Selected Cantatas (BWV 1-200)
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Number of cantatas analyzed: 25
The first and fourth movements, chorus and chorale, have a close 4:3 beat ratio, 318:237, and a 4:3 tempo ratio, 96:72, resulting in virtually equal durations, 3:18 and 3:17 (4:3 beat ratio ÷ 4:3 tempo ratio = 1:1 duration ratio). The second and third movements, alto aria and a soprano-bass duet, have a close 4:7 beat ratio, 198:333, and 4:7 tempo ratio, 48:84, resulting in similar durations, 4:07 and 3:57. Two fewer measures for the third movement, 64, and one more measure for the third movement, 112, result in a 1:1 duration ratio, 4:00-4:00 (4:7 beat ratio ÷ 4:7 tempo ratio = 1:1 duration ratio).
Movts 1-2 — 1:2 duration ratio — 6:00-3:00
Movts 3-5 — 1:1 duration ratio — 4:10-4:10
The first and second movements, a chorus and soprano aria, have a close 4:7 beat ratio, 332:572, and 8:7 tempo ratio, 96:84, resulting in a close 1:2 duration ratio, 3:25-6:50 (4:7 beat ratio ÷ 8:7 tempo ratio = 1:2 duration ratio). In addition, the two sections of the da capo aria divide into a close 3:2 ratio. The fourth and fifth movements, a bass aria and alto-tenor duet, have a close 1:1 beat ratio, 224:210, and 1:1 tempo ratio, 48:84, resulting in similar durations, 2:40 and 2:30. A little over two measures for the fifth movement, 37.33, results in a 1:1 beat ratio, 224:224, and a 1:1 duration ratio, 2:40-2:40 (1:1 beat ratio ÷ 1:1 tempo ratio = 1:1 duration ratio). The third movement at its natural tempo of 48 bpm has a duration of 1:20, which is precisely half the duration of the fourth and fifth movements, showing a 1:2:2 duration ratio, 1:20-2:40-2:40. Finally, the sixth and seventh movements, tenor recitative and chorale, have equal measures, 222, a 2:1 beat ratio, 88:44, and a 2:3 tempo ratio, 42:63, resulting a 3:1 duration ratio, 2:05-0:41 (2:1 beat ratio ÷ 2:3 tempo ratio = 3:1 duration ratio).
Movts 1-2 — 1:1 duration ratio — 3:25-6:50
Movts 2-3 — 1:1 duration ratio — 2:40-2:40
Movts 3-4-5 — 1:2:2 duration ratio — 1:20-2:40-2:40
Movts 6-7 — 3:1 duration ratio — 2:05-0:41
The first and second movements, alto aria and tenor recitative, have a close 28:9 beat ratio, 330:104, and 14:9 tempo ratio, 84:54, resulting in close 2:1 duration ratio, 3:55-1:55. Two more measures for the first movement, 112, and one more measure for the second movement, 27, result in a 2:1 duration ratio, 4:00-2:00. The third movement, a chorus, consists of two sections in which the first is fast and the second is a little faster, which Bach indicated with Vivace ed allegro after measure 36. The tempos 96 and 108 contribute to a total duration of 3:01. The fourth and fifth movements have a precise 1:2 beat ratio, 96:192, and 3:4 tempo ratio, 48:63, resulting in a 2:3 duration ratio, 2:00-3:00. In addition, the second and sixth movements, a recitative and chorale, have the same meter as well as meter, tempo, and duration, 2:00 for each. Thus, the cantata consists of six movements with exclusively whole number durations: 4:00-2:00-3:00-2:00-3:00-2:00
Movts 1-2 — 28:9 beat ratio, 14:9 tempo ratio, 2:1 duration ratio (28/9 ÷ 14/9 = 2/1)
Movt 3 — two sections (fast, faster) = 3:00
Movts 4-5 — 1:2 beat ratio, 3:4 tempo ratio, 2:3 duration ratio (1/2 ÷ 3/4 = 2/3)
Movts 2-6 — equal measures, tempos, durations — 2:00
All Six Movts — 4:00-2:00-3:00-2:00-3:00-2:00
The first movement, chorus, consists of 74 measures of 4/4 at 48 bpm, resulting in a duration of 6:10. Two fewer measures, 72, results in a duration of 6:00. The third and fifth movements, bass and soprano arias, have a close 4:3 beat ratio, 192:147, and 4:3 tempo ratio, 63:48, resulting in virtually equal durations, 3:02 and 3:03. Three fewer measures for the fifth movement, 144, results in a 4:3 beat ratio, 192:144, and 1:1 duration ratio, 3:00-3:00. Thus, the three major movements, 1-3-5, have a 2:1:1 duration ratio, 6:00-3:00-3:00, or the opening chorus lasts two times longer than two arias. In addition, the second and third movements, tenor recitative and bass aria, have a 1:2 duration ratio, 1:30-3:00.
