by
Paul Guy © Paul Guy 1990 - 99
The fretboard
Compensation
& intonation
Troubleshooting
Nut
compensation
Stretch tuning
Tuning methods
evaluated
Tuning tips
References
Tuning has always been
a bugbear for guitarists. Every guitar player - and every guitar builder
and repairer - is familiar with the problem. No matter how good the instrument,
and how well tuned and adjusted, it never sounds perfectly in tune in all
positions and keys.
This is not the fault
of the guitar. It is not designed to play perfect intervals (except for
octaves and unisons) in any position, or any key. It is designed to play
the equal-tempered scale, and it is perfectly possible to adjust and intonate
almost any well-made guitar so that it plays this scale pretty accurately.
The problem with equal temperament, though, is that it is artificial, a
mathematical construct, and it conflicts with the physical properties of
real-world strings.
Real-world strings produce
harmonics which are pure fractions of the speaking length of the string.
The ancient Greeks and Chinese knew about the pure intervals, and constructed
their musical scales around them. But Nature throws a spanner in the works
by making the natural tone row irregular, so instruments tuned in this
way cannot modulate to different key signatures without adding more intervals
to the octave.
There is another problem
in that 7 pure octaves and 12 pure fifths do not add up the same:
7 octaves = (2/1) ^7 = 128
12 fifths = (3/2) ^12 =
129.74
The discrepancy works out
to 24 cents (almost exactly a quarter-tone), and is known as the "Pythagorean
Comma". Finding a way around these problems has been the cause of much
controversy and many bitter arguments among music theorists for two and
a half millenia.
To make a fixed-interval
instrument with 12 notes in the octave useable in all the key signatures,
the purity of the intervals has to be compromised. This is called "tempering".
A temperament is a specific way of dividing the Pythagorean comma among
the intervals of the octave. There many alternative ways to do this on
keyboard instruments, and it is only in the last 150 years that equal temperament
has taken over as the accepted standard.
As far as the guitar and
other fretted instruments having 12 straight, unbroken frets to the octave
are concerned, equal temperament is the only choice. Back in 1581, Vincenzo
Galilei (Galileo's father), explained the need for equal semitones logically
and correctly - "since the frets are placed straight across the six strings,
the order of diatonic and chromatic semitones is the same on all strings.
In chords, therefore, a C# might be sounded on one string, and a Db on
another - this will be a very false octave unless the instrument is in
equal temperament."
Equal temperament divides
the octave into twelve exactly equal semitones. The resulting equal divisions
are a logarithmic function of the speaking length of the string, rather
than pure fractions, and thus are not a true analog of the natural harmonic
series.
Equal temperament is the
ultimate compromise. Tonal purity is sacrificed for ease of modulation.
Depending on your viewpoint, equal temperament either a) makes every key
equally in tune, or b) makes every key equally out of tune... The idea
is to make it possible to play all intervals and chords, in all keys, with
the same relative accuracy. Although every key is very slightly out of
tune, every key is also useable. No key sounds worse than any other key.
The same applies to all chords. Theoretically, that is. In practise certain
intervals and chords can still sound dissonant. Thirds are especially troublesome,
as the even-tempered minor third is 16 cents flat to the "pure" minor third
and the even-tempered major third is 14 cents sharp of pure. The equal-tempered
major sixth is 16 cents sharp of just, and the equal tempered major seventh
is 12 cents sharp of just. The only interval which is identical in the
two scales is the octave.
Those readers who are interested
in the theory behind all this can check out my essay Tuning
and Temperament, which goes into the history and development of
tuning theory, from Pythagoras to the present.
The purpose of this article
is to show how to get the best out of the equal tempered guitar.
THE
GUITAR'S FRETBOARD
The number 1.0594631, the
twelfth root of two, is the key to dividing a fingerboard into equal semitones.
Applied to the guitar, the frets are placed so that the ratio of the distance
from the nut to the bridge (the scale length), to the distance from the
first fret to the bridge, is 1.0594631:1. The ratio of the distance from
the first fret to the bridge to the distance from the second fret to the
bridge is the same, and so on up the fingerboard. This is a fairly complicated
way to calculate fret positions, but we can juggle the numbers around to
make it simpler.
