I believe it's most definitely important to learn how to tune by ear. There is much written on methods of tuning by ear, but just in general it's good to note that each guitar is going to behave differently in respect to how it's tuned with respect to the other strings (relative tuning!). You can strictly use a tuner, or you can strictly learn tuning by fretting the string at the 5th fret, but what matters is how the guitar soundswhen it's strummed.
The primary and secondary harmonic sounds will tell you. Play and E chord. Is the B string and high E strings creating that great one note sound, or are the 'beating' together where either the B note sounds sharp or flat?? You'll know what I'm talking about when you hear it. Are all the E's in tune (low and high open E's, plus the D string fretted at the second fret?) How about the open B string and the B note played by fretting the A string in the second fret? How about the open D string and the D note played by fretting the B string in the third fret?
Check these notes against each other and teach the ear how to hear whether or not these strings are indeed in tune with each other.
Often times I'll start with my tuner, and then fine tune the guitar by ear from there.
In live situations, I may not have much of a choice except to follow my guitar tuner. In that case, it's good to get to know your guitar tuner and what it says about your guitar. For example, do you tune the D string so that it's at the top edge of 'in tune' or the bottom?
These will be great exercises for those guitarists learning to train the ear! These will help you learn to hear other guitars and whether or not they are actually in tune.
This is just a brief overview. If you have any questions, please ask! Or seek out the great lessons available here, or other answers in this thread.
Have fun,
Steve
Steve Cass
Solid Walnut Music/ASCAP
Becoming a great guitarist has less to do with fancy moves than it does becoming a master of the basics and learning musicianship.
It's not what you can't do. It's how you play what you already know. Lessons for the Beginner and Beyond"Rhythm guitar is a trip that alot of people miss" -- Tom Petty
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