Being able to do a trill or a tremelo is an essential technical skill if you want to play advanced music. Every era of Classical music has them. Having a really fast -- and beautiful -- trill is a worthwhile goal.
A trill is usually between two adjacent tones; a tremelo is between two tones further apart, usually an octave. But the concept is the same. They are always fast, and they are NOT measured, which means they do not fall evenly into sixteenth or thirty-second or sixty-fourth notes and do not line up in an even way with what is going on the other hand, for example; instead they are free-form. It is this free and un-measured quality which gives them their excitement and almost ecstatic quality. They often come at a part of the music that has been building to a climax. (I am referring here to a trill which goes on for several beats, not just a simple turn of three notes. Technically that is not considered a trill.)
There are many other examples in our music which are not intended to be measured, such as grace notes. You, the pianist, have the freedom to make them a little faster or a little slower, depending on the character of the music, but they are not a specific speed. If they were intended to be measured and even, the composer would simply write them that way. The small notes you see used for grace notes, mordents and other ornaments indicates that they are un-measured.
Earlier today I came across someone's blog who said a trill should measured, and needs to work out evenly so that you always have the same note coming on the beat, for example. Nothing could be more wrong! This would make your trill sound amateurish and stiff. I'm thinking of a gorgeous piece by Debussy titled L'isle Joyeuse (Isle of Joy) which opens with a long solo trill lasting half the measure. It beautifully conveys the joy that the piece is about. You don't even get a sense of the beat until the end of the measure. If it were measured it would be a completely different feeling. There is no question that Debussy would have intended it to be free ( he was once quoted as having said "I have no use for German bookkeeping.").
In the same post this person said that to get clarity in the trill, you need to lift your fingers. Again, nothing could be more wrong. If the trill is to be fast, you must be efficient. Lifting your fingers any distance off the keys will cause loss of efficiency. Think of an Olympic skier in the slalom race, where they have to ski around a series of gates. They need to get as close to the gate as possible; even a few inches too wide will cause them to lose a tiny fraction of a second and will make the difference between winning or not. Maximum efficiency means being close to the keys. It's just physics. You don't need to worry that the sound will be blurred; you want to be playing so fast that the listener doesn't really hear the trill as individual notes.
Here is how I teach trills. Take the two notes of the trill and play them blocked, meaning together at the same time. You need to use your whole arm, not just fingers. Then, think of how it feels when you are skip a stone on a lake; you have one impulse (the throw) and then several "bounces." Let there be several bounces (not too many) off the first impulse. When the bounces occur, you need to stay as close to the keys as possible. After all, it just makes sense that if you bounce high off the keys there will be too much time between bounces. After you have the hang of this, just let the notes come out separately, but try to keep it feeling almost identical to how it felt when it was blocked. You'll be tempted to try to do something to get the notes to separate, but just try to keep the feeling of one impulse. When your bounces get really fast, meaning as little time between them as possible, you have the beginnings of a fast trill.
There are many people who will tell you the trill is done solely with the fingers. There are some who can do this. But for the average person, you will find that soon the small muscles of the fingers tire and even seize up. Using the arm gives you the power to keep going without pain or fatigue.
A tremelo is essentially the same and I recommend the same method. I've heard many people say that a tremelo with an octave requires that you use forearm rotation, which means the radius bone rotates over the ulna. They even say to exaggerate the rotation when you are practicing. However, rotation is extremely inefficient. You are tipping the forearm (and therefore the hand) towards the pinky side and then towards the thumb side, which means almost your whole hand is far away from the keys. Again, there is no way your tremelo can be fast unless you stay close to the keys.
I want to emphasize again that, while you might want to see a video of what I am describing, I am still not including videos in my posts. I don't want my readers to think you can learn to play the piano online by watching videos. You need to have a teacher by your side who is watching your hands and arms in order to correct and refine your technique. What I present here is hopefully giving you ideas for experimentation, or perhaps to explain why you may feel you are not making progress if you are using methods that you have been taught in the past and which do not work.
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