S = Scale length
X = Distance from nut to
first fret
S - X = Distance from first
fret to bridge
(S - X)/S = 1/1.0594631
S = 1.0594631 (S - X)
S (1.0594631 - 1) = X (1.0594631)
S/X = 1.0594631/0.0594631
S/X = 17.817152
The number 17.817 is much
easier to deal with when we want to divide a guitar fretboard into semitones.
Just divide the scale length by 17.817, the result is the distance from
the nut to the first fret. The remaining length of the string (scale length
minus first fret) is again divided by 17.817 to give the distance from
the first to the second frets, and so on, for the desired number of frets.
This method is very precise in practise, as the 12th fret comes at exactly
half the scale length, and the 24th fret at exactly half the distance from
12th fret to bridge. This gives us "pure" octaves.
The following is a table
of fret locations for a Fender Stratocaster, calculated by the "17.817"
method. Note that the 12th fret is exactly at the halfway mark, and the
24th fret at three quarters of the scale. (A standard Strat has only 21
or 22 frets, but it's usual to work out the figures for 24 frets as a double-check
on the calculation.)
Fender Stratocaster, scale
length 25-1/2"
Fret From nut To next fret Remaining
1 1.4312 1.3509 24.068
2 2.7821 1.2751 22.717
3 4.0571 1.2035 21.442
4 5.2606 1.1359 20.239
5 6.3966 1.0722 19.103
6 7.4688 1.0120 18.031
7 8.4808 0.9552 17.019
8 9.4360 0.9016 16.064
9 10.3376 0.8510 15.162
10 11.1886 0.8032 14.311
11 11.9918 0.7582 13.508
12 12.7500 0.7156 12.750
13 13.4656 0.6754 12.034
14 14.1410 0.6375 11.359
15 14.7786 0.6017 10.721
16 15.3803 0.5680 10.119
17 15.9483 0.5361 9.551
18 16.4844 0.5060 9.015
19 16.9904 0.4776 8.509
20 17.4680 0.4508 8.032
21 17.9188 0.4255 7.581
22 18.3443 0.4016 7.155
23 18.7459 0.3791 6.754
24 19.1250 6.375
Back to top
COMPENSATION
As we have seen, equal tempered
fret spacing can be calculated mathematically to a high degree of accuracy.
If this were all there was to it we would be laughing. However, if the
bridge is placed at exactly the theoretical position (nut - 12th fret distance
multiplied by 2), the fretted notes will get progressively sharper the
further up the fingerboard one plays. This is because fretting the strings
stretches them by a small amount, raising the tension and therefore the
pitch of the notes produced. Action height is normally lowest at the nut
and highest at the last fret, so the sharping effect increases with distance
from the nut. To compensate for this, length is added to the string at
the bridge end. The amount necessary varies from string to string, generally
increasing from treble to bass. "Intonation" means adjusting this compensation
until the open notes and the 12th fret notes of each string are exactly
one octave apart.
Most modern electric guitars
have a separate length-adjustable bridge saddle for each string, and the
octaves can be intonated very precisely by the owner using an electronic
tuner. Acoustic guitars usually have a fixed, narrow bridge saddle which
gives little room for compensation.
Steel-string acoustic guitars
usually have a straight slanted bridge saddle. Most nylon-strung guitars
have either a straight bridge saddle with the same compensation for all
six strings, sometimes with extra compensation on the G-string. This works
fairly well due to the smaller differences in diameters in nylon string
sets.
Most often the only way to
improve the intonation of acoustic guitars is to install a wider saddle
and file in the correct intonation points. Such work is best left in the
hands of a professional with the appropriate equipment and experience.
INTONATION
Intonating most electric
guitars is so simple that every guitarist with access to an electronic
tuner should be able to do it himself. And since intonation is also affected
by one's individual playing style - how hard one presses down the strings,
for example - it makes sense that a guitar should be intonated by the person
who is going to play it.
