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I heard that anyone who received theoretical education in music should use a metronome to practice their timing. But I don't know how does a metronome help me? Or even how would better timing help me?
Also is it related with beats,and time signatures?
As humans, we're not naturally inclined to play music in time. Our speech while rhythmic at times is vastly more complicated rhythmically than the majority of music out there. Just check out this article by Steve Vai in which he talks about polyrhythms. He talks about how one of the toughest challenges he has ever faced in music is transcribing speech.
But what does this have to do with metronomes?
I'm glad you asked, other Alex. Well, our minds and ears are flexable to the complicated sounds of the world. We're not naturally used to the constant pulse of set tempos. Our heartbeats are variable, and slow and speed in phases, and there's not really that much in the natural world which exerts a constant audible tempo. So, when we try to play a steady tempo without a metronome, what we will actually do is slightly speed up, slow down, and compensate when we fall behind the beat. As soon as a group of musicians trained in such a way gets together, everyone will be in time with themselves, and out of time with others(I've been there, it's not pretty).
Enter the metronome.
The metronome is constant, unyeilding. It does not forgive, it does not forget. When you play 50 ms out of time and there's a metronome there, you can hear the difference, and it's not the metronome's fault that you were out. Playing to a metronome makes you consistent. It makes every one of the people playing along consistent, and it enables players to develop a sense of timing to use while they play with themselves and each other.
It can also help you with playing faster, and more accurately quicker, see these questions:
Technique or exercise to play this part from a song which i'm stuck with
As a parting note I'd say I never used to practice with a metronome, and my skill went up rapidly as soon as I started doing it. Getting into the habit of practicing with a metronome is a huuuuuuuuge benefit in both the short and the long run.
Hope that helps :)
A metronome can do several things. If a piece has a metronome marking, it can give you some idea of a composer's (or often an editor's) idea of how fast it should go. Also, it can give you an idea of whether your tempos through a piece are consistent. Especially when you are beginning to work on a piece, you can find that you are playing easier sections faster than harder ones without realizing it, and your tempo can get inconsistent. A metronome will point this out to you in a hurry.
It can give you a sort of benchmark on how well you are coming along with a difficult piece as you are working it up. It's especially useful in this last regard. Try putting the metronome on at a speed where you can practice the entire piece without making (many) mistakes. You'll be surprised to see how slow some easier parts sound when you're trying to play them at the same speed as more difficult parts elsewhere, at a tempo slow enough to accommodate the tougher sections.
Now, all that said, be very careful NOT to overdo it. You have to always keep the music in mind before the notes. If you just try to get the notes without playing the music, you'll find that you have trained your hands to play the piece unmusically. ("Metronomic" is a criticism of a performance that sounds too slavish in its adherence to a tempo, to the point that all the music is squeezed out of it.)
The further along you are with the piece, the less useful the metronome is. You can always use it to "spot check" your tempos; see if you're playing the whole piece faster than you think you are, see how consistent your tempos are from section to section, and so on.
Two additional points beyond BobRodes's answer
For using the metronome as a gauge for progress with specific agility/speed exercises: e.g. taking a given exercise and increasing the metronome rate each day for a period of time.
Focusing on listening to the click is a basic step towards being able to listen to other performers when in an ensemble situation.
In relation to the last part of your question, yes, it's directly related to time sigs.There are metronomes which can be set to 'ping' on beat one, whether the time sig. is 2, 3 4 5 or 6 on the top.So you can hear when each new bar starts. The tempo can also be used as a good guide, in that, say it's 80 b.p.m. - if you wanted, you could set 160 to give a tick twice as quick, which sometimes helps to keep you in time better. When you got pretty good, you could go down to half speed, 40 b.p.m. and work harder to keep in time. B.p.m. incidentally, is beats per minute, in other words, how many ticks the metronome will sound in one minute. 60 b.p.m. = one tick per second.
Having said all that, I still prefer to have a drum track playing to keep time to. Probably used to playing with real drummers for many, many years...
When I practice with the metronome I often imagine the ticks are on the off-beats, so if I were counting out loud "one and two and three and four and" then a tick would fall on each "and", rather than on a number. If you don't already do this, you have to try it.
The skill in this is that you must mentally construct the unheard on-the-beat tick. With practice you can mentally flip between hearing the tick on the beat and off the beat. It's like the rhythmic equivalent of one of those optical illusions where you can interpret what you're seeing in more than one way.
Further practice with this is to play tuplets against the off-beat tick. This is hard(!) but worth while.
