The “Great 18” Chorales (BWV 651-668)
Movts 1-2 (2:3 duration ratio, 6:20-9:30)
Beat ratio = 424:597 — adjustment (-24 beats, +3 beats) — 400:600 ÷ 2:3
Tempo ratio = 63:63 = 1:1
2:3 beat ratio ÷ 1:1 tempo ratio = 2:3 duration ratio — 6:20-9:30
Movts 3-5 (1:1 duration ratio, 4:00-4:00)
Beat ratio = 249:292 — adjustment (+3 beats, -4 beats) — 252:288 = 7:8
Tempo ratio = 63:72 = 7:8
7:8 beat ratio ÷ 7:8 tempo ratio = 1:1 duration ratio — 4:00-4:00
Movts 3-4 (1:2 duration ratio, 4:00-8:00)
Beat ratio = 249:387 adjustment (+3 beats, -3 beats) — 252:384 ≈ 2:3
Tempo ratio = 63:48 ≈ 4:3
2:3 beat ratio ÷ 4:3 tempo ratio = 1:2 duration ratio — 4:00-8:00
O Lamm Gottes, unschuldig is the only movement in the Great 18 other than No. 12 that does not have a duration partner. In rare cases like this, Bach’s usual procedure was to create a whole number duration. In this beautiful “Lamb of God” movement, Bach apparently chose a duration of nine minutes, 9:00, and achieved this with pinpoint accuracy. Bach’s desire for this movement to last nine minutes rather than seven or eight (like No. 12) probably reflects the three verses of the text and the theological implications of 3 + 3 + 3 = 9, not to mention the three sharps or the two forms of triple meter, simple and complex. In sum, this piece is thoroughly imbued with symbolism of threes on no fewer than six levels (Table 1):
· Movt 6 (duration, 9:00)
3/2 sections (121 measures) — beats = 363
Tempo: Half = 48
363 beats ÷ 48 tempo = 7:33.75
9/8 section (31 measures) — beats = 93
Tempo: DottedQuarter = 64
93 beats ÷ 64 tempo = 1:27.19
Total duration of 3/2 and 9/8 sections — 7:33.75 + 1:27.19 = 9:00
Movts 7-8 (1:1 duration ratio, 4:00-4:00)
Beat ratio = 284:304 — adjustment (+4 beats, -16 beats) — 288:288 = 1:1
Tempo ratio = 72:72 = 1:1
1:1 beat ratio ÷ 1:1 tempo ratio = 1:1 duration ratio — 4:00-4:00
Movts 9-10 (2:1 duration ratio, 5:00-2:30)
Beat ratio = 272:168 — adjustment (-2 beat, -10 beats) — 270:158 ≈ 12:7
Tempo ratio = 54:63 = 6:7
12:7 beat ratio ÷ 6:7 tempo ratio = 2:1 duration ratio — 5:00-2:30
Movts 10-11 (1:1 duration ratio, 2:30-2:30)
Beat ratio = 168:184 — adjustment (-10 beats, - 4 beats) — 158:180 ≈ 7:8
Tempo ratio = 63:72 = 7:8
7:8 beat ratio ÷ 7:8 tempo ratio = 1:1 duration ratio — 2:30-2:30
Movt 12 (duration, 8:00)
Beats = 424 — adjustment (+8 beats) — 432
Tempo = 54
432 beats ÷ 54 tempo = 8:00
Movts 13-14 (1:1 duration ratio, 6:00-6:00)
Beat ratio = 381:384 — adjustment (-3 beats, -6 beats) — 378:378 = 1:1
Tempo ratio = 63:63 = 1:1
1:1 beat ratio ÷ 1:1 tempo ratio = 1:1 duration ratio — 6:00-6:00
Movts 15-16 (3:2 duration ratio, 5:00-3:20)
Beat ratio = 208:152 — adjustment (+2 beats, + 8 beats) — 210:160 = 21:16
Tempo ratio = 42:48 = 7:8
21:16 beat ratio ÷ 7:8 tempo ratio = 3:2 duration ratio — 5:00-3:20
Movts 17-18 (2:3 duration ratio, 2:30-3:45)
Beat ratio = 104:180 — adjustment (+1 beat) — 105:180 = 7:12
Tempo ratio = 42:48 = 7:8
7:12 beat ratio ÷ 7:8 tempo ratio = 2:3 duration ratio — 2:30-3:45