Movt 1 — 72 measures of 4/4 at 48 bpm — 6:00
Movts 3-5 — 4:3 beat ratio, 4:3 tempo ratio, 1:1 duration ratio (4/3 ÷ 4/3 = 1:1)
Movts 1-3-5 — 2:1:1 duration ratio — 6:00-3:00-3:00
Movts 2-3 — 1:2 duration ratio — 1:30-3:00
The first and second movements have a close 1:3 measure ratio, 65:198, a close 2:3 beat ratio, 260:396, and 4:3 tempo ratio, 96:72, resulting in a close 1:2 duration ratio, 2:42-5:30. One more measure for the first movement, 66, results in a 1:3 measure ratio, 66:198. a 2:3 beat ratio, 264:396, and 1:2 duration ratio, 2:45-5:30. The second and fourth movements, a tenor and bass aria, have a close 12:7 beat ratio, 396:472, and 8:7 tempo ratio, 72:63, resulting in a close 3:2 duration ratio, 5:30-3:44. Two and a half fewer measures for the fourth movement, 115.5, results in a 3:2 duration ratio, 5:30-3:40. Thus, the three major movements share two duration ratios with the longest common value of five and a half minutes: 2:45-5:30 (2:1) and 5:30-3:40 (3:2). In addition, the fifth and sixth movements, a soprano recitative and chorale, have a close 8:9 beat ratio, 36:40, and 8:7 tempo ratio, 48:54, resulting in equal durations. In other words, the finale chorale is a little faster than the previous recitative.
Movts 1-2 — 1:3 measure ratio, 66:198
Movts 1-2 — 2:3 beat ratio, 4:3 tempo ratio, 1:2 duration ratio (2/3 ÷ 4/3 = 1/2)
Movt 2-4 — 12:7 beat ratio, 8:7 tempo ratio, 3:2 duration ratio (12/7 ÷ 8/7 = 3/2)
Movts 5-6 — 8:9 beat ratio, 8:9 tempo ratio, 1:1 duration ratio (8/9 ÷ 8/9 = 1/1)
Movt 2 — the aria and da capo sections, 116:82, have a close 3:2 ratio
The first movement consists of 86 measures of 3/4 at 63 bpm, resulting a duration of 4:05. Two fewer measures, 84, results in a duration of 4:00. The third and fifth movements have a close 9:8 beat ratio, 320:288, and 3:4 tempo ratio, 72:96, resulting in a close 3:2 duration ratio, 4:26-3:00. One more measure for the third movement, 81, results in a 9:8 beat ratio, 324:288, resulting in a 3:2 duration ratio, 4:30-3:00.
Movt 1 — 84 measures of 3/4 at 63 bpm — 4:00
Movts 3-5 — 9:8 beat ratio, 3:4 tempo ratio, 3:2 duration ratio (9/8 ÷ 3/4 = 3/2)
Movt 6 — two sections total 1:00
Movts 5-6 — 3:1 duration ratio — 3:00-1:00
The first and fifth movements have a close 6:7 beat ratio, 400:444, and 6:7 tempo ratio, 72:84, resulting in similar durations. 5:33 and 5:17. The third movement, bass aria, consists of 254 measures of 3/8 at 96 bpm, resulting in a duration of 7:56. Two more measures, 256, results in a duration of 8:00. This is close to one-half longer than the outer movements, showing that some minor adjustments – two fewer measures for the first movement, 48, and one more measure for the fifth movement, 112 – result in a symmetrical 2:3:2 duration ratio, 5:20-8:00-5:20. In addition, the two da capo arias, the third and fifth movements, have close 3:2 ratios between the two sections, 149:105 and 65:46.
