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The intonation of a classical guitar is a subject that is increasingly being talked about, both by the players and the makers. There are many and varied reasons as to why intonation adjustment is necessary on classical guitars. With this article I hope to show what is necessary and why.

Many guitars do not play in tune and the causes of this can be many and varied. A guitar that does not play in tune will usually suffer from more than one of these causes.

Many players do not realise that their guitar does not play in tune until they play in an ensemble with other instruments. Guitarists are often used to the way their guitar plays and accept it as Ok, but the truth of the matter is that a large number of these guitars do not play in tune at all.

Some of the factors that are important for a guitar to play in tune are,
  • The fret calculation, placement and condition
  • The strings, condition and quality
  • The action and fret height
  • Intonation adjustment by way of compensation at the nut and saddle


  • Fret calculation, placement and condition.

    Guitars use what is called the "equal tempered scale" which is also used for most instruments with fixed pitch notes. This tempered scale leads to equally spaced intervals regardless of the tonality used.  This is a mathematical solution that divides the scale into 12 equal parts. These divisions do not give us frequencies that provide perfect or beatless 5ths for example, as with some other scales. 

    This table shows the frequencies of two of the scales used for tuning instruments, Equal temperament and Just temperament. The examples have been calculated starting on A (220Hz).

     
    Equal Temperament
     
    Just temperament

    Variation

     
     
     
     
     
     
    A
    220.000000 Hz
    Unison
    1:1
    220.000000 Hz
    .000000 Hz
    A#
    233.090000 Hz
     
    25:24
    229.166667 Hz
    -3.923333 Hz
    B
    246.958855 Hz
     
    9:8
    247.500000 Hz
    .541145 Hz
    C
    261.652907 Hz
    Minor third
    6:5
    264.000000 Hz
    2.347093 Hz
    C#
    277.221255 Hz
    Major third
    5:4
    275.000000 Hz
    -2.221255 Hz
    D
    293.715919 Hz
    Perfect fourth
    4:3
    293.333333 Hz
    -.382586 Hz
    D#
    311.192017 Hz
     
    45:32
    309.375000 Hz
    -1.817017 Hz
    E
    329.707942 Hz
    Perfect fifth
    3:2
    330.000000 Hz
    .292058 Hz
    F
    349.325564 Hz
     
    25:16 / 8:5
    343.750000 Hz
    -5.575564 Hz
    F#
    370.110435 Hz
    Perfect 6th
    5:3
    366.666667 Hz
    -3.443769 Hz
    G
    392.132006 Hz
     
    9:5
    396.000000 Hz
    3.867994 Hz
    G#
    415.463861 Hz
     
    15:8
    412.500000 Hz
    -2.963861 Hz
    A
    440.183960 Hz
    Octave
    2:1
    440.000000 Hz
    -.183960 Hz


    When a player uses harmonics to tune the guitar, the frequencies of the harmonics are not the same as the equivalent fretted notes, except in the case of the octave. How to tune a guitar is a personal thing, but it would help if the player understood that string harmonics are not the same as the fretted note in an equal tempered scale.  The equal tempered scale, because of its equal spacing of notes allows the player to modulate between keys without having to retune the instrument, but it has it problems in that the perfect 4ths and 5ths are not perfect. If the intonation is 'out' on a guitar, this will be even worse and is most noticeable.

    Fret placement on the guitar using the equal temperament scale, is determined by what is commonly called the rule of 17. The fret position calculation is simple and is best described using an example.

    How to calculate the fret positions for the given scale:

    The nominal scale length (without any compensation) is divided by 17.817 ( the 1/12th root of 2) and this gives the distance to the first fret from the nut. This distance to the first fret  is then subtracted from the nominal scale length to yield the new shorter scale length. This new shorter scale length is then divided by 17.817 to give us the distance to the next fret. This process is repeated for the number of frets required.

    Example: Call the scale Length = L  and the Distance to fret(n) = D(n),  and then let us say the scale length is 650mm, a common scale length on guitars.

