The Clavier-Übung Series. In: Wolff Chr. BACH. Essays on his Life and Music. Cambridge, Massachusetts, London: Harvard University Press, 1991. Pp. 189–213.


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