To understand guitar string compensation, some basic components of the vibrating string need to be noted. Essential among these is the Vibrating Length of the string which, without string compensation, is not the same for each string. The Total Length of the string, between nut and saddle, is made up of the Vibrating Length plus a Dead Length at each end. These terms are explained in the graphic that follow.
A line across the top of the frets should, therefore, not be straight but should form an arc to accommodate the path of the string. A two-way truss rod is the most convenient way to bend the neck so that the fret line forms this arc. A perfectly straight fret line will cause string buzz at the first few frets.
With the width and string spacing drawn, put the nut blank in the clean nut slot at the end of the fretboard. Draw an arc on the face of the nut 0.060" above the fretboard. This arc should be parallel to the top of the fretboard. Use a 0.060" spacer and a light gauge pencil (0.5 mm works well). This arc will determine the bottom of the string slots.
Lastly, after the string slots are at final depth, each string slot should be half the diameter of the string. This will keep the string from creating a buzz as the open string rattles back and forth between the walls of a too-deep groove. Lastly, the top of the nut is rounded and smoothed.
If one plucks the string while touching it lightly above the fret as shown below (i.e., at a node), a note will be produced that has a frequency that is an integer multiple of the fundamental frequency. For example, on the 5th string (A):
Open 5th string (A): A2=110hz,
2nd Harmonic, 12th fret: A3=220hz,
3rd Harmonic, 7th fret: E4=330hz,
4th Harmonic, 5th fret: A4=440 hz, etc.
These harmonic notes allow us to tune the guitar accurately using only one's ear. Once one develops the ear for this type of tuning, it's faster than electronic tuning and has the advantage of always being with you and no batteries are needed.
Next, play the harmonic at the 5th fret on the A string (again). While the note is still ringing, match it with the harmonic on the D string at the 7th fret.
Now play the harmonic at the 7th fret on the A string and match the harmonic at the 5th fret on the low E string. This note is an E4. The open 1st string can also be matched to this same E4 note. At this point, four of the guitar's six strings are in tune. The last two (G and B) are tuned similarly.
The diagram below is a graphic of how the harmonics match up across all 6 strings.
SETUP: String Clearance
The eventual final set up of the guitar will depend on the player's preferences and style of play. The height of action, the string width at the nut, the string width at the saddle, radius of the fretboard, gauge of strings, etc. impact the setup. Any guitar that one buys from a music store should be set up to suit the style of the player.
Likewise, any dimensions mentioned here would be impacted by the player's preferences. Hard-driving flatpickers need more string clearance than folk singers. Woody sets up a new guitar to an average string clearance that can be changed if need be.
Keep in mind that every part of the setup and action is in continuous flux, mainly due to the weather, but also due to the player's preferences (which also change over time).
Pictured below is a gauge that I made (about 40 years ago) from a scrap piece of brass. It has served well in checking set ups for proper string clearance.
HARMONICS and STRING VIBRATION
Many readers might know how to tune a guitar by matching the string harmonics. These vibrations occur at the nodes of the vibrating string and are simply called the 'harmonics'.
First, we need some standard note naming to get everyone on the same page. All of the open string notes (frequencies) on a guitar, except 1st string E, are below middle 'C' on a piano. Middle C is designated as C4 because it is the first note in the 4th octave from the bass end of the piano keyboard. On a guitar, all open string notes except E above middle C, (E4 above C4) have a vibrating frequency of less than 262 hz (Middle C).
SET UP: NECK RELIEF
Simply stated, Neck Relief is necessary because the strings on a guitar vibrate in an arc. The oscillations are wider in the center of the string (12th fret) than at the ends (nut and saddle). This should be obvious to anyone who has ever jumped rope.
That's why the saddle is laid into the bridge on an angle... so that all of the strings will have the same vibrating length (dashed line in the graphic above). String Length Compensation is essential for an instrument with a fixed scale length and fixed fret spacing, but different string thickness (stiffness).
A way to check the relief is to tune up to pitch, then place a straight edge on top of the frets and slide it toward the nut (as Woody is doing in the photo below). At the fourth or third fret one should feel a little bump as the forward corner of the straightedge bumps the fret. Same at the second fret. Same at the first fret.
One does not have to see the straight edge bump up the frets. The bumps can be felt in a steel straight edge and heard if one is listening.