    Calculate distance to the first fret
    Divide 650 by 17.817 (rule of 17). The result is 36.48mm. This is the distance from the nut to the first fret.
    L / 17.817 = D(1)
    650 / 17.817 = 36.48
    Re Calculate scale length
    Subtract 36.48 from 650. This gives us 613.52. This is our new scale length (L)
    L = L - D(1)
    650 - 36.48 = 613.52
    Calculate distance to the next fret
    Divide 613.52 by 17.817. The result is 34.43. This is the distance from the first fret to the second fret.
    L  / 17.817 = D(2)
    613.52 / 17.817 = 34.43
    Re Calculate scale length
    Subtract 34.43 from 613.52.  This is our new scale length (L).
    L = L - D(2)
    613.52 - 34.43 = 579.08
    Calculate distance to the next fret
    Continue the calculations for the number of frets required.
    L  / 17.817 = D(3)
    579.08 / 17.817 = 32.50


    For those who are interested I have included a simple spreadsheet that will calculate the fret positions for any scale length.

    Download FretCalculator.xls The output of the program is similar to the table below.

    650mm Scale

    Distance From Previous Fret

    New Scale Length

    Distance from Nut

    Fret 1

    36.48201156

    613.5179884

    36.48201156

    Fret 2

    34.43441592

    579.0835725

    70.91642748

    Fret 3

    32.50174398

    546.5818285

    103.4181715

    Fret 4

    30.67754552

    515.904283

    134.095717

    Fret 5

    28.95573234

    486.9485507

    163.0514493


    These fret calculations are only to be used on the nominal scale length, not the actual or measured scale length which will generally include some form of compensation. Some guitars will have scale lengths in a metric configuration and some will be imperial. Generally classical guitars are metric, but not always.

    The condition of the frets will obviously play a big part in how well in tune a guitar plays. Frets are crowned with the highest point being theoretically in the centre. If the frets are worn, or a poor fret job has been performed on the guitar, the break point may not be where it is meant to be and this will cause the guitar to play out of tune.

    Different fret heights can also be an issue. Tall frets are sometimes easier to play, especially for new players who experience trouble with the barre. The main problem with tall frets is that it is possible for the player to use more pressure than is actually required to stop the string ratting on the fret when played, and this increase in pressure will stretch the string and cause it to play sharp.

    Where the finger is placed within the frets is also important. It alters the amount of stretch either infront of the finger or behind and this can effect intonation again, but that in itself is a whole other topic.

    The strings, condition and quality

    The quality of the strings, their condition and age also play an important part here. Strings that are brand new will generally need some time to settle down before they can be assessed properly. Every string, because of its different properties will settle down at a different rate. It can take a day or two for some strings to reach their optimal playing condition and play in tune.

    For a string to play in tune it must be well made and consistent for its entire length. Any deviation in diameter or material properties will cause a string to play out of tune in some areas. This problem is not as bad now as it used to be due to the improvement in quality control and production techniques. Problems generally occur as the string is stretched to its required tension. If the string does not stretch evenly the diameter will vary along the length of the string and this will cause tuning problems. Some players go to the trouble of checking the diameter of the string along its length.

    It is important for the player to ensure that the nut and saddle are in good condition and do not cause damage to the strings as they pass over them. If either the nut or saddle are rough or incorrectly shaped they can damage the strings and cause tuning difficulties.

    Needless to say, strings have a useful lifespan. As they get older they are subject to tuning and other performance problems.

    The action and fret height

    The action can play a major part in how well a guitar plays in tune. This is mainly to do with the fact that the strings increase in tension as they are depressed onto the fretboard and between the frets. The greater the distance from the string to the fretboard, the greater the increase in tension. Keep in mind that the fret positions are based on a "perfect" model which does not include any increase in tension of the string.

    If the action of a guitar is altered substantially, it could be necessary to alter the amount of compensation for the guitar to keep playing in tune. Fret height is also a factor here. The greater the height of the fret, the greater the increase in tension as the string is depressed. There are arguments for and against high frets, but the biggest problem with them is if the ability to cause tuning problems.

    Compensation at the nut and saddle

    To keep this subject as simple as possible, it is necessary to point out that there is usually compensation required at both the saddle and the nut for a guitar to play in tune. It goes without saying that the guitar should be as well set up as possible as different action heights will effect the amount of intonation adjustment required. Again there are many factors that will come into play here, such as  the end effects on the strings (end effect is caused by string stiffness, which makes the effective vibrating length of a string shorter than its actual measured length), inharmonicity (the successively greater sharpening of successive overtones caused by string stiffness) and the elasticity of the string and the increase in tension caused by depressing the string to the fingerboard.