Movts 1-5 — 6:7 beat ratio, 6:7 tempo ratio, 1:1 duration ratio (9/8 ÷ 9/8 = 1/1)
Movts 1-3-5 — symmetrical 2:3:2 duration ratio — 5:20-8:00-5:20
Movts 3-5 — the aria and da capo sections, 149:105 and 65:46, both have close 3:2 ratios
The first and third movements have a close 9:8 beat ratio, 459:405, and 9:8 tempo ratio, 108:96, resulting in virtually equal durations, 4:15 and 4:13. The third movement consists of 105 measures of 4/4 at 48 bpm, resulting in a duration of 8:45. This is close to two times longer than the outer movements, showing that some minor adjustments – three more measures for the first movement, one less measure for the third movement, 104, and three and two-third measures for the fifth movement, 138.66 – result in a symmetrical 1:2:1 duration ratio, 4:20-8:40-4:20. In addition, the fourth and sixth movements, tenor recitative and chorale, have a close 3:4 beat ratio, 64:88, and 3:4 tempo ratio, 54:72, resulting in virtually equal durations, 1:11 and 1:13.
Movts 1-5 — 9:8 beat ratio, 9:8 tempo ratio, 1:1 duration ratio (9/8 ÷ 9/8 = 1/1)
Movts 1-3-5 — symmetrical 1:2:1 duration ratio — 4:20-8:40-4:20
Movts 4-6 — 3:4 beat ratio, 3:4 tempo ratio, 1:1 duration ratio (9/8 ÷ 9/8 = 1/1)
The first and fifth movements, chorus and trio aria (S-A-B), have a close 7:6 beat ratio, 280:246, and 7:6 tempo ratio, 84:72, resulting in similar durations, 3:20 and 3:25. The third movement consists of 118 measures of 4/4 at 72 bpm, resulting in a duration of 6:30. This is close to two times longer than the outer movements, showing that some minor adjustments – three and a half fewer measures for the first movement, 136.5, and six fewer measures for the fifth movement, 117 – result in a symmetrical 1:2:1 duration ratio, 3:15-6:30-3:15, between the three major movements. In addition, the da capo aria, the third movement, has close 3:2 ratio between the two sections, 69:48.
Movts 1-5 — 7:6 beat ratio, 7:6 tempo ratio, 1:1 duration ratio (7/6 ÷ 7/6 = 1/1)
Movts 1-3-5 — symmetrical 1:2:1 duration ratio — 3:15-6:30-3:15
Movt 3 — the aria and da capo sections, 69:48, have a close 3:2 ratio
The first movement, a chorus, consists of two sections, one slower at 63 bpm and one faster at 108 bpm, resulting in a 3:2 duration ratio, 3:09-2:06. Which adds to 5:15. The third and fifth movements, bass and alto arias, have a close 4:3 beat ratio, 330:252, and 4:3 tempo ratio, 96:72, resulting in virtually equal durations, 3:26 and 3:30. Thus, a minor adjustment of two more measures for the third movement, 112, results in a 4:3 beat ratio, 336:252, and a 3:2:2 duration ratio, 5:15-3:30-3:30, between the three major movements.
Movt 1 — 3:2 duration ratio, 3:09-2:06 — total 5:15
Movts 3-5 — 4:3 beat ratio, 4:3 tempo ratio, 1:1 duration ratio (4/3 ÷ 4/3 = 1/1)
Movts 1-3-5 — 3:2:2 duration ratio — 5:15-3:30-3:30
The first and second movements, a chorus (marked Allegro) and soprano aria, have a close 14:27 beat ratio, 456:870, and a 7:9 tempo ratio, 84:108, resulting in a close 2:3 duration ratio, 5:25-8:00. Four fewer measures in the first movement, 224, and two fewer measures in the second movement, 288, result in a 14:27 beat ratio, resulting in a 2:3 duration ratio, 5:20-8:00. The fourth movement, bass aria, consists of 79 measures of 4/4 at 84 bpm, resulting in a duration of 3:45. Five more measures, 84, results in a duration of 4:00, and a 2:1 duration ratio with the second movement, 8:00-4:00. To summarize, the three major movements have two duration ratios that have the longest duration of eight minutes: 5:20-8:00 (2:3) and 8:00-4:00 (2:1)
Movts 1-2 — 14:27 beat ratio, 7:9 tempo ratio, 2:3 duration ratio (14/27 ÷ 7/9 = 2/3)
Movt 4 — five more measures, 84 — duration of 4:00
Movts 2-4 — 2:1 duration ratio — 8:00-4:00
The first and third movements, both tenor arias, have tempos the result in 4:53 and 3:54. This shows that minor modifications – three more measures for the first movement, 140, and one more measure for the third movement, 42 – result in durations of 5:00 and 4:00.
