The prelude and fugue are both in 4/4, and have a measure ratio, 40:74, and tempo ratio, 63:72, resulting in a close 2:3 duration ratio, 2:32-4:06. One and a half more measures for the prelude, 42, and two fewer measures for the fugue, 72, result in a 2:3 duration ratio, 2:40-4:00…

The Orgelbüchlein consists of 46 organ chorales organized sequentially by seasons according to the church calendar. The following bullet list summarizes Bach’s large-scale organization:

The Schübler Chorales belong to a small handful of works printed and published during Bach’s lifetime. In 1747, late in the composer’s life, Bach assembled a new set of six chorales in which five of the six (Nos. 1, 3, 4, 5, 6) were transcribed to organ from movements selected from five previously composed cantatas, published in 1748 by Johann Georg Schübler (ca. 1720-1755).

O Lamm Gottes, unschuldig is the only movement in the Great 18 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.

The third part to the Clavierübung (commonly referred to as the “German Organ Mass”) consists of a grand prelude and fugue (commonly referred to as “St. Anne”), the longest of all Bach’s preludes and fugues, at the beginning and end of the opus. Between these bookends lies 21 chorale preludes and 4 duets. The following bullet list summarizes Bach’s large-scale organization:

The 15 Inventions first appeared as “Preambles” in a different order in the Notebook for Wilhelm Friedemann Bach. Analysis reveals a deliberate plan of order and symmetry in the Inventions applying the same tempos to both sets, suggesting that Bach organized the Inventions and Preambles simultaneously. Such an impressive mathematical feat could be understood as the “preamble-invention conundrum,

The prelude and fugue have a close 4:3 beat ratio, 140:108, and virtually precise 4:3 tempo ratio, 63:48, resulting in a 1:1 duration ratio. 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).

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.

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 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.