Make a cuatrolele

A what?

Well, there is the ukulele, and then there is the cuatro. So the cuatrolele is their love child. Essentially a ukulele that sounds like a Venezuelan cuatro, but can still play along with other ukuleles. The good news is that building one requires less than one hour of your time, plus a two-dollar budget ($38, starting from scratch). The result is a sweet-sounding instrument that your friends will want to borrow constantly. (Image courtesy of camburpinto.org)

I’ve been collecting ukuleles at an excessively fast rate for the last few months. They sound sweet, are real easy to play, and you can also find them real cheap. Last summer, I ran into a Venezuelan cuatro, which is the size of a baritone ukulele (with a deeper body, which helps with the resonance), but tuned differently. Most cuatros are tuned (4th string first) as A D F# b, all in ascending pitch except the first string (b), which is tuned one octave lower. The result is a re-entrant tuning, different from the re-entrant tuning common with ukuleles, that has a deeper quality to it and at the same time works well with ukulele chord shapes. Now, this tuning is in the key of D, which is not far from the key of C of most ukuleles, so the question is: could I tune a Venezuelan cuatro in a way that a ukulele player would be able to pick it up right away? It would be great if it could be tuned as G C E a instead, with a low “a”, so it still sounds like a cuatro.

It doesn’t sound too far fetched, since the new tuning would be exactly two semitones below the original for each string. The ratio between those frequencies would then be exactly the square of the semitone interval (which is 2^(1/12), or 1.059463), so that the ratio is 1.12246 or, rather the inverse 0.891 because we are going down in pitch. Now, the frequency of a string’s vibration is given by this formula: f = SQRT( T / mu) / 2L, where T is the string tension, mu the linear density, and L the length. For a given string, the frequency is controlled by changing the tension with the tuning pegs, so that going down by two semitones, a factor of 0.891 times in terms of frequency, would require an decrease in tension that is the square of that, which works out to be a factor of 0.7937. Tuning a string from A to G, for instance, would mean a 21% decrease in tension. Doesn’t look like much, but it might be noticeable because the cuatro tends to a have fairly low string tension to begin with (so the strings can be muted easily, a common event in traditional cuatro technique).

But there is an alternative, and this is to take a ukulele and give it a cuatro-like tuning. The ukulele that is closest to the cuatro in size is the baritone, which is usually fitted with strings tuned as D G B E (no re-entrant tuning). Observe that two of the pitches we want, G and E, are already there, though at different positions. The C is easy to obtain from the B string, since the distance is only one semitone, which works out to be only a 12.2% increase in tension (and the B string is typically is the one with the lowest tension anyway). This leaves the low A to be obtained.

As a matter of fact, other people have worked this out before me. Here’s a fellow on YouTube named collapsibletank who did pretty much the same with the two thinner strings, and then took the original G string (3rd) as 1st string (A, so he increased the pitch by two semitones), and tightened the original D string (4th) in place, to reach a G (5 semitones). As we saw earlier, this would imply a substantial increase in tension (79%), which your uke may resent. Even worse would be leaving the G string as G, and pitching the D string up to A (124% increase in tension). I think collapsibletank gets away with this because his strings are not wound, and therefore they have a lower tension to begin with. He does mention that the way he did it requires unwound strings, by the way.

So, if you start from a set containing wound strings, you’d do better adding a new string (typically around $2 online, plus shipping) that is thinner than the baritone’s G string, and therefore easier to tune up to A (you may need to enlarge the first string groove in the nut slightly). This is why I gave you the full formula a couple of paragraphs above. Observe that the frequency is inversely proportional to the square root of the linear density which, for a given volumetric density of the material, should be proportional to the cross-sectional area, which is proportional to the square of the diameter. In other words, the frequency is inversely proportional to the string diameter, all other things being equal. In order to get the A pitch without changing the tension, the string would need to have a diameter of .030 / 1.06^2 = .0267 inches. So, a similar wound string with a diameter of .027 inches would be ideal. This diameter is fairly rare, but you can find it as a low-tension 4th string for guitar. Here’s one from Amazon, which is what I ended up using. Another alternative is to use an unwound string. In this case we’ll start from the B string (.033 inches) and recalculate its diameter so its pitch with the same tension is an A, which is two half steps lower. The calculation is .033 * 1.06^2 = .0371 inches. This is even harder to find, but here is a .039 inch string from justStrings. Now you only need to add a baritone ukulele. If you don’t have one and are on a budget, here’s a cheapo for roughly $36 at the time of writing.

Update: After a few weeks with the .027 inch wound first string, I decided to try using a plain string instead. Since the other plain strings are D’Addario Titanium series (not actually made of titanium ;-), I chose a .040 inch Titanium string, which comes together with the other two strings in the Titanium Treble strings set, like this one. I was afraid that the .040 string would require too much tension since the calculation specified a diameter of only .037 inches, but after installation and tuning the tension is all right. What’s best, it is smooth to the touch, which is good for switching chords (a wound string in first position feels weird that way), and the tension is closer to that of the other strings. In fact, I’ve replaced the G string (.030 inches, wound) with the .027 inch would string I just replaced, resulting in lower tension of the fourth string as well, which makes it closer to the other strings. It sounds and feels even better.

So, does it sound good? I’m giving you three sound samples so you can compare, all of them playing these chords (twice): C – E7 – A7 – D7 – G7 – C7 – F – Bb – G – C.

Here’s the cuatrolele (original string arrangement, with a wound 1st string):

The same instrument (baritone uke) with the original string arrangement (same chords, so the chord shapes are different):

And finally a tenor ukulele, doing the same chord progression (same chord shapes as the cuatrolele):

 

So, to recap, do the following with a baritone ukulele:

1. take the ukulele and remove the 4th string
2. then shift the remaining strings up (1st to 2nd, and so forth)
3. install a .027 inch wound string as 1st string, or whatever you have handy that comes close. Alternatively, you can use a .037 inch nylon string, or similar.
4. tune the strings to G, C, E, low A
5. enjoy your cuatrolele!

Update June 2019

More than a year has passed since I wrote the above, and my cuatrolele became an octave ukulele with a “barbershop” tuning. Everything is explained in this article. So I decided to make a new cuatrolele, this time starting from a tenor uke. It turned out to be a piece of cake. The only thing you need to do is replace the “high G” 4th string with a “low G” string, which is fairly standard practice for tenor ukes, and then replace the 1st “high A” string with a “low A” tuned one octave lower. You have two options for this:

1. Get another “high G” string (likely wound) and tune it up to A. This will make it a 21% more tense than the G string, which may be too much for the string (wound guitar 4th strings, very similar to the string we’re talking about here, are notorious for breaking spontaneously).
2. Get another fat 3rd “C” string, and tune it down to A. It will feel perhaps a little twangy, but in my tests not excessively so. This is what I ended up doing, and it sounds terrific after the string stretched.