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granger
12-15-2014, 08:06 AM
Customizing a set of Baritone Ukulele Strings
Some baritone ukuleles allow you to put on a set of stock strings and they just sound great. Other baritones simply need string sets that are customized to the instrument in order to bring out the best the Ukulele has to offer. The search for the perfect set of strings can become a search for the Holy Grail. There are good reasons for this obsession of course. Perhaps the string tensions are so unbalanced in the set that a similar attack across the strings produces dramatically different responses. Or perhaps one string is a bit ‘floppy’ and muddy in tone, or it does not give the response the player is looking for on hammer-ons, pull offs, slides or other techniques. Maybe the strings sound good but don’t hold up well for any duration. I have a pair of baritone ukuleles that sent me off on the quest for the perfect custom string set. The following is my tale, what I have learned and the approach I finally adopted after a bit of frustration.

Like many players I started by buying up stock string sets from the various brand names, stringing them up, breaking them in and playing them to evaluate them. After going through most of the name brands I really wasn’t any closer than I when I started. I began to mix and match bass strings and treble sets from various brands and got mixed results. I concluded that this rather haphazard approach was not the solution and decided to start fresh and adopt a more structured approach beginning with the basics.

The basic variables that I wanted to be able to quantify or qualify and asses were individual string tension, total string set tension, effect of saddle height, string unit weight and string material as they affect tone, tone balance, playability and string longevity. Some of this is obviously subjective, what sounds good to me may not appeal to another player. The style of a player will greatly affect the results. But I needed to be able to evaluate strings in a more informed manner if I was ever going to make headway.

After some research I decided to adopt the method employed by D’Addario by using the frequency and string tension to calculate a string Unit Weight as an aid to string selection. Their excellent publication “A complete technical reference for fretted instrument string tensions” can be downloaded from their website and is an excellent reference.

D’Addarrio has a large selection of nylon and composite classical guitar strings that are suitable for use on the baritone ukulele. Basically the approach uses two formulas that can be easily adapted to an Excel Spreadsheet in order to compute string tension and Unit Weight values useful for the scale length of the baritone ukulele.

A quick look at the formula puts this in perspective. The string tension formula:
Tension lbs = (unit weight x (2x scale length x frequency)^2) / 386.4

If the unit weight is not known, but the string tension and frequency are known for a given scale length then we can calculate the unit weight as follows:
Unit Weight lbs/in = (Tension X 386.4)/(2 x length x frequency)^2

Since the unit weight is a handy means to quantify strings we can construct a table of unit weights for baritone ukulele frequencies and scale lengths.

Unit Weight by String Tension and Frequency 20.125 inch scale
Frequency
lbs E 329.6 Hz B 246.9 Hz G 190 Hz D 146.8 Hz
10 0.00002195 0.00003913 0.00006607 0.00011068
11 0.00002415 0.00004304 0.00007268 0.00012174
12 0.00002635 0.00004695 0.00007928 0.00013281
13 0.00002854 0.00005086 0.00008589 0.00014388
14 0.00003074 0.00005478 0.00009250 0.00015495
15 0.00003293 0.00005869 0.00009910 0.00016601
16 0.00003513 0.00006260 0.00010571 0.00017708

Before we can use the table of Unit weights to guide us in string selection we need to consider the total string tension, individual string tension and the choice of materials.

How much string tension?
Total string tension that is optimal for any stringed instrument is dependent on a large number of variables that are mainly fixed by the design and actual construction of the instrument. The type of sound board wood, its density, thickness, grain uniformity, bracing pattern, brace profile, saddle height are but a few of the important variables. Of these, the saddle height is the easiest for the ukulele owner to measure and it has a very large influence on sound. The total string tension placed onto the bridge is translated by the saddle height into the rotational force of torque when the string(s) are acted upon. An actual example will help to illustrate the importance of torque. I have two baritone ukuleles that are quite different in their design and construction, a Pono Acacia Deluxe and a custom baritone. The Pono acacia soundboard is relatively thin, lightly fan braced, and has a saddle height of .490”. The custom baritone has a sitka spruce top, A-frame bracing with an offset soundhole and side sound port, its saddle height is .355”. Both instruments have excellent, low actions. The Pono sounds best with a total string tension of about 42 lbs, while the custom uke plays best with a total string tension of about 55 lbs. They have very different string tensions but when we calculate the approximate string torque for the two instruments we see much less of a difference.

Pono torque = 42Lbs tension x .490in saddle height= 20.58 in lbs
Custom torque = 55 lbs x .355in = 19.53 in lbs

On the surface of it the two instruments are very dissimilar and they do in fact have very different tone and volume characteristics. Both have excellent tops and were carefully braced and the sound they produce is driven by basically the same amount of torque. Both instruments are highly responsive and balanced. In reality these are both fairly low torque instruments. A baritone ukulele with 53 lbs of tension and a saddle height of .450 would have a torque of 23.85 lbs, perhaps a “normal” string tension and resulting torque.

The saddle height should be carefully measured after the instruments action has been fine tuned and it can give an indication as to where to start with total string tension. A high saddle height may indicate the need for lower total string tensions and visa versa. If the instrument is heavily braced , has a thicker top or stiffer top wood this may not hold up, but at least it gives a starting point.

What about individual string tension?
As a starting point I am an advocate for fairly uniform string tension for each string in a set. I believe this enhances the playability of the instrument so that a similar attack or strum on the strings gives a similar or balanced response. There should be a good reason for moving the tension of an individual string away from the sets uniform tension. For example the player really wants to brighten the treble e string or wants bright trebles and warmer basses. My advice here is to keep the tension consistent and change the string material. Black nylon for example is generally thought to be mellower in tone than clear nylon at the same tension. Or 80/20 brass is considered to be warmer than silver plated copper wound strings of the same tension. Only choose a string of higher or lower tension than the set as a last resort.

Let’s customize a string set
In looking for a balanced tension set for my custom baritone I first took my 55 lbs of total string load and divided by 4 yielding a target tension of 13.75 lbs per string. I looked at the unit weight chart and selected the values for 14 lbs. The unit weight values were as follows:
E = .00003074
B = .00005478
G = .00009250
D = .00015495

I wanted the tonal characteristics of clear nylon and silver plated copper wound nylon strings. D’Addario classical guitars strings had a number of options and I chose the following set based on their Unit Weights.


String set for custom baritone with 20.125” scale length and .355” saddle height

Hz String name lbs Unit weight Target unit weight
E Nylo33 14.02 .00003078 .00003074
B Nylo41 12.14 .00004751 .00005478
G Nylo26w 14.29 .00009438 .00009250
D J2905 13.87 .00015347 .00015495


Total Tension = 54.32 lbs

These strings are well balanced and have the sound I’m looking for. When the quest for the holy grail of string sets is finely realized the results are truly worth it. The instrument can give you its best, it sounds fantastic and its playability is enhanced. Life is good!!

Doug
12-16-2014, 04:47 AM
Too much math for me.

Timbuck
12-16-2014, 07:02 AM
Try using this Lads baritone string sets..They sound great ;) https://www.youtube.com/watch?v=yWZfEIX3AYI

lauburu
12-16-2014, 09:23 AM
Thanks for passing on the results of your research and experimentation. I got a headache reading it but it's a valuable resource I can draw on if I ever need to customise strings for an instrument.
Miguel