# Psalmodikon Builders Tips

By Floyd Foslien

For those of you who want to accurately calculate fret spacing, here is an easy formula for you to use. This formula will work to establish the fret positions for any open string (nut-to-bridge) length.

The number to remember is 17.817. This is the key to calculating fret positions for any stringed instrument with frets, including guitars, banjos, and psalmodikons.

Divide the string length by 17.817. The result is the distance from the nut (or fret) to the next fret. For instance, if you decide you want to make an instrument with an open string length of 34 inches, the distance from the nut to the first fret is 34/17.817 = 1.9083. The distance from the first fret to the second fret is (34-1.9083)/17.817 = 1.8012. However, to alleviate measurement error, all fret positions should be measured from the nut position so the second fret would be 1.9083+1.8012 = 3.7095 inches from the nut. The third fret position is (34-3.7095)/17.817 = 1.7001. 3.7095+1.7001 = 5.4096 inches from the nut. Repeat this calculation until you have all the fret positions calculated.

When a string length is halved and the string is caused to vibrate, the resulting note is exactly one octave higher. The 12th fret raises the sound by one octave and the 24th fret raises the sound by another octave.

The position of the 12th fret is exactly ½ the open string length and the position of the 24th fret is exactly ¾ of the open string length or, in this example, 17 inches and 25.5 inches from the nut position. Due to rounding errors, you may find that your calculated 12th and 24th fret positions are slightly different than ½ and ¾ of the open string length. For example, 17.0001 inches instead of 17.0000 inches. Use the ½ and ¾ dimensions for these fret positions and for the calculations for the frets after them.

Now, having calculated the fret positions with this great precision, you still need to transfer the information to the fret board and actually cut slots for the frets. When using hand tools to measure and cut fret slots, it is difficult to achieve greater precision than 2 or 3 decimal places. Use a good quality accurate steel rule and mark the fret positions as well as you can. The closer you can get to the calculated position, the happier you will be with the result.

Floyd Foslien, August 2009