The Well-Tempered Clavier, Book 2 (BWV 870-893)
The prelude and fugue have a close 6:7 beat ratio, 136:166, and 4:7 tempo ratio, 48:84, resulting in a close 3:2 duration ratio, 2:50-1:58. Two more measures for the prelude, 36, and one more measure for the fugue, 84, result in a 6:7 beat ratio, 144:168, and a 3:2 duration ratio, 3:00-2:00. In other words, the beat ratio equals 3/2 times the tempo ratio resulting in a 3:2 duration ratio (6:7 beat ratio ÷ 4:7 tempo ratio = 3:2 duration ratio).
Prelude and Fugue in C Major — 3:2 duration ratio — 3:00-2:00
The prelude and fugue have a precise 1:1 beat ratio, 112:112, and 3:2 tempo ratio, 72:48, resulting in a 2:3 duration ratio. In other words, the beat ratio equals 2/3 the tempo ratio resulting in a 2:3 duration ratio (1:1 beat ratio ÷ 3:2 tempo ratio = 2:3 duration ratio).
Prelude and Fugue in C Minor — 2:3 duration ratio — 1:33-2:20
The prelude consists of two sections that approach a 3:1 ratio and add to 1:59. At its natural tempo, the fugue has a duration of 2:55. One more measure for the fugue, 36, results in a 2:3 duration ratio, 2:00-3:00.
Prelude and Fugue in C-sharp Minor — 2:3 duration ratio — 2:00-3:00
The prelude and fugue have a virtually precise 2:3 beat ratio, 186:284, and 7:16 tempo ratio, 42:96, resulting in a precise 3:2 duration ratio, 4:25-2:57. One more measure for both, 63 and 72, result in a 21:32 beat ratio, 189:288, and a 3:2 duration ratio, 4:30-3:00. In other words, the beat ratio equals 3/2 the tempo ratio resulting in a 3:2 duration ratio (21:32 beat ratio ÷ 7:16 tempo ratio = 3:2 duration ratio).
Prelude and Fugue in C-sharp Minor — 3:2 duration ratio — 4:30-3:00
The prelude and fugue have a close 8:7 beat ratio, 224:200, and 8:7 tempo ratio, 72:63, resulting in similar durations, 3:06 and 3:10. One less measure for the fugue, 49, results in an 8:7 beat ratio, 224:196, and a 1:1 duration ratio, 3:06-3:06. In other words, the beat ratio equals the tempo ratio resulting in a 1:1 duration ratio (8:7 beat ratio ÷ 8:7 tempo ratio = 1:1 duration ratio).
Prelude and Fugue in D Major — 1:1 duration ratio — 3:06-3:06 (without repeats) or 2:1 duration ratio of 6:12-3:06 (with repeats)
The prelude and fugue have a close 7:4 beat ratio, 183:108, and 7:4 tempo ratio, 84:48, resulting in similar durations, 2:10 and 2:15. Less than one measure less for the fugue, 26.14, results in a 7:4 beat ratio, 183:105, and a 1:1 duration ratio, 2:10-2:10. In other words, the beat ratio equals the tempo ratio resulting in a 1:1 duration ratio (7:4 beat ratio ÷ 7:4 tempo ratio = 1:1 duration ratio).
Prelude and Fugue in D Minor — 1:1 duration ratio — 2:10-2:10
The prelude and fugue have a close 3:2 beat ratio, 213:140, and a 1:1 tempo ratio, 72:72, resulting in a close 3:2 duration ratio, 2:58-1:56. One more measure for the prelude, 72, and two more measures for the fugue, 72, result in a 3:2 beat ratio, 216:144, and a 3:2 duration ratio, 3:00-2:00. In other words, the beat ratio equals 3/2 the tempo ratio resulting in a 3:2 duration ratio (3:2 beat ratio ÷ 3:2 tempo ratio = 3:2 duration ratio).
