You get out your tuner, and set each string perfectly so you've got to be in tune!
And then you play a few chords, and something is just wrong!! So you check
your equivalent frets! There, that's got to have it!! No,something is still off.
What is going on here?? Why can't I get this #%$#&# guitar in tune???
Well, the short answer is: because guitars can't really be tuned.
The long answer (and a workaround) is this:
Remember Pythagoras?? "The square of the hypotenuse of a right triangle.."
Well, geometry aside, he was a music lover, and spent a lot of time investigating
the physics of music. He discovered many things, but the one we are concerned
with is this: Sound is vibration, vibration that occurs at frequencies (they repeat at
regular intervals). Today's standard concert pitch is the note A vibrating 440 times
Well, when Pythagoras investigated combinations of notes that sounded right
(in tune) to the ear, he found an amazing thing: if you divide the higher frequency
by the lower, you get an exact integer -- no fractions, no remainders. If you follow
that through every possible pair of note, you will discover that within what we call
an octave (say from one C note to the next C note) there are actually 56 distinct
intervals! So, where we have12 frets (or keys), we actually need 56. Ask any violinist
about this. Violins don't have frets, so violinists actually use all of these intervals,
and any decent violinist will tell you that F# and Gb are not the same note!! This
whole mess, which is the way our ears actually hear, is called just or true intonation.
So, what to do?? Many experiments were tried -- movable frets, multiple frets,
special tunings, even a keyboard instrument with four keyboards all intended
to be played simultaneously!! Finally a compromise was reached -- the one we
still use today. The octave was divided into 12 equal parts, a system called
equal temperament. The result is this: octaves are perfect. Perfect fifths
are almost perfect. And everything else is off!! There was much concern
about this at the time of its introduction -- would music played in all of the 12
available keys sound good? Bach answered this beautifully by writing The
Well-Tempered Clavier, which is a collection of pieces, one in each of the 12
major keys, one in each of the 12 minor keys.
Getting back to our guitar. Now you'll see it. If you fool around with your guitar
and adjust it so you get your G major chord to sound perfect, your E major
chord will sound terrible. There's no way around it, because the B natural pitch
needed as the 3rd of a G major chord is different from the B natural pitch
needed as the fifth of an E major chord. One string cannot be tuned to 2
pitches at the same time.
Here's the workaround. Professional players tune for the music they will be playing.
If you are playing Country, Folk, Bluegrass, or anything else that uses a lot of open
chords and/or the keys of G, A or D, get the G major chord right (tune your B string
slightly flat). If you are playing in E, or are playing a lot of barre chords (Rock, Jazz,
Blues), then get the E chord right. Because the nut creates a lot of pressure, and
there is a tendency to squeeze too hard with the fretting hand (which can make
notes go sharp), it's a good idea to use an A barre chord played at the fifth fret
(which is just the open E chord shape played in front of a barre) to check. (Listen
to any live Jimi Hendrix recording, and you'll hear him do exactly what I just
described: the last thing he does before starting to play is to check the A barre
chord at fifth fret!)
I hope you have found this helpful, and it eases your frustration.