Finally, if you are guitar repair person, harmonic tuning is the easiest way to tune a guitar that is lying flat on its back on the workbench.
First, let me say this: If one is not familiar with the harmonic tuning method, tuning this way is waaaaaay easier than explaining how to do it. One might have to read the instructions below a couple of times.
Start with tuning the A string. Strike an A-440 tuning fork, then match the tuning-fork A with the harmonic at the 5th fret on the A string. This note is an A4 (440 hz).
The gauge is only about 3" long and tapers from one end to the other. The scratch lines across the gauge mark the thickness of the brass at 0.060", 0.070”, 0.080", 0.095" and 0.100" thickness (right to left). The heavy part on the left end is the 'handle’.
Woody uses this gauge to measure the distance between the string and the top of the 12th fret (0.095") and the distance between the fretboard and the bottom of the string at the nut (0.060"). All else aside, and light gauge strings on the guitar, these target dimension produce a nice, low action on an acoustic guitar that leaves room for adjustment if necessary.
Making a nut for a guitar is not the simplest thing to do. One can purchase a one-size-fits-all plastic nut and hope it works. String widths vary, however, with the preferences of the player.
The first thing that one needs to do, therefore, is to decide on the width of the nut. The finished width of the fretboard will be the same dimension as the nut (43 mm is common on dreadnoughts).
The width between the center of the 'E' string and the center of the 'e' string must also be fixed. Woody uses 36 mm for this dimension. The rest of the strings are evenly spaced between the first and sixth-string centers.
To lay out these string centers, put the bone blank in a small vise that has good lighting. With a sharp pencil mark all of the string centers on the top of the bone blank.
If the neck on your guitar is "too straight", and you don't have a two-way truss rod, you need to see an experienced, qualified repairman. Neck relief can be achieved without re-setting the neck, but that operation cannot be explained here. When you build, or buy, your next guitar, make sure it has a two-way truss rod.
The Home-Shop Guitar Building Overview, which started in June 2020, is about to be completed. There are only two steps left... Finishing and Set Up.
There will be a change, however, to the posting for May. Woody was expecting to post a chapter on Finishing then Setups. Instead, we decided to insert a chapter on Guitar Setup first. As a standard practice, Woody sets up the guitar for playing before applying finish. The Finishing post will come next month and, after thirteen chapters and thirteen months, the Overview will be complete.
Setting up the guitar before finishing allows the bridge, saddle, and nut to be installed before lacquer locks in everything in place. The neck relief will also be set, and the guitar can be intonation tested and played to make final adjustments as might be needed to improve the feel and playability of the neck.
On a guitar, an open string vibrates between the nut and saddle at a specific frequency determined by the player using the tuning gears on the peghead. This is called the fundamental frequency of the vibrating string. The open vibrating string has only two nodes (points of minimum amplitude) and they are at the nut and the saddle. The point of maximum amplitude is called the anti-node and the open-string fundamental has only one anti-node (at the 12th fret).
The guitar string is also vibrating in many sub-fundamental string lengths that have an integer number of nodes and anti-nodes. The node at the 12th fret is called the 2nd harmonic because it divides the string into 2 equal, vibrating string lengths, thus, two anti-nodes.
There is another node at the 5th fret (4 anti-nodes), and another node at the 7th fret (3 anti-nodes). There are more nodes but, for now, this will do.
Don't take it for granted that every note played on a guitar fretboard will be at perfect pitch. The pitch (frequency) of a vibrating string is determined by 3 factors: String Length, String Mass and String Tension.
> We change string length by shortening the string as we move up the fretboard... raising the pitch.
> We cannot change the string mass, so be it.
> We increase string tension mainly with the tuning gears in the peghead.
The fret saws pictured above are various thickness (kerf) and all cut on the pull stroke, Japanese style. They are very controllable.
Note: For years Woody cut all of the string slots with one 0.025" back saw. By rocking the angle of the blade from left to right on the cutting stroke, one can widen the string slot as necessary. It takes practice.
The nut files pictured here are handy in that they cut a different width on each side of the file. They add even more control when one wants to cut the final depth of the string slot without going too deep. Woody tries to keep the bottom of the string slot at 0.060" above the fretboard. A line drawn on the nut blank, 0.060" above and parallel to the fretboard, helps in this regard.
Making the Nut by Hand
Next month, Finishing, will be posted ahead of schedule, that is, in the next couple of weeks.