Movts 1-3 — two whole number durations — 5:00 and 4:00
The first and third movements, both bass arias, have a close 6:7 beat ratio, 501:568, and 6:7 tempo ratio, 72:84, resulting in similar durations, 6:57 and 6:45. One more measure for the first movement, 168, and five more measures for the third movement, 147, result in a 6:7 beat ratio, 504:588, and equal durations of 7:00. In addition, the two sections of the fourth movement add to 1:19, which is close to the duration of the fifth movement, chorale, 1:23.
Movts 1-3 — equal durations of 7:00 — 6:7 beat ratio, 6:7 tempo ratio, 1:1 duration ratio (6/7 ÷ 6/7 = 1/1)
Movts 4-5 — equal durations averaging 1:20.
The first and third movements, soprano-bass duet (marked Adagio) and soprano aria, have virtually equal beats, 309 and 308, and equal tempos, 63 bpm, resulting in virtually equal durations, 4:54 and 4:53. The fifth movement, soprano-bass duet, consists of 108 measures if 2/4 at 84 bpm, resulting in a duration of 2:34. This is close to half the duration of the first and third movements. Thus, two more measures for the first movement, 105, and three fewer measures for the fifth movement, 105, shows equal measures and an overall 2:2:1 duration ratio of 5:00-5:00-2:30 between the three major movements.
Movts 1-3 — equal durations of 5:00
Movt 5 — half the duration of five minutes, 2:30
Movts 1-3-5 — 2:2:1 duration ratio — 5:00-5:00-2:30
The first and second movements, soprano-bass duet and soprano recitative, have durations close to 3:2, 2:54-1:55. Two more measures for the first movement, 63, and one more measure for the second movement, 24, result in a 3:2 duration ratio, 3:00-2:00. The third and fourth movements, chorale and bass aria, have a precise 3:2 beat ratio, 112:168, and 4:3 tempo ratio, 84:63, resulting in a 1:2 duration ratio, 1:20-2:40.
Movts 1-2 — 3:2 duration ratio — 3:00-2:00
Movts 3-4 — 1:2 duration ratio — 1:20-2:40
Assigning the natural tempos to each of the four major movements, results in four durations a little under 2:00, 3:00, or 4:00. Rounding up to four whole number durations indicates one more measure for the first and second movement, 84 and 27, and two more measures for the third and movements, 96 and 54. This results in the outer two movements, 1 and 4, being equal at 4:00 while the inner two movements, 2 and 3, have a 2:3 duration ratio, 2:00-3:00.
Movts 1-4 — 1:1 duration ratio — equal durations of 4:00
Movts 2-3 — 2:3 duration ratio — 2:00-3:00
Movts 1-2-3-4 — four whole number durations — 4:00-2:00-3:00-4:00
Bach used the first and fourth movements, chorus and soprano aria, from Cantata No. 59 (composed in 1724) for the first and second movements in Cantata No. 74 (composed in 1725). These two movements are unrelated in duration, which Bach used to plan the newly composed movements, 4-5-7, for this cantata. The first movement relates to the seventh movement, while the second movement relates to the fourth and fifth movements. The first and seventh movements have the same meter, 3/8, a 1:3 beat ratio, 244:732, and 2:3 tempo ratio, 84:126, resulting in a precise 1:2 duration ratio, 2:54-5:48 (1/3 ÷ 2/3 = 1/2). Seen from another perspective, Bach gave the newly composed seventh movement 244 measures, which equals the beats in the previously composed first movement, 244. After creating the 1:2 duration ratio between the first and seventh movements, Bach did likewise for the previously composed second movement, which has a duration of 2:40, and the newly composed fourth and fifth movements. First, Bach calculated how many measures each movement should have at their chosen tempos to facilitate durations of 2:40 and 5:20, which is 75 and 112. Next, Bach composed the fourth and fifth movements achieving 77 and 110 measures.
Movts 1-7 — 1:2 duration ratio — 2:54-5:48
Movts 2-4-5 — 1:1:2 duration ratio — 2:40-2:40-5:20
The first and fifth movements, both bass arias, are in 3/8 with a close 8:7 measure ratio, 208:188, and 4:7 tempo ratio (tempo of one measure), 32:56, resulting in a close 2:1 duration ratio, 6:30-3:21. In other words, the measure ratio, 8:7, is two times the tempo ratio, 4:7, resulting in a 2:1 duration ratio. This indicates the ideal length of 182 measures for the fifth movement, which results in a 2:1 duration ratio, 6:30-3:15. Hence, Bach was probably aiming for 182 measures, but achieved six measures over this goal, 188. In addition, the third movement, bass aria, consists of 121 measures of 4/4 at 54 bpm, resulting in a duration of 8:57. One-half more measure, 121.5, results in a duration of precisely nine minutes, 9:00.
