Clavierübung III (BWV 552, 669-689, 802-805)


Introduction

The third part to the Clavierübung (commonly referred to as the “German Organ Mass”) consists of a grand prelude and fugue (commonly referred to as “St. Anne”), the longest of all Bach’s preludes and fugues, at the beginning and end of the opus. Between these bookends lies 21 chorale preludes and 4 duets that correspond sequentially to the established German Lutheran liturgy. The following bullet list summarizes the large-scale organization of Bach’s greatest and most ambitious organ collection:

  • (Α) Prelude – The first bookend secures all that lies within

  • Kyrie – Six chorales, BWV 669-674, are organized into two duration groups.

  • Gloria – Three chorales, BWV 675-677, are organized into one duration group.

  • Ten Commandments – Two chorales, BWV 678-679, are organized into one duration pair.

  • Credo – Two chorales, BWV 680-681, are organized into one duration pair.

  • The Lord’s Prayer – Two chorales, BWV 682-683. The first chorale, the longest movement in the collection, stands alone with a duration of precisely 10 minutes, while the second chorale is grouped with the “Baptism” section.

  • Baptism – Two chorales, BWV 684-685, are organized into one duration pair with the addition of the last chorale in “The Lord’s Prayer” section, which forms a duration group of three.

  • Confession – Two chorales, BWV 686-687, are organized into one duration pair.

  • Communion – Two chorales, BWV 688-689, are organized into one duration pair, and four duets, BWV 802-805, are organized into two duration pairs of first-last and second-third.

  • (Ω) Postlude – The last bookend secures all that lies within.

 

✯ The Alpha & The Omega

 In Chapter 3 it is shown that Bach often gave first and last movements equal durations in multi-movement works or in groups of movements, which symbolizes the unity of the first and last or The Alpha & The Omega. The first and last letters of the classical Greek alphabet, Α and Ω, symbolize that Jesus has existed for all eternity, from the beginning to end of time. Securing the bookends with related durations (usually 1:1) was Bach’s preferred technique to unify large-scale collections. It is a simple yet highly effective technique that imbues multi-movement works with an enduring theological truth and esthetically satisfying large-scale symmetry. For example, Bach used this technique in the Schübler Chorales (discussed in two chapters previously) as well as in many other key works discussed in Chapter 3.

Perhaps the most obvious but overlooked example of Bach’s use of The Alpha & The Omega is in the Goldberg Variations, published just two years later (1741) as the fourth and final part to the Clavierübung series. Performers and listeners take for granted the final appearance of the opening Aria at the end of the Goldbergs; however, Bach was not obligated to do this, and, he strayed from tradition by incorporating such a seemingly simple technique into his opus. This is because up to this time a set of variations in which the opening theme is repeated at the end can hardly be found. Hence, the Goldbergs is the most obvious yet most overlooked example of Bach’s use of The Alpha & The Omega (Figure 1.)

✯ Prelude & Postlude: BWV 552

Just as he would do in the Goldberg Variations two years later (1741), in the Schübler Chorales nine years later (1747), and as he did previously in many other key works (discussed in Chapter 3), the first prerequisite in composing such a monumental collection as Clavierübung III was to secure the bookends with equal durations to symbolize The Alpha & The Omega. Thus, it can be assumed as an axiom that Bach intended the “St. Anne” prelude and fugue to have equal durations (Figure 2).

Limiting the tempo choices only to those tempos in the mathematically ideal matrix (explained in Chapter 2), reveals only one possibility of tempos for each section that contribute to equal durations for this prelude and fugue. More specifically, the prelude and fugue consist of four sections (one section for the prelude, three sections for the fugue) in which the natural tempos for each style and time signature result in two equal durations of 7:30 that add to a total of 15:00. Bach planned the duration of 15:00 from the outset, before putting pen to paper, and then portioned out the three sections of the fugue so that they would add to 7:30. Here is a mathematical summary of how Bach achieved equal durations of 7:30 in this prelude and fugue astonishingly within a mere 0.3% average margin of error:

Movt 1 – Prelude (duration 7:30)

  • Beats 410 — adjustment (-5 beats) — beats 405 — 405 beats ÷ 54 tempo = 7:30

Movt 27 – Fugue (duration 7:30)

  • Fugue (4/2 section) — beats 144 ÷ tempo 72 = duration 2:00

  • Fugue (6/4 section) — beats 270 ÷ tempo 108 = duration 2:3

  • Fugue (12/8 section) — beats 144 ÷ tempo 48 = duration 3:00

  • Total of Fugue — 2:00 + 2:30 + 3:00 = 7:30


✯ Kyrie: BWV 669-674

Movts 2-3 (2:3 duration ratio, 2:00-1:20)

  • Beat ratio = 168:244 — adjustment (-6 beats, -1 beat) — 162:243 = 2:3

  • Tempo ratio = 54:54 = 1:1

  • 2:1 beat ratio ÷ 1:1 tempo ratio = 2:3 duration ratio — 3:00-4:30

Movts 3-4 (1:1 duration ratio, 4:30-4:30)