The nut, truss rod and action
height should be adjusted to taste before you start intonating, otherwise
you may as well not bother. It is also a waste of time (except in an emergency
situation) to try to intonate with worn strings. For best results, restring
and adjust the instrument, and then wait 24 hours to let the strings settle
before fine-adjusting the intonation. (By all means give it another check
and final adjustment 24 hours after that, too.) For most guitars you will
only need a new set of strings, a screwdriver or key of the correct size
for the bridge saddles' length adjusting screws, a good electronic tuner,
and patience. Don't attempt to adjust your intonation by ear (unless you
have perfect pitch) you'll only drive yourself crazy!
The goal of intonation is
to adjust the length of each string individually until it plays pure octaves
between the open string and the twelfth fret, between the first fret and
the 13th fret, the 2nd and the 14th, and so on, as closely as possible.
Start by tuning all six strings with the tuner (and keep checking the overall
tuning throughout the procedure). The guitar should be held in playing
position - the tuning will be noticeably affected by gravity, among other
things, if the guitar is laid on its back.
Using the tuner, first compare
the open string note to the note at the twelfth fret. The tuner should
give exactly the same reading. If not, and the twelfth fret note is flat
compared to the open note, the string length is slightly "too long", and
the bridge saddle must be moved towards the neck. Conversely, if the twelfth
fret note is sharp to the open note, the string is "too short", and the
saddle must be moved away from the neck. Adjust the saddle, retune the
open string and compare again. Repeat the procedure until the two notes
agree. Do the same for the remaining strings.
Adding length to the string
at the bridge end to correct the intonation at the 12th fret has an unfortunate
side-effect, in that this also lengthens the distance from the higher frets
to the bridge, which can throw the intonation off at the top end of the
range.
To check for this, compare
the 5th fret with the 17th fret, and the 7th fret with the 19th fret. If
there is a problem, it may be necessary to compromise the 12th fret a tad
to get acceptable intonation in the high register. If the guitar is seldom
played above the 10th fret, though, it's obviously better to optimise the
low end instead.
All the strings will end
up slightly longer than the theoretical scale length, which is the distance
from the nut to the twelfth fret x 2. The thicker the string, the more
its tension increases when fretted. The lower strings therefore need more
"compensation", as this small increase in length is called. A plain string
needs more compensation than a wound string of the same diameter, so, in
most cases, the high E string will be shortest, the B string a little longer,
a plain G a little longer still, the D string a little shorter than the
G, the A string a little longer than the D, and the low E longest of all.
Heavy gauge strings need
less overall compensation than lighter gauges. This is because they are
already at a higher tension than lighter gauges, and thus the percentage
of tension added by fretting the strings is relatively less than for lighter
gauges.
Back to
top
TROUBLESHOOTING
There are a host of problems
that can cause a string or strings to tune falsely. If one string behaves
very differently to the rest of the set, the first thing to suspect is
a bad string. If replacing it doesn't cure the problem, check the following:
Make sure the
string is making clean contact with the fingerboard edge of the nut.
Sometimes a string of different thickness than the one replaced will not
fit into the slot properly. The slot widths should be as close as possible
to the diameters of the individual strings, without the strings binding.
The slots should be rounded over a little towards the tuner side of the
nut, so that each string makes solid contact at the fingerboard edge of
the nut. The depth of the slots is checked by fretting each string between
the second and third frets, and checking the clearance over the first fret.
The string should NOT touch the first fret - you should just be able to
get a piece of thin paper in between. Much higher than this, though, and
the extra amount the string must stretch to be fretted at the first few
frets will cause these frets to play sharp. (Too low and the open string
will rattle on the first fret when played.)
Check that the string
is making clean contact with the bridge saddle. On acoustics, is the
bridge saddle standing up straight in its slot? If it leans forwards (toward
the neck) the guitar will almost certainly play sharp up the neck.
Flat frets can also contribute
to bad intonation.The frets should be properly crowned (rounded), so
that the strings make contact at the centrelines of the frets and not at
the front edges.
