I'm kinda strange guy. I like really zillions of things, very different one another. For example, I'm studing math, I'm learning to play violin, I like Irish music... I also like making things. To conciliate this last passion with music I made a pan flute, an ancient instrument belonging to various cultures. Here is the process that will bring us to an almost perfectly tuned pan pipes.

This Instructable is splitted in two parts: theory and practice. If you are not interested in all the math and physics behind the project, you can jump directly to the practice section. If you want to know how to retrive all measurement, or even to customize your pipes, then proceed with next step.

Step 1: Theory

The (not-so-)boring part.

As I've aforementioned, you can skip this passage if you don't want (or need) to understand the physics beyond a pan flute.

OK, if you're reading those words you want to know more. I'm here for this!

A pan flute is a mere group of tubes with a closed end (called closed cylinder, even if one end is open). Each tube have a different length but, usually, the same diameter of all other tubes.
The length of the tube influence the pitch: longer tubes produce lower notes, shorter tubes produce higher notes.
The inner diameter of the tube influence the speed of blow needed to make the sound audible: smaller diameter means less blow, greater diameter means more blow.

Pretty simple, uh? No math, no strange formulas...

Now we need to find a precise relation between tube length and note pitch. Luckily, some physician (well, actually a lot of physician) already studied this matter creating and developing a branch of physics called acoustic. So we can "stole" their results to serve our scopes.

The formula we need is the one in the first pic. Here is the meaning of various symbols:

- L is the length of the tube
- v is the speed of sound
- f is the frequency

Fine. Now we need to determine which notes we want to produce, and their frequencies. I'm going to make a full octave pan flute, so I need 13 tubes: C, C#/Db, D, D#/Eb, E, F, F#/Gb, G, G#/Ab, A, A#/Bb, B and C again. Each tube will produce a note a semitone higher than the previous one and a semitone lower than the next one.

Since it's is too generic saying "I want to play an E", we must specify also the octave. In my case the first C is a C4 and the last C is a C5. This make the A an A4, with a frequency defined to be 440 Hz (modern concert pitch). From this we can determine all other frequencies using the second formula (second pic, obviously). The n is the number of semitones between the note we want and the A4. If the note is lower than n will be negative, if the note is higher it will be positive.

Step 2: Theory Part II - Calculations

Now we have the basis to determine the tubes length. First we find the frequencies of all notes we choose. This can be done easily with Excel, Derive, Mathematica, even with Windows' Calc.

As a math student I love Mathematica, so I will use it. However, "my" frequencies are
261.6, 277.2, 293.7, 311.1, 329.6, 349.2, 370, 392, 415.3, 440, 466.2, 493.9, 523.3
rounded to first decimal digit, measured in hertz. Using the first formula shown in the previous step we obtain the list of length:
31.69, 29.91, 28.23, 26.65, 25.15, 23.74, 22.41, 21.15, 19.96, 18.84, 17.78, 16.79, 15.84
rounded to second decimal digit, measured in centimeters.

A "virtual" pan flute made using those length and laying all tubes on a table is shown in the first pic. The external diameter of those pipes is 2 cm, maybe too wide (and bigger than the one I've realized).

The disposition of tubes, in my opinion, is not so good, because of my lack of memory. If you ask me where is a note on a piano I can find it almost instantly, but if you ask me the same thing on this arrangement I will need at least two seconds, a really long time if you are playing something. So the disposition I chose is similar to that of key on a keyboard, but the accidentals (black keys) are nearest to the player and have been lowered. The second image is another virtual model of the pan flute made this way.

Later I will explain how to dispose everything even better.

Theoretic lessons are gone, now let's do something more practical!

Step 3: Materials and Tools

We cannot start making something if we don't have anything to start with.

Materials we need:

- about 3 m of metal or plastic pipe (if you use metal try to avoid copper)
- duct tape of any kind
- strings/shoelaces/yarn/whatever you want to keep tubes together
- 13 pieces of whatever you can use to close one and of a pipe (coins, metal or plastic scrap, wood, cardboard... remember that it will cover the end from outside, and cannot be inserted like a cork on a bottle because this will shorten the air column and change the note produced).

Please make sure that you can cut all pieces from your pipes because it may be difficult to join two pieces together without compromise the sound. My local store sells only 1 or 2 m long tubes, and with 3 short (1 m) tubes you can do every pipe. The inner diameter should be not too big nor too small: a 1-1.5 cm of inner diameter is fine.

