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I was recently looking through Bach sheet music to find something new for training and I found BMV994 which made me a bit confused:

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This does not look like any "modern" fingerings I have seen. I have following questions:

  • How exactly am I supposed to play such fingering with legato? Should third finger go over the fourth or under it?
  • Is such fingering still used or the piano technique evolved since then? Should I focus on learning proper 3-4-3 fingering or it's relic of the past? Is it often used nowadays?
  • Does playing with such fingering has any advantage over playing it like 1-2-3-1-2-3-4 or similar "normal" fingerings?

    BMV994 on YouTube

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Your mistake of thinking is, that in Baroque music (and in classical music, and mostly even in romantic music), the standard articulation is non-legato. You only shall play legato if there is a legato-bow or some strong indication.

E.g. In this example the fingering indicates the articulation. Every two notes with fingering 3-4 are played legato, then you articulate a bit the next note. How much you articulate is personal flavour, but they must not be tied together - which is anyway impossible with this fingering.

A second benefit from this fingering is the following. In French Baroque music, there is something called: notes inégales. Roughly speaking, all melodic notes, which come across in pairs, are played rhythmised - the first note is longer then the second. The fingering in this example also helps you to play such a rhyhtm.

Do not forget that, there are also some piano-technical aspects:

  • old claviers had a key-drop which was far less then todays piano key-drop,
  • the keys were not so heavy,
  • the keys often had rounded edges, which allowed to slide with one finger from one key to another (most people forget that point).
  • According to Alexander Woo, players sat in an angle to the keyboard. This may also influence the fingering.

All this together made it much easier to play such a fingering then it is nowadays.

Now to your questions:

  • Usually the third finger goes a little bit below the fourth finger, but this depends on everybodys hand.
  • Some people still use this fingering. If you want to learn it, learn it.
  • This fingering has the advantage that you automatically play the correct articulation. If you play a good articulation with your favourite fingering, it is also ok.

A side-note: All of the ornaments start on-beat. That is, the first note of the ornaments is played on the beat. In particular for the first three ornaments: together with the chord in the left hand.

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  • I think it should also be noted that, in the Baroque period, harpsicordists sat an angle to the keyboard, not parallel to it. Aug 2, 2018 at 16:30
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This isn't "modern" fingering. It was a relic of the finger technique for the first keyboard instruments, where the "white" keys were physically too short to make "passing the thumb over or under" a convenient way to play scales.

It's not too difficult to play this type of fingering evenly, especially on a harpsichord which has a "hair-trigger" touch compared with a modern piano, the note sounds during the top 25% of the key depression, not at the bottom of the key stroke like a piano, and the loudness of each note is not affected (at least to any significant degree) by the speed at which the key is depressed.

But even does not mean legato in the sense that later piano technique uses the term.

On instruments like the harpsichord and organ, with no dynamics, articulation is the most important tool the performer has to define rhythm. Playing everything "legato" on a harpsichord (or even worse, on an organ in a building with a very resonant acoustic) simply produces a shapeless mush of sound.

It is certainly valuable to research such original fingerings and understand how they "work" on the original instruments, but since the piano is very different mechanically from the instruments that Bach was using, there is little point in trying to slavishly use the same fingering IMO. What matters is that you produce the same effect, so far as that is possible on a piano.

This is played on organ not harpsichord, but the reason for including it here is that it clearly shows just how NON-legato the fingering technique is, compared with the sound it produces.

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