Tuning The Guitar

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 upp 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

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    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.

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    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.

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    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.

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    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.

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    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.

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    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.

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    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.)

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    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.

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    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.

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    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