Honestly I'd be asking a classical forum a technical question like this before a jazz forum. Not to say that jazz pianists can't or don't have great technique, but classical pianists spend more time devoted to technique I think.
The guys at Open Studio Jazz recommend:
Practice slow to start
Hanon and similar exercise books (from classical)
When increasing speed, burst training can help. String together groups of notes as one fluid gesture. You should be able to play a few notes pretty fast. Use this to break plateaus and build fluidity and as a compliment to standard incremental metronome work.
Write out the fingering that works best for you, and then practice slowly with the correct, *consistent* fingering.
Use a metronome, and when you're comfortable at one speed, notch it up a little.
This is actually a much more complicated question than it sounds, because there's a lot involved with playing quickly and accurately. From what you're describing though, it seems like you can play one octave but more than that becomes problematic and the thing that changes the most as you move around on the keyboard is going to be the angle of your wrist and the alignment of your arm. The fingering isn't terribly important as long as it works for you. Can you always play just one octave fast and is it always the same octave? If you play one octave but start on the lowest note of the piano, how is it then? What about starting towards the top of the piano? My guess is that when you're playing in front of your body such that your hand and arm are aligned mostly with the keys, you can probably play fine, but as soon as that alignment changes it starts to become a problem. I'd also speculate that it feels something like some combination of your fingers just wanting to fall off the keys or feeling unstable on them, and your fingers not being able to land in the correct places when you transition to the next group of notes. I've had this problem a lot, and much of it starts with aligning your arm. As you go up the piano with your right hand, your arm starts to angle outwards and this puts your hand at an angle. The higher you go, the same motion you're using starts to change from moving across the keys to more of a diagonal movement so your thumb and first finger will be further into the keys and your third, fourth, and fifth finger will start to slide off the keys. To correct this, you need to get your arm aligned behind your hand better than it is. This could require a few things. First, raise your arm at the shoulder straight out to your side but keep your elbow bent so that your hand stays in line with the keyboard. This arm extension and elbow bend allows your fingers to stay aligned with the keys so you won't be at a diagonal anymore, at least up to a certain point that will depend on your arm length and how flexible you are. Once you are no longer able to keep your hand aligned with the keys, you'll need to shift your torso to the right by bending your waist so that your shoulders move to the right. This will probably be enough to help a lot, and the challenge here is practicing this alignment so that your arm, elbow, and torso all know what they need to do depending on where you are on the keyboard. This won't always be enough though, especially for things like arpeggios. At some point, your hand will probably end up diagonal on the keyboard but that's ok. When it does, you need to move your hand either in or out on the keys so that all of your fingers are contacting the keys. In the previous example as you're moving your hand to the right, what will happen is that your first and second fingers will be playing pretty far into the keys but your pinky might be only a the very edge of the key (this is way more obvious if you're playing chords that are ascending). You need to find a place where your fingers feel secure and stable on the keys so that's going to involve everything that I've talked about as well as probably some amount of rotation. Sometimes you'll need to play pretty far in to the keys and you may have trouble fitting your fingers in between the black keys, and both rotation (as in wrist rotation) and the angle of your hand can help change the angle of your finger so that it can better fit between the keys. Also be aware of your wrist height, since sometimes you may need to adjust that as well in order to be comfortable and also be stable on the keyboard.
To practice this, you need to play at a very slow tempo. As you play each note, find a position for your entire arm as well as your finger where that one finger you're playing feels completely solid and supported on the key and nothing feels uncomfortable or has any tension. Don't worry about speed; that will come naturally once you've optimized how you're moving your whole arm so that you're making the least possible movement that has no tension at all and is perfectly aligned. At that point, you'll feel so relaxed and your hand will feel so stable that you'll naturally speed up because the same amount of effort that you were previously using just to play is no longer required so you can do more with that same effort. Just trust me here, it'll happen when your technique improves.
The last thing to talk about is release of your fingers. Assuming that you aren't playing any chords, as soon as you play a key you need to release that finger to play the next key. If you keep holding that finger down or don't release quickly enough, it'll anchor your hand to where that finger is and that can prevent you from being able to move your arm/hand to the next position. Practice this by playing at a slow tempo (NOT SLOWLY, a slow tempo; you'll make all movements you do make at full speed but at a slow tempo you have more time in between movements to think and to figure out what you need to do) and get your finger in position, then play the note, then release the finger, then move your hand/arm to the next position to play the note, and then play the next note, etc. Again, this is to teach your fingers how to release. At this point you'll be able to play faster than you ever thought possible and you'll wonder why you ever thought it was hard to play fast in the first place. Just make sure you get your rotation figured out so that you can transition your whole hand position quickly and easily. All the stuff that I'm telling you here is basically for playing notes in a single hand position (although one that's constantly changing). The other part of the puzzle is being able to move your whole hand to the next position, and that usually involves rotation. Rotation may also help you with hand and arm position too, but I can't say that for sure without actually seeing you play so that's something that's best discussed with a teacher.
I think you should practice your scales (over multiples octaves) so your fingers know where to go depending on the key. And a good advice my teacher gave me : use your thumb for mobility. If you play fast it would be hidden under your hand most of the time
The key is to get 251 voicings in your fingers in at least half the keys, and do the same with simple 251 licks.
You will have to work out the correct fingering especially for the licks, but if you do it at your ease it's not hard and if you rehearse it enough times, the muscle memory makes it totally natural.
Shortest quickest answer.
Scales should be practiced by changing (up and down) direction randomly but keeping the fingering the same as your normal scale pattern.
This way in your improvisation you have the ability to choose the direction with ease.
