Fingerboard formula

[Justin Carvitto]

I'm looking for the formula for calculating fret placement on a mandola. I've done searches but haven't located anything.

Does anyone know the formula or could link me to a resource.

Thanks,
justin

[sunburst]

Try this.
All you need is the scale length.

[Dave Cohen]

If you have Excel or a competing spreadsheet, you can generate the fret positions for any scale length you want in short order. I use Excel, and put headings in row 2. In cell A2, I put the heading "fret #". In cell B2, I put the heading "1/2^(1/12). Column B will give the distances from the bridge to each fret. In cell C2, I put the heading "nut to fret". Column C will give the distances from the nut to each fret for a scale length of "1".

In cell A3, I put the number 1. In cell A4, I put the formula =(A3+1). I then use the fill down command to generate the rest of the fret numbers in column A. In cell B3, I put the formula =(A3*1/2^(1/12)). In cell A4, I put the formula =(B3*1/2^(1/12)), and fill down for the rest of the numbers in column B. In cell C3, I put the formula =(1-B3), and fill down for the rest of the numbers in column C. That's all there is to the basic structure of the spreadsheet. If you want the positions in inches for a 17" scale, put the heading "17.00" scale" in cell D2. In cell D3, put the formula =(C3*17.00), and fill down for the rest of the fret positions of the 17" scale. If you make a spreadsheet as I have described, you will never have to depend on anyone else for fret positions for any scale length on any instrument.

[Antlurz]

The MIMF had a free/downloadable calculator called WFret v.2.0.

I'd imagine it's still available over there. Very simple to use.

Ron

[billhay4]

Telier,
There is a mathematical formula for calculating fret placement. It is a function of the desired length of the scale. I don't know the precise formula, but all these little pieces of software use pretty much the same one (there are several ways of making this calculation).
Basically, you decide what length scale you want and then apply the formula. What length scale do you want? Well, this depends on where you want the bridge to be located on the body, how long the neck will be, etc. There are a lot of factors to consider here. For instance, the longer the neck, the wider the frets at the top. This can make certain cords harder to finger. The tension of the strings is also different with different lenght scales and this, in turn, can place more or less pressure on the top.
I'd suggest using standard scale lenghts until you get a lot of the other details and their interrelationship figured out. But, you can use ANY scale length up to a certain point (where it becomes impossible physically to make a certain string tight enough to produce the desired note without breaking).
Bill

[Dave Cohen]

I just gave the mathematical formula for fret placement in my post above. It is simply that, for an equal-tempered scale, the uncompensated distance from the bridge saddle to the center of a given fret position is 1/2^(1/12), or one over the twelfth root of two, of the distance from the bridge saddle to the previous (i.e., lower) fret position. Also, Bill, the fret scale formula is not really a function of the length of scale; it is simply a function of equal temperament. When you multiply all of the fret positions by your desired scale length, you get the actual fret positions in whatever units you have chosen. So your chosen scale length is a parameter or constant, and as such is not a variable.

[billhay4]

I stand corrected by someone who does know.
Bill

[Paul Hostetter]

On my Windows machine I have a great fretspace calculating program, but he never finished one for the Mac. Besides the one John mentioned above, Stew-Mac also has one here. With these resources you can just plug in your desired scale length, whatever it is, and print the results out. I used to calculate them on the 12th root of two, but that was tedious. This just gets you farther faster. Note that the Stew-Mac thing has a feature for compensation but no setting for mandola, so you're on your own for that part.