Piano chord fingering notation with only 1 finger number for multi-finger chord

Question

The following score has suggested fingering, where some left hand chords only have one finger number indicated. Does it mean the other fingers on the same chord are obvious or whatever your preference is, but the indicated one is highly recommended? Both the green-circled and the next red-circled are the same, so why the fingering is not indicated on the first one (green) instead of the second appearance (red)? (I understand fingering is only suggestive, but I'm more curious about the convention or common practice involved in the notations here, i.e. partial finger number for a multi-finger chord)

Answer 1

"More for less!" - Walmart

Fingerings are intended to help you position yourself correctly so that you don't have to go through overtly difficult changes or unnecessary hard work. But, sometimes too much can have the opposite effect; instead of giving you clarity, it obfuscates your reading. Imagine if every single note on the page had a finger. That would be a lot of information to process along with the actual notes themselves (and, god forbid, dynamics...)

So, instead of doing that, sheet music makers assume that you are a bit competent and approach it minimalistically by only putting in fingerings that are not apparent or to serve as reminders. In your example, all the chords would have a thumb on top. This is apparent - there is no reason to have any other finger up there. From the first red circle to the first green circle, you'd go from 4 to 5 because the ambiguity here is just what makes sense for your hand - your pinky is already on that note!

It's hard to generalize though. Fingerings, especially in free sheet music, are largely hit or miss.

Semi-related, but there's an interesting read on fingerings in this thread here which goes contrary to what I just said. It's an exception to the rule

Answer 2

There's a principle when marking up fingering for the benefit of less experienced players that you mark (a) where a non-obvious fingering is needed and (b) when a change of hand position is required. This piece pretty well follows that. The first marked chord might be assumed to take 1-5, particularly if the player didn't look ahead to the next one! Then there's a repeated chord which, however, needs a different fingering second time - so 4 is marked. The upper note, C, obviously takes 1 both times. Then, on the next line, D uses 5 then 4, which is obviously worth marking.

So yes, we mark fingerings where it's helpful. Just where it's helpful.