Written by Ian Noyce
(First published in the Quarterly Journal of the Guild American
Luthiers in 1977)
Let's assume the guitar being tuned is properly set up so that
the intonation is correct. (More on this later.)
The two most common methods of tuning are
(1) the 4th and 5th fret method and
(2) the harmonic method.
Both of these methods are often misunderstood through confusion
regarding perfect (or Pythagorean) intervals and even tempered
intervals.
1. The 4th and 5th fret method.
Theoretically this is the simplest method as it simply involves
tuning unison intervals. The A string can be tuned to an A tuning
fork, then the bass E is fretted at the fifth fret and tuned
in unison with the A. The D string is tuned in unison to the
fifth fret on the A, the G to the fifth fret on the D, the B
to the fourth fret on the G and the top E to the fifth fret
on the B string. In practice this can be difficult for a number
of reasons, the most common ones being:
a. Any errors are accumulative.
b. Any falseness in strings will probably introduce errors,
depending on the skill of the person tuning.
c. If the bridge is not properly adjusted or compensated,
errors will definitely occur.
2. The Harmonic Method.
This is probably the most misunderstood method, and in fact
it is inherently inaccurate! The reason for looking at perfect
intervals and even tempered intervals was partly to throw light
on this method of tuning.
Harmonics are produced when a vibrating string is made to
vibrate in multiples of its fundamental pitch. For this reason,
harmonic intervals are always "perfect" or pure, and
this method, when done exactly, does not work on a guitar, which
is made to tune to the equal tempered scale.
The common tuning method is as follows:
Tune the A string to a tuning fork, the tune the bass E to
the A by playing the fifth fret harmonic on the E string (produces
a note E, two octaves higher than the open string) with the
7th fret harmonic on the A string (also produces a high E).
This is represented on the A and D strings, then the D and
G strings. Then the fourth and fret harmonic of the G string
(a B note) is played with the fifth fret harmonic of the B
string (also a B, two octaves higher than the open B). The
fifth fret harmonic on the B string is then used to tune the
7th fret harmonic of the top E.
If you follow this method accurately, the guitar will just
not play in tune, and the G-B interval will be particularly
bad. In fact, the G will be a pure major third away from B,
and the tempered major third is a much wider interval than the
perfect third.
In order to see how much difference there is between tuning
the guitar to perfect intervals (such as when using the harmonic
method) and tempered intervals, let's look at the open strings
of the guitar, when tuned correctly to tempered intervals.
Whenever two notes tuned properly are played together, "beats" will
be heard, (i.e. an alternate increase and decrease in volume
will be heard. A perfect interval has no beats). The beats occur
when adjacent open strings on a guitar are played together,
as follows:
String: 6 5 4 3 2 1
Note: E A D G B E
Interval: Fourth Fourth Fourth Major Third Fourth
Beats: 0.3 / sec 0.5 / sec 0.6 / sec 0.8 / sec 1 / sec
It should now be apparent that the harmonic method of tuning
is inaccurate, but if you understand why, you can compensate
for its inadequacies and still use it.
I find a composite method of tuning works for me as follows:
Tune the E, A, D, and G strings using the harmonic method described
earlier but widen each interval by the finest margin possible,
e.g. While tuning the D by playing the seventh fret harmonic
on the D with the fifth fret harmonic on the A, pull the D up
until it is perfect i.e. no beats, then raise it ever so slightly
to widen the interval just a touch (The difference here is two
hundredths of a semitone, or two cents -- pronounced "sonts").
Then, having tuned the lower four strings this way, check them
by playing the 12th fret harmonic on the E to check the E note
on the 2nd fret of the D string, and likewise for the G string
using the 12th fret harmonic on the A. A further check using
the fifth fret unison method is also helpful. With a little
practice you'll find that you've tuned correctly with the slightest
adjustments made initially to the harmonic method. To tune the
top E, use the 12th fret harmonic on the G string and the third
fret of the E string, and tune the B string similarly using
the 12th fret harmonic on the D string. As these last 2 strings
involve unison notes in tuning, then no compensation for the
harmonic method is necessary. Then, if the guitar is in tune,
the fifth fret harmonic on the bass E string should be in unison
with the open top E string.
If you've done everything correctly, and the guitar is still
out of tune, then it's likely that the strings are faulty or
the bridge compensation is not correct.
If the above information is confusing then it's probably due
to the fact that I've tried to cram in too much information.
For those who'd like to read up on this subject more fully,
below is a list of recommended material:
The Acoustic Foundations of Music,
by John Backus, published by W.W. Norton and Co. Inc., NY;
Complete Guitar Repair
by Hideo Kasimoto (Oak Publications); and
John Carruther's column in Guitar Player.
The remainder of this article can be read at http://www.noyceguitars.com/Technotes/Articles/T4.html
Reprinted here with kind permission from Ian Noyce.
http://www.noyceguitars.com
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