Here's my stab.
If you don't have a solid foundation before attempting fast scales, you are probably of the majority that will MAKE a wall for yourself. I find that most students want to and end up playing scales much faster than they could ever possibly passably play a piece. After two years of piano, I had begun approaching velocity pragmatically and carefully per the recommendation of my instructor. Of course I had trouble with it, and of course I wanted to play much faster than my capacity would allow. I had a "D'OH!" Moment during a practice session and was suddenly able to play much faster easily within a half hour after a few adjustments. The following weeks saw my speed and coordination go up dramatically. But also, my repertoire benefitted tremendously, because the fastest passages were now precise and elegant. I had a fantastic teacher, and I studied a conservative 2hours every day for those two years, so was prepared for the scales to be stepped up. If you are being called upon by a teacher to play faster or you have a good foundation, here are some pointers.
1. You must vill it into existence! A reference to barenboims single-note crescendo. Aural preparation and the will to synthesize the beats in the mind is often the biggest hurdle between a student and smoothe, fast scales. That means you. If you cannot hear steeply subdivided notes, then you cannot imagine them. If you can hear them, but are having trouble synthesizing faster subdivisions with mind or mouth, you cannot play fast smoothe scales. There is no room for ego with fast scales unless you can already play them. If you can very easily synthesize very even divisions of a very even pulse, the 90% of the work is done.
1. True legato is not possible at faster speeds. The more control and better technique you have, then the more options you have on the virtual range of legato and staccato. But if you are trying to teach your mind and body faster scales, I recommend choosing two levels: legato-ish and a more fleeting leggierissimo. True legato is IMPOSSIBLE PERIOD at faster speeds. Prepare accordingly.
1. Know your scales utterly and intimately, at slow to medium speeds, inside and out upside down, ht and hs, left hand and right hand accompaniment, duplets, triplets, quintuplets, sextuplets AND septuplets AND every division thereof. You should be able to start on any key and know where it will end up any number of beats later. Seems excessive, I know, but even if you try this stuff, your scale familiarity will rise above its current point and that's the point.
1. The less your thumb passes under your hand, the faster your scales can be. The hypothetical fastest speed you can achieve will see the thumb never passing under the hand, and the hand is already in an optimal position for the thumb to simply and minutely lower as it depresses the key. Thumb under is only useful for legato, which again is impssible to achieve at a faster speed. The key is to move the hand and rotate the wrist in a coordinated fashion so fluidly and quickly between thumb and finger, finger and thumb that the length of the two adjacent tones are identical and continue to be identical throughout.
1. Still stipulate your goal dynamics where you want them. Achieving the goal dynamics during scales ensures focus and will burden your mind and balance enough to draw undue attention away from your technique and toward your musicianship.
1. If you arent controlling your dynamics with your arm weight, you can't play fast scales. At the same time, if you are supporting your arm weight with the played finger, then you will have significantly less control and stamina.
1. Wrist rotation is what allows the weak and slow nature of the finger to be circumvented. You simply cannot play your fastest with your fingers unassisted by wrist rotation. The finger is brought to its nominal capacity at the key by the hand position, arm position and the wrist rotation into place. However, there is a major pitfall here: do not apply wrist rotation more than what is necessary to meet your fingers halfway. It is only to assist the arm in the application of minimal force to the intended key for the intended effect at the goal velocity.
1. Minimize movement. The single most general and therefore greatest hindrance to speed( and indeed all musical actions) is excessive movement. Excessive or altogether extraneous movement is effective only for timekeeping or showmanship purposes. Don't swing your thumb under too much(or at all), no excessive wrist rotation, don't raise your fingers, don't hold your arm weight by the finger... All examples of minimizing movement. Do what you can with it. to play a beautiful volumous, dynamic, smoothe, lightning fast scales is by and far a display of delicate balance in the hand finely manipulated by a trained mind.
1. There are slow scales and there are slow-motion scales. When practicing for velocity, there is nothing more vital than slow-motion scale work. Here is where you observe (visually, tactally, aurally) your technique for speed under a microscope to see what you are doing right or wrong. Here is where you condition new techniques to be fitted into into your toolbox. Every extreme of the spectrum for hand position, finger height and shape, note length, wrist position, dynamic level, fingering, thumb action etc can be experimented. Then they can be adjusted and tailored to the occasion. This is where you will fit all the ideas you have for getting faster into your practice routine.
Topic: how fast can you play scales?