String tension experiment -- Glen's Questions

> > From: "McDougall, Darren Scott - MCDDS001"
> > <MCDDS001@students.unisa.edu.au>
> >
> > Before I had my 19-tet five-string bass made, I took a DAT to the
> > luthiers shop and recorded all 24 notes of the A-string (the middle
> > string) of a bass he had already made. This bass was fretted to
> > 12th root of two. Back home I transferred the recording to my
> > digital audio workstation then used it to find the exact frequency
> > of the 24 notes. I then calculated the error between the expected
> > frequency (given the fret placing) and the actual frequency (due to
> > increased string tension).
>
My post above prompted some questions from Glen Peterson. Before I answer them,
let me provide a few details on my experiment.

I did all my tuning error calculations in hertz in reference to A=55 Hz (the
open A string). Digidesign's DINR-Hum removal plugin was used to identify the
fundamental of each note. Microsoft Excel did my calculations, but I used the
computer pool at uni so my files were saved to floppy. These files went to data
heaven when my proper uni work required the disk space, but I do still have the
spreadsheet printout that I faxed to the luthier. It has 39 string lengths
(from the 19th root of two), 38 adjustments in millimetres (to compensate for
string tension), and the resulting 38 distances from the nut that the luthier
needed.

The bridge of the 865 mm scale bass tested, although appearing perfectly set up
according to the electronic tuner at the shop, was actually 3.849 cents out at
the octave fret. (It was one of those "light chaser" style meters as opposed to
a moving needle.) This resulted in my 19th fret being shifted 0.9626 mm toward
the nut.

Anyway, on to Glen's questions:

How much error was there in cents and millimeters of fret placement?
Judging by the excel printout I have, my first fret was adjusted by 2.9143 mm.
This suggests that simply using 2^1/19 would have made it 6.04 cents sharp. At
the 38th fret, an adjustment of 2.3803 mm was required, compensating for an
error of 18.95 cents. The smallest adjustment was 0.2357 mm at the 9th fret for
0.65 cents.

How did the 19 tone bass come out?
Excellent! Brian West of Fretco in Adelaide, South Australia did a fine job.

What was the accuracy?
Never measured it, but I hear no difference between it and my 19-tet synth. My
mass produced 12-tet bass on the other hand, while sounding perfect around the
12th fret and also around the 4th, is flatter than a synth between those frets
and sharper elsewhere. (That is what actually prompted the whole exercise.)
Note that the 12-tet bass sounds perfect on its own, probably because when
playing in any one general area of the neck similar amounts of string tension
are applied to each note; it only sounded wrong compared to 12-tet synths.

What did the luthier have to change to make it more accurate?
Nothing. I just faxed him the measurements.

DARREN McDOUGALL

Thank you for the data!

So what you are saying is that your 12tet bass and the one in the store were
about 3-5 cents sharp at the first fret, became flatter until they were in
tune around the fourth fret, continued to flatten for a few frets, then
sharpened back into tune by the 12th fret? (9th fret in the case of the
store bass).

Relying on my ears and a guitar tuner, I have come to a similar conclusion
about most guitars that I work on. You can correct it as you did by
modifying the fret placement (and congratulations on getting the math
right!). You could also correct it by moving the nut forward a millimeter
or two, then setting the intonation at the 12th fret. You stretch the
string a little extra when you fret it near the nut, and that is not
compensated for on most guitars. I've done this to a few inexpensive
guitars, and it seemed to really help. It's nice to read the results of a
(somewhat) scientific analysis that confirms my suspicions. There's a
fellow named Buzz who I think has a patent on this technique. (really!) He
put out a video demonstrating the wonders of his new fretting system. He
never said how it worked, but it wasn't that hard to figure out that he'd
just slid the nut forward a millimeter or two.

P.S. I recently read an article about repair-people NOT adjusting the
intonation on vintage acoustic instruments because it would ruin their
value. Keep that in mind before you "fix" the nut on your pre-war Martin.

---
Glen Peterson
Peterson Stringed Instruments
30 Elm Street North Andover, MA 01845
(978) 975-1527
http://www.organicdesign.org/peterson

> So what you are saying is that your 12tet bass and the one in the store were
> about 3-5 cents sharp at the first fret, became flatter until they were in
> tune around the fourth fret, continued to flatten for a few frets, then
> sharpened back into tune by the 12th fret?
>
Yes. But they also continued to get sharper beyond the 12th fret, reaching over
18 cents sharp by the 24th fret. I hate fret buzz and have my action fairly
high, so this does increase the stretching in that area of the neck.

