This is one of those questions that can easily devolve into "Well technically" ... "Oh yeah, well actually" and so forth. I'm not aware of an official designator of instrument categories, but more to the point I'm not interested in a right or wrong answer here. I'm interested in why the question should be tricky in the first place.
The answer I learned from high school orchestra or thereabouts was "Yes, it's a percussion instrument, because the strings are hit by hammers." The answer I personally find more convincing is "No, because it's a piano, duh."
OK, maybe that's not particularly convincing. Maybe a better way to phrase it would be "No, it's a keyboard instrument. Keyboard instruments are their own class, separate from strings, woodwinds, brass and percussion." By this reasoning, the pipe organ is a keyboard instrument, not a wind instrument, the harpsichord is a keyboard instrument, not a string instrument, and a synthesizer is a keyboard instrument, assuming it has a keyboard (not all do).
The intuition behind this is that being played by way of a keyboard is more relevant than the exact method for producing the sounds. Even though a marimba, xylophone, vibraphone or glockenspiel has an arrangement of things to hit that looks a lot like a keyboard, the fact that you're limited to mallets in two hands has a big effect on what you can play. Likewise, a harpsichord and a guitar or banjo produce somewhat similar sounds, but fretting a one or more of a few strings is different from pressing one or more of dozens of keys.
It's a lot easier to play a four-part fugue on a harpsichord than a marimba, and a seven-note chord is going to present real problems on a five-string banjo. Different means of playing make different things easy and hard, and that affects what actually gets played.
At this point, I could put forth a thesis that how you play an instrument is more important in classifying it than how the sounds are ultimately produced and be done with it, but that's not what got me typing in the first place. To be clear, I like the thesis. It's easier to play a saxophone if you know how to play a clarinet, easier to play a viola or even a guitar if you can play violin, and so forth. What got me thinking, though, was the idea of how any classification on the order of string/woodwind/brass/percussion or keyboard/bow/plectrum/mallet/etc. tends to break down on contact with real objects to classify.
For example, there are lots of ways to produce sound from a violin. There are several different "ordinary" ways to bow, but you can also bounce the wooden part of the bow on the strings, or pluck the strings (with either hand). Independently of what you do with the bow, you can put a mute on the bridge to get a kind of ethereal, spooky sound. You can rest a finger lightly on the string to get a "harmonic" with a purer tone (and generally higher pitch) than if you pressed the string to the fingerboard. Beyond all that, you can tap on the body of the violin with your finger, or the stick of the bow or the end of the bow. You could even tap the violin on something else, or use its strings as a bow for another instrument.
Does tapping on a violin make it a percussion instrument? I'd say it is when you're tapping on it, otherwise not. But if you ask, "Is the violin a percussion instrument," I'd say "no" (or, if I'm feeling cagy, "not normally").
How about an electric guitar? Obviously, it's a string instrument, except there's more to playing an electric guitar than picking and fretting the strings. The effects and the amp make a big difference. It's probably best to think of electric guitar plus amp and effects as both a string instrument and an electronic instrument, both in its construction and in how you play it. The guitar, amp and effects together are one instrument -- that's certainly how guitarists tend to see it, and they can spend quite a bit of time telling you the details of their rigs.
There are plenty of other examples to pick from -- a morsing, a glass harp, a musical saw, a theremin ... if you had to pick, you could probably call a morsing or even a glass harp a percussion instrument -- I mean, if a piano is, why not? A musical saw would be, um, a string instrument? A theremin would be ... I don't know, let's say brass because there are metal parts?
But why pick? Clearly the four sections of an orchestra work fine for the instruments they were originally intended to classify, and they provide useful information in that context. If you're putting together an orchestra, you can expect a percussionist to handle the bass drum, snare drum and tympani but not a trumpet, oboe or cello. If you're composing for orchestra, you should know that wind players need to breathe and that a string instrument can play more than one note at a time, but only within fairly strict limits. In neither case do you really care that someone might consider a piano a percussion instrument. For the purposes of hiring players and composing music, a piano is a keyboard instrument.
If your purpose is to classify instruments by common properties, there are much better systems. Wikipedia likes the Hornbostel Sachs classification, which takes into account what produces the sound, how the sound is produced, the general form of the instrument and other factors. For my money, it does a pretty good job of putting similar instruments together while making meaningful distinctions among them. For example (based on this 2011 revision of the classification):
- violin 321.322-71 (Box lute sounded by a bow)
- cello 321.322-71 (Same)
- guitar 321.322-5 or -6 (Box lute sounded by bare fingers(5) or plectrum(6))
- French horn 423.232.12 (Valved horn with narrow bore and long air column)
- oboe 422.112-71 (Reedpipe with double reeds and conical bore, with keys)
- bass drum: 211.212.12 (Individual double-skin cylindrical drums, both heads played)
- piano 314.122-4-8 (Box zither sounded by hammers, with keyboard)
- harpsichord 314.122-6-8 (Box zither sounded by plectrum, with keyboard)
- morsing 121.2 (plucked idiophone with frame, using mouth cavity as resonator)
- glass harp 133.2 (set of friction idiophones)
- musical saw 151 (metal sheet played by friction)
- theremin 531.1 (Analogue synthesizers and other electronic instruments with electronic valve/vacuum tube based devices generating and/or processing electric sound signals)
There's certainly room for discussion here. Playing a cello is significantly different from playing a violin -- the notes are much farther apart on the longer strings, the cello is held vertical, making the bowing much different, and as a consequence of both, the bow is much bigger and held differently. Clearly the analogue synthesizer section could stand to be a bit more detailed, and there's a certain amount of latitude within the categories (Wikipedia has a musical saw as 132.22 -- idiophone with direct friction).