Prelude and Fugue in E-flat Major — 3:2 duration ratio — 3:00-2:00
The prelude and fugue have a close 3:4 beat ratio, 144:184, and 3:2 tempo ratio, 72:48, resulting in a close 1:2 duration ratio, 2:00-3:50. Two more measures for the fugue, 48, results in a 3:4 beat ratio, 144:192, and a 1:2 duration ratio, 2:00-4:00. In other words, the beat ratio equals half the tempo ratio resulting in a 1:2 duration ratio (3:4 beat ratio ÷ 3:2 tempo ratio = 1:2 duration ratio).
Prelude and Fugue in D-sharp Minor — 1:2 duration ratio — 2:00-4:00
The prelude and fugue have a close 1:1 beat ratio, 162:172, and 3:2 tempo ratio, 72:48, resulting in a 2:3 duration ratio. Two more measures for the prelude, 56, and one less measure for the prelude, 42, result in a 1:1 beat ratio, 168:168, and a 2:3 duration ratio, 2:20-3:30. In other words, the beat ratio equals 2/3 the tempo ratio resulting in a 1:1 duration ratio (1:1 beat ratio ÷ 3:2 tempo ratio = 2:3 duration ratio). This pair has much in common with the next pair, BWV 879, in that both have identical measure ratios, 54:43 and 108:86, related tempos, 72:48 and 48:48, and identical durations and ratios, 2:20-3:30.
Prelude and Fugue in E Major — 2:3 duration ratio — 2:20-3:30
The prelude and fugue have a close 2:3 beat ratio, 108:172, and 1:1 tempo ratio, 48:48, resulting in a close 2:3 duration ratio, 2:15-3:35. Four more measures for the prelude, 112, and two fewer measures for the fugue, 84, result in a 3:2 measure ratio, 112, 84, a 2:3 beat ratio, and a 2:3 duration ratio, 2:20-3:30. In other words, the beat ratio equals 2/3 the tempo ratio resulting in a 1:1 duration ratio (2:3 beat ratio ÷ 1:1 tempo ratio = 2:3 duration ratio). This pair has much in common with the previous pair, BWV 878, in that both have identical measure ratios, 108:86 and 54:43, related tempos, 48:48 and 72:48, and identical durations and ratios, 2:20-3:30.
Prelude and Fugue in E Minor — 2:3 duration ratio — 2:20-3:30 (without repeats) or 4:3 duration ratio, 4:40-3:30 (with repeats)
The prelude and fugue have a close 9:8 beat ratio, 216:198, and 9:16 tempo ratio, 54:96, resulting in a 1:1 duration ratio. Three fewer measures for the fugue, 96, results in a 3:4 measure ratio, 72:96, a 9:8 beat ratio, 216:192, and 2:1 duration ratio, 4:00-2:00. In other words, the beat ratio equals two times the tempo ratio resulting in a 2:1 duration ratio (9:8 beat ratio ÷ 9:16 tempo ratio = 2:1 duration ratio).
Prelude and Fugue in F Major — 2:1 duration ratio — 4:00-2:00
The prelude and fugue have a close 6:7 beat ratio, 140:170, and 4:7 tempo ratio, 48:84, resulting in a close 3:2 duration ratio, 2:55-2:01. Two more measures for the prelude, 72, and one less measure for the fugue, 84, result in a 3:2 duration ratio, 3:00-2:00. In other words, the beat ratio equals 3/2 times the tempo ratio resulting in a 3:2 duration ratio (6:7 beat ratio ÷ 4:7 tempo ratio = 3:2 duration ratio).
Prelude and Fugue in F Minor — 3:2 duration ratio — 3:00-2:00 (without repeats) or 3:1 duration ratio of 6:00-2:00 (with repeats)
The prelude and fugue have a close 9:7 beat ratio, 225:168, and 6:7 tempo ratio, 54:63, resulting in a close 3:2 duration ratio, 4:10-2:40. Three fewer measures for the prelude, 72, results in a 3:2 duration ratio, 4:00-2:40. In other words, the beat ratio equals 3/2 the tempo ratio resulting in a 3:2 duration ratio (9:7 beat ratio ÷ 6:7 tempo ratio = 3:2 duration ratio).
