One of my friends started taking bamboo flute lessons and it’s pretty cool (link to his YouTube channel). He now owns a couple different types of flutes including an ocarina (which he said he bought “exclusively for the purpose of playing Zelda music”). This all got both of us thinking, how do flutes actually work? So I decided to take some time and explore that a little.

First let’s start off by defining how instruments work in general. Sound is just vibrations occuring at various frequencies. Instruments work by having a particular thing that can vibrate to create tones, and then a way to alter its wavelength to create different notes. For example, string instruments like guitars have strings that will oscillate when struck, creating sound. You can then press down on the frets to change the effective length of the string that is being vibrated. This changes the wavelength and creates different notes. Every instrument has one “thing” that is responsible for the vibrations. Surprisingly, I looked around the internet and there is not a single name for this part, despite being something every instrument has. I’m gonna dub it as the “inceptor” then.

So what is the inceptor of a flute? Wind instruments have their inceptors typically near the mouthpiece. For instruments like brass instruments, the inceptor is actually the player’s mouth. Your lips vibrate and flap around as they blow into the little cup shaped mouthpiece. The mouthpiece then amplifies your flappy lip sounds into the rest of the instruments and different valves are pressed to change the wavelength of the vibrating airstream.

Flutes belong under a classification of instruments called the woodwind. Typically, woodwind instruments have a wooden reed that is inserted into the mouth piece. As you blow into the mouthpiece, air travels across the reed, causing it to vibrate. The same principle as other instruments then applies. Everything you cover or press down on is to change the wavelength of the airstream vibrating throughout the instrument.

But modern concert flutes do not have any wooden parts. They are still classified under woodwind because they were originally made out of wood. I find this to be a problematic classification because it seems that generally, woodwind instruments refer to the wooden reed that acts as the inceptor. Reed mouthpieces work differently than how flutes operate because reed mouthpieces will open and close depending on the pressure of air being blown in. The harder you blow, the more it vibrates and lets more air in. Flute holes have no moving parts and usually just have either an open hole or a flipple, which is a sharp sort of edge that will cut the air blown across it. This includes instruments like the recorder. A whistle technically can also qualify as a one-note flute. Another difference between flutes and most other woodwind instruments is that flutes are open pipe instruments. Both ends of the flute are open, as the player’s mouth does not fully cover the mouthpiece. This is in contrast to something like a clarinet. The University New South Wales has a great page that goes into the differences in physics for how exactly a closed end vs an open end instrument works. To summarize briefly, flutes will have a close to fast moving atmospheric pressure air flow when played while a clarinet would have higher pressure air flow but less motion. So the period of a note on the clarinet would be twice as long as the one on the flute since it would have to travel the length of the instrument four times as opposed one twice, as the air pulse and subsequent suction would bounce off the closed end.

So this sets a fundamental difference between how flutes and closed end instruments work. Lumping in flute and the rest of the woodwind instruments just feels wrong. And if we want to get real nitpicky, in the case of a bamboo flute, bamboo is a grass and not a wood. So it at no point should be considered a woodwind instrument even if you are referring to material structure and not the reed mouthpiece.

So we have an idea of how flutes instigate sound now. But how does pressing the different holes work change the notes? Well that’s actually just a little bit of math on vibrations and resonance. My primary information was found on this page from Michigan Tech. The main thing to understand is that notes are dictated by their wavelength. So you know the Do Re Mi etc scale right? Assume Do has a wavelength of one unit, the subsequent notes would roughly have wavelengths as follows:

Do would be the lowest note, the equivalent of pressing all the holes on a flute. This corresponds with the highest wavelength, since the air pulse spans the entire length of the flute. As you uncover more holes starting from the further end, you are shortening the length that the air has to through, since it can now escape through the hole you’ve uncovered. So as long as the holes are carved into the flute at the approximate locations corresponding to the wavelength ratios, you should have an instrument that can play the standard scale. Of course key dimensions are needed to actually guarantee the geometry of the instrument is correct. The outside radius, the inside radius, and the distance from the mouth hole to the end opening of the flute all are necessary for the calculations on where the holes should be located.