Two Time Signatures: Bach Prelude in D Major BWV 874 [duplicate]

I'm currently learning Bach's Prelude and Fugue in D Major, No. 5 WTC 2, BWV 874. At the beginning of the prelude, there are two time signatures given - cut time (2/2) and a 12/8 time signature.

I found another post on here that helped me understand parts of the timing for this prelude. For example, in certain measures, like mm. 1 and 3, the quavers are to be treated as "triplets" or can be counted in 12/8 time.

My immense confusion starts in Measure 5. A post I saw mentioned that the quaver-semiquaver figure in the left hand coincides with the third quaver from the quaver "triplet" (marked in the red boxes). It also looks like within the first semiquaver-quaver group, the semiquaver in the dotted quaver-semiquaver figure falls with the 3rd and 4th semiquavers that open the bar (marked in the blue boxes). I'm really not sure how the math works out here. This confusing pattern repeats throughout the prelude and I'm so lost.

Regardless of whether we treat the dotted quaver-semiquaver figure as triplets or as written in 2/2 time, should the semiquaver in the left hand be played after the third quaver from the quaver "triplet" in the right hand? Am I missing something or not understanding something here? Would appreciate any help!!

• This is really a question about performance practice more than math. The simple, abstract answer, if this were a contemporary piece, is: sure, you can superimpose a subdivision of 4 against a subdivision of 3. A semiquaver is shorter than a triplet quaver, and thus the final D in the first red box would fall later than the second B. HOWEVER, this is a baroque prelude, and questions of dotted notes (or even duples) get very complicated—it's not so much about what the values claim to be on paper, as about how they ought to be interpreted. I'll hold back hoping that someone with more... Apr 4 at 14:21
• ... keyboard-specific knowledge, preferably of this specific piece, has insight. But questions include "should the duples in m 2 be perfectly strict"? Even if so, they should be strongly differentiated in dynamic, in a "strong-weak" pattern. And "should the dotted figures be exactly 3 + 1, or should they align with the triplets, or should they "over-dot" to something more like 5 + 1? If the tempo is fast enough, do we hear and care about these distinctions? Just what is an appropriate tempo, anyway?" Apr 4 at 14:26
• NB, this piece has been addressed here before in an answer to a broader question. Apr 4 at 14:30

In Bach, it is common that partial triplet figures are written as dotted figures. In this case, the marked figures should be played such that the dotted notes receives the first two parts of the triplet, and the semiquaver receives the third part of the triplet.

Bärenreiter's Urtext edition explains, specifically with regard to this Prelude, but also indicates where there is room for scholarly research and debate:

Another problem is the rhythmic placement of dotted notes of the sort we find, in WTC II, mainly in the Prelude in D major, [and] the Fugue in E minor.... In the first instance..., Bach grants himself a certain license by employing a double time signature. We therefore decided, in our new edition, to make all dotted figures occurring in a triplet context (bar 5, bass, etc.) conform with the triplets as if Bach has written [crotchet - quaver], hoping thereby to do justice to his intentions....

Now it so happens that we possess a document in which one of Bach's pupils, Johann Friedrich Agricola (1720 – 1774), expressed his views on this subject. He writes as follows...: "This [adaptation] is only correct at extremely fast tempos. Except in such cases, the note following the dot must not be made to coincide with the final note of the triple, but should instead be struck after that note. This practice was taught by J. S. Bach to all of his pupils".

Although it is not our wish to deter anyone from proceeding in this fashion, a number of reservations may be raised against Agricola's testimony. For example, Bach may have changed his mind on this point in his later years and the pieces in question may have originated at an earlier date. Or it may merely represent an admission on Bach's part as to how he ought to have notated those pieces.

The general practice can be confirmed with most any recording by a prominent performer. Andras Schiff, for example, is considered a Bach authority and plays the dotted figures in triplet rhythm.

Interestingly, Richter also plays the dotted figures this way, but additionally plays the "straight" quaver pairs as triplet figures.

• Relying on what others do is a dangerous way to decide what's right, regardless of how prominent the performer may be, and especially if your models are pianists and the music was not written for the piano. Apr 4 at 17:05
• But was it a common practice in that time to write a dotted quarter of modern time as a quarter note of modern time, in the context of 12/8? because it is the case in the op. Apr 4 at 18:31
• Okay Bach seems to write it as such in the manuscript. But perhaps it was more of a omission of change of time signature to 4/4? That would be understandable as the meter switches between 4/4 and 12/8 frequently, sometimes independently in the two hands (e.g. bar 5-8) Apr 4 at 18:40
• @Divide1918 The notation is independent of time signature. In a triple subdivision of the beat — such as in triplets or in 12/8 time — where modern writers would use a quarter-note and eighth note, Bach (and others) would use a dotted eighth and a sixteenth. Apr 4 at 19:21