It is unclear who, in a bygone era, decided that "one must not use the pedal when playing Bach," but such a nonsensical period has ended. There are no rules for playing Bach. No one dictates them, nor does anyone have the right to establish them. Performance practices also vary by country; in France, for example, performances are quite free, even to the extent of using the soft pedal. I believe Bach's pieces should be performed according to one's own inspiration. Bach's scores fundamentally lack tempo markings, indications of character, dynamics, articulation, and phrasing. Furthermore, since pieces originally performed on the harpsichord or organ are now played on modern pianos, there is no need to force an imitation of the harpsichord or organ (if one were to imitate, it would be simpler to bring the authentic instrument onto the stage). It is by leveraging the characteristics of the modern piano that playing these pieces on the piano gains its meaning.

However, what must be preserved is the independence of each voice. The pieces written by Bach possess very strong polyphonic elements, which must be accurately reproduced in performance. Neglecting this independence of voices would render Bach's compositional style meaningless. This alone must be carefully observed.

In this sense, this Allemande is also impossible to perform without the pedal, as the voices must be connected by means of the pedal. Furthermore, the blurring of sixteenth notes that occurs when the pedal is engaged cannot be avoided. How can we connect the voices while avoiding the blurring of small notes? Let's explain step by step.

For example, in the first beat of measure 1, the chord is GBD, and the only other note is the sixteenth note C written in the soprano. Since this C is written at the very end of the beat, even if one sustains the pedal throughout the entire first beat, changing or releasing the pedal on the second beat will prevent this C from being noticeable. Therefore, if we assume this beat is sustained with one pedal for its full duration, the bass G can be seamlessly connected to the A in the second beat.

However, at the same time, all sixteenth notes in the first beat will be sustained beyond their written value.

Another method is to briefly engage the pedal just before the bass G changes to A in the second beat. With this pedaling, there is no need to sustain the sixteenth notes unnecessarily.

Either of these two methods is acceptable. My reasoning is that the bass G in the first beat and the bass A in the second beat are likely both played with the fifth finger (which is probably easier in performance). If one re-strikes from the fifth finger to the fifth finger, a break will occur at that moment. This is something we absolutely want to avoid. Therefore, one of the two methods above should be used to connect the bass.

I usually adopt the latter method: briefly engaging the pedal just before the bass changes to connect the bass, thereby avoiding unnecessary sustain of the sixteenth notes within.

From this point forward, the discussion becomes highly subjective. However, I interpret this Allemande as a piece that should possess warmth and flow smoothly horizontally. Unless non-harmonic tones are written in places where they would be sustained by the pedal, resulting in blurring, I believe the pedal can be held down in such cases. What are your thoughts?

Now, let's look at the second beat of measure 1. There is a trill in the right hand, and the sixteenth notes descend along a scale. In such situations (where non-harmonic tones are written as part of a scale), sustaining the pedal for a full beat will genuinely cause blurring. Therefore, we avoid the pedal here. Just before moving to the bass H in the third beat, briefly engage the pedal to connect the bass seamlessly.

Subsequently, the pedal should always be used in sections where the bass or other voices would be disconnected due to fingering constraints. Sections where no pedal is needed at all are from the third beat of measure 8 to the third beat of measure 11. No pedal is required here. At the third beat of measure 11, a break occurs in the right hand, so we use the pedal again.

In the latter half, for example, to connect the last right-hand note, the sixteenth note C, in measure 14 to the first right-hand note, the sixteenth note C, in the first beat of measure 15, we briefly use the pedal here.

Subsequently, the same treatment applies from the last right-hand A in the second beat of the same measure to the A in the third beat, and from the last right-hand F in the fourth beat of the same measure to the F in measure 16.

As for the overall character of the piece, a performance that is never rigid, avoids emphasizing the beat, and flows gracefully horizontally is desirable. Never overemphasize the sixteenth notes; instead, use overlapping techniques and pedaling to ensure a smooth, horizontal flow.