If accuracy of intonation at
the lowest frets is a problem, even when the guitar plays "perfect" octaves
at the 12th fret and between the upper frets, it may be time to look at
the next parameter.
Back to
top
NUT COMPENSATION
All guitar players are familiar
with the common tendency of most guitars to play slightly sharp at the
first couple of frets. Lowering the nut as far at it will go before the
open string rattles on the first fret minimises this effect, but does not
totally eliminate it.
There are two key differences
between each string's open note and all its fretted notes.
1) Finger
pressure on every note except the open note.
The finger stretches
the string slightly, sharpening the note produced. This sharpening effect
normally increases in a fairly linear way towards the higher frets and
is compensated for by lengthening the string at the bridge saddle over
and above the theoretical scale length. So far so good. However, an anomaly
arises in the intervals between the open note and the first couple of frets,
because of the second key difference between open and fretted notes, which
the design of the conventional fingerboard fails to take into account.
This is:
2) "End effects" on
the open note alone.
As the string is held
motionless at the nut and the bridge, the first tiny part of it at each
end is prevented from vibrating freely. The effective speaking length
of the open string is therefore slightly shorter than the theoretical string
length used to calculate the fret locations. This means that depressing
a string at the first fret shortens it a tad too much for it to create
the correct frequency - it sounds sharp relative to the open string. This
cannot be compensated for at the bridge saddle without compromising the
intonation of the rest of the frets.
By shortening the distance from
the nut to the first fret, the note created by depressing the string at
the first fret is flattened relative to the open string. Since the frets
are not moved - they are placed in accordance with theory - their pitches
are unaffected by the moving of the nut. It is only the relative pitch
of the open string to the notes at the first couple of frets that is perceptibly
altered.
A handful of top-line luthiers
go in for nut compensation in a really big way, compensating the nut different
amounts for each string. Others use a compromise position for the nut which
compensates all strings equally. Still others claim ferociously that nut
compensation is a crock...
There is little real agreement
on exactly how much compensation is necessary - if any! - but figures of
from half a millimeter to as much as one and a half millimeters are quoted.
My own experience is that a little goes a long way.
Back to
top
STRETCH TUNING
The mathematical intervals
only take the strings' fundamental frequencies into account. But strings
do not just generate fundamentals; they also produce a whole spectrum of
overtones (or "harmonics"). The string has to vibrate in smaller and smaller
divisions of its length as the overtones increase in frequency, but it
is not infinitely flexible. The higher the overtone the more the string
has to struggle to vibrate. The stiffness of the string causes the overtones
to become sharper and sharper the higher they get. This phenomenon is called
"inharmonicity".
If notes played together
are to sound consonant, then above all, their overtones must blend together.
The high overtones of the lower notes in a chord should not clash with
the low overtones of the higher notes. On pianos, therefore, the octaves
are tuned progressively flatter starting about an octave below Middle C,
and progressively sharper starting about an octave above Middle C. Piano
tuners "stretch" the tuning of the piano +/- 50 cents or more across 7
octaves on smaller instruments. Inharmonicity is minimised on grand pianos
by lengthening the lower strings as much as possible, but even the largest
concert grands are normally "stretched" at least +/- 25 cents across 8
octaves.
The graph below is an averaged
curve of the actual measured stretch of a large number of professionally
tuned pianos.
Inharmonicity is nowhere
near as extreme with guitar strings, which are at much lower tension than
piano strings. It can be ignored for most purposes, unless you are using
barbed wire strings. But a subtle stretch tuning may please your ear, and
help you blend in better with keyboards. The above graph shows where the
guitar's range falls in relation to the piano stretch curve, and can be
a valuable guide if you want to experiment along these lines. Remember
that A = 440Hz is A at the 5th fret of the high E string. The 2nd fret
A on the G string is 220Hz, and the open A string is 110Hz.
The guitar cannot be evenly
stretch-tuned throughout its range without altering the spacing of the
frets. But one can cheat by simply widening the open string/12th fret interval
- this will give a stretch which increases on a parabolic curve as you
progress up the fingerboard. A few cents is a great plenty in this connection.
