Playing piano by ear is among the most essential of musical skills, yet it is generally looked down upon by teachers of traditional reading-based approaches (of which I am also one). In this article I wish to demonstrate that the two can live in harmony with one another.
I find this state of affairs perplexing, since music is sound and commonsense should tell us that musicians need to train their ears first and foremost. A musician who can't recognize basic harmonies by ear would be like a painter who can't distinguish between the primary colors.
I consider it essential to develop a vocabulary of common harmonies which we recognize in a musical context. These start with the tonic and dominant, and proceed to the dominant seventh, subdominant and diminished chords, then branch out from there to more advanced harmonies such as the supertonic and submediant.
Where ear training concerns melody, we should know where we are in the musical scale. This means knowing the scale degrees by number (scale degree 1 is the tonic or key note, etc.: in C major scale degree 1 is C, 2 is D, and so on).
It true that many pieces of music become very complex, and it can be difficult to follow the harmony in a dense work that has a rich instrumentation or is full of suspensions, dissonances and non-harmonic tones. Fortunately, we don't need to, as listening to music doesn't mean analyzing every note but simply getting caught up in the musical flow.
Playing piano by ear should not be seen as an alternative to reading music. Conversely, reading music should not be done to the exclusion of playing by ear. The trouble with relying on reading music is that the score becomes the source of musical knowledge, and the fingers are then relied on for musical memory.
By contrast, playing piano by ear is really a form of improvisation. Even you're not actually composing the melody and harmony, you're transferring them from your mind's ear to the piano. In any form of improvisation, the locus of the music is the mind rather than a piece paper. This is a different category of musical thinking, and it will inform the written music you learn as well.
One of my favorite ways of playing piano by ear is transposing passages of music, or even entire pieces, into various keys. Transposing is one of the most effective ways to train the crucial connection between the mind's ear and the fingers. This type of practice is incredibly helpful in learning and memorizing music, since you're learning with the ear rather than simply with the fingers.
Here's an important tip when playing by ear: never allow your fingers to strike a key until you're certain that the key is the correct one. You should hear the next note in your mind before you actually play it. If you make a mistake, don't immediately grab the next key or keep searching until you happen to hit the right one. Instead, raise your hands from the keyboard and start the passage over again.
When you practice consistently in this manner, you'll discover that playing piano by ear actually informs not only the way you learn music, but your ability to read piano music as well!