Consider four cases:
- A-flat major
- A-flat (natural) minor
- A-flat melodic minor
- A-flat harmonic minor
I start them with the third finger on the A-flat key (both hands), but I have no idea how a professional pianist would do it. Help!
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There's nothing wrong with starting on the third finger. I would think most people would be taught it that way, because then it's consistent with the fingering you would use as you go up an octave (i.e., if you start on A♭4 you should play A♭5 with the third finger).
Some pianists might start with the second finger on the right hand, however. The inconsistency is initially difficult to manage mentally, but it allows you to start with your stronger index finger.
I think what helps instead of memorizing where each individual finger should go, is to memorize the "imprint" of your hand on the keyboard. For Ab major for instance, this would be thumb, index and middle on C, Db and Eb resp. and then thumb, index, middle and ring on F, G, Ab, and Bb resp. That is for the right hand, for the left hand, middle, index and thumb on Ab, Bb and C resp. and ring, middle, index and thumb on Db, Eb, F and G resp. Then, you can start on whatever finger you like, you just have to see that you fall back to that pattern somehow.
For A flat major, these are the fingerings I'd use:
Left hand ascending: 3 2 1 3 2 1 4 3
Right hand ascending: 3 4 1 2 3 1 2 3
Descending scales would have the fingers placed in the same positions on the piano as the ascending scales. Thus, the fingerings would be the same sequence as written above, but in reverse. Minor scales would use the same fingering.
I chose this fingering by using a method that works on all scales that use a lot of black keys. I was taught this method by my piano teacher.
The idea is that each time you play the group of two black keys (C sharp and D sharp, or D flat and E flat) you use the second and third fingers of your hand. And every time you play the group of three black keys (F sharp, G sharp and A sharp, or G flat, A flat and B flat) you use the second third and fourth fingers of your hand. This applies to both the left and right hands. Then you place your thumbs appropriately. And if you have to use fewer than 5 black keys, you use the finger on the white key that would have been on the black key next to it. So you can hover your hands over the groups of black keys and figure out the fingerings pretty easily.
A good scale to practice this on is G flat major, since it uses all 5 black keys. If you master playing G flat major with this type of fingering, and think of it as a sort of default or standard pattern, then you'll be able to adjust it slightly to play other scales that use several black keys.
Advantages to fingering this way include:
1) It is easy to find where your hand position should be on the piano, and to figure out the fingering.
2) The thumbs always get played by both hands at the same time. This means that it's easier to coordinate the hands. Also you can more easily anticipate where the fingers cross over the thumb.
3) The thumbs never land on a black key. This makes hand positions less awkward.
4) It switches the question from "What are the black keys I need to use?" to "What are the white keys I need to use?" This gives you fewer things to remember if the key uses a lot of black keys, and makes the black keys seem less intimidating.
5) You can keep going for several octaves, since it is easy to repeat the patterns. The pinky finger isn't used, so the awkwardness of crossing over it is avoided.
That said, there are other ways to choose the fingering, and some of them might also count as "proper" ways to do it.
To answer your question: evenly. :) That's why we use the fingerings that we do, because they are generally considered "best practice" to get the scales even.
Now, I always start the Ab scales with the second finger in the right hand. There's no technical reason to pass the thumb under the fourth finger instead of the third, and for me passing under the fourth is a little more difficult. Most pros do this as well in my experience; I had three different piano professors in college and they all taught the same scale fingerings. Now, Bb and Eb I always start with 2 instead of 3, for much the same reasons. Conversely, I end Bb, Eb, and Ab with 2 in the left hand as well.
Therefore, it looks like my rule is to start black-key scale fingerings with the finger closest to the thumb that will still get the thumb on the right note to begin the combination of 123 and 1234 (or 321 and 4321 in the other hand) that the rest of the scale uses.
Here are the fingerings I prefer for the four scales asked about, followed by some notes for general guidance.
RH: 3(2) 4(3) 1 2 3 1 2 (3) LH: 3 2 1 4 3 2 1 (3)
Ab (Natural) Minor
RH: 3(2) 4(3) 1 2 3 1 2 (3) [same fingering as Ab major and B major] LH: 3 2 1 3 2 1 4 (3) [same fingering as B major; different from Ab major]
Ab Melodic Minor
RH: 3(2) 4(3) 1 2 3 1 2 (3) [same as major] LH: 3 2 1 4 3 2 1 (3) [ascending] (3) 4 1 2 3 1 2 (3) [descending]
Ab Harmonic Minor
RH: 3(2) 4(3) 1 2 3 1 2 (3) [same as major] LH: 3 2 1 4 3 2 1 (3) [same as major]
@user28 is correct that it's fine to use
3 being commonly taught. I also follow both @Raskolnikov (think in groupings of
1 2 3 and
1 2 3 4) and @StrangeAttractor (
2 3 on pairs of consecutive black keys;
2 3 4 on trios).
In general, there is flexibility at the bottom and top end of (black key) scales. The standard fingerings are designed to facilitate running scales through multiple octaves, but at the bottom and top, since you're not continuing through another octave, you can defer to comfort.