Slurs and Finger Substitution

Question

In ABRSM "The AB Guide to Music Theory, Part I, Ch 11.2" on "The Slur": they show the following example (Bartok, For Children, Vol. 1 No. 3)

And they say that the end of a slur implies a slight shortening of its last note, with a brief silence before the next note.

Therefore the melody of the example above would be played approximately:

Question:

Given the above, why in the following example (Beethoven Sonata in G, Anh 5 no 1, first movement) the suggested fingering has a substitution 4-1 (highlighted in the circle)?

Is it to play legato? But the half note is outside the slur, so based on what it is said above there should be a brief silence before it and not legato.

Any idea?

I would have just used 1.

UPDATE In the same ABRSM book cited above in Ch 11.5, I found a note that seems relevant: Composers of the classical period would usually have divided a legato phrase into smaller sections each with a separate slur, usually ending at the bar-line or before the last note

Answer 1

The 4–1 in the Beethoven indicates that you begin playing that C with your fourth finger, but while playing the C you switch to the first finger. The switch is to help facilitate the upcoming leap to F♯; now that your first finger is on the C, it's easier to reach the F♯ with finger four. (Without the switch, you'd keep 4 on the C and use 5 on the F♯!)

Also, a note on your first point: the general sentiment is correct, but different interpreters would interpret the length of that rest differently. Many, I think, would make the rest even shorter, like a thirty-second note. But I'd recommend not mathematically calculating these out; use your musical intuition to find what you like best.

Answer 2

In addition to Richard's answer, another reason for not jumping straight to the C and landing on it with thumb is that in doing so, some players will just hit it too hard, and make it too pronounced. (Think about learning scales - a lot of us dropped onto the thumb notes too heavily). So, by using 4, holding it and transferrring to thumb, it takes away that possibility. True, good players may not let the hand weight make C play too loudly, but then they may well do the transfer, as there's plenty of time, and the hand movement won't be marred by dropping that thumb.

Answer 3

You COULD hop the 4th finger directly from C to F♯. But the finger change and implied change of hand position makes hitting the F♯ much more secure. This is what the finger change is for in this case, not to facilitate a legato.

Your approximation in the question shows a FAR too big gap after the slurs. The gap will be minimal. The slur is more about giving the first note a little more weight, the second a little less.