Back to
top
TUNING METHODS EVALUATED
List
It is worth repeating that
the tempered scale is a compromise. It follows that the tuning of the guitar
is also a compromise. However it is a very successful compromise which
enables us to play almost all intervals and chords in all keys with the
same relative accuracy.
The only pure fretted intervals
that can normally be produced on the guitar are unison and octave. In tempered
tuning fifths are lowered by 2 cents compared to pure. Fourths are raised
by 2 cents from pure. Thirds are raised 14 cents, and minor thirds lowered
16 cents, from pure.
The guitarist needs to develop
a "tempered ear" to be able to discern whether a guitar tunes well or not.
Even without a "tempered ear", though, it's easy to tune a guitar to the
equal tempered scale, as long as you remember that the only pure fretted
intervals that can normally be produced on the guitar are unison and octave,
and that these intervals are therefore the only ones usable for tuning
purposes. One must also be aware that ALL harmonics are pure intervals,
and that only the octave harmonics (above the 12th and 5th frets) should
be used when tuning.
There are a whole slew of
methods - some better, some worse - used to tune guitars. The following
is a discussion of the most common methods. Note, however, that some methods
that do not work on the guitar work fine on fretless instruments, including
the violin family. It is perfectly possible to play pure intervals on instruments
which lack frets. They can therefore be tuned in ways that do not work
for the guitar. We are discussing only guitar tuning here though, and the
tuning methods are evaluated with this in mind.
Listen for the beats!
Those who find it difficult
to hear whether an interval is in tune or not have usually just not learned
the trick yet. It's like riding a bike, or swimming - once you've got it,
it's dead simple. Learning to listen for the beats is the answer. Play
the two notes together - say the open low E string and the E on the D string
at the second fret - and let them ring. If they are not precisely in tune
you will hear a tremolo (regular variation in volume) produced by interference
effects. This is called "beating". Tuning either one of the strings will
either a) cause the beats to increase in speed, which means that you are
going the wrong way, or b) cause them to slow down and eventually stop
altogether when the two notes are perfectly in tune.
Tuning methods:
Unison
method
Octave
method
My
favourite method
5/7
Harmonics method
Counting
beats
Tuning
to a chord
Electronic
tuners
UNISON METHOD (4th/5th
fret method) - CORRECT
The old faithful "4/5"
method is perfectly correct in principle, since unison intervals are used.
For those readers from Mars who aren't familiar with it, the method is
as follows: one string (usually high E) is tuned to a reference frequency
("Oi! Fred! Gimme an E!").
The 5th fret E on the B
string is tuned to match the open E,
the 4th fret B on the G
string is tuned to match the open B,
the 5th fret G on the D
string is tuned to match the open G,
the 5th fret D on the A
string is tuned to match the open D,
finally the 5th fret A on
the low E string is tuned to match the open A.
If you have tuned accurately
the interval between the two E strings will be exactly two octaves - the
5th fret double octave harmonic on the low E should sound at the same pitch
as the open high E. The problem with this method is that if you get one
string wrong, the following strings will also be out. But if you have a
well-adjusted guitar and a good ear, it can work well.
Back to
list
OCTAVE METHOD - CORRECT
Any tuning method using
octaves is correct in principle. There are many variations - one way is
to tune the open B string one octave below the 7th fret B on the high E
string, the open G string one octave below the 8th fret G on the B string,
the open D string one octave below the 7th fret D on the G string, the
open A string one octave below the 7th fret A on the D string, and - you
guessed it - the open low E one octave below the 7th fret E on the A string.
But we're back to small errors
affecting the following strings again. To avoid this, and because tuning
errors become more obvious further up the fingerboard, make your comparisons
using only fretted octaves between the 7th and 12th frets, and try tuning
in this order:
1. Tune low E two octaves below
high E.
2. Compare high E and D - tune
D.
3. Compare high E and G - tune
G.
