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Palindromes, Symmetries and Mini-Canons in Bach Chorale BWV 32/6 by Luke Dahn 24 July 2008; Rev

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Palindromes, Symmetries and Mini-Canons in Bach Chorale BWV 32/6 by Luke Dahn 24 July 2008; Rev Palindromes, Symmetries and Mini-Canons in Bach Chorale BWV 32/6 By Luke Dahn 24 July 2008; rev. 9 April 2014 Bach closes Cantata 32 Liebster Jesu, mein Verlangen with a setting of the final verse of Paul Gerhardt’s “Weg, mein Herz, mit den Gedanken” using Louis Bourgeois’s tune “Freu dich sehr, o meine Seele.” A total of seven chorale settings of the Bourgeois tune are found in the choral works of Bach, indicating a particular fondness for it. Only two other tunes appear more frequently in the entire catalogue of extant four-part chorales – Heinrich Isaac’s “O Welt, ich muss dich lassen” (BWVs 13.6, 44.7, 97.9, 244.10, 244.37, 245.11, 392, 393, 394 395) and Hans Leo Hassler’s “Befiehl du deine Wege” (BWVs 135.6, 153.5, 161.6, 244.15, 244.17, 244.44, 244.54, 244.62, 248.5, 248.64, 270, 271, 272).1 The seven settings of the Bourgeois tune are as follows, arranged by date of first performance: Seven Four-part Chorale Settings of Bourgeois’s “Freu dich sehr, o meine Seele” BWV First Performance Text Chorale Collections 25.6 29 August 1723. 14th Sunday after Trinity Treuer Gott, ich muss dir klagen, by Breitkopf 254 & 282, Riem Johann Heermann 254 & 282, Dietel 11 194.6 2 November 1723. Dedication of church and Treuer Gott, ich muss dir klagen, by Breitkopf 63 & 256, Riem 64 organ Johann Heermann & 256, Dietel 18 70.7 21 November 1723. 26th Sunday after Trinity Freu dich sehr, o meine Seele, by None Christoph Demantius 32.6 13 January 1726. 1st Sunday after Epiphany Weg, mein Herz, mit den Gedanken, Breitkopf 29, Riem 29 by Paul Gerhardt 39.7 23 June 1726. 1st Sunday after Trinity Kommt, lasst euch den Herren lehren, Breitkopf 67, Riem 67, by David Denicke Dietel 116 19.7 29 September 1726. Feast of St. Michael and Freu dich sehr, o meine Seele, by Breitkopf 297, Riem 298, Angels Christoph Demantius Dietel 87 30.6 24 June 1738?, Feast of the Nativity of St. John Tröstet, tröstet meine Lieben, by Breitkopf 76, Riem 76 the Baptist Johann Olearius 1 Several other tunes appear seven times as well: Johann Schop’s “Werde munter, mein Gemüthe,” Claudin de Sermisy’s “Was mein Gott will das g’scheh allzeit,” Severus Gastorius / Werner Fabricius’s “Was Got tut, das ist wohlgetan,” Ahasverus Fritsch’s “O Gott, du frommer Gott” (melody #3), Johann Crüger’s “Jesu, meine Freude,” and Georg Neumark’s “Wer nur den lieben Gott lässt walten.” CHORALE In Chorale 32.6, Bach seems particularly interested in symmetrical and palindromic structures, perhaps inspired by the palindromic components of the Bourgeois tune – the first five notes of the Aufgesang (G-A-B-A-G), the entire second phrase (G-A-B-C-B-A-G), the first five notes of the Abgesang (B-C-D-C-B), and the fifth phrase (B-D-C-B(-A-)G-A-B-G). MOTIVE X The single most important motive of the chorale is given at the tune’s very opening: G-A-B-A-G (labeled “X”) The palindromic structure of motive X informs other parts of the chorale, as palindromic structures appear frequently. EXAMPLE 1 EXAMPLE 2 The melody of phrase 2 (Example 2) is an expansion of X: G-A-B-C-B-A-G. Naturally, this version of X is also palindromic. This expanded form of X is then transferred to the bass in measures 5-6 (Example 3), where it appears in inversion. The bass here is the exact mirror of the soprano’s phrase in measures 3-4, with an pitch axis, and common starting point, of G. Bach then continues his method of expansion in measures 7-8 in the bass part, presenting a further expansion of motive X, now encompassing five notes. Example 3 also shows three other manifestations of X in measures 1-8: a quick appearance via passing tones in the tenor in measure 3, a third consecutive appearance in the hymn tune in measures 5-6, and a rhythmically askew appearance in the alto leading to the half cadence in measure 8. EXAMPLE 3 Almost every note in every part of phrase 5 (mm.9-11) figures in a presentation of motive X (Example 4). The melody in the soprano has three overlapping presentations of motive X, with the two outer occurrences being partial. The first instance is missing its second note (C), while the third instance is missing its fourth note (A), thus revealing another palindromic arrangement. A similar thing happens in the tenor part, with an inverted form of motive X overlapping an uninverted form. (Notice the palindromic rhythmic nature of the two forms when taken as a unit.) The alto and bass lines