I do not generally warm up, but then I don't really stretch my playing as much as my ear when I practice. But I know I should.
What are some good exercises to do before I start getting into the details of working for speed, developing scales, etc.?
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I usually warm-up with a slow-blues I found in a magazine years ago. Here's a video. Can't really notate more, because it's never the same after this.
It's pretty easy to change the drone to A for the second verse and then pop a B7 and do a lick to turn it around. It's really hard to make your fingers slow down for this. But it really sounds nice slow and sweet, too. But it's so simple that the temptation to jazz it up can be irresistible.
Illustration made with MuseScore. (Haven't figured out how to make the title smaller, yet.)
Beginner here, I also warm up with blues, I am not sure about how to name what I play but it looks like that (I copied the notes from a 12 bar progression):
E|---------------- B|---------------- G|---------25---47 D|----25-26---48-- A|--26--2----4---- E|-3--------------
I do it because my left hand needs to move vertically and horizontally (which is the hardest for me right now).
I usually warm up playing scales. Sometimes I play a single major scale form in a cycle of fifths. Other times I will just play through major and pentatonic scale forms in one key up and down the neck. Then I usually just noodle around on some phrase or song with which I'm familiar. Caveat: I'm an amateur and have no sound reason for why this is good. It just works for me.
In addition to the examples shown here, I would advise you to warmup without the guitar, stretching your hands, wrist and shoulders, but also and in my opinion more importantly, to warm DOWN after a big session of playing. I used to hurt myself when I was a beginner, as my left wrist would go from "inside" flexion during hours to a sudden outside flexion.
The content of the exercise itself is not that important, and chromatisms are quite boring and frankly quasi-useless as a guitarist. What is important is to start slow, simple, with some are of your guitar playing which is mastered. It might be simple chords, it might be polyphonic tapping or tremolo, it depends on your personnal practice.
I use arpeggios: major 7, minor 7, and dominant 7 in 5 positions (essentially CAGED). Go through the circle of fifths, playing major 7ths in one of the 5 positions; repeat for other positions; repeat for minor 7 and dominant 7. Practice with a metronome, and gradually increase speed (over weeks/months/years).
At the moment, I'm also working on tremolo picking, playing a scale using 4 sixteenth notes per degree of the scale (also, of course, with a metronome).
I saw some really good answers and I agree with some of them.
My favorite warm up practice helps strengthen all my fret hand fingers, as well as providing coordination with pick hand and fret hand.
Starting on the
low E string 2 - 3 - 4 - 5
then the A 2 - 3 - 4 - 5
then the D 2 - 3 - 4 - 5
continue through all six strings and back up again.
Next move up one fret, so... 3 - 4 - 5 - 6 , then another fret 4 - 5 - 6 - 7 , all the way to 12 - 13 - 14 - 15 and back down 15 - 14 - 13 - 12. This can be boring for your picking hand, so try all down strokes, or all up strokes, or alternate picking ( down - up - down - up ).
When I first learned this technique, I had a hard time getting clean sounding notes out of my pinkie ( since I used it so little ). Then speeding up was tricky, but this exercise pays off!
One last thing I can recommend, is alternate the order your four fret fingers ascend and descend. For example:
......2 - 3 - 4 - 5
then 3 - 4 - 5 - 2
then 4 - 5 - 2 - 3
last 5 - 4 - 3 - 2
This helps train each of your fret fingers to work independently and quickly. Try it and you may find a fun new exercise.
This warm up exercise helps stretch your fretting hand. I found a picture that explains http://www.fretjam.com/image-files/hand-stretch3.jpg Push as far as you can and use all three crooks of fingers.
Play violin and flute music: Paganini 24th and 5th caprice, Vivaldi G minor summer storm, B minor flute Bach, for tapping and stretch play EVH, Satriani (Midnight and Forgotten part 2) for arpp-s --- YJM, for developing strong thumb --- Hendrix, SRV. All dull and dumb chromatic exercises are better substituted with an outstanding R-K flight of a bumble bee, perform your own cover variant to fit your hand. This music will be with you through all the life and will impress people around. And play the other instruments to teach the ear and hands.