Tools we need:

- a saw or a tube-cutter
- a measuring tape/long caliber/big printer (I will explain this later)
- something to write on tubes
- needle files
- tuner/good ear (optional)
- clear glue (optional)

If you don't have one, I suggest to buy a tube-cutter: I've bought a small one, suitable for tubes from about 0.5 to 2.2 cm, and it costs me only 2 € (less than 1.5 $). If you don't know how to use a tube-cutter and you cannot figure out by yourself feel free to ask.
The caliber will allow you to make more precise measurements, but you can use a measuring tape with a sign every millimeter without loosing too much tuning. Only a really good ear can sense a difference of a few cents. If you have access to a printer that can use large formats (at least 35 cm on one side), you can print out a schematic with precise measures made with any CAD software. This is my favourite method, but this time I cannot follow this way because my printer is incapable of such dimensions.
The tuner (or a good trained ear) can be useful to test each tube once cut and cleaned. It shouldn't be necessary, but it's a further warranty.

For finishing (optional):

- sandpaper of various grit
- a Dremel-like tool (optional but very useful)
- a lot of patience, a googolplex tons of patience if you want to do everything by hand

Step 4: Measuring and Cutting

Now we have to start measure things.
We need 13 tubes with various length, from slightly more than 15 cm to slightly less than 32.
To optimize the space and to use only three 1 m pipes, we will cut each pipe as follow:

1st pipe: 31.69 cm + 29.91 cm + 22.41 cm + 15.84 cm (low C + C#/Db + F#/Gb + high C, about 2 mm left)
2nd pipe: 28.23 cm + 26.65 cm + 25.15 cm + 19.96 cm (D + D#/Eb + E + G#/Ab, almost nothing left)
3rd pipe: 23.74 cm + 21.15 cm + 18.84 cm + 17.78 cm + 16.79 cm (F + G + A +A#/Bb + B, less than 2 cm left)

As you can see, I wrote also the note corresponding to each section. Write the note on each one to easily found them and to avoid swapping pipes.

If you use an handsaw make sure it can cut the material or you will be ruining it. Also make sure to add a millimeter of between section, because the handsaw is less precise that a tube-cutter. If you have a tube-cutter, try to put it with the blade exactly where it should go and use a working glove to turn the knob: it's very tough.
If you cannot print a life-size plan or you don't have a caliber with a tolerance of 0.01 (and big enough to measure 32 cm), you can round to the first decimal digit, but make sure to round properly (for example, 31.69 will become 31.7, 29.91 will become 29.9. The general rule is: if the discarded part starts with a digit less than 5 then you left all unchanged; if it starts with a digit greater or equal than 5, then add 1 to the last digit of the remaining part).
The best way to cut the tube almost exactly (unless you use the printer) is to measure only one section and cut, then measure the next one and cut, and so on.

Every time you cut a piece of pipe, file down all burrs, inside with a rounded needle file, and outside with a flat side. File also the section to make it planar, especially if you use an handsaw.

Step 5: Cleaning (optional)

If you like the finiture of your tubes you can skip this step.

I've brought aluminium pipes (light and good-looking), but they have a paint I don't like. For another project (a tin whistle) I've started to sand them by hand with a medium grit sandpaper. How boring!!!
With a Dremel tool you can speed up the process, unless you prefer doing it by hand, but be aware that you will change the sandpaper bit many, many times.

This time, since the whistle was less than 40 cm long and the sum of lengths now is more than 295 cm, I've decided not to sand it. Maybe I will decorate my pan pipes in another way.

So, the image of this step is from my previous instrument, a six-holed pennywhistle made of aluminium, wood (juniper), and electrician tape. I'm very sorry that I haven't take any picture... Maybe I will do another tin whistle, and use the project for another Instructable.

By the way: the tin whistle sounds good, is well tuned, and it's a C-whistle. The next one I will make will be a D-whistle, the traditional Irish tuning for this instrument.

Step 6: Closing the Tubes

Take one tube. Take the thing you want to use to close the end and close the end. Then repeat for another tube, until you have no tube open.

Do you want some more directions? OK, then.

Since the process depends also on what you have choosen as cap, those can be only general directions. I choose to use light cardboard.