Movts 1-5 — 2:1 duration ratio — 6:30-3:15
Movt 3 — duration of nine minutes, 9:00
The first and third movements, both soprano arias, have a close 27:14 beat ratio, 474:256, and a 9:7 tempo ratio, 72:56, resulting in a close 3:2 duration ratio, 6:35-4:34. Four more measures for the first movement, 162, and four fewer measures for the third movement, 252, result in a 3:2 duration ratio, 6:45-4:30. In other words, the beat ratio is 3/2 times the tempo ratio which results in a 3:2 duration ratio (27/14 beat ratio ÷ 9/7 tempo ratio = 3/2 duration ratio). The second and fourth movements, soprano recitatives, are both in 4/4 with equal tempos of 54 bpm with a close 2:1 beat ratio, 84:44, resulting in a close 2:1 duration ratio, 1:33-0:48 (2/1 beat ratio ÷ 1:1 tempo ratio = 2:1 duration ratio). At its natural tempo the fifth movement, chorale, has a duration of 0:46, showing a 2:1:1 duration ratio of 1:33-0:46-0:46 between the three minor movements.
Movts 1-3 — the two major movements have a 3:2 duration ratio — 6:45-4:30
Movts 2-4-5 — the three minor movements have a 2:1:1 duration ratio — 1:33-0:46-0:46
The first and third movements, tenor and bass arias, have a close 4:3 beat ratio, 315:240, and a 8:9 tempo ratio, 56:63, resulting in a close 3:2 duration ratio, 5:37-3:48. Five more measures for the first movement, 320, results in a 4:3 beat ratio, 320:240, and 3:2 duration ratio, 5:42-3:48. 3:2 duration ratio, 6:45-4:30. In other words, the beat ratio is 3/2 times the tempo ratio resulting in a 3:2 duration ratio between the two major movements (4/3 beat ratio ÷ 8/9 tempo ratio = 3/2 duration ratio). At their natural tempos the second, fourth, and fifth movements, alto and tenor recitatives and chorale, have a 2:1:1 duration ratio, 1:30-0:45-0:45. In addition, the two sections of the first movement aria have a close 3:2 ratio, 186:129, showing the ideal measure divisions of 192:128.
Movts 1-3 — 3:2 duration ratio — 5:42-3:48
Movts 2-4-5 — 2:1:1 duration ratio — 1:30-0:45-0:45
Movt 1 — 3:2 measure division in aria — 192:128
The first and third movements, chorus and alto aria, have a virtually precise 8:9 beat ratio, 300:336, and 4:9 tempo ratio, 48:108, resulting in a virtually precise 2:1 duration ratio, 6:15-3:06. Half a measure more for the third movement. 112.5, results in an 8:9 beat ratio, 300:338, and a 2:1 duration ratio, 6:15-3:07. (8:9 beat ratio ÷ 4:9 tempo ratio = 2:1 duration ratio). The third and fourth movements, tenor aria and soprano-alto duet, have a close 12:7 beat ratio, 336:200, and a 12:7 tempo ratio, 108:63, resulting in similar durations, 3:06 and 3:10. (12:7 beat ratio ÷ 12:7 tempo ratio = 1:1 duration ratio). This shows a 2:1:1 duration ratio between the first, third, and fourth movements, 6:15-3:07-3:07. In addition, the measure ratios between the first and third movements and first and fourth movements reduce to 2:3 and 3:2, respectively, 75:112 = 2:3 and 75:50 = 3:2. The fifth and sixth movements, tenor recitative and soprano aria, have a close 2:3 beat ratio, 116:180, and 2:3 tempo ratio, 48:72, resulting in similar durations, 2:25 and 2:30. One more measure for the fifth movement, 30, results in a 2:3 beat ratio, 120:180, and a 1:1 duration ratio, 2:30-2:30 (2:3 beat ratio ÷ 2:3 tempo ratio = 1:1 duration ratio). In addition, the seventh movement, chorale, has a duration of 0:50 at its natural tempo, which relates 3:3:1 with the fifth and sixth movements, 2:30-2:30-0:50.
