Fret Anything!

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Contents

prelude

My buddy Scott and I were sitting around talking about making tricked out necks for instruments... not only guitars but ukes, and banjos etc. Scott makes most of his own instruments many of which are covetable. He fashioned an acoustic bass that is great, has converted vintage electrics with custom bodies etc. etc. It seemed to us that the limitations of custom instrument manufacturing was limited to 'parts' that were available. Yes, you could trick out a body... and the head you could customize, but what about the necks?... most instruments that are custom use stock necks. Why? cause no one could be bothered to fret their own.

That being said, we started wondering why some of those little trinket guitars you buy in Mexico or in asia sound Ok.. mean to say they can be tuned. Then some are obviously for show and sound like crap. My son has a little kid sized Mexican guitar that sounds perfect when tuned... it doesn't keep a tune cause the keys are shit, but it will intonate.

So we thought there must be a formula for determining fret distance according to the size of the neck, or more accurately the length of playable string. This would have to work for any 'western' stringed instrument from a fender to a violin. Mandolins are violins, and mandolins are intonated like guitars so logic follows they're all the same. I think the 'western' intonation could even be applied to Sitars and more obscure stringed instruments as we're not judging culture...but rather frequency, and string vibration doesn't check passports.

So...Scott busted out some old papers he has about making instruments and they contained instructions for determining the placement of frets.


The instructions boiled down to:


f=s/17.817

where f=fret and s=string length (from bridge or fret to nut[playable string])

initial notes: It is more desirable to use metric measurements when fretting 'planks' as fractions of inches require way too much effort.


The hard way

I call this the hard way because it requires many more calculations than the other method, but it should be addressed to fully grasp the concept. Also a calculator must be handy for each fret where as the 'easy' way requires only one calculation with the rest done with calipers(manually).



Given

We begin with string length: lets take a playable string length of 24" or 609.6mm as the playable string length from nut to bridge.


Measurements

firstly we take 609.6 and divide this by 17.817 giving us 34.21mm. A mark from 'fret 0'(nut) to 34.21 gives us 'fret 1'.

Next, because we have taken 34.21 off of the playable string length our new 's' is 575.39

Again: 575.39 divided by 17.817 equals 32.29

so from 'fret 1' 32.29mm up is 'fret 2'.

Again: 543.1 (our new string length) divided by 17.817 is 30.48 ('fret 3')

and so on.



The easy way

So obviously the above method requires too many hand to calculator movements.

We figured a way using what we didn't smoke from pre-calc to do the entire operation using only the initial calculation.

Since we're going old-school you'll need accurate calipers. So effectively you could pull this off in a cave in a pinch...as it was done in days of old.


Given

We begin with string length: lets take a playable string length of 24" or 609.6mm as the playable string length from nut to bridge.


Image:fret1.jpg


Measurements

609.6 divided by 17.817 is 34.21

so we take our first measurement for 'fret 1' and mark it on the horizontal line.

Image:fret2.jpg

Now swing that same measurement up above the horizontal line at the nut ('fret 0'):

Image:fret3.jpg

from the top of our new vertical line we can draw a line to the bridge end of 's', our horizontal line, which becomes tangent(tan)...like so:

Image:wiki4.jpg


now you can throw away the calculator as we have all we need.


For 'fret 2' we simply take our calipers from 'fret 1' and swing them down to the location on the horizontal line:

Image:fret55.jpg


You can now take the distance from 'fret 2' to (tan), adjust the calipers and draw 'fret 3' and continue on down the plank.


Image:fret6.jpg

Because (tan) gets smaller in respect to our horizontal line... no more calculations are needed. This can be done until the desired number of frets is reached.

Image:fret7.jpg


Conclusion

It should be noted that at 'fret 12' you will be at exactly 1/2 of the initial 's' so if your initial string length was 24" ... at 12" exactly you will be at the harmonic half of the open string. Ah hah!

Now obviously, the length of the actual neck will be smaller than 's' but at what point you cut it off doesn't matter. the neck length is superfluous as we are dealing only with playable string length 's'.

The width of the neck also has no bearing on the intonation of the strings... so you can make some wierd ass instruments with x number of strings.. and they will be intonated correctly according to the above formula.

now tuning the fucker is up to you.




More

I'm hacking out a little application that'll give you fret measurements. in BASIC it would look like this:

        A = 0
        B = 0
        INPUT "String Length?",S
        INPUT "Playable Frets?",F
        PRINT "Fret distances from the nut"
        PRINT "Scale length: ";S;" mm"
        FOR Z = 1 TO F
        D = S - A
        B = D / 17.817
        A = A + B
        PRINT "Distance to fret ";Z;": ";A;" mm"
        NEXT Z


Anyone who could move that over to a web based language I'd host the file...i'll do it when i have time. Throw up a little page that'll calculate it for the masses..might be cool.

anyway now that you understand the concept...let your mind fill in the possibilities.

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