A note is a vibration at a certain frequency. A drum produces a tone with a certain pitch much like a string percussed with a mallet.
Why is a drum unfit for playing a melody while a string inside a piano (or any other melodic instrument) is very good for it?
Instruments don't just produce one frequency at a time. When you play a single note on a melodic instruments (like piano, wind instruments, string instruments, etc.), you produce many different frequencies at a single time--a whole spectrum is produced. But this spectrum isn't random. It pretty closely follows the harmonic series, which can be thought of as the "ideal" values that most appeal to our ear. When a single note is played, the higher, often fainter frequencies that are produced are called overtones. (To read more on those, check out my answer here.) When the overtones match the harmonic series, it sounds harmonious and we get the sensation of hearing a single note/pitch. Here's an example of a waveform produced by a flute:
http://hyperphysics.phy-astr.gsu.edu/hbase/Music/imgmus/fluw3.gif
But when you strike a drum, the spectrum of frequencies deviates quite a bit from the harmonic series. Yes, there's often a single loudest frequency, but the overtones don't match what we expect to hear from a single-note/melodic instrument. As a result, our ears don't get the same sensation of hearing a single, defined pitch. It sounds more like a blunt collision than a defined note. For this reason, it would be much more difficult to recognize a melody on a drum than on a violin. This is called inharmonicity. A single strike on the timpani produces a spectrograph like this:
According to hyperphysics, the timpani's overtones would theoretically would be these multiples of the lowest/fundamental frequency: 1, 1.35, 1.67, 1.99, 2.30, 2.61. This deviates quite a bit from the ideal-sounding harmonic series, where the overtones are integer multiples of the lowest/fundamental frequency.
This might raise the question: why aren't the overtones of a drum harmonic? What physical quality of an instrument causes this inharmonicity? (Harmonic = integer multiple of the lowest/fundamental frequency.) It comes down to this: a vibrating circular membrane has an extra dimension within which it can vibrate compared to a 1D string or a 1D column of air. This extra dimension gives rise to both symmetric and asymmetric vibrations. For timpani, the symmetric vibrations all produce inharmonic frequencies which aren't integer multiples of the fundamental frequency. And only 5-6 of the asymmetric vibrational modes are harmonic. Those are called the "preferred modes," and they're far and few between compared to the overtones of a melodic instrument.
But beyond this, there's another logistical reason why drums aren't as well-suited for a melody as melodic instruments. Drums are tuned in advance of a performance and many can't really be re-tuned on the spot. However, there are jazz drummers who use a technique called "melodic drumming." One of the most well-known is Ari Hoeing. Here's a video from his YouTube channel of him playing You Are My Sunshine. You'll see him pushing down on the drums to increase the tension and produce a higher pitch. It's definitely recognizable, but perhaps compared to the saxophone, it's a little harder to distinguish the notes that the drums are playing.
The drums CAN play melodies, but the number of pitches and notes you have available are limited by the number of drums you have (not counting creative applications of "bending" the drum head to produce higher pitches).
Terry Bozzio is an example of a drummer who uses a massive drumset so that he can play more complex melodies on the drums. In a video of his kit being setup he mentions that his kit is half chromatic and half diatonic.
This beast must be a nightmare to keep in tune!
No-one's mentioned pans - aka steel drums They certainly are used to play melodies. The main problem is that melodies usually contain long and short duration notes, and drums generally can only produce short, so rolls have to be performed to 'sustain' longer notes.
For those who haven't had the pleasure, 40 gallon steel oil drums are cut in half, or less, and a fire set in them. At a point when they are really hot, the top is battered in to make a dish shape. Then the clever bit. On a soprano pan, the top is divided into maybe twenty small circles, each representing a note - usually diatonic, often in D major. Others which are destined to be tenor have three or four larger circles scribed.
Those circles are then heated and made into separate dishes. The order is important, and they are then beaten till in tune, making a couple of octaves. played with sticks that have rubber bands wrapped round the ends.
Probably the ultimate cheap - if not free- instrument, from the West Indies originally. A band can sound very impressive - symphonies have been performed, and their sound typifies the West Indies.
In contrast to the question, the timpani are a drum set that can play melodies (although they are almost always given accompaniment parts only). Indeed, they are tuned to pitches (one pitch per drum) before a piece starts.
