A harp works on the simple principle that a string stretched tight across a frame will vibrate and make noise when plucked. If one end of the string is attached to a hollow box, the box resonates and amplifies the sound. Given a way to control the tension on the strings, one can tune them to a musical scale and use the instrument to make pleasing music. The frame consists of three pieces; the soundbox, the neck (which is attached to the soundbox at one end and holds the other end of the strings and the tuning pegs), and the column, which supports the other end of the neck. On a really fancy harp, the column is sometimes carved to look like a Corinthian column. Depending on the size and style of the harp, it may have a box or flat platform with feet at the bottom of the soundbox. The whole thing is held together with wood glue and a few strategically-placed screws. All of the above (and most of the rest of this writeup) applies to acoustic harps; there are also electric harps, where the strings are attached to pickups, but I've never even got a really close look at one, let alone played one.
The "structural" parts of the instrument - the neck, column, and most of the soundbox - are made of a hardwood such as maple or cherry. The soundboard - the top surface of the soundbox, where the strings are attached - is made of a softer wood such as birch or spruce. The soundboard may or may not have a reinforcing strip of wood running down the centre where the strings are attached, and the holes for the strings are sometimes reinforced with metal rings. On a new harp, the soundboard is a flat plane; once the strings have been brought up to full tension and tuned, the soundboard will develop a noticeable curve due to the pull of the strings. The entire construction needs to be able to support the tension on the strings: the neck and column have to be strong enough that they will not deform (or break!) under the force exerted by the strings, and the soundboard has to be both flexible enough to vibrate when the strings are stuck and strong enough not to tear apart.
The strings are made from gut, nylon, or metal (usually copper, bronze, steel, or some combination thereof). Nylon strings are usually only used for middle C and higher pitches; the bass strings are either plain wire or nylon-wrapped wire. Gut strings go about an octave lower than nylon ones, but the lower strings will still be wire. For the convenience of the harpist, the C strings are coloured red and the F strings are coloured blue or green.
The amount of tension on the strings varies considerably depending on the size and make of the instrument. Generally speaking, smaller harps will have lower string tension than larger harps, but even in harps of roughly the same size instruments by different makers can have markedly different tension. A friend of mine plays a Silvershell harp about the same size as my Triplett, but the string tension on his is much lower. It's easier to play fast if the strings don't have a lot of tension on them, but you'll lose a lot of volume and tone quality.
Nylon and gut strings are usually anchored to the soundboard by simply tying a knot in the end to stop it slipping through the hole. Wire strings have little stops already attached. In either case, the top end of the string is wrapped around a tuning peg which is stuck through the neck. The tuning pegs are slightly tapered; the end that the string is wrapped around is a bit narrower than the other end. This lets the harpist tighten a peg which keeps slipping by forcing the peg further into its hole. Eventually, of course, this means that the peg will go all the way through and fall out; the solution at that point is to replace it with a bigger peg.
That brings me to...
The tuning key that comes with a harp is basically a socket wrench with a nice wood handle and a square hole exactly sized to fit the square end of the tuning pegs. In a pinch, one can rifle through a socket set and find one that will work, although it won't fit quite as well as the harp's own key. The process of actually tuning the instrument is just a matter of tightening or loosening each string until its pitch is correct. Unless you have perfect pitch, an electronic tuner is invaluable. It is possible to tune one string, then tune all the others as intervals from that string, but it takes a lot longer and is a lot harder to get right.
It really isn't as bad as you might expect, looking at the prospect of tuning 30 or 40 strings each with its own tuning peg before you can play anything. A brand-new harp will slip out of tune every time you look at it, but after being tuned regularly for a couple weeks it will settle in and stay reasonably stable. Unless I've ignored it for months, it usually only takes me about five minutes to check all 30 strings on my harp and adjust any that are out of tune.
The strings of a harp are sort of like the white keys of a piano; each one corresponds to one note of a major scale (usually, unless the harpist decided to tune his instrument some other way). That's fine as long as you're playing music with no key changes or accidentals, but it's pretty limiting. Fortunately, there are a couple devices that allow a quick half-step change, although they have their limits. Playing a chromatic scale, for example, is not practical on most harps.