  • Beat ratio = 244:240 — adjustment (-1 beat, +3 beat) — 243:243 = 1:1

  • Tempo ratio = 54:54 = 1:1

  • 1:1 beat ratio ÷ 1:1 tempo ratio = 1:1 duration ratio — 4:30-4:30

Movts 5-6 (1:1 duration ratio, 1:30-1:30)

  • Beat ratio = 96:60 — adjustment (-1 beats, -1 beat) — 95:63 = 3:2

  • Tempo ratio = 63:42 = 3:2

  • 3:2 beat ratio ÷ 3:2 tempo ratio = 1:1 duration ratio — 1:30-1:30

Movts 6-7 (1:1 duration ratio, 1:30-1:30)

  • Beat ratio = 60:102 — adjustment (+3 beats, -6 beats) — 63:96 ≈ 2:3

  • Tempo ratio = 42:64 ≈ 2:3

  • 2:3 beat ratio ÷ 2:3 tempo ratio = 1:1 duration ratio — 1:30-1:30

✯ Gloria: BWV 675-677

Movts 8-9 (2:3 duration ratio, 4:00-6:00)

  • Beat ratio = 198:252 — adjustment (-6 beats) — 192:252 = 16:21

  • Tempo ratio = 48:42 = 8:7

  • 16:21 beat ratio ÷ 8:7 tempo ratio = 2:3 duration ratio — 4:00-6:00

Movt 10 (duration of 1:00)

  • Beats = 80 — adjustment (+4 beats) — 84

  • Tempo = 84

  • 84 beats ÷ 84 tempo = 1:00

✯ Ten Commandments: BWV 678-679

Movts 11-12 (2:1 duration ratio, 4:18-2:09)

  • Beat ratio = 360:140 — adjustment (-4 beats) — 360:137 ≈ 8:3

  • Tempo ratio = 84:64 ≈ 4:3

  • 8:3 beat ratio ÷ 4:3 tempo ratio = 2:1 duration ratio — 4:18-2:09

✯ Credo: BWV 680-681

Movts 13-14 (2:1 duration ratio, 2:46-1:23)

  • Beat ratio = 200:60 — adjustment (-2 beats) — 200:58 ≈ 24:7

  • Tempo ratio = 72:42 = 12:7

  • 24:7 beat ratio ÷ 12:7 tempo ratio = 2:1 duration ratio — 2:46-1:23

✯ The Lord’s Prayer: BWV 682-683

Movt 15 (duration, 10:00)

  • Beats = 546 — adjustment (-6 beats) — 540

  • Tempo = 54

  • 540 beats ÷ 54 tempo = 10:00

✯ Baptism: BWV 684-685

Movts 16-17 (1:3 duration ratio, 1:30-4:30)

  • Beat ratio = 144:324 = 4:9

  • Tempo ratio = 96:72 = 4:3

  • 4:9 beat ratio ÷ 4:3 tempo ratio = 1:3 duration ratio — 1:30-4:30

Movts 17-18 (3:1 duration ratio, 4:30-1:30)

  • Beat ratio = 324:81 = 4:1

  • Tempo ratio = 72:54 = 4:3

  • 4:1 beat ratio ÷ 4:3 tempo ratio = 3:1 duration ratio — 4:30-1:30

Movts 16-18 (1:1 duration ratio, 1:30-1:30)

  • Beat ratio = 144:81 = 16:9

  • Tempo ratio = 96:54 = 16:9

  • 16:9 beat ratio ÷ 16:9 tempo ratio = 1:1 duration ratio — 1:30-1:30

✯ Confession: BWV 686-687

Movts 19-20 (1:1 duration ratio, 5:33-5:33)

  • Beat ratio = 300:408 — adjustment (-8 beats) — 300:400 = 3:4

  • Tempo ratio = 54:72 = 3:4

  • 3:4 beat ratio ÷ 3:4 tempo ratio = 1:1 duration ratio — 5:33-5:33

✯ Communion: BWV 688-689

Movts 21-22 (2:3 duration ratio, 3:41-5:31)

  • Beat ratio = 354:268 — adjustment (-2 beats) — 354:266 = 4:3

  • Tempo ratio = 96:48 = 2:1

  • 4:3 beat ratio ÷ 2:1 tempo ratio = 2:3 duration ratio — 3:41-5:31

Movts 23-26 (1:1 duration ratio, 3:00-3:00)

  • Beat ratio = 219:216 — adjustment (-3 beats) — 216:216 = 1:1

  • Tempo ratio = 72:72 = 1:1

  • 1:1 beat ratio ÷ 1:1 tempo ratio = 1:1 duration ratio — 3:00-3:00

Movts 24-25 (1:1 duration ratio, 3:34-3:34)

  • Beat ratio = 298:156 — adjustment (+2 beats, -6 beats) — 300:150 = 2:1

  • Tempo ratio = 84:42 = 2:1

  • 2:1 beat ratio ÷ 2:1 tempo ratio = 1:1 duration ratio — 3:34-3:34

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