# Homemade well tuned pan flute

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.

Hello! You said both plastic and metal pipes would work, but does the diameter of the pipes matter? I'm actually thinking of using bamboo if possible so I can make a working replica of the Spirit Flue from the Legend of Zelda: Spirit Tracks, would bamboo work the same way? Thank you!

Hi! Yes, bamboo will work just fine. You only have to make sure that the diameter is constant for all the length of each pipe, or at least that it changes just a little. The inner diameter affects only the force you need to apply to play the flute, but the pitch is almost unaffected.

3 months ago
alright, thank you so much
Thanks for the information on tuning. I was able to apply that when I made my pan flute paldrun.
Drako84 (author)  deephidden3 months ago

Wow! It looks awesome! I'm glad to have helped.

ayame.che5 months ago

Would it be okay if divide the pipe pieces in half, to make the pan pipe smaller?

Drako84 (author)  ayame.che5 months ago

If you cut the pieces in half you will double the frequency, and so you'll rise the pitch by 1 octave. If you are okay with that, you can cut those pieces, otherwise I'm afraid there's not much you can do to reduce the size

alita.toh.95 months ago

Did you use the formula L=nv/4f?I think that you took the speed of sound to be 331.65 m/s right? Perhaps you didn't know about the end correction formula, which states that

L=nv/4f -0.4d.Where d is the diameter of the tube.Please check your calculations and see if it matches mine.My excel spreadsheet is attached.

5 months ago

Correction:

For pipes with significant flange: L=nv/4f -0.4d

For unflanged pipe: L=nv/4f -0.3d

Drako84 (author)  alita.toh.95 months ago

Thanks for this remark, I should have mentioned before!

Anyway, I've noticed that the difference between the values ranges from 2% (C4) to 10% (B5), using you spreadsheet. Also, if you use a smaller internal diameter, the difference decreases accordingly (obvious from the formula itself).

If you plan to make an extremely accurate pan-flute you should take care of this difference, for sure, but for me this is good enough.

But again, thank for pointing out!

kaleigh.jackson.36 months ago
Does the sound differ if you use metal or plastic pipe?
Drako84 (author)  kaleigh.jackson.36 months ago

I think the sound will be different, because of the different properties of the material. Some times ago I've bought a cheap bamboo pan flute and the sound differ, so I believe it will be different also with plastic.

demiperson1 year ago

Drako84 (author)  demiperson1 year ago

You can obtain the data you need from the formulas in step 1. However, I made those calculation for you.

I assume you need a full chromatic pan flute, so the notes will be F4, F#4/Gb4, G4, G#4/Ab4, A4, A#4/Bb4, B4, C5, C#5/Db5, D5, D#5/Eb5, E5, F5.

The frequencies you need are 349.2, 370.0, 392.0, 415.3, 440.0, 466.2, 493.9, 523.3, 554.4, 587.3, 622.3, 659.3, 698.5 hertz.

With a speed of sound set at 342.2 m/s, the lengths you need to cut are 24.5, 23.1, 21.8, 20.6, 19.4, 18.4, 17.3, 16.3, 15.4, 14.6, 13.7, 13.0, 12.2 cm, or 9+21/32, 9+3/32, 8+19/32, 8+1/8, 7+21/32, 7+7/32, 6+13/16, 6+7/16, 6+1/16, 5+3/4, 5+13/32, 5+3/32, 4+13/16 inches.

Hope this helps!

10 months ago

Hi Drako84,

I want to made a 22 tubes pan flute in G1-G4. Could you help me please? I need the tube length for that.

Thanks in advance and best regards

Florian

Drako84 (author)  f_mal10 months ago

Hi there!

First of all, just to be sure, you only need the "white notes" right? Those without any alterations? If so, you're right, you'll need 22 tubes, but if you need a chromatic scale (all notes inbetween), you'll neet 36 of them. That's a lot of notes!

I assume you made your math, so I'll take those notes: G1, A1, B1, C2, D2, E2, F2, G2, A2, B2, C3, D3, E3, F3, G3, A3, B3, C4, D4, E4, F4, G4. This time I'm going to skip then frequencies (you don't really need them), so here are the lenghts, in the same order of the notes:

174,59 - 155,55 - 138,58 - 130,80 - 116,53 - 103,81 - 97,99 - 87,30 - 77,77 - 69,29 - 65,40 - 58,26 - 51,91 - 48,99 - 43,65 - 38,89 - 34,64 - 32,70 - 29,13 - 25,95 - 24,50 - 21,82 cm

or, if you prefer:

68,74 - 61,24 - 54,56 - 51,50 - 45,88 - 40,87 - 38,58 - 34,37 - 30,62 - 27,28 - 25,75 - 22,94 - 20,44 - 19,29 - 17,18 - 15,31 - 13,64 - 12,87 - 11,47 - 10,22 - 9,64 - 8,59 inches.

I must say that’s quite a big pan flute!

10 months ago

hi Drako84,

thanks for your help. This is a realy very big pan flute :). but my G1-G4 is the german notation. I need a pan flute like this here:

http://www.beautifulflute.com/Panflute_Gallery.php

the first pipe has maximum 26cm length

Regards Florian

Drako84 (author)  f_mal10 months ago

As far as I know, the German and English notations are different only for Bb and B, that in German notation are B and H. Beside this, I think that the numbers associated with the octaves are the same, so my calculations should be right. Can you provide the frequency of the lowest note in your range?

