The Stretch-Compensation Option
THE STRETCH-COMPENSATION OPTION
in the Experimental Musical Instruments Fret-Spacing Calculator
When you press the string of a fretted instrument down behind the fret, the string is stretched slightly in the process. This increases tension on the string and causes the pitch go a little sharp of what it would otherwise be. If you ignore this and make your fret placements based strictly on the mathematics of string lengths and scale factors, the fretted pitches will all be a little sharp of the ideal.
There are several ways you can deal with this. Here are three practical options.
1) Select the stretch-compensation button the ExMI fret-calculator program before running it. The program will then include a small correction in the fret placements to offset the stretching effect. The offsets we’ve built into the program are fairly typical, approximating conditions on typical instruments, based on observations and measurements from a number of sample instruments. Chances are it will produce good results for your instrument, but since your instrument may vary from the norm, it’s not a sure thing. For instance, if the action on your instruments is unusually high and/or the strings are set at unusually low tension, the compensation may not be enough and the resulting tones still a bit sharp.
2) Make the bridge on your instrument moveable, or at least don’t fix it in place until the instrument is complete and you can run some tests. You then may or may not select stretch-compensation when you run the program. (Selecting it may give you slightly better results in relation to the first few frets closest to the nut.) When the instrument is complete but the bridge still movable, string it up with the bridge in its approximate expected location. On one of the strings, play the octave harmonic. (Do this by touching the string lightly above the octave fret, not pressing down, and plucking.) Compare the resulting note to the note you get when you press the string down behind the octave fret. If the pitches match, the bridge location is good … keep it there. If the harmonic is higher than the fretted note, move the bridge closer to the nut. If the harmonic is lower than the fretted note, move the bridge farther from the nut. Test again. Repeat until the pitches match. Do this for all the strings, and angle the bridge slightly if you can get better results across all the strings that way.
3) Build the instrument and string it up temporarily before putting the frets in. Play the octave harmonic as described in option 2 above. Then press the string down against the fingerboard and find the exact point at which you get the same note as the harmonic. (For best results: hold a thin piece of wire against the fingerboard, as if it were a temporary fret, when you do this.) Measure the distance from the nut to that point. Double that distance, and input the doubled distance as a fictitious open string length when you run the ExMI fret calculator program. Don’t select stretch compensation. (You will have already compensated by using the fictitious open string length value.) Be sure to use the nut-to-fret distances given in the output (not bridge-to-fret) when you do your actual measuring.