Bach’s “Fours”

Abstract

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 H ö h ' 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