And it goes on to fret 19 and to the infinite.
*vibrations per second
In practice, if we use this method - which we will reject later - the space #13 is in the middle of the 1st, the #14 in the middle of the 2nd, etc.
However, this method when applied for fretting any stringed instrument, is incorrect, since once the cord is pressed so that it touches the fret, as one looks for the sound one wishes to produce, the cord undergoes an extra pressure that modifies - though slightly - the expected sound, and increases the frequency.
People have been trying to solve this problem by compensating the extra pressure we already mentioned changing the place where the cord is in contact with the bridge, or by making the cord longer in the part between the pressed fret and the bridge. Therefore, the measure of the variation on the bridge (let's suppose 2.5mm) has to be added to each length of the resulting cord, as shown above (for eg, the 1st fret to the bridge 613.520 + 2.5).
This procedure is not correct because the degree of pressure that the fingers have to do in the first space to produce the sounds is less than in the following spaces of the diapason. In space #19, this pressure is three times higher, no matter which cord is pressed, nor its quality. The pressure needed to produce a sound in the diapason is related with the frequency: the more the pressure, the higher the sound.
This procedure will be the basis for the new method.
It is evident that these observations were made bearing in mind a precious rule that every single luthier follows:
“The cords have to be as near the diapason as the produced sound allows it to”
; this is to make the use of the instrument easier. The regular measures are around 0.7mm between the top of the first fret and the cord, and 4.5mm between the cord and the twelfth fret.
The method explained below has taken into account the progressive resistance of the cord as the hand moves towards the bridge, producing higher sounds. It consists on moving the frets progressively - by twisting them - and in this way - which is more reasonably - replacing the previous unilateral procedure of moving the place where the cord touches the bridge, which has been frequently used. The proposed formula will make this idea clearer.
These are some last considerations, which have to do with the tuning of the guitar, which is the instrument I know about better.
In order to reach the proper tune (E, A, D, G, B, E
), each cord has to support different degrees or kilos of pressure: the first one around 6 kilos, the second less than the first, the third even less. Therefore, for a perfect tuning, we should make permanent corrections. Another factor to bear in mind to forgive the guitar's failure in harmony is the one related to the height of the frets each luthier uses, since there are guitarists that put such an exaggerated pressure that the frequency of the pressed note rises, making them suffer from a tendinitis.
Another highly important factor is the lateral variation of the cords, produced by the guitarist when on a strained position.
The saying that goes “the guitarist spends half an hour for tuning, only to play half an hour with an guitar which is not tuned” is quite right. They referred mainly to the lutenists.
