So.. where's my math error?

[Mike Kolb]

I expect to catch heat for being a mathematical idiot, but here goes:  

Refretted a customer's electric with s/s frets. Ordered the frets (4ft) and it all worked out fine. The end.

Before doing the work, and while standing-around waiting for something to dry on another job, my mind wandered to the frets. The guitar (an Ibanez RG) has 24 frets... so I measured the 1st fret (1.730") and then the 24th fret (2.270").  

My thinking was: by adding the 2 lengths together and dividing by 2 I'd get the average fret length ... which I did and it was exactly 2-inches. 

Then panic set-in. "If the average length is 2" and there's 24 frets, that's 48" and that's the length of the fretwire I ordered, with no room for error whatsoever".

As it turned-out, there was plenty of fretwire left-over... maybe 10" or so. The job's done, the customer's happy.... but where'd I go wrong here?  My better half thinks the supplier may have been generous, but I never measured the actual wire when it was received.  

There's bound to be someone here who'll get a chuckle before setting me straight?

[Robbie Collins]

Another thought ... since avg1 + e computes the exact length required, we might want to add a constant along with e so we all always have a small amount left over. The constant might need to be larger if ordering in 2' lengths as opposed to clipping if from a coil.

[Mike Kolb]

Alas,  I was afraid it might end this way: I'm totally lost in the equations!  

So it's back to square one for me, which will be trusting the suppliers that 4-ft of fretwire is sufficient for the average fret job, and that seems to work just fine.

Thanks to all for the valiant efforts, but my math skills are the proverbial lost cause:)  

PS: in case there's any doubt, my wife keeps track of the checkbook!

[Robbie Collins]

Okay, I built an Excel spreadsheet. The only manual calculation is for avg2 where each length measured and summed and inserted into column F. The file is the old .xls format.

[Paul Verticchio]

Hi Mike.

Consider the possibility that they accidentally sent you 58" of fretwire.

Otherwise, I am the biggest math idiot on the forum.

Hope you solve this mystery :)

[eliya]

There are two issues here. The first is that your method for finding the average is correct only if the frets are spaced evenly, the other is the supplier probably gave you more than four feet of fret wire. 

I'll start with the latter since it's easier to see. Consider the frets were all the same length, and that length is that of the first fret, so each fret is 1.730" long. Multiply that by 24 and you get 41.52", which is 6.48" short of 48", and that doesn't account for trimming. That's the most conservative estimate, and it doesn't prove it (no Math journal would accept this proof), but it gives you an idea as to why there's a good chance you got a little more fret wire than you ordered.

I haven't read all of Robbie's posts, but I think he touched on it. The reason your method for calculating the average is wrong is because it only works when the lengths you're averaging are equally spaced. Obviously, the frets on a guitar aren't evenly spaced, so the method of using the first and last frets to average the lengths is out. Now, of course you could unevenly arrange the frets on the board to get a 2" average (there are infinitely many ways of doing that), it just happens that the way arrange the frets (to get and even spacing musically) isn't it. There's probably a better explanations than "isn't it", but I'm a little too tired right now to figure it out.

[Jelle van Tilburg]

Holy Moly Robbie, that's just outerspace stuff to me!

I can only say I'm with Billy on this subject http://www.youtube.com/watch?v=JqZo07Ot-uA

(aka: way easier to measure) (I'm sure Einstein would agree)

[Robbie Collins]

Funny! I love Billy Connolly.

I was terrible at math until I went back to school in my early 40s. Then it was beat into me while I screamed "please make it stop" and cowered with my arms above my head.

Now, I think in calculus ... I guess I've been "ruint" as some down here say. Some have described me as running around with my hair on fire but I'd never do that - hair is a precious commodity to me.

[Ned Knepp]

I'm with Paul on this. Every way I figure it the result is 48 inches so I'm betting that the supplier sold you 48 inches of wire but shipped something like a foot extra. It sounds to me like it was a good thing they shipped extra because the 48 inch measurement I get is exact length with no room to trim each fret. Since you ended up with 10 inches of extra wire, I'm guessing that you probably got around a foot extra to begin with. 

 That means that an order of 48 inches of wire for this guitar wouldn't have done the job if they actually sent you 48 inches.

[Paul Verticchio]

Hi Ned.

I applied an ancient, yet recognized and accepted, principal in forming my theory. It's called "Occam's Razor"

"The definition of Occam's Razor is the idea that the most likely explanation for an event is usually the simplest explanation."

It's oft overlooked in today's modern world.

:) P

[Robbie Collins]

One of my guiding principles.

[Mike Kolb]

Since the kid's coming tomorrow to pick-up his guitar, I figured there's only one more chance to do some real-world measuring.  So, with calipers in hand, I carefully measured each finished fret... and the combined grand total was 48.740" 

Leaving the ONLY explanation possible being that the supplier (thank you, LMII) provided more than I'd ordered. In fact, since there was about 10" left-over (and accounting for trimming) they probably gave me 5ft. when the order called for 4ft.  The prize goes to Ned & Paul. 

By the way, here's a shot of the actual guitar in question, and ...yes... I kept a large rag over the finish not just to protect it, but to shield my poor old eyes from the glare!   Kids these days, whatcha' gonna' do?

[RETROROD]

I would agree with covering the finish color....pretty putrid! The "kid" must play the 'pee' out of it... if it needed a refret....Kids nowadays....Jeesh!

Glad that you got the math worked out!

Rod