The Compensated Nut by Ste Stephe phen n D el f t edited dited text text of a 1992 1992 ar ar ticle wri tten tten for " NewZe NewZealand aland M usician" usician" magaz magazin in e, plus some stuf f on checki checki ng f r et posi posi tion s
I find this a useful tool for analysis of instruments with subtle tuning problems, and it gets me fairly quickly to a useful level of adjustment and intonation. Musicians seem happy enough with the result that I can charge a sensible rate for the work. I normally use my ears and a a strobe tuner, and include a little tempering in the final settings; but I have also described how to optimise the nut position without a tuner. And if you have a head cold or poor pitch sense, then a straight equitempered equitempered intonation can be done entirely with the tuner. Of course, this isn't the only adjustment a djustment needed or possible for good intonation (and I have simplified the mathematical mathematical model for fretted strings) but it does deal with one corner of the problem. I keep records of each compensated nut job, with details of player's l/hand style, scale, strings, action, etc, and final nut distances to c/line of fret 1, for each string. Sometimes the same nut distances will suit another guitar, and need only a little final trimming with the strobe tuner. The original N Z M article described retro-fitting compensated nuts to existing instruments; but later paragraphs on nut-edge adjustment may also be useful for makers setting up new instruments. instruments. ( A more sophisticated compensation would combine similar nut-edge adjustment adjustment with altered position of fret 1, or the first few frets ) 1
An earlier article in NZM also showed how to adjust string heights at the nut, and the bad effect on intonation if strings are set higher than optimum above the first few frets - I don't think I need to explain that here; nor that worn strings, or even faulty new ones, can mimic the effects of misplaced nut, frets, or bridge, and make a perfectly good instrument play out of tune.
Part 1 - To Check Fret Positions: (this will also give you a close estimate of the original scale length on which they are based) Some pre-war guitars may have individual fret spacings which do not exactly follow the 2^1/12 ratio. These may be considered as either subtly compensated or cut in the wr ong place - depending on how nicely the instrument plays. ( I still haven't made up my mind about one particular square-fret 000-18 ! ) In modern factory-made guitars, incorrect spacing between frets is less likely; but incorrect spacing from first fret to nut, (and nut slots left too high), are both still fairly common. And if the bridge position was established from the actual nut and 12 fret positions, then this may also be wrong. A typical result would be the instrument which plays perfectly in tune at the 12th f ret, but nowhere else! ( Or it may be tolerable down to about fret five, gradually worsening until fret 1 is intolerably sharp - particularly the note c on the b-string.) If the errors are small, the same problem may present as a good quality guitar, mandolin, etc.... but difficult to get nicely in tune over the whole fingerboard, and for no obvious reason. If you can't rely on nut or bridge position as a reference point, then you can measure distances between frets, and see if they fit a regular sequence. So: measure frets 5-17
multiply by 1.0595, note the answer
measure frets 4-16
compare with above multiply 4 to 16 by 1.0595, note the answer
measure frets 3-15
compare with above multiply 3 to 15 by 1.0595, note the answer
measure frets 2-14
compare with above multiply 2 to 14 by 1.0595, note the answer
measure frets 1-13
compare with above 2
multiply 1 to 13 by 1.0595, note the answer If all the compared figures agree closely, then the distances between frets are probably correct; the last number (1 to13 x 1.0595) is the theoretical distance from nut to 12 fret (and twice this is the theoretical scale length for fret positions). (I find it more convenient to derive the calculated nut-to-fret1 distance and compare this with the measured one, but it is easier to understand what is happening here, by using nut-to-fret12.) Compare this with measured nut-to-12 on guitar. In practice, it needs to be a little less than the calculated distance... For plain straight nuts, I have been shortening nut-to-f1 by between 0.5 and 1 mm for the last 30 years; I understand some (but not all) Brit and US makers do something similar. Many players find this approximate compensation satisfactory, particularly when combined with a small extension to shorten the thickest plain string in the set. If your measured nut-to-12 is greater than your calculated one, then your nut is very likely in the wrong place (or your fret measurements were bad - which is unlikely if all the compared figures match within say 0.05%). Personally, I would extend this, and say that if the measured and calculated distances are even exactl y th e same , then the nut is still in the wrong place. The real, measured distance needs to be slightly less.
2) Materials: You need super glue (cheap kind is fine) and some narrow strips of hard bone or other nut material (corian, tusq, etc.) about 2mm wide, and thicknesses approx 0.2mm, 0.5mm, and 1mm. To hold small strips while filing, stick them to a small block of wood with double-sided tape. They can be slipped loose with a thin table knife rubbed with dry soap. Cut each of the strips into pieces which are a little shorter than the spacing between strings on your guitar nut. Put each set of pieces into separate envelopes, marked: 0.2, 0.5, etc. Please note: It is tempting to use slips of bamboo or plastic - not glued to the nut - or bits of wire under the strings. You are warned that either of these may sometimes give seriously wrong results....even when their height is correct and the original nut slots are deepened to give enough string down-pressure. 3
It seems to be necessary for accuracy, that any temporary "nutlets" are glued rigidly in place, and that they have a normal size and shape of string slot continued cleanly through them, at the usual slight back angle. If you want to try with loose bits, then start by trimming about 1.5mm LESS off the end of the fingerboard than the temporary nuts suggest, and check intonation with a real nut before you go further.