4. Compare D and B - tune B.
5. Compare G and A - tune A.
Back to
list
MY FAVOURITE METHOD
If you tune all the
strings to the same reference string, you can avoid a small error on one
string affecting all the others.
Tune the high E string to
a reference: compare
5th fret E on the B string
9th fret E on the G string
14th fret E on the D string
7th fret E on the A string
(one octave below)
5th fret harmonic on the
low E string.
I then cross check
(if I feel the need) as follows:
12th fret harmonic on low
E / fretted 7th fret E on A string.
12th fret harmonic on A
/ fretted 7th fret A on D string.
12th fret harmonic on D
/ fretted 7th fret D on the G string.
12th fret harmonic on G
/ fretted 8th fret G on B string.
12th fret harmonic on B
/ fretted 7th fret B on high E.
This method has worked well
for me - and for many of my customers - for many years. (It is also extremely
effective at getting the best available results out of a poorly adjusted
instrument.)
Back to
list
5/7 HARMONICS METHOD
- DOES NOT WORK!
This method seems to have
a strange attraction for many guitarists. Perhaps it's a relic from the
beginner stage, when it was difficult to get the harmonics to ring at all.
Somewhere deep in the unconscious the impression is formed that the method
must be good because it "sounds so professional" and was so difficult to
learn. Not least because it's such a convenient method, which leaves the
fretting hand free to tune with, many guitarists cling stubbornly to harmonics
tuning, despite the recurrent tuning difficulties it causes.
All the mystery effectively
hides the simple fact that the method cannot possibly work, as all harmonics
are pure intervals, and the frets are placed to give equal tempered intervals.
With the exception of the octave and double octave harmonics (octaves are
pure in both the pure and the tempered scales) harmonics should not be
used for fine-tuning.
The most common harmonics
method is the "5/7" where the high E is tuned to a reference, and the 5th
fret harmonic on the low E, to the open high E.
The 7th fret harmonic on
the A is tuned to the 5th fret harmonic on the low E.
The 7th fret harmonic on
the D is tuned to the 5th fret harmonic on the A.
The 7th fret harmonic on
the G is tuned to the 5th fret harmonic on the D.
The 5th fret harmonic on
the B is tuned to the 7th fret harmonic on the high E.
Many users of this method
also delude themselves that the 4th fret harmonic on the G string should
sound the same frequency as the 5th fret harmonic on the B string.
A guitar tuned this way will,
quite simply, not play in tune. The reason is simple - the 7th fret harmonic
on the A string sounds the note E, the fifth . But this is a pure fifth
interval (to be pedantic, an octave and a fifth). The tempered fifth is
lowered two cents from pure. The resulting open A note will therefore be
two cents flatter than the tempered A we want. The interval between the
low E and the A strings should be a tempered fourth, which is raised two
cents from pure. Since the A string has been tuned two cents flat the E
- A interval will be flat by the same amount.
Two cents isn't much but
when you tune the D to the A the same way, the D ends up four cents flat.
When you get to the G you will be six cents flat. Tuning the 5th fret harmonic
on the B string to the (pure fifth) 7th fret harmonic on the high E leaves
the open B sharp by two cents. The resulting open G to open B major third
interval will be eight cents sharp.
Trying to tune the B string
to the G by harmonics will really get you into trouble. The 4th fret harmonic
on the G string sounds the major third of G - a B note. But again, this
is a pure interval. The tempered third is raised fully 14 cents from pure.
Tuning the 5th fret harmonic on the B string to the pure third on the G
will leave the B 14 cents flat. Try it and then compare the 4th fret B
on the G string to the open B - you'll see what I mean. It should be obvious
by now that harmonics - other than octaves - are not to be trusted! They
are useful for the initial coarse tuning, however, as the fretting hand
is free to tune while both strings are sounding. Just don't try to use
them to fine tune.
Back
to list
TUNING PAIRS OF OPEN STRINGS
BY COUNTING BEATS ?
GOOD LUCK!
