The golden ratio and the design of the guitar fingerboard
The proportion between frets, the location of the harmonics, the tuning of the guitar are some of the questions that every guitarist ever poses.
The fingerboard is a fundamental part of the Spanish guitar. The pressure of the fingers and the friction of the strings occurs constantly. That is why the wood used for this element has to be of high hardness.
Thus, noble woods such as rosewood or ebony are used for the fingerboard. Woods that are normally selected to achieve a homogeneous aesthetic, normally dark, where the contrast of the frets acquires great prominence.
In addition, the fingerboard must be calculated and adjusted very accurately. It is not only to place the tuner and to tune the guitar, the guitar must be tuned in all its notes.
One way to check the guitar fingerboard quickly is to play the harmonics of the 5th, 7th, 12th and 19th frets.
The location of harmonics
Sometimes we wonder why the harmonics sound so good in some of the frets as the 5th, 7th, 12th or 19th.
These frets are located in fractions of the guitar's shot, located on the fingerboard.
We call "guitar shot" at the distance between the saddle and the nut.
If we divide the shot into four parts, in the third division we find the 5th fret (3/4), in the second division the fret 12th (2/4) and in the first division (¼) the harmonic that is in the area of the mouth.
In the same way, if we divide the shot into three parts, in the first division we find the fret 19º (⅓) and in the second division the fret 7º (⅔).
As we can see in the guitar, harmonics can be made in all these frets.
But how is the location of the frets calculated to correspond to these proportions?
Placement of the frets
For the placement of the frets, a mathematical formula based on the 12 semitones of the octave and half of the guitar's shot is normally used.
With this formula, the first fret would be calculated by subtracting from the total shot of the guitar, the figure resulting from the division of the total shot between root twelve in base 2.
The number two fret would be calculated in the same way but discounting the guitar's shot, the size of the first fret.
Some luthiers directly use the so-called rule of 18, because:
Therefore, if we divide the guitar shot by 18, we get an approximation to what the first fret would measure. And in the same way, from the remaining distance to the saddle, we would get the rest of the frets.
The golden ratio on the fingerboard
The so-called Golden number or Golden ratio is a number of infinite decimals that, according to numerous studies, appear in many works of art, as well as in elements of nature itself.
If we measure the distances of the fingerboard, we can see that the proportion we get between those who measure the first 7 frets and the first 4, is the same as the ratio between the first 4 and the sum of the 5th, 6th and 7th frets.
The result of both relations is close to the famous 1'618 ... called Golden Number or Golden Ratio.