Since the late 18th century, concert harps have been built with a pedal assembly that allows the harpist to change the pitch of a set of strings by moving a pedal with his foot. There are seven pedals, each controlling all the strings for a given note in every octave (one controls all the C strings, one controls all the B's, etc.) The pedals have three positions - the bottom position sharps the strings, the middle position returns them to natural, and the top position turns them flat. This allows very quick key changes and lets the harpist change keys without lifting his hands from the strings. This device is only usable on large floor harps, and is very heavy - a typical pedal harp stands about 6 feet tall and weighs around 80 pounds (nearly 2 meters and a little under 40kg).
Smaller harps have hooks (rarely) or levers (much more commonly) mounted next to all or some of the strings. Turning the lever so that it presses against the string shortens the length of string that can effectively vibrate and increases the tension slightly, raising the pitch a half-step. This is less flexible than a pedal harp, since it only allows changing a string from flat to natural or natural to sharp. Many lever harps only have a partial set of levers, so some strings can't be easily changed at all. On the other hand, I've been playing a harp that only has levers on the C, B, E, and F strings for several years, and it's not a really onerous restriction. Typically a harp with this set of levers will be tuned so that with all levers disengaged, the B's and E's are flat and all other strings are natural. This allows the harpist to play in any of five keys (B-flat, F, C, G, and D) conveniently. A harp with levers on all its strings will often be tuned similarly, except the A's will also be flat.
Playing the Harp
It's pretty much impossible to explain how to play any instrument in text; if you really want to learn you're much better off finding someone who knows how to play and learning from them. Still, here's an attempt, in case you want to know why harpists hold their arms at that odd angle and how all that finger-wiggling works.
Note: I was trained by a Salzedo concert harpist, so everything below is biassed toward that tradition. If there are any harpists around from a different background, I'll be happy to hear your comments.
Some of the basics are the same in any case: the harpist sits behind the harp (or, in the case of a very small harp, with the harp held between his knees) with the soundboard leaning back against his right shoulder. The harp is played with the thumb and first three fingers of each hand; the pinky fingers aren't strong enough or long enough to effectively strike the strings. The fingers of each hand are numbered one through four, the thumb being "one" and the ring finger being "four". Usually, the left hand plays the lower strings and the right hand plays the higher strings (which is why when I'm tired I can't read bass clef and play with my right hand...) The side of the finger - the flesh right next to the fingernail - is used to strike the strings; if you try playing with the ends of your fingers, it's harder to pull them off the strings, and you'll catch your nails on the strings.
In some ways, playing the harp is very intuitive: each string has only one pitch, so there are no fingerings to memorise. On the other hand, since that string is the same note no matter which finger you pluck it with, which finger do you use? Whichever is most convenient given the passage you're playing - sometimes this is an obvious choice, and sometimes it requires some thought and experimentation. On especially tricky passages, the harpist will often pencil in finger numbers over the notes.
Harpists (concert harpists, anyway; I'm not sure about people from a purely folk-harp background) are trained in either Salzedo or Grandjany method. The most obvious difference between the two is hand position. A harpist trained in the Grandjany style plays his thumb with his hand pointing downward, then flexes his wrist the other way (thumb pointing up) to play the other three fingers - done properly, it's very graceful and pretty, but it doesn't lend itself to speed and all that wrist motion tends to cause joint problems. A Salzedo harpist, on the other hand, plays with his arms parallel to the floor and hands bent upward as close to vertical as possible (it sounds much more uncomfortable than it is).
Care and Feeding of a Harp
Water and temperature extremes are bad for most instruments, harps included. Gut strings fall apart if they get wet, nylon strings will soften in extremely hot conditions (like, for example, the inside of nylon tent in the sun), and both heat and excessive dampness are bad for the wood glue that holds it all together. Cold is less of a problem, although very low temperatures can cause the varnish on the wood to crack. Temperature can also affect the tuning of the strings; a harp that was tuned while it was cold will always slip out of tune as it warms up. Rapid changes in temperature can also cause the strings to go out of tune, as the different components expand and contract at different rates.
Sources: My harp teacher and seven(ish) years of playing the instrument