Krieger Science Blog

A few ideas for home science education projects...

A Pan Flute

How to make the Pipes of Pan from soda straws, and learn something about the Diatonic Scale in the process.

Brass instruments in the "horn section" 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. Flutes are instruments that work just by blowing—but you have to blow across an opening in a special way. You have to blow across an opening 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.)

(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 sound? 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.)

To make different notes come out of a flute, we could put holes in the sides, as we do for concert flutes. I also once tried to make a "slide-flute", like a telescope that could get longer or shorter, 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 we just pick the one we want to make the note we want. This is the idea behind the Pipes of Pan, or a Pan Flute, and it is very easy to make one from soda straws.

A Pan Flute

(Assembly Tip: Children will often try to line up the ends of the straws one straw at a time, and get frustrated when their efforts with the last few straws disturb the first few straws. It is much more effective just to lay the straws side by side in order by length, without worrying about aligning the ends, then gently press against the end of the array with a ruler or some other straight edge. Also, to fasten the straws together, I suggest using a long piece of tape, gently lowering it against the array of straws, rubbing it with your finger to ensure it is sticking to all straws, then picking up all straws and wrapping the ends of the tape around the other side. Then reinforce your flute by repeating the same procedure on the opposite side.)

How long should the straws be? 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 capable of playing an octave, and all of the proper Do-Re-Mi notes in between, if you want to be able to play recognizable melodies, you need to have straws with the right lengths. To make a Pan Flute capable of playing a single octave, the shortest straw must be exactly half the length of the longest straw. For the rest of the Diatonic Scale, you need six straws in between with the following proportions:

Do110 cm
Re8/9 9 cm8.89
Mi4/5 8 cm8.00
Fa3/47½ cm7.50
So2/36½ cm6.67
La3/5 6 cm6.00
Ti8/155½ cm5.33
Do1/2 5 cm5.00

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 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" and "Twinkle, Twinkle, Little Star" 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.

The Diatonic Scale

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. Other things being equal, the shorter the string or pipe, the higher the note. It might then occur to you that 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 play more than one note 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. Some notes sound better together than other notes. Some chords are 'better' than other chords. 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? Oddly enough, if everything else is the same, you find that consonant notes come from strings or pipes that have simple ratios in their lengths. One pipe is 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 13:21 sound a bit harsh.

(Incidentally, I never did find a really good 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.")

This discovery — that simple integer ratios are harmonious — is usually credited to the Pythagoreans of ancient Greece, 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. 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 adopt. 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 systems, we usually make 'octaves' of eight notes. Modern music theory has many variations and improvements, but it boils down to something like this:

The Diatonic Scale

The most pleasing and best combination is 1:2. 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: 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.