All "by ear" tuning ultimately
depends on the use of beats - the tremolo (regular variation in volume)
produced by interference effects when two notes are played together - in
unison or other intervals - and the interval is not precisely pure. The
closer to pure, the slower this tremolo, until it disappears altogether
when the interval is pure. The speed of this tremolo is also relative to
the interval's absolute pitch - the higher the pitch, the faster the tremolo.
Inexperienced guitarists
often try to tune the guitar by the beats between pairs of adjacent open
strings. For example, they play the open E and A strings together, and
tune the interval so that the beats disappear. Next they play the open
A and open D together, and so on. The problem with this method is exactly
the same as with the harmonics method - i. e. that the intervals are being
tuned pure, and the guitar must be tuned to tempered intervals. If the
open E and A strings are tuned beat-free, the interval will be two cents
too narrow. If the open G and B strings are tuned the same way, the interval
will be fourteen cents too narrow. A guitar in exact equal tempered tuning
sounds the following beats between pairs of strings:
| String |
|
6 |
|
5 |
|
4 |
|
3 |
|
2 |
|
1 |
| Note |
|
E |
|
A |
|
D |
|
G |
|
B |
|
E |
| Interval |
|
|
Fourth |
|
Fourth |
|
Fourth |
|
Third |
|
Fourth |
| Beats |
|
0.3/sec |
|
0.5/sec |
|
0.6/sec |
|
.8/sec |
|
1/sec |
It's easy enough to hear
when the beats disappear, and to tune the intervals pure. It's much harder
to learn to count the beats accurately enough to tune the guitar correctly
by them. Most of us will find it much easier to use another method.
Back
to list
TUNING TO A CHORD - NO
WAY
Tuning one chord so that
it sounds perfect just causes all other chords to sound terrible. In tempered
tuning all chords are slightly "out", but all by the same small amount.
Remember that the tempered scale is a compromise that enables us to play
all chords and intervals, in all keys, with the same relative accuracy.
It therefore follows that there is not one chord on the guitar that tunes
absolutely pure. Thus it is a total waste of time to tune the guitar to
a chord and expect it to sound pleasing anywhere else. If you can't swallow
these facts, then for your own peace of mind, you're probably better off
if you give up the guitar and get a flute or a sax or something instead.
With experience, though, you can develop an ear for even tempered tuning.
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ELECTRONIC TUNERS
No-one was happier than I
when the first affordable tuners appeared on the market in the 70's. At
last - an end to band arguments about who was in tune or not. Just plug
in to the box and check. Electromechanical strobe tuners had already been
around for a long time, and were used by the majority of professional repair
shops for intonating instruments. But they were rather large and delicate,
and cost an arm and a leg.
Electromechanical and "virtual"
strobe tuners are extremely accurate - within plus/minus one tenth of a
cent. High-end strobe tuners use a solid-state rotating LED display, and
can do even better. My PST-2 Precision Strobe Tuner, made by Jim Campbell,
has a specified temperament accuracy of better than one hundredth of a
cent. Its successor, the PST-3, is even more accurate, at one thousandth
of a cent - see http://www.precisionstrobe.com.
(Unfortunately these tuners do not seem to be in current production.)
Microelectronics made it
possible to build "guitar tuners" which were small and relatively cheap.
The early models were accurate to around plus or minus 3 cents, but most
recent units do much better - plus or minus 1 cent. This is better than
the average human ear can manage, except perhaps for one in ten thousand
people who are blessed with perfect pitch. Electronic tuners are a good
investment - they can save a lot of time, arguments and stress - but what
happens when the battery runs out, and the Seven-Eleven is closed? Every
guitarist should be capable of tuning a guitar accurately without electronic
assistance when necessary.
Update, October 2007 -
the Turbo Tuner:
My Precision Strobe Tuner
is a great piece of equipment, but it has now been retired in favour of
a Sonic Research Turbo Tuner. The PST was designed primarily as a piano
tuner, whereas the Turbo Tuner was designed by an electronics engineer
who also happens to be a guitar builder, and is thus far better adapted
to the needs of the guitarist and guitar technician.