Another thing: I know for sure that some producer labels their instruments with a note and a number, meaning that the instrument is in that note and it's the nth in the series. For example, Fabio Menaglio, an ocarina maker based in Italy, sells ocarinas labeled Do1, Sol2, Do3, Sol4 and Do5 (Do = C, Sol = G), but the Do1 is the highest of them all, while the Do5 is the lowest one.

Last but not least, I added a step with a link to a Google Spreadsheet that contains the lenghts for all notes, from C1 to C8. Feel free to check this out, if it can help.

10 months ago

Thanks for your help. The calculator is very useful.

Best regards Florian

RyanKranz1 year ago

Hey buddy, your calculations are all a little off, by like a cm. Did you take the speed of sound as something funny? Press a wrong key?

34029 = speed of sound in cm/s

34029/(4)(261.6) = 32.52cm, not 31.69cm.

Drako84 (author)  RyanKranz1 year ago
As I said in a previous reply, the speed of sound can vary greatly based on air pressure, air temperature and even air composition. Basically, any source you look into for the "real" value reports a different number: for instance, Google says 34029 cm/s (your value), but Wolfram|Alpha says 34320 cm/s, Wikipedia says 34300 cm/s, and so on.

I'm sure there is a way to cope with those differences, but remember that just by playing in a room with an air conditioner can change the pitch compared the outside because of the lower temperature and humidity.
chikengirl1 year ago

I am going to try making one of these. Hopefully it works well. :)

RICARDOMILITAO1 year ago

Thank you, you helped a lot, friend! But since taking the opportunity, would you please make a tutorial of these teaching to make a tin whistle?

Drako84 (author)  RICARDOMILITAO1 year ago

I know it's taking a lot of time. A tin whistle is surely harder to make than a pan flute, because you must have all the holes with the right size and in the right position. For not to speak of the mouthpiece and the embrochure hole!

However, reading your kind comments make me want to try again as soon as I can. I don't have much time, now that I'm not a student anymore, so please be patient.

RICARDOMILITAO1 year ago

Thank you, you helped a lot, friend! But since taking the opportunity, would you please make a tutorial of these teaching to make a tin whistle?

RICARDOMILITAO1 year ago

Very good tutorial. But how do I produce them in those different diameters you used here? There is some calculation that allows to know which length tubes of other diameters?

Drako84 (author)  RICARDOMILITAO1 year ago

Thank you!

The pitch of the note doesn't depend on the diameter, only on the tube length. However, tubes with small diameters can be hard to manage (a small difference in blow force can cause a big difference in tone), and tubes with large diameters can require a lot of blow.

Think of a bottle and a glass: with the bottle is easy to produce a sound by blowing on the opening, but with a glass it's almost impossible.

The diameter counts only when you try to make some holes for fingering, but this will make things very complicated...

Hope this helps!

Jonas.B3 years ago
Superb instructable! :)
I have one question though:

On wikipedia the speed of sound in room temperature is said to be 34320 cm/s, but when i check your calculations, it seems the used number was 33150 cm/s. Which one of us calculated wrong?
Drako84 (author)  Jonas.B3 years ago
Thank you!

I think none of us calculated wrong, simply because the speed of sound depends not only on temperature, but also on a lot of other things, for example on altitude or density of the air. Since the pan flute cannot be tuned once made, you must adjust the blow speed and force to raise or lower the frequency.
Very good and educating instructable!! Thanks!!!

One advise: Maybe it would be "safer" to cut the tubes a little bit longer (a few mm). Then, using the needle file and a good tuner you can tune each tube at the exact pitch. ;-)
ComplacentBard4 years ago
I think you meant physicist, not physician.
Daftehh4 years ago
One more thing added to my to-do list
also, you could use epoxy to bind the tubes together
arami4 years ago
Great place to start for making wind instruments! I would like to point out that physicists (not physicians) are the ones that acoustics... But other than that, great basic explanation on how pan flutes work.

Thanks :)
trubshac5 years ago
Brilliant instructables.  I like the theory as well as the practical explanation.  We've just made one out of the plastic coated mild steel handles of 3 floor brushes that we got from the poundshop!
Our first attempt just used insulating tape to close one end of the tubes - this didn't work at all.  We then tried stiff cardboard held in place with insulating tape which worked perfectly.

Neat Instructable, but a video of you playing them would really add to it.
I only found out recently that the way they're played in the Andes is for two players to blow alternate notes on the pipes, so each player is only playing half the tune with the notes bouncing back and forth between them.
Thank you! Well, I haven't posted a video mainly for 2 reasons: videos my camera can take have a very poor quality; and I'm not so good in playing...
After all, Stradivari was an excellent violin maker, but a poor violin player.

The way Andes performers play their instrument is very interesting, I'd like to see them in action.
5 years ago
Good point about Stradivarius.  I've never seen a video of him playing anywhere ;¬)
I can't find a video of the alternate blowing either.  We get a few Andean bands busking in the High Street during the year and one of them explained and demonstrated the technique once.  Since then I've seen others do it.
Doctor What5 years ago
Lovely!  My family used to participate in Renaissance Faires (well, they still do, but I don't!).  Using instruments was incorporated heavily into our character designs.

My stepmom played the fiddle and a mouth harp.

My dad played the Tabor Drum, the fife, the flute, and a dozen other random instruments.

I also played the flute.  (I liked juggling better than musical instruments)

We performed with an Irish Stepdancing group.  It was quite fun!

This would be great for those who can't find a pan flute.  (I'm also excited for your tin whistle!)

Very nice job!
Drako84 (author)  Doctor What5 years ago
Great! Renaissance Faires! I love them!
Sadly, I've seen only one... and desolate...

However, I hope I will not make you wait too long for the tin whistle. Stay tuned!