I have a confession to make. Back in April, I wrote that for my quarantine hobby, I intended to be practicing my concertinas more. But by the time that column was published, that statement was no longer true.
Concertinas may be small, but they make a mighty sound that carries well. With everyone home all the time, there was always someone around to hear me practice, and I got self-conscious. So I started searching for a more fully-occupied-apartment-friendly instrument. And I bought a harp.
I’ve long been fascinated by the Celtic harp. It has a beautiful sound, and it seemed (and I can now confirm) that it would be fun to play. I’d heard of something called “harp therapy,” although I’m still not sure exactly what that entails, apart from using soothing harp music to calm frazzled nerves. And my nerves were in need of a good defrazzling.
The sticking point was cost. Even a small, basic Celtic harp costs the better part of $1000, and larger and better ones go for considerably more. That’s a lot to pay for an instrument I was buying on a whim, didn’t know if I’d take to, and couldn’t try out in a music store beforehand because they were all closed. Like most instruments, harps also come in a range of cheap, no-name forms on various online commerce sites, but I knew better than to go that route; cheap instruments are too often so poorly made that they’re unplayable. I’d once bought a $100 mandolin whose strings were set so high above the fretboard that it was impossible to play in tune. And I’d heard of cheap concertinas whose buttons were hooked up to the wrong notes.
Miller’s Diary
Physics Today editor Johanna Miller reflects on the latest Search & Discovery section of the magazine, the editorial process, and life in general.
But then I learned of another option. As I read articles and watched videos about good harps for beginners, the Fireside harp, made by Backyard Music, came up over and over again for being shockingly inexpensive (by harp standards, anyway) yet well constructed and with a good sound. So I bought one. The key to its economy is that its sound box is made of heavy-duty corrugated cardboard.
I guess I hadn’t thought much about a harp even having a sound box, but of course it does. A vibrating string by itself doesn’t move enough air to create an appreciable sound wave. As with all stringed instruments, harps make sound only because the strings transfer their vibrations to something else: a big, flat, resonant soundboard. But is cardboard as effective in that role as the usual wood?
I assumed there would be a difference in durability—a cardboard sound box doesn’t seem like the kind of thing to last for generations. But I was surprised to learn, from an article on harp acoustics by Chris Waltham and Andrzej Kotlicki, that expensive wooden harps may not last for generations either.
The difficulty is that harps have a lot of strings (roughly 20 to 50; mine has 22) that are collectively under a lot of tension. The strings pull directly on the soundboard, which needs to be strong enough to support the stress. But the soundboard also needs to be thin enough to resonate well, and that uneasy balance often isn’t struck well by cheap harps, whose soundboards can crack within months. Even good harps last “merely for decades, as opposed to centuries,” Waltham and Kotlicki say. Furthermore, when a harp has all its strings mounted on the same side of the neck at the top of the instrument (as both Celtic harps and concert harps do), the torque they exert can wreak further havoc: Here’s an example of a harp that’s only 25–30 years old but whose post is already severely bent and has had to be reinforced. All in all, used harp listings don’t seem to include many antiques (in marked contrast to concertinas, which, as I wrote in April, are almost all antiques).
What about the sound of a cardboard harp? The Backyard Music website says that cardboard is “acoustically responsive” but doesn’t elaborate on what that means. From what I can gather, musical acoustic performance depends on two material properties: the sound radiation coefficient and the loss coefficient. The sound radiation coefficient, in turn, depends on both the material’s Young’s modulus and its density: Stiff, light materials radiate sound most effectively. The loss coefficient—the reciprocal of the Q factor—measures how much the material’s internal friction damps its vibration and blunts its acoustic resonances.
It’s hard to find specific numbers for either of those parameters. There are many types of cardboard, measurements of their material properties aren’t usually made with an eye toward their use in musical instruments, and I’m not equipped to make any better measurements myself. But as far as I can tell, it looks like cardboard is inferior to most woods in both sound radiation coefficient and loss coefficient, but not by too much. After all, corrugated cardboard is designed to be sturdy and lightweight, exactly the properties that make good soundboards.
An instrument’s sound depends not only on the soundboard’s material properties, but also on the shapes of its two-dimensional modes of vibration and how the strings excite them. If a vibrational mode happens to have a node at the point where the string couples to the soundboard, that note will sound quiet and dead. If, on the other hand, the coupling point is at an antinode, the note will sound loud—perhaps too loud. The main topic of the Waltham and Kotlicki paper is the unusual challenge that the coupling presents for harps: Unlike violin- and guitar-family instruments, whose strings couple to the soundboard via a bridge, harp strings attach to the soundboard directly, each at a different point. For the notes of a harp to all sound with equal volume, each mode must vibrate with equal amplitude at the point where the corresponding string is attached to the soundboard. Sometimes even good harp makers have trouble getting that balance right, and harps can have considerable note-to-note variation in sound.
I haven’t noticed any such variation in the notes of my cardboard harp, although my playing technique isn’t yet to the point where I can consistently pluck all the strings with equal intensity. I suspect that the cardboard’s relatively high damping leads to less pronounced modes. Also, the strings are attached at the bottom to a thick wooden beam, not directly to the cardboard, which could never withstand their tension. For both those reasons, the cardboard harp’s sound is sweet but quiet—if I ever tried to take it to a jam session, it would be quickly drowned out. But for now, for playing by myself without annoying the neighbors, it’s just what I need.