General Set-up: I am assuming that... 1) You have already adjusted the nut so that each string's height above the first fret is no more than necessary - If you don't know exactly what this means, stop now! 2) You have adjusted the curve and height of the bridge saddle(s) for your preferred action, using fresh strings of your usual kind and gauge, etc. 3) You know how to adjust bridge saddle position(s) for best octave fret intonation. The only difference this time, is that you don't use 0-to-12. Instead, you put a capo at 2nd fret position and check fretted octaves at fret 14. Try to get the geometry of the capo's down-pressure on the strings close to what your fingers would be doing when you are playing normally. 4) THEN LEAVE THE BRlDGE ALONE ! You now have a guitar which plays nicely at frets 2,3,4,5....and all points north of Watford. If you fiddle with the bridge adjustment during the following stages, you will lose your reference points and go round in circles.
NUT ADJUSTMENTS for individual strings: Take off the capo, and check intonation at fret 12 relative to open strings. Check and adjust one string at a time: if the fretted 12 fret note is sharp, first suspect the string and try the whole adjustment process again with a new string. lf this is still sharp at the 12 fret, then the nut-end of the vibrating string probably needs to be moved closer to the bridge. Slacken the string and lift it out of the slot. Hold it out of the way with a bit of masking tape. As a starting point, take a O.2mm strip of bone and glue it to the front edge of the nut with a tiny amount of superglue. You may find sharp tweezers useful. 4
Give it about 10 minutes for the super glue to set hard. then file down the bone strip to just above the nut height, and extend the string slot across the added bit of bone.
Replace the string, adjust the slot depth until the string is the same height above fret 1 as it was before, and re-tune it. As far as that string is concerned, you have moved the nut closer to the bridge. Make sure the string is tuned to correct pitch and see how the intonation goes at the 12th fret. Now you consider three choices: l) If the 12 fret intonation is better, but still very sharp, go back to the nut, glue a 0.5 bone shim onto the 0.2 one which is already there, and trim and adjust as before. 2) Alternatively, if the intonation is better, but only a little sharp, add a second 0.2 shim instead of 0.5. Try various combinations of O.2, 0.5 and 1mm shims, until... 3) If the intonation is near enough right, start on the next string. (If the intonation is flat at the 12 fret, suspect the string before you start any major adjustments. If you are sure, then you can shift the front edge of the nut away from the bridge, by filing away a small area around the front edge of the string slot)
Adjusting Nut with Tuner: ( This is also the only recommended method, if you suspect some fret spacings may also be inaccurate.) 5
With a chromatic tuner which displays accurately to 2 cents or better, you can directly measure the pitch of open strings and their notes on the lowest few frets, and adjust the nut for what you feel is the best compromise. You can split unwanted shims away from the front of the nut with a sharp pocket knife blade. Eventually you will become more accurate at guessing what thickness of bone shims are needed. . You will probably end up with a nut something like the second diagram
If you wish, you can copy your final nut profile from a solid block of bone or other nut material, with the steps going down the full depth of the nut, and then carve away bits of the fingerboard end, to fit the nut shape. You could do this....but I suggest you play on the original modified nut for several weeks or months until you are quite sure that you like it - and that it is a real improvement on the original uncompensated nut, before you start cutting into the fingerboard. As an example, I recently worked on an Ovation acoustic for one of our local guitar heroes. Even with minimal string height at the nut, it could not play first position C maj and E maj chords without one of them sounding sour - either a sharp third in one chord, or a sharp root and flat fifth in the other. The owner, and several repair techs at the other end of the country, had almost given up on it. (To be fair, I worked on a Gibson semi a few years ago, with exactly the same problem.) Measured nut-to-12fret distance found on this Ovation was about 0.2mm more than the calculated figure derived from the fret spacings. After compensating the nut, final distances to c/line of fret 1 were.... e' - 35.1 6
b - 34.9 (fine for me, but he squeezes harder, so I will reduce this to maybe 34.5mm) g - 35.1 d - 34.2 A - 33.7 E - 32.7 (still a bit too much, but tolerable, without making the modified nut shape too obvious) (I just had a letter from the owner, thanking me for "miraculously" getting all the open-string chords in tune, so I'll call that one a success....) Like bridge saddle adjustments, the optimum position depends on a lot of things, including strings, action, shape and pressure of fingers, height, shape, and amount of wear of frets etc. - so don't be surprised if your adjusted nut ends up a bit different from my drawing. If in doubt, undercompensate: a modest amount of nut compensation will usually work better than no compensation at all. One curiosity you will discover, is that when you compensate the nut, you generally need less compensation at the bridge. I sometimes wonder just how much of the traditional bridge saddle adjustment on steel string acoustic guitars has actually been covering small lntonation problems at the nut end. The two photos below show a fully compensated 12-string nut...
...and an extreme case of nut compensation - optimised for short scale and heavy-gauge strings, in a dropped open tuning, and with strings set high at the nut to allow playing with slide and fingers.
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Unlikely as it looks, this guitar plays in tune. This is also a reminder that higher strings at the nut demand greater nut-end compensation...it is useless to fiddle with nut-edge shims, unless you also keep the string heights constant.
If you find some ideas in this article useful in your own instrument making and repair work, please donate at least $5 to the World Wildlife Fund's Indian Tiger Project. If you're making instruments for sale, then be a Mensch and send them $5 each time! You are welcome to apply this information on your own personal instruments; and in repair work for individual musicians; but not on imported factory-made instruments for sale, nor as a service offer accompanying such a sale.
http://www.mimf.com/nutcomp/
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