Speed equals Distance divided by Time. For those who don't already know, this is a very simple sum that lets you work out how far it is , or how long it takes to get from point A to point B. By knowing two of the elements, you can work out the third.
If for example A and B are exactly 100kph apart, and it takes 2 hours to travel between them, then by dividing the distance by the time we can find the speed. 100 (D) divided by 2 (T) = 50. So the speed is 50kph. Or if we travelled from A to B at 50kph and it took 2 hours, then the distance must have been 25 kilometres. S/T = D.
Finally if we travelled at 50kph, and the distance was 100 kilometres, then the journey would take 2 hours. D/S = T.
So what does all this have to do with music? Well we saw that by knowing two of the elements we can work out the third. So if one element is fixed, then by changing one of the remaining elements, we can affect the other. For example, if the distance is fixed at 100 kilometres, then by changing our speed, we can change the journey time.
In music it's the time (tempo) that is fixed, so by changing the distance, we can change our physical speed, I.e, how quickly our hands have to move.
In order to keep the maths simple, let's set the tempo at 60bpm, so 1 quarter note = 60. This means that for every second that passes we have to play 1 quarter note.
As shown above, by changing our Distance, we can change our physical Speed.
D = Length of Stroke.
If we begin the down stroke 1cm above the string, and end it 1cm below, then the length of stroke is 2cm. So now we have two elements fixed, T and D, we can work out the third S.
We're playing quarter notes at 60bpm, 1 per second, and the distance we're having to travel is 2cm, so our Speed is 2cm per second (2cmps).
So obviously if we begin the down stroke 0.5cm above the string, and end it 0.5cm below, then we've halved the distance to 1cm, and our Speed is now 1cmps. Halve it again and our Speed is 0.5cmps.
So we're still playing 1 quarter note per second, but we've quadrupled our efficiency. This means we could now play quarter notes at 240bpm without any more effort.
This is why beginner/intermediates have serious problems trying to keep up with Petrucci. If JP is playing 16ths at 200bpm, then beginners with say a stroke that is twice as wide, would have to play (physically twice as fast to keep up. 16ths at 400bpm anyone?
So when practicing speed, PRACTICE DISTANCE!
NOTE: it applies just as much to the fretting hand as the picking.
TICKING TWITCHES AND FLICKING SWITCHES
How do we practice speed without making a mess? There is a way to develop fast muscles without doing too much damage to your accuracy.
Let's look at JP again. If he's playing a chromatic scale using all 16th notes at 200bpm, then if we isolated one note, we'd find it lasted for just 0.075 of a second; a tiny pip .
He is fretting, stroking, and unfretting at the speed of a muscle spasm. So he's playing as if he's having some kind of fit; all ticks and twitches, and that's what we need to practice. Not a whole chromatic scale, but just one or two notes as fast as a twitch. BANG BANG on and off.
The fretting fingers should switch from one to the next as abruptly as a light switch flicks from the on state to the off. The picking hand should make the stroke as snappy and ticky as the second hand of a clock. Tick tock down and up. Very ticky and snappy. And it should all be done as efficiently as possible in terms of distance travelled.
Here's the important bit: YOU DON'T HAVE TO PLAY A WHOLE SCALE ALL AT ONCE TO DEVELOP FAST MUSCLES! You can practice efficiency and fast twitchy muscles just as well one or two notes at a time.
Ever wondered why people who play musical instruments and also suffer from Tourette's Syndrome, Mozart for example, often become amazingly good at it? As the song says, don't touch me I'm a real live wire.
If you naturally have the nervous energy levels of a Tourette's sufferer, then developing twitchy muscles will come well naturally. If however you're an idle sod like me, you'll need to give them a bit of a boost.
20mins of exercise every morning should do the trick. Don't torture yourself because you won't feel like doing it the day after. Just do enough to get the heart pumping, the sweat flowing, and the lungs working. As soon as you feel taxed, stop. No pain no gain is for fools, or people on stimulants. A bit of exercise in the morning will increase energy all day and all night.
Why is this so? Because if you laze about, then food is stored as fat, whereas if you exert yourself, it turns into energy. Simple!
Systems are only as strong as their weakest link. Don't neglect your upstroke. A bicycle with only one wheel is as useless as one with none. I said bicycle!
Good luck. Don't hurt yourself.