Sonatas for Viola da Gamba and Harpsichord (BWV 1027-29)
The first and second movements have a close 1:1 beat ratio, 336:339, and 1:1 tempo ratio, 84:84, resulting in virtually equal durations, 4:00 and 4:02. The third and fourth movements have a close 1:2 beat ratio, 144:284, and 1:1 tempo ratio, 72:72, resulting in a close 1:2 duration ratio, 2:00-3:56. One less measure in the second movement, 112, and two more measures in the fourth movement, 144, result in a 1:2 duration ratio, 2:00-4:00, showing an overall 2:2:1:2 duration ratio of 4:00-4:00-2:00-4:00.
Movements 1-2 —> 1:1 beat ratio, 1:1 tempo ratio, 1:1 duration ratio (7/4 ÷ 7/8 = 2/1)
Movement 3-4 —> 1:2 beat ratio, 1:1 tempo ratio, 1:2 duration ratio (1/2 ÷ 1/1 = 1/2)
Movements 1-2-3-4 —> 2:2:1:2 duration ratio, 4:00-4:00-2:00-4:00
The first and third movements have a close 7:8 beat ratio, 138:160, and 7:8 tempo ratio, 63:72, resulting in virtually equal durations, 2:11 and 2:13 (without repeats). The third and fourth movements have a close 3:2 beat ratio, 348:250, and 3:2 tempo ratio, 84:56, resulting in similar durations, 4:08 and 4:27. These are both not far from two times the duration of the first and second movements, 4:22 and 4:26. Two-thirds more of a measure for the first movement, 23.66, one more measure for the second movement, 81, two and a half more measures for the third movement, 31.5, and one more measure for the fourth movement, 126, result in a four-way 1:1:2:2 duration ratio, 2:15-2:15-4:30-4:30 (without repeats) or 1:2:2:2 duration ratio, 2:15-4:30-4:30-4:30 (with repeats).
Movements 1-2 —> 7:8 beat ratio, 7:8 tempo ratio, 1:1 duration ratio (without repeats) or 1:2 duration ratio (with repeats) (7/8 ÷ 7/8 = 1/2)
Movement 3-4 —> 3:2 beat ratio, 3:2 tempo ratio, 1:1 duration ratio (3/2 ÷ 3/2 = 1/1)
Movements 1-2-3-4 —> 1:1:2:2 duration ratio, 2:15-2:15-4:30-4:30 (without repeats) or 1:2:2:2 duration ratio, 2:15-4:30-4:30-4:30 (with repeats)
The first and second movements have a close 7:3 beat ratio, 440:180, and close 4:3 tempo ratio, 84:54, resulting in a close 3:2 duration ratio, 5:14-3:20 (without repeats). The third movement has a duration a little under four minutes, 3:57. One-half less measure for the second movement, 31.5, and one less measure for the third movement, 112, result in a 7:3 beat ratio, 440:189, and a 3:2 duration ratio, 5:15-3:30 (without repeats), or a 3:4 duration ratio, 5:15-7:00 (with repeats).
Movements 1-2 —> 7:3 beat ratio, 14:9 tempo ratio, 3:2 duration ratio (2/1 ÷ 3/4 = 3/2)
Movement 3 —> 112 measures of 7/8 at 56 bpm = 4:00
