Trills
Keyboard Technique - Speed
I often get asked how I can 'move my fingers so fast'. I don't feel that my fingers are fast: listen to Artur Schnabel or Vladimir Horowitz - I grew up with their sound. Anyway, the simple answer to what I can do is practise - practise until all movements seem entirely memorised by fingers and arms, so that I do not have to be consciously aware of them. But there are others.
Muscle relaxation
It was from my violin teacher Artur Garami that I first learned how important it is to avoid muscle tension. During all my lessons with him, half his time was spent circling me, watching with eagle eye for any hint that one muscle was fighting another. At first, I would have to stop playing, put my fingers on my muscle with his, feel the tension, then concentrate on it while thinking "relax - relax ...", even force it to extend with an opposing muscle. Eventually, I was able to tell almost every muscle in my body to relax as directly as I could tell it to contract. Tension kills the sound of a fiddle - its sound must lift the bow off the strings, its body must move air, not be clamped by the player's body.
Playing a keyboard, the benefit is different. If a muscle starts to get tense, the opposing muscle has to work harder to move. Then that muscle has to relax further or the return motion is impeded still more. Tension kills speed, and it kills control.
Place one hand in normal playing position, on a table. Concentrate on relaxing it, totally. Use the other hand to lift a finger, then release it. Watch the exact motion the finger makes when it falls: the base joint returns to normal position first, then the mid one, while the end joint will probably not return to its relaxed angle until after your finger tip has contacted the table. Then use the hand's own muscles to pick the finger up. Then, relax it and watch the motion - it should be exactly the same as when the other hand lifted it. If it isn't, you aren't relaxing the finger muscles fast enough, so keep working at it. Practise this with every finger, wrist, arm and shoulder muscle. (Pick your location for this - I nearly got expelled from school in grade 5 for 'fiddling with my fingers' !)
Approach trills the same way - with one finger at a time first. Using two fingers, it's easy to hide tension - playing repeated notes with one finger makes tension obvious. Once you can play a note repeated with any single finger at half the note speed of a scale or two-finger trill, you can be satisfied that you are relaxing your muscles totally between each motion. The finger should never leave the key, but just move the pluck depth of the plectrum. It can't be done that way on a piano action, and it drives pianists nuts! Scarlatti obviously did this, cf. K.141 or K.455. K.141 in particular can be used to display the technique, with each finger in turn, two-finger 'trill' fingerings on the same note, then with all fingers flailing as pianists have to.
The goal is to be able to relax every muscle used in playing as quickly and as directly as it can be contracted.
Double trills
The muscles of our hands are interconnected to aid in holding and manipulating things - harpsichord playing had no role in its evolution! So, our playing must adapt to our hands.
I often am asked whether my use of double-third trills in Scarlatti (cf. K.450) is appropriate, by those who misquote Couperin to argue that it is 'impossible'. (Actually, in the original French, Couperin just said that he didn't think it worth learning at his age, but recommended that young students try.)
I believe that Couperin was talking of a trill played with fingers 2 and 3 in parallel with another played with 4 and 5. Anatomically, that is indeed next to impossible, even slowly. (In fact, I find even the sustained trill of Scarlatti's K.357 with it's simple 5th finger obligato extremely awkward.) But, pairing the thumb and 5th finger, to alternate with paired fingers 2 and 4, fits our hand very naturally, especially with 2 and 4 both on sharp keys.
I'm certain from his notation that Scarlatti knew this technique, but I confess to finding few places in Couperin where it works. Double trills are a very powerful sound, best used sparingly.