File slightly the end surface of the tube to create something the glue will adhere to. Then put some glue on the edge, avoiding the internal of the tube, take a square of cardboard slightly larger than the tube and glue both things together.
When the glue is dry remove the external carboard with a knife, a scalpel or a pair of scissors. With some duct tape, maybe a colored one, cover the edge to avoid any air fugue.

That's all, folks!

Well, for this step...

Step 7: Putting Everything Together

Now we have a set of 13 tubes. We need to arrange them in a practical way, so we start by taking all "white" tubes, e.g. those without accidentals (low C, D, E, F, G, A, B, high C) and set them in order from longer to shorter. Obviously open ends will go on the same plane. Start lying a strip of duct tape on the table, then add one tube at time on the tape, following the right order.
Take the yarn and wrap 6-7 times around all the tubes, then wrap 2-3 times between tubes (see images). Knot the end when you are done.

Once done the first row, we need the accidentals row. So take the C#/Db and D#/Eb tubes, and follow the same process as before. Then repeat with F#/Gb, G#/Ab and A#/Bb tubes.

Now you should have three partial pan flutes: one with 8 tubes, one with 2 tubes and one with 3 tubes.

Take the 8-tubes and the 2-tubes pan flutes and lye the latter on the first (see first image), lowering the accidentals by 1-2 cm. Try to play some notes. If you hear 2 notes when you play the C, D or E tube, then lower the 2-tubes group. If your nose touches the open end of the C, D or E tube when you try to play a C#/Db or a D#/Eb, then raise the 2-tubes group.
When you find the right place, take a piece of yarn and wrap it around the ends of the first group of five of tubes (C, C#/Db, D, D#/Eb, E). Make 2-3 turn, then knot the end and trim the exceeding yarn. Do the same on the top.

Finally repeat with the 3-tubes pan flute.

You can use some glue to the yarn to fix it in place.

The result of those operations should be similar to the one depicted in the last two images.

Step 8: Further Improvement: Adding an Higher Octave

The pan flute have a problem: each tube can produce a single note, so if you want a full 3 octave flute you have to make 36 different tubes.

But we can take advantage of physics!

OK, maybe there's the need of some other explanations. Two tubes of equal length, but one closed at one end and the other completely open, produce the same note within two adjacent octaves. For example, a closed tube that produce an A4 (440 Hz) is 18.84 cm long. The same tube opened will produce an A5 (880 Hz). We can see this fact from two formulas in the first image.

Actually, an open tube requires a correction factor that depends on frequency and inner diameter, but the difference should be barely noticeable.

So, finding a way to open and close the tubes at wish will give us an extended range: for example, if the original range is C4-C5, the final range will be C4-C6. Without even adding a single tube!

Step 9: Further Improvements: Adding Another Higher Octave

But what if we want a note higher than a C6?

Again, the answer came from physics. How we can do that? Simple: creating an hole in the tubes.

Wait, don't take your driller too soon. We need some calculation, obviously.

First, if we make a single hole, its size doesn't matter. If you want to add two or more holes for each tube, than the things became complex. So we'll drill only one hole.

We can calculate the distance of the hole center from the open end using the same formula I've shown in previous step (see first image). This time we know the frequency (if you don't then go to the second step). All we need to do is take the frequency of the pipe, double it two times and calculate the value of L. For example, the D4 has a frequency of 293.7 Hz, so the D6 has a frequency of 1174.7 Hz. So the hole center must be 7.06 cm from the open end. If you make a large hole (like 5 mm of diameter), the approximation will be better than a smaller hole.

However, reaching the central tubes with your finger can be difficult, so again finding a way to keep closed all holes and open them simultaneously is a great idea. I'm thinking about the key system of a flute (or sax, or similar systems), but I'm not so good in making such precise works...

This method only works when you can also open the ends, because the note produced is noticeably different if the end is open or closed. This is due to harmonics produced by the section behind the hole. So, the best thing (maybe it's only a dream) is a mechanism that open both ends and holes with a single lever, and only the ends with another lever. This way you can have a pan flute whose range is, for example, C4-C7, three octaves!

Step 10: Automatic Calculation!

Since it seems there is a shortage of willingness about find out the tubes length on your own (it sounds bitter, right? It's just a pinch of sarcasm…), I made this simple spreadsheet in Google Drive. You can use it "as is", or you can change the speed of sound to a value you think it's more appropriate for you. The numbers should

Before I forget it, here's the link to the awsome