A Soda-Straw Pan Flute

Brass instruments in the “horn section” of the orchestra are musical instruments that work by fluttering your lips as you blow into them. Woodwinds are instruments that work by making a reed (sometimes made of wood) flutter as you blow across it. In both cases, it is obvious that something has to vibrate in order for the instrument to sing properly. Breath alone is not enough. But flutes are different. Flutes are instruments that work just by blowing — except you have to blow across an opening in a special way. You have to blow sideways, in the same way you blow over the mouth of a jug or bottle to make it sing. (Some instruments, like a recorder or a referee's whistle, have a special channel that points your breath across a second opening in just the right way, saving you the trouble of aiming properly. We call this a fipple, and fipple flutes are a sub-category of the larger family of flutes.)

(With horns and woodwinds, the fact that something is vibrating is obvious, but with flutes, there is no visible motion. Is there something special and invisible going on when the flute makes the note, that doesn't happen when the flute doesn't make the note? I would sometimes try to demonstrate that there is, with a short section of clear plastic tube that was open at one end, and had a hole in the other. I would attempt to blow across the hole and make the flute sound its note, and then try to place my finger into the other end of the tube, thus making the note change, but without touching the walls of the tube. When I succeeded, I could change the note by touching only the air inside, and it was a pretty clear demonstration that something was going on in the air itself, even if there was no visible activity in the pipe. But this was a pretty difficult demonstration to get right. If you'd like to see me try to illustrate this, I made the following video many years ago for an online science class...)

Making Different Notes

You can make a very simple and crude “flute” just by blowing carefully across the end of a soda straw. But it won't be very interesting unless you can make many different notes come out of it. How can we make a soda straw sing different notes? Maybe we could make holes in the sides, and make it look like a concert flute? I once snipped a few holes in a soda straw, and it could make a few different notes when I blew across the opening. Or at least you could tell that the hiss had a different pitch when various holes were uncovered. I also once tried to make a “slide-flute” from a pair of soda straws, one fitted inside the other, but the two tubes had to be almost identical in size to sound right, in which case they tended to get stuck. A much simpler approach is just to make several simple flutes all of different lengths and fasten them all together, and then when we want to play a different note, we just blow across a different pipe. This is the idea behind the Pipes of Pan, or a Pan Flute, and it is very easy to make one from soda straws. We can just cut several straws of different lengths, and then tape them side-by-side.

How long should the straws be? Do they need to be any special lengths? If you don't care about playing tunes, you could just cut a few straws to any lengths you want and tape them together. However, if you want to make a flute that can play a standard scale and recognizable melodies, then you need to have straws with the right lengths. To make a Pan Flute capable of playing a full octave, the shortest straw must be exactly half the length of the longest straw. For the rest of the “Do-Re-Mi” Scale (more formally known as the “Diatonic Scale”) you need six straws in the middle with the following proportions:

The third column gives one possible set of measurements that I have found convenient for cutting from soda straws. Rather than have small children fuss with measuring every straw to the nearest millimeter, I just rounded my measurements to the nearest half-centimeter, and it didn't make any recognizable difference to the notes produced, especially for small children. You can calculate your own set of measurements by adjusting the number at the top of the final column, i.e. the length of the fundamental note, and the rest of the measurements in the table should adapt to show the corresponding measurements for the rest of the scale.

With a little practice, you can play tunes on such an instrument. “Do-Re-Mi”, “Twinkle, Twinkle, Little Star”, and “Happy Birthday” are good first attempts. It is a little difficult to aim your breath precisely across such small openings, but you can also save a spare length of straw, and use it as a blow-pipe to direct your breath more precisely against the end of the pipe that you want. Even if you can produce nothing more than a hissing sound, the hiss will have a definite pitch to it, and you can still hiss out melodies.

(Assembly Tip: Children will often try to line up the ends of the straws one straw at a time. This can be frustrating, because your attempts to line up the last few straws will disturb and disarrange the straws you've already lined up. It is much more effective just to arrange all of the straws side by side, without worrying about aligning the ends, and then gently press against the end of the array with a ruler or some other straight edge. It's a little like straightening out a stack of papers by tapping the edge against a desk. Also, to fasten the straws together, I suggest sticking a single piece of tape to all straws at once. Use a long piece of tape, gently lower it against the array of straws, rub it with your finger to ensure that it is sticking to all straws, then pick up the entire array and wrap the ends of the tape around the other side. Then reinforce your flute by repeating the same procedure on the opposite side.)

The Diatonic Scale

Why did we need to make the straws with those exact lengths? What's so special about those proportions?

