Assume the distance between the Nut and Bridge in the drawing is 0.628 m. The fr

Question

Assume the distance between the Nut and Bridge in the drawing is 0.628 m. The frets are numbered for convenience. A performer can play a musical scale on a single string because the spacing between the frets is designed according to the following rule: When the string is pushed against any fret j, the fundamental frequency of the shortened string is larger by a factor of the twelfth root of two than it is when the string is pushed against the fret j - 1. Assuming the tension in the string is the same for any note, find the spacing (a) between fret 1 and fret 0 and (b) between fret 5 and fret 6.

Explanation / Answer

First, understand the modern 18 rule...2^(1/12)/(2^(1/12)-1)=17.81715375. This defines the ratio, however, fret length is d=s-(s/(2^n/12)) Your first fret is 0.628 m- (0.628/(2^1/12))=0.035246932 m. All you have to do now is solve for the fifth and sixth frets and find the difference.

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