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This tutorial looks at chord fingering in general, including how to break away from limiting 1-3-5 chord fingerings in favour of approaches that offer greater flexibility and comfort at the keyboard.

If you're playing classical music - where the fingers are often written in - it's generally a good idea to try to follow what the composer intended. However, when improvising, the main thing that should govern your chord fingerings is comfort. This will mainly be governed by the size of your hands. Pianists with very large hands will probably use different fingerings to those with smaller ones, in order to make their hand position feel more natural and comfortable.

When people are first given piano lessons, they are usually taught 1-3-5 fingerings for three note chords. Though these are perfect for playing piano when you're a child, they can cause wrist strain as your hands get larger. I tend to use 1-2-3 or 1-2-4 fingerings for triads, as they leave you with your fourth and fifth (or third and fifth) fingers free. This makes small jumps between chords more smooth and legato, and also helps to decrease large jumps slightly. Using the pedal is still important, but you can make legato playing easier just by changing your finger positions.

With chords of four or more notes, the fingering is often more dictated, though you should still take comfort into account and see where your fingers fall naturally.
It's also useful to bear in mind that you can move vertically along the keyboard as well as horizontally. Moving further in to the keys can make chords using black notes feel more secure. It requires a little extra leverage, but this will help you to develop strength and flexibility in your hands.

I would recommend that you sit down at the piano, practice playing some progressions and simply see how your hands fall on the chords. Finding the correct hand position will really help you to make your chord transitions smoother and improve your legato playing.
If you've found this tutorial useful, you might want to check out my other videos as well as my book, How to Really Play the Piano, which is full of useful information about chords, improvising and piano playing in general.