Fret Calculation on the Classical Guitar
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 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 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.
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.
