“Intonation is a social construct”. I’m not sure if I made this phrase up or accidentally adopted it, but I say it often. All music is out of tune – it is mathematically impossible for any three notes to be perfectly in tune at the same time. This is pure science. We’ve all adapted to this mathematical anomaly and, for the most part, enjoy our imperfect music. Some instruments are more imperfect than others, and the guitar is one of those instruments that humans have struggled with since its invention. Frets must be perfectly placed, and yet intonation is a compromise that involves setup, string gauge, and the player’s technique. If the frets are in the wrong place, it becomes all the more difficult to play in tune. Gibson placed the frets in the wrong places on their instruments for years, and nobody really noticed or cared. I recently encountered this problem while rebuilding an older Gibson Les Paul for our friend Shane from the mighty Crowbar. Listen.
Shane found a popular and much-abused vintage Les Paul Custom (I can’t remember which era, but I think it’s from the late 70’s or early 80’s). He immediately brought it to us for appraisal and unfortunately I had to be the harbinger of bad news: the guitar had been very poorly finished in the past and needed to be redone. Brushing up a guitar is something I do almost every day, so it should have been a straightforward task. Boy, am I wrong?
The previous technique completely destroyed the original fret slots, which were so wide that the fret pegs could not grip the ebony. To “fix” this problem, they flooded the slots with epoxy and simply floated the frets in the mass. Needless to say, the frets were extremely uneven and just fell out of the neck. This job suddenly became much more complicated.
After removing the frets I realized how wide the slots were so I had to add wood and then re-cut them all. I tracked down the sturdiest 0.5mm wood veneer we had in the store, cut it up and glued it into the fret slots.
After filling the slots, I leveled the fretboard using our PLEK machine to both straighten the neck and make the radius even. This process is accurate to within 0.1mm, giving us a perfect surface to press the frets into. If we properly prepare the fretboard before freting, we can maintain the new fret height as much as possible, thus minimizing the leveling required after freting. Plus, it’s just plain fun to look at.
Then I programmed the PLEK to cut the new fret slots into the fretboard:
This is where it got really interesting. The PLEK revealed an ugly truth: Gibson’s frets were in the wrong place! When I cut the waistband vents, the new cuts didn’t match the old waistband vents perfectly. The cuts were slightly closer to the bridge in the lower areas of the neck and closer to the saddle in the upper areas of the neck, like so:
I was baffled for a moment until I remembered a conversation I had with the engineers at PLEK when I was visiting them in Berlin. PLEK discovered that Gibson had used an outdated formula for fret placement, namely a “rule of 18” formula instead of the modern “12. Square root of 2” formula. I know, I know – you weren’t expecting a math class. But here’s the gist:
- The “18 inch rule” is derived by successively dividing the scale length minus the distance from the nut to the previous fret by 18. Let’s say you have a Les Paul with an overall scale length of 24.75 inches. Divide 24.75″ by 18 and you get 1.375″, which is the distance from the nut to the first fret. Now subtract 1.375″ from 24.75″, which gives 23.375″. Divide that by 18 again and you get 1.2986″, which is the distance from the first fret to the second fret. Then repeat the process for the remaining frets, you know? Most of the time this works fine, and people have enjoyed playing and listening to instruments with this fret formula for thousands of years.
- The “12. Square root of 2” is the more modern formula based on how we calculate how notes are derived in standard 12-tone Equal Temperament. We use this to evenly match all notes across the chromatic scale. To determine fret placement, just follow the same process as above, just replace 17.817 with 18.
So what does all this mean for your guitar? In practice, well… nothing. As I said, intonation is a social construct and we’ve grown accustomed to music that is out of tune. So don’t worry if your guitar isn’t perfectly in tune. You don’t have to retool your beloved vintage Les Paul to correct fret placement, just enjoy its features and make them RAWK. What does this mean for Shane’s guitar? Continue reading.
It’s possible that Gibson screwed up the fret placement beyond the rule of 18 (perhaps this was done on a Friday afternoon), or the frets could have been so destroyed by the previous technique that some of them were misaligned. But now that we’ve cut the waistband vents perfectly, we decided to make the most of it. I filed it with Shane’s favorite fret wire, made a new bone nut, plucked the newly installed frets and set it up completely. Most of the old fret lines were hidden by the new frets and only two at the top were exposed. I dyed them black and fused them to the ebony board and you’d never notice they’re there unless you look really closely, applying blindingly bright lights (which of course we use in our shop). And even we can hardly see them.
Intonation theory is a big nerd interest of mine, so I was keen to put that to the test. I’ve played a lot of tight chords all over the neck and it was in tune very, very well (or at least as far as it was mathematically possible). It’s certainly more precisely intoned than many other vintage Les Pauls we’ve played.
Shane loves it, and so do I. This guitar sounds massive, it plays beautifully, it has great intonation and it looks damn good. I mean look at this thing:
This is what a popular Les Paul should look like. Take it easy on yourself, Shane! Enjoy!
PS How come I didn’t get the crowbar bass gig when Todd Strange left? We literally have the same last name! Call me next time, Kirk!