The challenge is that drums’ pitches cannot easily be changed. You could follow Berlioz’s Requiem (Grande messe des morts) and have eight pairs of timpani played by ten people and have melodic content, but one player probably couldn’t move fast enough between the drums to play a melody at any sort of reasonable tempo.
The scientific theory behind this is covered in the article "The Physics of Kettledrums" in the Nov. 1982 issue of Scientific American.
The vibration of a string (e.g. violin string) or column of air (e.g. organ pipe) has modes which are sine waves. Since the zeroes of a sine wave occur in ratio 1:2:3:4..., the sound produced by a violin or an organ has harmonics in those ratios which the human ear hears as a definite tone/pitch.
By constrast, the vibration of a circular drum skin has modes which are Bessel functions. The three smallest zeros of the bounded (i.e. 1st-kind) Bessel functions are 2.4048, 3.8317, 5.1356 (source), which are approximately in a 2:3:4 ratio. That ratio isn't exact enough for a human ear to hear a tone, which is why most drums such as tom-toms sound atonal to us. In a kettle drum though, the shape of the "kettle" will fine-tune the harmonics into a more exact 2:3:4 ratio, and the human ear can hear that as a definite tone - just without a fundamental.
A drum produces a tone with a certain pitch much like a string percussed with a mallet.
The answer to your question is that for many types of drums the assumption above is mostly completely wrong.
The most essential part of the sound of a snare drum is noise (this is why machines that synthesise drum sounds electronically mostly just use noise as a basis for snares or hi-hats), that means not a certain pitch at all but rather the whole spectrum over several octaves being filled with smooth noise. Basically there's two elementary types of sounds, pure tones and noise (a third would be transients, but this is not relevant here). Pure tones are sinusoidal waves, at any given moment they have only one frequency, though they might go up and down with time, and perceptually several separate pure tones may be linked together as harmonics, as with most musical instruments that produce notes.
Noise on the other hand isn't made from pure tones at all, many people are confused about this because Fourier analysis says that every sound is made from a sum of a bunch of sinusoidal waves, however discrete Fourier analysis interprets a sound as being repeated in a loop. If you don't interpret a sound as being a loop of a fixed duration then its spectrum is continuous and not made of a sum of discrete waves.
In other words something like a short burst of noise like the hit of a snare drum should best be thought of as a filled area in the time-frequency plane, meaning it has nothing matching to a note that stands out. Instead of having a sharp spike at a given pitch (and its harmonics), noise is just pretty much smooth all over, so there's no "certain pitch" coming out of that at all.
In the case of kick drums the sound is mostly a pure tone (with optionally some harmonics, and possibly some noise either coming from the initial hit or from the reverberation) there is a "certain pitch", however it's quickly descending over the range of an octave or two, so typically you wouldn't think of them as having an identifiable pitch. Timpani produce mostly noise, however they do have a sharp spike in volume of a certain flat pitch, so they do have notes associated with them. So an issue with your question is that you didn't really specify which type of drums you're thinking about.
For the sake of pedantry snare drums can have some rather flat pure tone components (as jdjazz's answer focused on), however it's not essential to the snare drum sound (hence why many synthesisers don't bother) and since there's a bunch of them a bit all over the place they don't produce anything you can recognise as a note, this is why no one even bothers to make sure they fit the tonality of the music being played. And finally of course you can transpose any sample by any number of semitones as some electronic keyboards allow you to do, however you'll have trouble producing a worthwhile melody if you use the types of unsuitable sounds outlined above.
For a drum like a snare drum, when the snare isn't engaged, there is a definite pitch. But that's the problem: it's A pitch. You could have a one-note melody, but that's it. It takes a while to change the pitch of a snare drum.
When the snare is engaged, there are so many notes at once (overtones) that one pitch can't be easily discerned.
Yep, steel drums. I don't know why you hardly ever see/hear these anymore -- they were quite popular back in the 60s, IIRC.
steel drum youtube.
Commented
Apr 13, 2020 at 22:58
I think that drums & percussion provide a drive/feel to the melody. It forces us to latch to certain notes. However if you want to talk about melody while drumming Aric Improta utilizes sample pads ingeniously to create some nasty grooves:
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