DM

> Yes. But they also continued to get sharper beyond the 12th fret, reaching
> over 18 cents sharp by the 24th fret. I hate fret buzz and have my action
> fairly high, so this does increase the stretching in that area of the neck.
>

In my experience the factors that contribute to the
low-action-fret-buzz-bad-tuning problem are a combination of the foll. :

1. Fretboard radius (flatter = better, shred machines are 16")

2. String Gauge (.009s seem to be the norm, but people do use .008s, etc.,
Plus see no. 3)

3. Tuning : is the instrument tuned to std. E, or down a half-step like
many well know players, or even down a whole step to D.

4. The... what's it called... neck relief ? i.e. the (always ?) necessary
warp in the neck, unless it's a graphite/composite neck.

5. The pick & picking technique. Nice stiff, sharp, & smooth ones work best.
I use the 3.0mm Jazz style Dunlop Stubbys.

I gave up my shredder aspirations long before I got a bit tired
of the music (Yngwie & Vai still rock though !), but I did develop a
quite precise (if slow) picking technique using the Stylus Pick.

For those who don't know about it, it's really nifty. Only a training
device, not for performance, takes some dedication, but it's worth it.
I pick with barely 2 to 3 mm of the tip of the plectrum/pick hitting the
string.
6. How precisely the fingers on the fretting hand press down on the strings.

- Drew

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While I like high action because it makes bending, muting, and pulling-off
much easier, I thought I'd respond:

>In my experience the factors that contribute to the
>low-action-fret-buzz-bad-tuning problem are a combination of the foll. :

>1. Fretboard radius (flatter = better, shred machines are 16")

If I'm not mistaken, classical guitars have a flat or slightly concave
fretboard (along the frets). Paul Gilbert's was flat, but many pros go for
the compound radius.

>2. String Gauge (.009s seem to be the norm, but people do use .008s, etc.,
> Plus see no. 3)

>3. Tuning : is the instrument tuned to std. E, or down a half-step like
> many well know players, or even down a whole step to D.

If you're looking for a smooth, buzz-free sound (I am), I'd recommend .010s
or heavier. My Martin only sounds good with .013s. A lot of players (like
Tony Iommi and Wes Borland) tune down to C#. If using light or de-tuned
strings, tuning problems are easily encountered because a slight bit of
extra finger pressure in any of the three dimensions will produce a
noticeable change in pitch, and buzz often occurs because one picks harder
to compensate for the loss in volume and sustain.

>4. The... what's it called... neck relief ? i.e. the (always ?) necessary
> warp in the neck, unless it's a graphite/composite neck.

You'll usually be able to adjust the truss rod to get the desired very tiny
concavity (along the strings), although I had to get the neck heated after
having a microtonal fingerboard put in, because even with the truss rod
completely loose, it was convex. By the way, a completely loose truss rod
totally changes the sound of the guitar -- the low notes could be described
as "buzzy".

>5. The pick & picking technique. Nice stiff, sharp, & smooth ones work
best.
> I use the 3.0mm Jazz style Dunlop Stubbys.

> I gave up my shredder aspirations long before I got a bit tired
> of the music (Yngwie & Vai still rock though !),

The fastest, smoothest pick for me in my speed-obsessed days was the Jim
Dunlop Nylon 0.88mm (many metallers go for it in much thinner gauges), and I
still use the 1.0mm for acoustic. Now I use Fender Mediums for electric, as
they have more "bite" -- not as easy to play fast, but when you do, every
note is articulated more clearly. I certainly get more buzz with stiffer
picks.

>6. How precisely the fingers on the fretting hand press down on the
strings.

Very important -- the pressure problem I already mentioned, and buzz often
comes from being too close to, or too far from, the fret.

We were talking about compensating the nut on guitars because they tended to
play sharp on the first few frets. I set up a Strat style neck to fender
specs, and set the intonation at the 12th fret.

Fretboard radius: about 12"
Neck relief: .009"
High E height at nut: 1/64", at 12th fret: 3/64"
Low E height at nut: 2/64", at 12th fret: 4/64"
Strings: new set of D'addario XL 120. "Nines"
Tuned to A=440 Hz.

The high E string showed no tuning distortion whatsoever at the nut. The
low E showed the most distortion: Almost 2 cents sharp at the first fret. I
also noticed that even lightly plucking the low E sharpened it by 2 cents,
then it would drop quickly to pitch. The other strings were in-between the
results for the highest and lowest. I don't think that the effort required
to compensate the nut for just the low E is really worth it. 2 cents is
within the margin of accuracy for plucking the string! The other strings
didn't seem to need it.

I'll try an acoustic when I get a chance. Hard to find one with a perfect
saddle though... Most play out of tune by 5 cents or more at the 12th fret.

---
Glen Peterson
Peterson Stringed Instruments
30 Elm Street North Andover, MA 01845
(978) 975-1527
http://www.organicdesign.org/peterson