If you play notes with a stretched string or a long tube or pipe, as the very first primitive musicians did, you soon discover you can play any note you want by changing the length of the string or pipe. The shorter the string or pipe, the higher the note (other things being equal). It might then occur to you that, instead of just playing with a single sound, you could make a tool, a device, an instrument, by making a whole set of pipes or strings all lined up next to each other. You could make a lute or a Pan flute, and then you could sing songs like a bird by playing many different notes on your instrument.

But how long should the strings or pipes be? When you try to put many strings together, and experiment with playing several notes at the same time, you may make a curious discovery. Some combinations of strings (or 'chords', from a Greek word for string), sort of clash with each other, they grate on your nerves a little, they conflict and sound a little 'off'. But other pairs of notes are more pleasing, they blend, they sound like they belong together. For some mysterious reason, some combinations of notes are 'better' than other combinations. Some chords are harmonious or consonant, and others are dissonant. Try hitting different combinations of keys on a piano and you might discover the same thing.

Why? What's the difference between consonant notes and dissonant notes? If you are paying attention to the lengths of the strings or pipes, you may make a fascinating discovery about the measurements. For some reason, consonant notes tend to come from strings or pipes that have simple whole-number ratios in their lengths. One pipe has to be twice as long as the other, or two-thirds, or three-fifths, or something like that. The less simple the ratio of lengths, the more dischord there is. Pipes in the ratio of 1:2 or 2:3 sound very good together, but pipes in the ratio of 13:17 sound a bit harsh.

(Incidentally, I never did find a really foolproof way of illustrating this point to children. I tried using a string-board that I constructed myself — just a couple pieces of fishing wire stretched between two pairs of screw-eyes, with fractional lengths marked underneath — with limited success. It was easy to convince some students that strings in simple ratios sound 'better', but many of the kids were hard to convince. I could usually convince most of them that a whole-string plus half-string sounded better than a whole-string plus almost-half-string, and that often had to be good enough. Considering that some people tend to be more musical than others, I could also say: “Not everyone thinks so, but many people agree that this sounds better.” You could also try using digital tone generators; you can find many of them online.)

This discovery — that simple integer ratios are harmonious — is usually credited to the Pythagoreans of ancient Greece, who lived about 2500 years ago, and who saw profound metaphysical and spiritual importance in it. There is probably nothing literally 'magical' in simple numbers, but there is definitely something special in simple integer ratios — something wondrous and harmonious and 'proper' somehow, at least as far as making music. The numbers are “in there” somehow. Music and mathematics go together in a special way.

Philosophy aside, let's come back to the question of how to construct a practical musical instrument. What set of lengths should we choose for making the best, most beautiful and harmonious chords and melodies? What's the best 'ladder' or scale of notes to work with? There are several different strategies you could try. The ancient Greeks made 'tetrachords' (literally 'four strings') in which the shortest string was 3/4 the length of the longest, and the two in between were adjustable. In modern music, we usually make 'octaves' of eight notes. Modern music theory has many variations and improvements, but it boils down to something like this:

The most pleasing and simplest combination is 1:2, meaning the one string should be half or double of the other. We make 'doubling' or 'halving' our basic interval, and we can expand in both directions if we want, by repeated doubling or halving. (Two notes that are half or double of each other form an 'octave'.) But an octave is a pretty big jump. We'd like to use many more notes in between. So within the octave, we'll choose the four simplest ratios between ½ and 1. We'll choose ⅗, ⅔, ¾, and ⅘. This gives us a ladder or scale of five jumps, and all of the notes should sound pretty good together. But the jumps are not all the same size. In particular, the first and last jumps are especially large. (Just imagine humming the Do-Re-Mi scale without Re or Ti. It just doesn't sound right.) So we'll cut the two large jumps in half by inserting two more fractions: we'll pick 8/9 and 8/15 as two more notes that don't sound too horrible with the rest of them, and then we'll have a ladder or a scale of eight notes that we can use together as a more-or-less harmonious set to make music. (After the 1:2 octave ratio, the next best ratios are 2:3 and 3:4. These are the fifth and fourth notes of our final eight-note octave ladder, and in modern terms, any pairs of notes in the ratio 2:3 or 3:4 form a 'perfect fifth' or 'perfect fourth'.)

Unfortunately, the jumps in this elementary scale are still a bit irregular, which makes transposing and coordinating multiple instruments a bit difficult. Is there a way to construct a ladder or scale of notes, in which all of the jumps are evenly spaced, but the scale still contains all of the 'best' simple integer ratios? The modern solution is the 'even-tempered scale', which you can see displayed visually in the ladder of frets on a guitar neck...but that's another story.