Let’s Fret a Football Field!

Every once and a while a budding luthier will come in with half-finished stringed instrument looking for advice.

“I’m not sure where to put the frets. I’ve measured a bunch of other instruments but mine isn’t the same. What do I do?”

FIRST DOWN!

Many first-time builders start by trying to make the “perfect” scratch built custom instrument on their first attempt, only to crash and burn by “building” themselves into a corner they can’t escape.

It always helps to start by copying a well-known design, as the process of building reveals a lot of the “why” of an instruments construction as well as the “how”. This makes planning your next one much easier.

If you’re already stuck in the middle of a project trying to figure out where to put the frets and bridge, there’s still hope! It’s actually quite easy to lay out a custom-length fret scale once you know how. In fact, you can even fret a football field!

KICKOFF!

Lets use metric measurements to calculate our “fret-ball” field (it’s much easier to calculate by tens than inches and yards). A standard football field measures 91.44 meters (100 yards) from goal to goal. This will represent our scale length with the 50 yard line standing in for the 12th fret.

football field smallStringed instruments are laid out using what’s known as the equal-tempered scale, where all 12 notes are spaced apart equally in pitch within an octave (based on the 12th root of 2 – 1.059463094). This makes it possible to modulate to different keys and still be able to play in tune (more or less).

Divide this number by 1 and you’ll get:

.9438743

Now multiply that by your scale length:

91.44 meters x .9438743 = 86.307865992

Here’s where your first fret will go (as measured from the “bridge”). Now multiply that result also by .9438743:

86.306865992 x .9438743 = 81.463776597

This is where your second fret goes. Keep on going like this until you reach the 50 yard line:

48.438645552 x .9438743 = 45.71999263 = 12th fret

This is almost exactly half the field length, right where you want the 12th fret to be. Now keep on calculating as many frets as you want.

football field fret scale smallSCORE!

It’s much easier and more accurate to lay out your fret scale from the nut rather than from the bridge. Let’s subtract the total scale length from each result. For example:

91.44 – 86.307865992 = 5.06134008 = the first fret (as measured from the nut)

Here’s a complete chart:

91.44 meters (100 yards)

Frets          Nut

1                5.132
2                9.976
3               14.548
4               18.864
5               22.937
6               26.782
7               30.411
8               33.836
9               37.069
10             40.121
11             43.001
12             45.72
13             48.286
14             50.708
15             52.994
16             55.152
17             57.189
18             59.111
19             60.926

WHERE DOES THE BRIDGE GO?

In order to get our giant football field-sized instrument to actually play in tune we’ll have to move our saddle back a bit from its “theoretical” placement to compensate for real-world problems like string size and stretching. Instrument designers have used all sorts of methods to calculate this position, most of which are approximate at best. For our ridiculously huge instrument let’s move it back about a meter for the treble side and about 1.5 meters for the bass side. Good luck finding strings though!

football field guitar smallTOUCHDOWN!

To work out a scale length from an existing instrument, measure from the front edge of the nut to the middle of the 12th fret, then multiply by 2. Add the compensated distance from the saddle to the total scale length for your final bridge saddle position.

I’d advise sticking to more conventional string lengths for a while until you’ve build up enough confidence to try out some of your own. Here are some common ones:

Martin D-28 – 64.516 cm (25.4 inches)

Frets           Nut

1                 3.621
2                 7.039
3                10.265
4                13.31
5                16.184
6                18.896
7                21.457
8                23.873
9                26.155
10              28.308
11              30.34
12              32.258
13              34.069
14              35.777
15              37.39
16              38.913
17              40.35
18              41.706
19              42.986
20              44.195

Fender Stratocaster – 64.77 cm (25 1/2 inches)

Frets          Nut

1                3.635
2                7.066
3               10.305
4               13.362
5               16.247
6               18.971
7               21.541
8               23.967
9               26.258
10             28.419
11             30.459
12             32.385
13             34.203
14             35.918
15             37.538
16             39.066
17             40.509
18             41.87
19             43.156
20             44.369
21             45.514

TRADITIONAL CLASSICAL GUITAR – 65 cm (25 19/32 inches)

Frets          Nut

1               3.648
2               7.092
3              10.342
4              13.409
5              16.305
6              19.038
7              21.618
8              24.053
9              26.351
10            28.52
11            30.567
12            32.5
13            34.324
14            36.046
15            37.671
16            39.205
17            40.653
18            42.019
19            43.309

GIBSON F-4 Mandolin – 35.401 cm (13 15/16 inches)

Frets          Nut

1                1.987
2                3.862
3                5.632
4                7.303
5                8.88
6               10.369
7               11.774
8               13.1
9               14.351
10             15.533
11             16.648
12             17.701
13             18.694
14             19.632
15             20.517
16             21.352
17             22.141
18             22.885
19             23.587
20             24.25
21             24.876
22             25.467
23             26.024
24             26.551

TENOR UKULELE – 43.18 cm (17 inches)

Frets          Nut

1                2.424
2                4.711
3                6.87
4                8.908
5               10.832
6               12.647
7               14.361
8               15.978
9               17.505
10             18.946
11              20.306
12              21.59
13              22.802
14              23.945
15              25.025
16              26.044
17              27.006
18              27.914

Thanks to Bob Petrulis for showing me this cool trick many years ago.

For more information about instrument building:

www.luth.org

© 2014 Leo Bidne

Leave a Comment

Your email address will not be published. Required fields are marked *