Do all piano scales have the same fingering?

Any scale (123,12345,54321,321 or 1234,1234,4321,4321) would logically end on the same finger. Playing scales in multiple octaves: This meaning isn't likely, but yes. Playing multiple C major scales in a row should start each new scale with the same finger (123,1234,1...).

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There's not a short answer to your question. Scale fingerings are a big topic. I think that scales are taught in an overcomplicated way. They're taught as if all 12 major scales have 12 separate fingerings, and then the fingerings change depending on how many octaves they are. That's a lot to learn. There's actually only two different scale patterns: The ones where scale degrees 1 and 5 are white keys (C, G, D, A, E), and the other ones. For the first category, the pattern is always: Scale degree 1 2 3 4 5 6 7 RH 1 2 3 1 2 3 4 LH 1 4 3 2 1 3 2 The use of the 5th finger is merely an optimization, to avoid a cross when you're done going in one direction and are either stopping or going back the other direction.

The other pattern: consider B major:

Scale degree 1 2 3 4 5 6 7 Note B C# D# E F# G# A# RH 1 2 3 1 2 3 4 LH 1 3 2 1 4 3 2 We're using all 5 black keys. We use fingers 2 and 3 to go across the two neighboring black keys, and 2, 3, and 4 to go across the three. The thumb goes in the white key gap. Again, any deviation from this is merely an optimization to avoid a cross (in this case, starting at the bottom with 4 in the left hand, and ending at the top with 5 in the right) We apply the same logic to the other two scales that use all 5 black keys, F♯/G♭ and C♯/D♭. Then, consider A♭ to be exactly the same as these three, but with a G♮. That is, consider playing it with a G♭ and apply the same logic, but then play G♮ instead. Continue around the circle of fifths this way all the way through F. In fact, if we look at the two fingerings I've written out, the only difference is whether you cross to 4 or 3 first in the left hand. It's entirely reasonable to play the "white key" scales with 1 3 2 1 4 3 2 in the left hand. If you do that, then there's only one pattern, and you merely start in different places for different scales.

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