Fretting Accuracy

What accuracy is needed in placing the frets for precise tonal production?

This question can be a vexing one, when we are trying to establish a method for cutting the fret slots. Here is a quantitative way to answer the question:

There is a tool on the Bear Meadow website to calculate fret spacing, and will give a reading of cents error, e, for any deviation, d, you supply.

But for those who like the math, here is a quantitative way to answer the question. The formula expressing fret placement error in terms of tonal errors is:

e=l200*ln((L+d)^^2/L^^2)/ln(2)

where:
e= error (in cents)
L= correct distance from fret to saddle
d= deviation from correct L (in inches, cm, furlongs, etc)

So set L to various fret-saddle values on your scale, then play around with various values of "d" to see which ones approximate but don't exceed an error of 5 cents (generally accepted as the smallest tonal error detectable by the ordinary human ear).

Paul Buerk, a well-known guitar maker, has produced this table as an example of the sorts of errors one will see within 5 cents of the correct fret placement for all the chromatic guitar frets in that scale. Note, for instance, that at the 24th fret a deviation of .020" gives a tonal error of 5.5 cents.

fret errors in a 25" scale

25" Scale

    Error in Cents for a given error in length of:
Fret Dist to Nut (0.05) (0.04) (0.03) (0.02) (0.01) 0.00 0.01 0.02 0.03 0.04 0.05
1 1.40 (3.67) (2.94) (2.20) (1.47) (0.73) 0.00 0.73 1.47 2.20 2.93 3.66
2 2.73 (3.89) (3.11) (2.33) (1.56) (0.78) 0.00 0.78 1.55 2.33 3.11 3.88
3 3.98 (4.12) (3.30) (2.47) (1.65) (0.82) 0.00 0.82 1.65 2.47 3.29 4.11
4 5.16 (4.37) (3.49) (2.62) (1.75) (0.87) 0.00 0.87 1.74 2.62 3.49 4.36
5 6.27 (4.63) (3.70) (2.78) (1.85) (0.92) 0.00 0.92 1.85 2.77 3.69 4.62
6 7.32 (4.90) (3.92) (2.94) (1.96) (0.98) 0.00 0.98 1.96 2.94 3.91 4.89
7 8.31 (5.19) (4.15) (3.11) (2.08) (1.04) 0.00 1.04 2.07 3.11 4.14 5.18
8 9.25 (5.50) (4.40) (3.30) (2.20) (1.10) 0.00 1.10 2.20 3.29 4.39 5.49
9 10.13 (5.83) (4.66) (3.50) (2.33) (1.16) 0.00 1.16 2.33 3.49 4.65 5.81
10 10.97 (6.18) (4.94) (3.71) (2.47) (1.23) 0.00 1.23 2.47 3.70 4.93 6.16
11 11.76 (6.55) (5.24) (3.93) (2.62) (1.31) 0.00 1.31 2.61 3.92 5.22 6.53
12 12.50 (6.94) (5.55) (4.16) (2.77) (1.39) 0.00 1.38 2.77 4.15 5.53 6.91
13 13.20 (7.35) (5.88) (4.41) (2.94) (1.47) 0.00 1.47 2.93 4.40 5.86 7.32
14 13.86 (7.79) (6.23) (4.67) (3.11) (1.55) 0.00 1.55 3.11 4.66 6.21 7.75
15 14.49 (8.26) (6.60) (4.95) (3.30) (1.65) 0.00 1.65 3.29 4.93 6.58 8.22
16 15.08 (8.75) (6.99) (5.24) (3.49) (1.75) 0.00 1.74 3.49 5.23 6.97 8.70
17 15.64 (9.27) (7.41) (5.56) (3.70) (1.85) 0.00 1.85 3.70 5.54 7.38 9.22
18 16.16 (9.82) (7.85) (5.89) (3.92) (1.96) 0.00 1.96 3.91 5.87 7.82 9.76
19 16.66 (10.41) (8.32) (6.24) (4.16) (2.08) 0.00 2.07 4.15 6.22 8.28 10.35
20 17.13 (11.03) (8.82) (6.61) (4.41) (2.20) 0.00 2.20 4.39 6.59 8.78 10.96
21 17.57 (11.69) (9.35) (7.00) (4.67) (2.33) 0.00 2.33 4.65 6.98 9.30 11.61
22 17.98 (12.37) (9.89) (7.41) (4.94) (2.47) 0.00 2.46 4.93 7.38 9.84 12.29
23 18.38 (13.13) (10.49) (7.86) (5.24) (2.62) 0.00 2.61 5.22 7.83 10.43 13.03
24 18.75 (13.91) (11.12) (8.33) (5.55) (2.77) 0.00 2.77 5.53 8.29 11.04 13.79

Last Updated on 2/6/03
By Paul Buerk
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