It's also interesting that a guitar is counted as a slightly different instrument depending on whether it's played with bare fingers or a plectrum, but that fits pretty well with common usage. Fingerpicking and flatpicking require noticeably different skills and many guitarists specialize in one or the other. The only sticking point is that a lot of fingerstyle guitarists use fingerpicks, at least when playing a steel-string acoustic ...
Nonetheless, I'd still say Hornbostel-Sachs does a decent job of classifying musical instruments. Given the classification number, you have a pretty good idea of what form the instrument might take, who might be able to play it and, in many though not all cases, how it might sound. There are even provisions for compound instruments like electric guitar plus effects, though I don't know how well-developed or effective those are.
For its part, the string/woodwind/brass/percussion system also provides a decent idea of form, sound and who might play, within the context of a classical orchestra, but if you're familiar with the classical orchestra you should already know what a french horn or oboe sounds like.
Which leads back to the underlying question of purpose. Classification systems, by nature, are systems that we impose on the world for our own purposes. A wide-ranging and detailed system like Hornbostel-Sachs is meant to be useful to people studying musical instruments in general, for example to compare instrumentation in folk music across the world's cultures.
There are a lot more local variations of the bass drum or box lute family than theremin variants -- or even musical saw variants -- so even if we knew nothing else we might have an objective reason to think that drums and box lutes are older, and we might use the number of varieties in particular places to guess where an instrument originated (places of origin, in general, tend to have more variants). Or there might be an unexpected correlation between geographic latitude and the prevalence of this or that kind of instrument, and so forth. Having a detailed classification system based on objective properties allows researchers to explore questions like this in a reasonably rigorous way.
The classification of instruments in the orchestra is more useful in the day-to-day running of an orchestra ("string section will rehearse tomorrow, full orchestra on Wednesday") and in writing classical music. Smaller ensembles, for example, tend to fall within a particular section (string quartet, brass quintet) or provide a cross-section in order to provide a variety of timbral possibilities (the Brandenburg concertos use a harpsichord and a string section with various combinations of brass and woodwinds -- strictly speaking the harpsichord can be replaced by other instruments when it's acting as a basso continuo).
Both systems are useful for their own purposes, neither covers every possible instrument completely and unambiguously (though Hornbostel-Sachs comes fairly close) and neither is inherently "correct". As far as I can tell, this is all true of any interesting classification system, and probably most uninteresting ones as well.
It's also interesting that a guitar is counted as a slightly different instrument depending on whether it's played with bare fingers or a plectrum, but that fits pretty well with common usage. Fingerpicking and flatpicking require noticeably different skills and many guitarists specialize in one or the other. The only sticking point is that a lot of fingerstyle guitarists use fingerpicks, at least when playing a steel-string acoustic ...
Nonetheless, I'd still say Hornbostel-Sachs does a decent job of classifying musical instruments. Given the classification number, you have a pretty good idea of what form the instrument might take, who might be able to play it and, in many though not all cases, how it might sound. There are even provisions for compound instruments like electric guitar plus effects, though I don't know how well-developed or effective those are.
For its part, the string/woodwind/brass/percussion system also provides a decent idea of form, sound and who might play, within the context of a classical orchestra, but if you're familiar with the classical orchestra you should already know what a french horn or oboe sounds like.
Which leads back to the underlying question of purpose. Classification systems, by nature, are systems that we impose on the world for our own purposes. A wide-ranging and detailed system like Hornbostel-Sachs is meant to be useful to people studying musical instruments in general, for example to compare instrumentation in folk music across the world's cultures.
There are a lot more local variations of the bass drum or box lute family than theremin variants -- or even musical saw variants -- so even if we knew nothing else we might have an objective reason to think that drums and box lutes are older, and we might use the number of varieties in particular places to guess where an instrument originated (places of origin, in general, tend to have more variants). Or there might be an unexpected correlation between geographic latitude and the prevalence of this or that kind of instrument, and so forth. Having a detailed classification system based on objective properties allows researchers to explore questions like this in a reasonably rigorous way.
The classification of instruments in the orchestra is more useful in the day-to-day running of an orchestra ("string section will rehearse tomorrow, full orchestra on Wednesday") and in writing classical music. Smaller ensembles, for example, tend to fall within a particular section (string quartet, brass quintet) or provide a cross-section in order to provide a variety of timbral possibilities (the Brandenburg concertos use a harpsichord and a string section with various combinations of brass and woodwinds -- strictly speaking the harpsichord can be replaced by other instruments when it's acting as a basso continuo).
Both systems are useful for their own purposes, neither covers every possible instrument completely and unambiguously (though Hornbostel-Sachs comes fairly close) and neither is inherently "correct". As far as I can tell, this is all true of any interesting classification system, and probably most uninteresting ones as well.
No one seems to care much whether a pipe organ or harpsichord is a percussion instrument. I'm not sure why. Both have been used in orchestral works together with the usual string/woodwind/brass/percussion sections.