The Turbo Tuner outperforms
any tuner I have ever tried - and that's quite a few. For the purpose of
tuning guitars, or any other multi-stringed instrument, plucked or bowed,
nothing has ever approached the performance, versatility, and user-friendliness
of the Turbo Tuner, at any price.
This is a true strobe tuner,
not a simulation, and its tuning accuracy is phenomenal - one-fiftieth
of a cent, or one five thousandth of a semitone! The only strobes I have
ever seen which can claim equal or better resolution are specialised high-end
piano tuners (like the PST) for very big bucks. The Turbo Tuner is five
times more accurate than electromechanical or "virtual" strobe tuners,
and at least fifty times more accurate than all common guitar tuners. Indeed
it is one hundred and fifty times more accurate than one popular pedal
tuner from a leading manufacturer with a list price $10 higher than the
on-line price of a Turbo Tuner.
For visibility and clarity
of display, the Turbo Tuner is unbeatable. The rotating LED strobe display
is clearly readable from across the room (even if you are short-sighted,
like me), and the backlit LCD display is never ambiguous or cryptic, giving
full information about the current settings at all times.
Very few tuners of any stripe
can read the attack transient of a guitar note. Mechanical displays (spinning
discs, needles) have latency due to inertia. "Virtual" displays have latency
due to the digital processing of the input signal. In common with the PST,
the Turbo Tuner's rotating solid-state LED display is strobed directly
by the input signal, and thus responds instantly both to the attack transient
and to the slightest change of pitch.
The Turbo Tuner is the optimal
tuner for the player, and for the guitar tech or builder. It can do anything
a guitar player could possibly want to do, and on the workbench it speeds
up intonation work no end. And unlike the old one, I can pick it up and
put it in my gig bag, or even my pocket, to take it with me to a gig.
www.turbo-tuner.com
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TUNING TIPS
1. Learn to attach
the strings to the machine heads properly!
2. Never try
to tune down to a note - first tune below the target pitch, then stretch
the string, then tune up to the note. (To avoid problems caused by the
"play" in 99% of tuning machines.) Make a couple of deep bends (you don't
have to actually play the note, just bend it to settle the tension) then
fine tune.
3. Before tuning
a string that you suspect is out, check it against both adjacent strings!
Many guitarists make the mistake of tuning the wrong string! Oftentimes
you think your G is sharp when in fact it's the D that's flat, for example.
I do sometimes, and when I watch other people tuning, it seems to me that
they do too...
4. When tuning
a guitar with a vibrato arm, tune the string, give the arm a good shake,
stretch the string, give the arm another shake, and fine tune. On the plain
strings I also like to bend the string a whole tone a couple of times (somewhere
around the middle) before fine-tuning.
5. Listen
for the beats!
© Paul
Guy 1990 - 2006
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References
Owen Jorgensen: Tuning: Containing
the Perfection of Eighteenth-Century Temperament, the Lost Art of Nineteenth-Century
Temperament, and the Science of Equal Temperament: Michigan State University
Press, 1991.
Mark Lindley: Lutes, Viols,
and Temperaments: Cambridge University Press, 1984
(An exposition of historical
evidence from the 16th- to the mid-18th century. Equal temperament is shown
to have been the norm for fretted instruments, with some use of meantone
and other systems in individual cases. A short cassette tape is available
separately from the publisher.)
Sir Jack Westrup & F.
Ll. Harrison: Collins Encyclopedia of Music, London 1984
Thomas D. Rossing: The Science
of Sound: Addison-Wesley Publishing, 1982
Franz Jahnel: Manual of Guitar
Technology: Frankfurt, 1981
John Backus: The Acoustical
Foundations of Music: W.W. Norton & Co., 1977
Hideo Kamimoto: Complete
Guitar Repair: New York, 1975
J. Murray Barbour: Tuning
and Temperament - A Historical Survey: Michigan State College Press, East
Lansing, MI, 1951
Sir James Jeans: Science
and Music: Cambridge, 1937
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See also:
Tuning
& temperament: a short history
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