# Calculation of the alternative apreggione (guitar) fret position.

### Increasing the sound of a note by an octave means increasing the frequency twofold. For example:“a1”is 440 Hz, “a2” of the second octave is 880 Hz.The difference in frequency of neighboring semitones is the twelfth root of two. ### 12 and 24 are the fret numbers. ### Some tuning error can then be compensated by adjusting the saddle position. ### The frequency of the string is calculated using the formula. ### f = 239,7676912 Hz ### The density of the string material should be determined using the inverse formula. ### Formula 3 ### Now I need to calculate the tension for my note and string length. ### Formula 4 ### In this case we can use the following scheme ### The shape that the string takes when it is pressed against the fret is described by a quadratic equation and is shaped like a parabola. ### Formula 5 ### Let’s assume that the string is bent only at the point where it is pressed to the fret and that the parts of the string to the left and right of the fret are a straight line. ### Figure 5 ### Thus, knowing the height of the string above each fret, we can determine the additional elongation of the string when it is pressed against the fret.And knowing the cross-sectional area of the string (A), the initial tension (N0) and the rigidity of the material to calculate the additional tension. ### Formula 6 ### Now we can calculate the total tension of the string on each fret. ### From this tension, we can calculate the length of string needed to sound at the frequency we want. ### The table below gives comparative values of the standard fret position calculation of the values obtained in this study.It also indicates the absolute value of the offset of each fret towards the nut. ### Table 9. Standard fret placement, estimated fret placement and absolute difference for each fret. 