Movts 1-3-4 — 2:1:1 duration ratio — 6:15-3:07-3:07
Movts 5-6 — 1:1 duration ratio — 2:30-2:30
Movts 5-6-7 — 3:3:1 duration ratio — 2:30-2:30-0:50
The first and fourth movements, chorus and chorale, have a close 4:3 beat ratio, 318:237, and a 4:3 tempo ratio, 96:72, resulting in virtually equal durations, 3:18 and 3:17 (4:3 beat ratio ÷ 4:3 tempo ratio = 1:1 duration ratio). The second and third movements, alto aria and soprano-bass duet, have a close 4:7 beat ratio, 198:333, and 4:7 tempo ratio, 48:84, resulting in similar durations, 4:07 and 3:57. Two fewer measures for the third movement, 64, and one more measure for the third movement, 112, result in a 1:1 duration ratio, 4:00-4:00 (4:7 beat ratio ÷ 4:7 tempo ratio = 1:1 duration ratio).
Movts 1-4 — 1:1 duration ratio — 3:18-3:18
Movts 2-3 — 1:1 duration ratio — 4:00-4:00
The first and sixth movements, chorale and soprano-bass duet, have a close 4:3 beat ratio, 615:476, and a 4:3 tempo ratio, 96:72, resulting in similar durations, 6:24 and 6:36. Three more measures for the first movement, 208, and two fewer measures for the third movement, 117, result in a 4:3 beat ratio, 624:468, and a 1:1 duration ratio, 6:30-6:30 (4:3 beat ratio ÷ 4:3 tempo ratio = 1:1 duration ratio). The third and fourth movements, soprano-bass duet (marked Adagio) and chorale, have a close 7:4 beat ratio, 528:296, and 7:6 tempo ratio, 84:72, resulting in a close 3:2 duration ratio, 6:17-4:06. Less than one measure more for the third movement, 88.2, and a little over one and a half measures more for the fourth movement, 75.6, result in a 3:2 duration ratio, 6:18-4:12 (7:4 beat ratio ÷ 7:6 tempo ratio = 3:2 duration ratio). In addition, the two sections of the da capo aria in the sixth movement show a close 2:3 division, 46:73.
Movts 1-6 — 1:1 duration ratio — 6:30-6:30 (da capo aria divided as 2:3)
Movts 3-4 — 3:2 duration ratio — 6:18-4:12
The first and third movements, tenor aria and soprano-bass duet, have a close 1:1 beat ratio, 318:308, and 2:3 tempo ratio, 64:96, resulting in a close 3:2 duration ratio, 4:58-3:12. One more measure for the first movement, 107, and six more measures for the fifth movement, 160, result in a 3:2 duration ratio, 5:00-3:20. Seen from another perspective, the first and fifth movements have three and two beats per measure, 9/8 and 2/2, and the ideal ratio of measures, 107:160 = 2:3, equals the ratio of tempos, 64:96 = 2:3, resulting in a 3:2 duration ratio. 5:00-3:20. At its natural tempo, the third movement, alto aria, has a duration of precisely 3:20, showing a 3:2:2 duration ratio between the three major movements, 5:00-3:20-3:20. In addition, the second and fourth movements, bass and tenor recitatives, have a close 3:2 duration ratio, 1:46-1:15. Less than one measure less for the fifth movement, 14.2, results in a 3:2 duration ratio, 1:46-1:11.
Movts 1-3-5 — 3:2 duration ratio — 5:00-3:20
Movts 2-4 — 3:2 duration ratio — 1:46-1:11
The first and third movements, soprano and alto arias, have a close 9:4 beat ratio, 228:104, and 3:2 tempo ratio, 63:42, resulting in a close 3:2 duration ratio, 3:37-2:28. Less than one less measure for both movements, 56.7 and 25.2, result in a 3:2 duration ratio, 3:36-2:24. In other words, the beat ratio, 9:4, is 3/2 times the tempo ratio, 3:2, which results in a 3:2 duration ratio (9/4 beat ratio ÷ 3/2 tempo ratio = 3/2 duration ratio). In addition, the natural tempos of the fourth and fifth movements, bass recitative and tenor aria, result in durations of 2:00 and 2:51. Two more measures for the fifth movement, 47, results in a 2:3 duration ratio, 2:00-3:00
Movts 1-3 — 3:2 duration ratio — 3:36-2:24
Movts 4-5 — 2:3 duration ratio — 2:00-3:00
