How closely is the \"rule of eighteen\" been followed for the first 3 frets? The

Question

How closely is the "rule of eighteen" been followed for the first 3 frets? The "rule of 18" is that the spacing to the next fret is 1/18 the remaining distance to the bridge. So for example, the string is 60 cm long, so the first fret should be 60/18=3.3 cm closer. The first fret was actually 3.5 cm closer, so we are 2 mm off. From first fret the remaining distance is (60-3.5)= 56.5 cm. x=56.5/18= 3.1 cm. The next fret was actually spaced (6.7-3.5)=3.2 cm so we are 1 mm off. From the 2^nd fret the remaining distance is (60-6.7)=53.3 cm. x=53.3/18= 2.96 cm. The next fret was actually spaced (9.7-6.7)=3.0 cm, so almost exactly right! From the 3^rd fret the remaining distance is (60-9.7)= 50.3 cm. x=50.3/18=2.79 cm. The next fret was actually spaced (12.4-9.7)= 2.7 cm, so just 1 mm off. From the 4th fret the remaining distance is (60-12.4)= 47.6 cm. x=47.6/18=2.64 cm. The next fret was actually spaced (15.0-12.4)= 2.6 cm, so almost perfect! From the &h; fret the remaining distance is (60-15.0)= 45.0 cm. x=45/18=2.5 cm. The next fret was actually spaced (17.6-15.0)= 2.6 cm, so 1 mm off. And so on. We see that the spacing is nearly following the rule of 18. Note that I made an average of the spacing and got a factor of about 17.9 which is close to what the book says that perhaps the spacing should be closer to factor of 17.817 If you wish to suppress the n,h harmonic, then you should make an antinode at L/n, i.e. pluck the string at this position. Hence solve: L/n=7, where L=60, we get n=L/7=60/7= 8.57 cm from the bridge.

Explanation / Answer

a) closely rule of eighteen followed for first three frets = (3.3 + 3.1 + 2.96 + 2.79 + 2.64 + 2.5)/6

                                                                                    = 2.881 cm

b) Here, L/n =7

=> 2.881/n = 7

=> n = 0.4115 cm from the bridge .

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