Posted by:
cflat
Date: 10 Jun 2007 18:23
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This method of tuning requires a basic grasp of
music theory and a fairly well developed ear. Absolute beginners may need a
little more experience before attempting to tune guitars using this method.
Most of us are familiar with the 5th fret (4th fret in the case of the G string)
method for tuning a guitar by ear. This technique uses unisons (two notes of
exactly the same pitch or frequency) to tune a guitar. This method is okay if
you want to get two neighbouring strings in tune with each other but it may not
be particularly accurate for getting the 1st string in tune with the 5th string
or the 4th string in tune with the 2nd string, and so on.
Using fourths, fifths and octaves, it is possible to achieve a high degree of
accuracy for any string in relation to any other.
TERMINOLOGY
Beat rate:
When tuning one string to another, you hear, for want of a better expression, a
"wah wah wah" sound. This slows as you approach the point where the two
frequencies coincide (vibrate at exactly the same frequency). The rapidity of
the “wah wah wah” is known as the Beat Rate.
Smooth:
When the two frequencies coincide the "wah wah" sound stops. This is known as
being Smooth. Unisons and octaves are Smooth.
Narrow and Wide:
Fifths are Narrow. Fourths are Wide.
The “wah wah” sound can not only be heard when tuning a unison, but can also be
heard when tuning intervals, e.g. thirds, fourths, fifths and octaves. For
instance, if you were to tune the 6th string (E) to the 5th string (A), you will
have tuned a fourth.
Assuming that your 5th string (A) is up to pitch (110Hz) and your 6th string (E)
is below pitch. As you raise the pitch of the E, the Beat Rate will begin to
slow (provided the E string was somewhere near pitch to begin with). You should
stop raising the pitch of the E string just before it becomes Smooth. This will
mean that the interval is Wide. If you were to continue raising the pitch past
the Smooth point, the Beat Rate would begin to speed up again and the interval
would become Narrow. Fourths are tuned slightly Wide.
Imagine the A note as a point in space and the E note as another point some
distance beneath the A. As you raise the pitch of the E it gets closer and
closer to the A. Now imagine an interval of a fourth as being the perfect
distance between these two points. If the E and the A were at this perfect
distance and you raised the E, the distance between them would become narrower.
If you lowered the E, the distance would become wider.
Musical intervals are thought of as distances in pitch.
COINCIDENTAL HARMONICS
Why is it possible to tune two different notes to each other, e.g. E and A?
This is possible because of coincidental harmonics. When you pluck an open
string on a guitar, not only do you get the note produced by the open string as
it vibrates along it's whole length, but also a series of upper partials. These
are known as the Harmonic Series.
You don’t hear these upper partials because the open string, vibrating along
it's entire length, displaces much more air than the upper partials and
therefore is much louder. The volume of the open string drowns out the quieter
upper partials.
It is possible to tune an E to an A because both notes have a coincidental
harmonic in their series of upper partials. That is to say, they both have an
upper partial that vibrates at exactly the same frequency. If you rest your
finger on the A string over the 12th fret and pluck the string, you get a
harmonic that is an octave above the A produced by the open string. This
harmonic is known as the first upper partial or the second harmonic (the first
harmonic being the A produced by the open A string, also known as the
fundamental). By resting your finger on the string at the 12th fret, you are
stopping the whole of the string from vibrating and allowing the string to
vibrate either side of your finger. This silences the fundamental and allows the
first upper partial (second harmonic) to be heard. If you repeat this procedure
at the 7th fret you will silence the first and second harmonics and hear the
third harmonic. This harmonic sounds an E, which is an octave and a fifth above
the fundamental A. By resting your finger above the 5th fret of the E string you
hear the fourth harmonic of the E string, which is an E at exactly the same
pitch as the one on the 7th fret of the A string. It is the beat rate between
these coincidental harmonics that can be heard when tuning an E to A fourth.
You do not need to pick out these harmonics to hear the beat rate. The beat rate
can be heard just by playing the two open strings together. The upper partials
themselves may be drowned out by the volume of the fundamentals but the beat
rate between the two coincidental harmonics can be heard.
USING INTERVALS TO TUNE A GUITAR
In standard tuning (E, A, D, G, B, e) you’ll notice that four of the
neighbouring pairs of strings are made up of fourths: E and A, A and D, D and G
and B and e. The 2nd and 3rd strings (G and B) are made up of a major third.
Firstly, set your A string using an A pitch fork (440Hz). The pitch created by
the 440 fork corresponds to the 4th harmonic of the A string (above the 5th
fret). Once again, you don't need to pick out the harmonic to hear the beat rate
but you can if you want to hear it really clearly. NEVER bang a pitch fork on
anything hard like a table. Strike it against some firm but with a bit of give
in it; like the sole of a shoe or your knee if you’re not too boney.