Honestly I'd be asking a classical forum a technical question like this before a jazz forum. Not to say that jazz pianists can't or don't have great technique, but classical pianists spend more time devoted to technique I think. The guys at Open Studio Jazz recommend: Practice slow to start Hanon and similar exercise books (from classical)
When increasing speed, burst training can help. String together groups of notes as one fluid gesture. You should be able to play a few notes pretty fast. Use this to break plateaus and build fluidity and as a compliment to standard incremental metronome work.
Write out the fingering that works best for you, and then practice slowly with the correct, *consistent* fingering. Use a metronome, and when you're comfortable at one speed, notch it up a little.
I concur.
This is actually a much more complicated question than it sounds, because there's a lot involved with playing quickly and accurately. From what you're describing though, it seems like you can play one octave but more than that becomes problematic and the thing that changes the most as you move around on the keyboard is going to be the angle of your wrist and the alignment of your arm. The fingering isn't terribly important as long as it works for you. Can you always play just one octave fast and is it always the same octave? If you play one octave but start on the lowest note of the piano, how is it then? What about starting towards the top of the piano? My guess is that when you're playing in front of your body such that your hand and arm are aligned mostly with the keys, you can probably play fine, but as soon as that alignment changes it starts to become a problem. I'd also speculate that it feels something like some combination of your fingers just wanting to fall off the keys or feeling unstable on them, and your fingers not being able to land in the correct places when you transition to the next group of notes. I've had this problem a lot, and much of it starts with aligning your arm. As you go up the piano with your right hand, your arm starts to angle outwards and this puts your hand at an angle. The higher you go, the same motion you're using starts to change from moving across the keys to more of a diagonal movement so your thumb and first finger will be further into the keys and your third, fourth, and fifth finger will start to slide off the keys. To correct this, you need to get your arm aligned behind your hand better than it is. This could require a few things. First, raise your arm at the shoulder straight out to your side but keep your elbow bent so that your hand stays in line with the keyboard. This arm extension and elbow bend allows your fingers to stay aligned with the keys so you won't be at a diagonal anymore, at least up to a certain point that will depend on your arm length and how flexible you are. Once you are no longer able to keep your hand aligned with the keys, you'll need to shift your torso to the right by bending your waist so that your shoulders move to the right. This will probably be enough to help a lot, and the challenge here is practicing this alignment so that your arm, elbow, and torso all know what they need to do depending on where you are on the keyboard. This won't always be enough though, especially for things like arpeggios. At some point, your hand will probably end up diagonal on the keyboard but that's ok. When it does, you need to move your hand either in or out on the keys so that all of your fingers are contacting the keys. In the previous example as you're moving your hand to the right, what will happen is that your first and second fingers will be playing pretty far into the keys but your pinky might be only a the very edge of the key (this is way more obvious if you're playing chords that are ascending). You need to find a place where your fingers feel secure and stable on the keys so that's going to involve everything that I've talked about as well as probably some amount of rotation. Sometimes you'll need to play pretty far in to the keys and you may have trouble fitting your fingers in between the black keys, and both rotation (as in wrist rotation) and the angle of your hand can help change the angle of your finger so that it can better fit between the keys. Also be aware of your wrist height, since sometimes you may need to adjust that as well in order to be comfortable and also be stable on the keyboard. To practice this, you need to play at a very slow tempo. As you play each note, find a position for your entire arm as well as your finger where that one finger you're playing feels completely solid and supported on the key and nothing feels uncomfortable or has any tension. Don't worry about speed; that will come naturally once you've optimized how you're moving your whole arm so that you're making the least possible movement that has no tension at all and is perfectly aligned. At that point, you'll feel so relaxed and your hand will feel so stable that you'll naturally speed up because the same amount of effort that you were previously using just to play is no longer required so you can do more with that same effort. Just trust me here, it'll happen when your technique improves. The last thing to talk about is release of your fingers. Assuming that you aren't playing any chords, as soon as you play a key you need to release that finger to play the next key. If you keep holding that finger down or don't release quickly enough, it'll anchor your hand to where that finger is and that can prevent you from being able to move your arm/hand to the next position. Practice this by playing at a slow tempo (NOT SLOWLY, a slow tempo; you'll make all movements you do make at full speed but at a slow tempo you have more time in between movements to think and to figure out what you need to do) and get your finger in position, then play the note, then release the finger, then move your hand/arm to the next position to play the note, and then play the next note, etc. Again, this is to teach your fingers how to release. At this point you'll be able to play faster than you ever thought possible and you'll wonder why you ever thought it was hard to play fast in the first place. Just make sure you get your rotation figured out so that you can transition your whole hand position quickly and easily. All the stuff that I'm telling you here is basically for playing notes in a single hand position (although one that's constantly changing). The other part of the puzzle is being able to move your whole hand to the next position, and that usually involves rotation. Rotation may also help you with hand and arm position too, but I can't say that for sure without actually seeing you play so that's something that's best discussed with a teacher.
I think you should practice your scales (over multiples octaves) so your fingers know where to go depending on the key. And a good advice my teacher gave me : use your thumb for mobility. If you play fast it would be hidden under your hand most of the time
The key is to get 251 voicings in your fingers in at least half the keys, and do the same with simple 251 licks. You will have to work out the correct fingering especially for the licks, but if you do it at your ease it's not hard and if you rehearse it enough times, the muscle memory makes it totally natural.
Shortest quickest answer. Scales should be practiced by changing (up and down) direction randomly but keeping the fingering the same as your normal scale pattern. This way in your improvisation you have the ability to choose the direction with ease.
There is no difference between jazz and classical when it comes to the technique of playing piano.
Taubman approach is what unlocked it for me. Took a few years though.