Brandenburg Concertos (BWV 1046-51)
(Brandenburg Concerto No. 1 still in progress)
The first and third movements have a close 7:4 beat ratio, 476:278, and 7:8 tempo ratio, 84:96, resulting in a close 2:1 duration ratio, 5:37-2:53. The second movement has a duration a little over four minutes, 4:03. One more measure for the first movement, 120, and three fewer measures for the third movement, 136, result in a 7:4 beat ratio, 476:272, and a 2:1 duration ratio, 5:40-2:50. In addition, the second and third movement have a 1:2 tempo ratio, 48:96. One less measure for the second movement, 64, results in a duration of four minutes.
Movements 1-3 —> 7:4 beat ratio, 7:8 tempo ratio, 2:1 duration ratio (7/4 ÷ 7/8 = 2/1)
Movement 2 —> 64 measures (192 beats) of 3/4 at 48 bpm = 4:00 (192 ÷ 48 = 4)
Movements 2-3 —> 2:3 tempo ratio, 48:96
The first and third movements have a 3:2 tempo ratio, 84:56, resulting in durations of 6:28 and 3:25. This indicates that the first movement is a full 25 seconds short of being twice the duration of the third movement, which probably explains the second movement of one measure (marked Adagio). That is, realizing that the first movement needed to be extended by about 20 seconds to achieve a 2:1 duration ratio of 6:50-3:25, Bach added a brief transitional second movement (improvised).
Movements 1-3 3:2 tempo ratio (84/56 = 2/3)
The first and third movements share a 3:2 duration ratio, 7:36-5:04, while the second and third movements share a 2:3 duration ratio, 3:22-5:04. Six fewer measures for the first movement, 420, one less measure for the second movement, 70, and four fewer measures for the third movement, 240, result in 3:2 and 2:3 duration ratios, 7:30-5:00 and 3:20-5:00.
Movements 1-3 —> 7:8 beat ratio, 7:12 tempo ratio, 3:2 duration ratio (7/8 ÷ 7/12 = 3/2)
Movements 2-3 —> 4:9 beat ratio, 2:3 tempo ratio, 2:3 duration ratio (4/9 ÷ 2/3 = 2/3)
The first and third movements have a close 3:2 beat ratio, 908:620, a 1:1 tempo ratio, 84:84, resulting in a close 3:2 duration ratio, 10:48-7:22. The first and second movements have a close 7:3 beat ratio, 908:392, and a 7:6 tempo ratio, 84:72, resulting in a close 2:1 duration ratio, 10:48-7:22. In addition, the three movements have a symmetrical 7:6:7 tempo ratio, 84:72:84. Four more measures for the first movement, 231, one-half less measure for the second movement, 49.5, and two fewer measures for the third movement, 308, result in 3:2 and 2:3 duration ratios derived from the whole-number duration of eleven minutes, 11:00-7:20 and 11:00-5:30.
Movements 1-3 —> 3:2 beat ratio, 1:1 tempo ratio, 3:2 duration ratio (3/2 ÷ 1/1 = 3/2)
Movements 1-2 —> 7:3 beat ratio, 7:6 tempo ratio, 2:1 duration ratio (7/3 ÷ 7/6 = 2/1)
Movements 1-2-3 —> 7:6:7 tempo ratio, 84:72:84
The first and third movements have a close 7:6 beat ratio, 520:440, and 7:6 tempo ratio, 84:72, resulting in virtually equal durations, 6:11 and 6:06. The second movement has a duration a little under four minutes, 3:52. In addition, the second and third movements have a 2:3 tempo ratio, 48:72. Four fewer measures for the first movement, 126, two more measures for the second movement, 64, and two fewer measures for the third movement, 108, result in a symmetrical 3:2 3 duration ratio, 6:00-4:00-6:00.
Movements 1-3 —> 7:6 beat ratio, 7:6 tempo ratio, 1:1 duration ratio (7/6 ÷ 7/6 = 1/1)
Movement 2 —> 64 measures (192 beats) of 3/2 at 48 bpm = 4:00 (192 ÷ 48 = 4)
Movements 2-3 —> 2:3 tempo ratio, 48:72