Now play the E and A together and raise the E to just short of smooth. Check the
accuracy of this by fingering the A string at the 2nd fret (B) and play the E
and B together. Both the E A fourth and the E B fifth should be just off smooth.
If you want to be really accurate, the fifth should be slightly smoother than
the fourth, but there’s not a lot in it. If the E A fourth is beating too
rapidly then you need to raise the E a little more. If the E B fifth is beating
too rapidly then you have raised the E too much and need to flatten it.
Now tune the D to the A as a fourth. Bear in mind that whilst tuning the E to
the A, the E was lower in pitch than the A and so you needed to stop short of
smooth in order to make the fourth slightly wide. Because the D is higher than
the A, you will need to go slightly past the smooth point to make the fourth
wide. It’s best in this case to tune it smooth and then check the the fifth by
fingering the 2nd fret of the D string to get an A E fifth. If it is beating too
much raise the D a little more and check both intervals again. Repeat the
procedure used for tuning the A D fourth to tune the D G fourth.
Now we come to the G B major third. Major thirds have a very rapid beat rate
compared to fourths and fifths, which are almost smooth. This beat rate
increases as you get higher in pitch. For example, the middle C (3rd string 5th
fret) and the E (2nd string 5th fret) is a major third. This beats 10.38 times a
second, almost a blur.
I trained as a piano tuner in my early twenties and it was the part of the
course that involved tuning this interval that separated the people who were
going to complete the course from those who were not.
If you have trouble hearing the beat rate between the G and B; tune the B string
by fretting the G string at the 4th fret and tune the unison. Now pick out the
harmonic that is just before the 4th fret of the G string and the one that is at
the 5th fret of the B string. These are the coincidental harmonics for the G B
third. You should now be able to clearly hear the rapid beat rate. To get a
fourth and fifth for the G and B string: Finger the B string at the first fret
and play it together with the open G for a fourth (G C) and the 4th fret for a
fifth (G D). Then you can apply the method for tuning the fourths and fifths
that was described above.
Once the B string is done you can use the same method to tune the final fourth B
e.
You can also use octaves as a further way of checking for inaccuracies. Finger
the D string at the 2nd fret and play it together with the open 6th E string as
an octave. Remember, octaves should be smooth. Finger the G string at the 2nd
fret and play it together with the open A string as an octave. Finger the B
string at the 3rd fret and play it together with the open D string as an octave.
Finger the 1st e string at the 3rd fret and play it together with the open G
string as an octave. In fact, anywhere on the fret board where you can play an
octave or a double octave along with an open string, you should do so; e.g. open
G with the G at the 8th fret of the 2nd string or open D with the D at the 7th
fret of the 3rd string.
You can also apply this to fourths and fifths, or extensions of fourths and
fifths i.e 11ths and 12ths or even 18ths and 19ths (these should sound just as
sweet as the fourths and fifths). For instance, the open A string together with
the open 1st e string as a 12th or the open D string together with the A at the
5th fret of the 1st string as a 12th. It’s best to stick to double octaves,
12ths and 19ths when checking further up the fret board as these are the
clearest to hear. You can of course check the 5th and 4th fret unisons too.
If all your unisons and octaves are smooth and your fourths, fifths, 11ths and
12ths aren’t beating too wildly, then you can be sure that your chords will
sound sweet wherever you play them on the fret board.
You could apply this method of tuning to achieve greater accuracy when setting
the intonation on an electric guitar. I’m not going to go into the method for
adjusting intonation as I’m sure someone else has already done so, but you could
use double octaves, 12ths and 19ths to check the accuracy of your guitar’s
intonation.
STRINGS
Strings can affect tuning and intonation. I find that about one out of every
four or five packs of strings has a faulty one in there. I think it has
something to do with the winding.
Finally, if you find your guitar drifts out of tune often, (if you train your
ears to hear interval beat rates you'll know about it alright) then it may be
because you haven't set the string after a re-stringing.
STRING SETTING
After stringing your guitar and tuning it up to pitch. Be sure to set the
strings by pulling them away from the fret board. Rounabout where the fret board
meets the sound hole or pick up, take hold of the string with your first two
fingers and with your thumb pressing against the front of your guitar, pull it
away from the guitar. You'll find the pitch has dropped a lot because you are
taking out the excess slack. retune and repeat several times until it no longer
drops. You should feel the string becoming much more tense as you reapeat this
proceedure. Be fairly gentle with the 1st ans 2nd strings. You should now find
that your guitar stays in tune for much longer. If you don't know how to string
a guitar the way they do in a guitar workshop then check around the internet or
read a guitar maintainece handbook. Basically, it involves wrapping the string
back under itself so that as you tighten it up it traps itself.
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