are also related to each other. The alto part has two inverted presentations of X, with the final note of the first serving as a link starting the second. (The E-F#-G-F#-E passage that overlaps the two alto instances of X here can also be considered an uninverted form of X.) The result is an undulating wave. The bass likewise has an undulating wave, but a wave created by overlapping two expanded four-note versions of X. EXAMPLE 4 In the final phrase of the chorale, motive X is found mirroring itself in the soprano and bass parts in measures 11-12. The bass presents an inverted form of the soprano retaining the exact intervallic structure (m2, M2, M2, m2), while its rhythm is retrograded. The result, of course, is that the bass is a retrograde inversion of the soprano. Finally, the alto and tenor parts end the chorale with closing instances of motive X—the expanded four-note version in the alto (with a missing penultimate note), and the three-note version in the tenor. The rearticulation of the motive’s peak note in the tenor (D) increases the satisfaction of its downward resolution. EXAMPLE 5 CANONS AND PALINDROMES Measures 1-4 Perhaps unsurprisingly, canonic devices frequently appear as phrases and phrase fragments are transferred from part to part. Such transference has already been seen in Example 3. The fragmentary nature of some of these canonic moments may cause them to seem coincidental, but the frequency with which such devices are used throughout the chorale does not allow for coincidence. Example 6 shows the first two phrases and two very simple mini-canons occurring between the tenor and soprano parts. Again, taken alone, one might certainly suggest the connection between these 3-note groupings is made arbitrarily. When taken along with all of the other canonic devices discussed in this essay, and when considering the fact that each of these canonic connections is perfectly audible, one is left only to conclude that canon and symmetry are a guiding principle. EXAMPLE 6 Measures 3-6 Example 3 above demonstrated a relationship between the soprano line in measures 3-4 and the bass line in measures 5-6. The bass is an exact mirror of the soprano’s expanded version of motive X, with an axis on the pitch G. (The soprano moves upward away from G; the bass moves downward away from G.) A closer look at the passage reveals a similar relationship between the alto and tenor parts. The alto’s counterpoint to the soprano’s melody in measures 3-4 (itself nearly palindromic), is transferred to the tenor in measures 5-6. The tenor gives with a mirrored version of the alto’s counterpoint. The mirror is not exact, for the tenor should end on E rather than D, but this slight alteration does in no way diminish the audible connection between the two. The tenor materializes out of the alto in the same way the bass materializes out of the soprano. The slight alteration of the tenor does two things here: it provides an emphasis on the pitch D (m.6), the dominant of the home key of G, and it creates a palindromic structure in the tenor (D-E-A-E-D). This transference of two grouped counterpointing voices in mirroring fashion from the soprano and alto to the bass and tenor (which then carry the responsibility of harmonically supporting a new melodic phrase) is an example of the stroke of genius we come to expect from Bach, though usually only in grander contrapuntal genres. EXAMPLE 7 The way in which the tenor and bass “develop” ideas presented previously in the soprano and alto might cause one to envision (anachronistically, to be sure) a kind of proto-sonata form. Phrases 1 and 2 serve “expositional” purposes; phrases 3 and 4 and perhaps 5 (though 5 is melodically connected with 6) demonstrate imaginative and thorough “developmental” devices; and phrase 6 provides closure. A few palindromic structures in Chorale 32.6 have already been demonstrated: in the various forms of motive X itself, in the structure of the soprano’s tune in phrase 5 (Example 4), and in the tenor’s rhythm in the same phrase. With the liberal use of various palindromic forms of the chorale’s primary motive X, palindromic structures naturally emerge. However, it is measures 5-6 that truly confirm the palindrome as a guiding principle, for not only does Bach alter the original tune to produce a palindromic phrase (substituting the original second note (B) for a C), and not only does he alter the tenor’s mirrored version of the alto’s previous line (Example 7), he also gives every part a palindromic phrase, producing a progression that clearly and quite audibly doubles back on itself (Example 8).
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