Prelude and Fugue in F-sharp Major — 3:2 duration ratio — 4:00-2:40
The prelude and fugue have a close 7:16 beat ratio, 129:280, and 7:8 tempo ratio, 42:84, resulting in a close 1:2 duration ratio, 3:04-5:50. One less measure for the prelude, 42, and two more measures for the fugue, 72, result in a 7:16 beat ratio, 126:288, and a 1:2 duration ratio, 3:00-6:00. In other words, the beat ratio equals half the tempo ratio resulting in a 1:2 duration ratio (7:16 beat ratio ÷ 7:8 tempo ratio = 1:2 duration ratio).
Prelude and Fugue in F-sharp Minor — 1:2 duration ratio — 3:00-6:00
The prelude and fugue have a close 14:27 beat ratio, 99:180, and 7:9 tempo ratio, 84:108, resulting in a 2:3 duration ratio. Four more measures for the fugue, 64, results in a 14:27 beat ratio, 99:192, and a 2:3 duration ratio, 1:10-1:46. In other words, the beat ratio equals 2/3 the tempo ratio resulting in a 2:3 duration ratio (14:27 beat ratio ÷ 7:9 tempo ratio = 2:3 duration ratio).
Prelude and Fugue in G Major — 2:3 duration ratio — 1:10-1:46
The prelude and fugue have a precise 2:1 beat ratio, 144:72, and 2:1 tempo ratio, 84:42, resulting in a 1:1 duration ratio. In other words, the beat ratio equals the tempo ratio resulting in a 1:1 duration ratio (2:1 beat ratio ÷ 2:1 tempo ratio = 1:1 duration ratio).
Prelude and Fugue in G Major — 1:1 duration ratio — 2:00-2:00 (without repeats) or 2:1 duration ratio, 4:00-2:00 (with repeats)
The prelude and fugue have a precise 2:3 beat ratio, 168:252, beat ratio, and 1:1 tempo ratio, 63:63, resulting in a 2:3 duration ratio. In other words, the beat ratio equals 2/3 the tempo ratio resulting in a 2:3 duration ratio (2:3 beat ratio ÷ 1:1 tempo ratio = 2:3 duration ratio).
Prelude and Fugue in G Minor — 2:3 duration ratio — 2:40-4:00
The prelude and fugue have a precise 2:1 beat ratio, 192:96, and 2:1 tempo ratio, 108:54, resulting in a 1:1 duration ratio, 1:46-1:46. In other words, the beat ratio equals the tempo ratio resulting in a 1:1 duration ratio (2:1 beat ratio ÷ 2:1 tempo ratio = 1:1 duration ratio). Seen from another perspective, both prelude and fughetta consist of the same number of eighth notes, 192, in which an equal eighth-note speed, 108 bpm, results in equal durations.
Prelude and Fughetta in F Major — 1:1 duration ratio — 1:46-1:46
The prelude and fugue have a close 7:6 beat ratio, 231:200, and 7:6 tempo ratio, 63:48, resulting in virtually equal durations, 3:40 and 3:42. In other words, the beat ratio equals the tempo ratio resulting in a 1:1 duration ratio (7:6 beat ratio ÷ 7:6 tempo ratio = 1:1 duration ratio). The first 23 measures of the fugue are identical to the Fughetta in F Major, BWV 901, thus, to fully realize Bach’s intended tempo for this expanded and final version, it is first necessary to correctly analyze BWV 901 (shown above). Once the most probable tempo is determined for the Fughetta in F Major based on its relationship with its prelude, then the same tempo, 54 bpm, shall be assumed for this Fugue in A-flat Major.
Prelude and Fugue in A-flat Major — 1:1 duration ratio — 3:40-3:40
The prelude and fugue have a close 2:3 beat ratio, 200:286, and virtually precise 4:3 tempo ratio, 63:48, resulting in a close 1;2 duration ratio, 3:10-5:57. Two fewer measures for the prelude, 48, and one more measure for the fugue, 144, result in a 2:3 beat ratio, 192:288, and a 1:2 duration ratio, 3:00-6:00. In other words, the beat ratio equals half the tempo ratio resulting in a 2:3 duration ratio (2:3 beat ratio ÷ 4:3 tempo ratio = 1:2 duration ratio).
