The Mudcat Café TM
Thread #54438   Message #842650
Posted By: JohnInKansas
06-Dec-02 - 06:05 PM
Thread Name: Tech: Mandola fret distances
Subject: RE: Tech: Mandola fret distances
I don't see a direct line to the information requested, although the link above will possibly get you there.

The basic fret positions are fairly simple to calculate, expecially if you have a decent spreadsheet to do the numbers. The key that you need is Beethoven's "twelfth root of two." For an equi-tempered chromatic scale, each fret is the "twelfth root of two" times as far from the bridge as the next higher fret.

The "magic number" is 1.059463094 to fair accuracy. In Excel, for example, you would enter "=2^(1/12)" without the quotes.

It is probably easier to work from the nut down, so use the reciprocal (1/1.059463094 = 0.943874313.

The string length, from bridge to nut, multiplied by 0.943874313 gives the distance of the first fret from the bridge.

The distance of the first fret from the bridge, multiplied by 0.943874313, gives the distance of the second fret from the bridge.

The distance of the second fret ... etc.

Once you've listed all the fret distances from the bridge, it's probably easiest to work from the nut end, so take the string length and subtract each number from it to get the distance from the nut for each fret.

The calculated fret locations are typically used, but the extra amount by which you have to stretch the string for "high frets" will require adjustment of the final bridge location to get best intonation. On a mando, with its short strings, the bridge must be "compensated" so that each string course has a slightly different length. I presume that similar compensation is used on the other instruments you're interested in, but I don't have one to look at.

I've measured mandos with string lengths from about 13-1/8 to 13-3/4 inches, but I think something around 13-5/8 inch is pretty standard (at least for A style). If you're building your own, you have the option of using just about any length you want, but copying a "known good" design is obviously an advantage.

John