On the guitar, there is a magical point, right around 100BPM and playing 16th notes where the tones blur together. The wrist starts tightening up, control of the stroke moves to the elbow, and hand has to sort of divebomb the strings in order to pick individual notes. Below 100BPM, each stroke can be pretty broad and almost flailing, but right around that threshold, suddenly all the movements have to get smaller and more efficient or it doesn't work.
So how do we get there? Well it's a metronome technique I call gear shifting.
Step 1. Take the sequence you want to speed up. Three or four measures maximum, and set your metronome between 40 and 60 beats per minute. Otherwise this will take forever. Make the duration of the shortest note equal to one quarter note, so it corresponds with one beat on the metronome.
Step 2. Play through the sequence at this very slow speed. What this does is that it begins myelinating the sequence in your mind. The way we are conditioned, the brain begins to insulate the sequences of neural firings which make up the sequence from everything else. The extra slow speed gives our mind extra time to make decisions, "Okay, this finger here... NOW.. this finger here... NOW" over and over. It's also fitting us into the grid of a rhythm. Without this precise timing, we can't go fast.
Step 3. Once you can move through the sequence at very slow speed without mistakes, even if it's not very comfortable, begin turning up the metronome by 10 BPM for every repetition. So go to 70BPM, and try to pull it off with no mistakes. You may find that as soon as you mess with the speed an error crops up, usually between the 3rd and second string, because this transition for most patterns is a bit weird. Focus on only that area of the sequence for a minute until you can push through it without a mistake. Continue raising the metronome speed 10 BPM.
Step 4. Here's our first "gear shift" When you reach 120BPM, turn the metronome back down to 60 BPM. This time we're thinking in 8th notes. 2 notes per beat. It's the same speed, but a different way of conceptualizing it. Make sure you've got it in 8th notes, and then continue raising the speed 10 BPM every repetition. Personally I find that somewhere around 80 or 90 BPM in 8th notes, the sequence starts getting handed over from my conscious mind to my unconscious mind. That is, it's going so fast that I'm no longer in control, I've either learned the sequence or I haven't, and I can make the sequence go faster or slower as a physical exercise, but the pattern itself is set.
Step 5. Shift gears again when you hit 120 BPM. Go back down to 60 BPM. Now we're in 16th notes. And if you're trying to go fast, this is probably the length of the note originally. Continue escalating the speed 10 BPM after every successful repetition. I find that 70 to 90 BPM is where it really has to clean up. If you're technique is sloppy, this is where it will show. If your problem is here, it's not knowing the sequence,
it's an imbalance in your hands, which can be addressed by checking a few things.
Right around 100BPM is what I call the "speed barrier". Room for error is gone, and the character of how you get it done begins to change. It's like making the transition from walking to running. Different things begin to happen. But if you pass this barrier, It's where speed playing begins, and the character of playing above 100BPM and in 16th notes stays roughly the same. The hard part is breaking into a sprint and making that "walking to running" transition.
If you hit 16th notes at 120BPM, congratulations! You have cleaned up your technique for this sequence, and you should be enjoying a nice blur of notes on the particular pattern you're playing. Continue on as far as you wish/can for whatever your particular style of play requires. Personally, my need for speed doesn't get much beyond about 120 or 130.
With my particular brand of technique, which I got from watching jazzers and copying how they move, my wrist begins to get pretty rigid, and control of my upstrokes and down strokes moves to my elbow. On an upstroke, it feels like my pick touches and then bounces up and away from the string. On a down stroke, it feels like I just glide down and then out to avoid strumming the string below it.
In my left hand, I've observed that my middle and ring fingers stay quite perpedicular to the fretboard, and my knuckles stay generally parallel to the bottom of the fretboard. My index and pinky fingers lean away from the middle two fingers. This seems to be the only way that the fretting hand doesn't get tired or make the tendons ache too much.
The metronome is very important in this process. It makes things black and white, and it keeps the notes spaced at exact intervals so that at full speed, the pattern sounds defined and beautiful. It also gives us a clear criteria for giving ourselves feedback about whether we did or didn't get it.
What I've aimed to do here is illustrate a reliable, reproducable way to go from a crawl to a sprint with whatever sequence you're aiming to brush up. Whether it's arppegios, ascending/descending 2's 3's and 4's. Whatever you need.
In my experience, this process can be done on just about any sequence. You can go from a relatively unfamiliar combination of notes to blazing in somewhere between half an hour to an hour. This is also assuming that you don't have larger technical issues holding you back, such as poor posture (try going classical - guitar on left leg, guitar all the way up to bottom of your chest), or imbalance of the left hand (middle and ringer finger not perpendicular to fret board).