    A relatively simple way to understand what is required and why, is to consider the 12th fret as the starting point, not the nut or saddle. The greater the deviation (when fretting a note) from this point, in either direction, the more the compensation required.

    Compensation at the saddle is necessary because of the increase in tension and from end effects on the strings. The amount of compensation required increases as we play successively higher on the fret board. Fortunately the amount of compensation does not need to be adjusted for each fret as the increase in tension is roughly linear and the end effects fairly constant. So, as we play higher the amount of compensation needed is relative to the vibrating string length, which shortens for each successive fret so effectively the amount of compensation increases.



    Without compensation at the saddle end guitars tend to play sharper as you play higher up the fret board. This is mainly due to the increase in string tension as the string is fretted. Compensation is generally achieved by moving the saddle back the required amount. This varies according to string length, action height, tension etc but is generally around 1 to 2mm. It is usually achieved by moving the bridge (and saddle) rearwards from its nominal position when attaching the bridge to the top of the guitar. It is sometimes possible to make this adjustment later by moving the saddle within the bridge, but this is not a good alternative.

    Without compensation at the nut end, guitars tend to play sharper in the lower frets, mainly the first five or so frets, and getting progressively worse as we approach the nut. One of the reasons for this is again string stretch as we depress the string to the fingerboard. The height of the nut is important here as it is generally set up fractionally higher than the fret height. The higher the nut, the harder the guitar to play and the worse the intonation problems in the lower frets and the greater the need for compensation. Intonation adjustment at the nut is sometimes called 'negative intonation'.

    To solve this problem of sharpening in the lower frets it is necessary to "move" the nut forward toward the bridge, or effectively shorten the distance to the first fret. Each string should have its own amount of compensation and this is often done with high quality guitars. But keep in mind that if you do this it may need to be altered if you change to a different type of strings or alter the nut.

    You may see some strange looking nuts around these days. Compensation at the nut is achievable in several ways. This picture shows compensation with a nut made specifically for that particular guitar and set of strings.

    Keep in mind that this may need to change each time you change to a different string type or brand  which had different physical properties of density, diameter, weight elasticity and so on.

    Many luthiers still use a straight nut that has just been moved forward. This is a reasonable compromise if you are the type of player who changes brand and types of strings often.

    Another point that is usually overlooked is the final sound of the guitar. With a correctly compensated nut and saddle and proper fret positioning, the guitar will not only play in tune but will also sound better and be easier to play. The sound will be less harsh and smoother.

    What can be done to improve the guitar.

    A good guitar should play in tune, and a few fundamental checks will tell you if your guitar needs attention. Depending on what is required the costs to fix it will vary, and may even outweigh the value of the guitar.

    How to check that your guitar plays in tune. This is best done with a good chromatic tuner. Make sure you have relatively fresh strings. Start by tuning the open strings with a tuner and then check the harmonic at the 12th fret. This should be in tune regardless of fret positions, scale length etc. If it is not in tune suspect the string and try changing it for another.

    If all is well, then play the octave of the open string at the 12th fret. Again this should be in tune. If it plays sharp then more compensation is possibly required at the saddle, or the fret could be in the wrong position. If it plays in tune then it is now time to check the notes at the lower end of the fingerboard. Play the first fret and check it with a tuner. If it is sharp then compensation may be required at the nut or it may also be a fret placement problem. Accurate measuring equipment is necessary to measure fret placement and this is generally not possible at most homes or studios.

    Repeat the testing procedure for all the 6 strings and keep a note of what has happened. If your guitar checks out Ok then good, if it has problems then it may be necessary to take it to a good repair person for rectification. Each string will probably give you different results as each string has different physical properties.

    Adjustments of the nut and saddle are not for the faint hearted. If you do attempt to alter things at home at least do so on a spare nut or saddle, so if you make a mess of it, it is no drama to put the old nut and saddle back in place.

    The saddle is sometimes thick enough that it can be shaped to alter the "break" point of the string. For the best results this adjustment should be performed on each string separately. If the string plays sharp at the 12 fret and you are positive the fret position is correct then you can file the top of the saddle to move the break point further towards the rear of the guitar. If it is flat  then you can file the saddle to move the break point forward towards the nut.


    Nut adjustment is best left to an experienced person as both the length and the height need to be set accurately.