Prelude and Fugue in G-sharp Minor — 1:2 duration ratio — 3:00-6:00 (without repeats) or 1:1 duration ratio, 6:00-6:00 (with repeats)
The prelude and fugue have a close 7:6 beat ratio, 132:112, and virtually precise 7:6 tempo ratio, 64:54, resulting in a 1:1 duration ratio. In other words, the beat ratio equals the tempo ratio resulting in a 1:1 duration ratio (7:6 beat ratio ÷ 7:6 tempo ratio = 1:1 duration ratio). Bach apparently planned one less measure for both prelude and fugue, 32 and 28, to achieve a 1:1 duration ratio, 2:00-2:00.
Prelude and Fugue in A Major — 1:1 duration ratio — 2:00-2:00
The prelude and fugue have a virtually precise 7:6 beat ratio, 128:112, and 7:9 tempo ratio, 42:54, resulting in a virtually precise 3:2 duration ratio, 3:02-2:04. Half a measure less for the prelude, 31.5, and one measure less for the fugue, 27, result in a 3:2 duration ratio, 3:00-2:00. In other words, the beat ratio equals 3/2 the tempo ratio resulting in a 3:2 duration ratio (7:6 beat ratio ÷ 7:9 tempo ratio = 3:2 duration ratio).
Prelude and Fugue in A Minor — 3:2 duration ratio — 3:00-2:00 (without repeats) or 3:1 duration ratio, 6:00-2:00 (with repeats)
The prelude and fugue have a close 7:6 beat ratio, 348:372, and 7:9 tempo ratio, 84:108, resulting in a close 3:2 duration ratio, 4:08-2:35. Three fewer measures for the prelude, 84, and three more measure for the fugue, 96, result in a 7:6 beat ratio, 336:288, and a 3:2 duration ratio, 4:00-2:40. In other words, the beat ratio equals 3/2 the tempo ratio resulting in a 3:2 duration ratio (7:6 beat ratio ÷ 7:9 tempo ratio = 3:2 duration ratio).
Prelude and Fugue in B-flat Major — 3:2 duration ratio — 4:00-2:40 (without repeats) or 3:1 duration ratio, 8:00-2:40 (with repeats)
The prelude and fugue have a close 1:2 beat ratio, 166:303, and 9:8 tempo ratio, 54:48, resulting in a close 1:2 duration ratio, 3:04-6:18. A little over three fewer measures for the fugue, 98.36, results in a 9:16 beat ratio, 166:295, and a 1:2 duration ratio, 3:04-6:08. In other words, the beat ratio equals half the tempo ratio resulting in a 1:2 duration ratio (9:16 beat ratio ÷ 9:8 tempo ratio = 1:2 duration ratio). Bach apparently planned two fewer measures for the prelude, 81, and four fewer measures for the fugue, 96, to achieve a 1:2 duration ratio, 3:00-6:00.
Prelude and Fugue in B-flat Minor — 1:2 duration ratio — 3:04-6:08
The prelude and fugue have a virtually precise 4:3 beat ratio, 184:208, and 12:7 tempo ratio, 72:42, resulting in a close 1:2 duration ratio, 2:33-4:57. One less measure for the prelude, 45, and one more measure for the fugue, 105, result in a 6:7 beat ratio, 180:210, and 1:2 duration ratio, 2:30-5:00. In other words, the beat ratio equals half the tempo ratio resulting in a 1:2 duration ratio (6:7 beat ratio ÷ 12:7 tempo ratio = 1:2 duration ratio).
Prelude and Fugue in B Major — 1:2 duration ratio — 2:30-5:00
The prelude and fugue have a virtually precise 4:3 beat ratio, 132:100, and 4:3 tempo ratio, 63:48, resulting in equal durations of 2:05. In other words, the beat ratio equals the tempo ratio resulting in a 1:1 duration ratio (4:3 beat ratio ÷ 4:3 tempo ratio = 1:1 duration ratio). Bach apparently planned three fewer measures for the prelude, 63, and four fewer measures for the fugue, 96, to achieve a 1:1 duration ratio of 2:00-2:00.
Prelude and Fugue in B Minor — 1:1 duration ratio — 2:05-2:05
