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.

<p>I used to play pan flutes. The semitones could be made by bending the panpipes for about 60 degrees - this makes note sound a semitone lower than normal, so you don't need tube for each tone - 22 tubes is enough :)</p><p>I wonder what physics stand by this bending technique. Anybody could help?</p>
<p>So if you look at the general theory, L = v/4f from standard physical principles. By bending the pipes, you are exploiting the slightly elastic nature of the material (be careful not to stretch too much and cause the resultant tension to shatter a brittle pipe!)</p><p>When we do this, the elastic properties cause a slight elongation. As you'll notice the frequency is inversely proportional to the length of the pipe. By making it fractionally longer, you slightly decrease the frequency :) </p><p>You should also notice that this is a fractional dependence w.r.t semitones. So if you were to bend a longer pipe the same amount, the change in pitch would be greater as the frequency change would be the same BUT the fractional change would be larger. </p><p>Please check this carefully and don't wear your pipes since although this is a cool representation of wave physics, I don't want you ruining your panflute :)</p>
<p>I'm not sure if I described exactly what I meant. My panpipe is wooden and no doubts it is not elastic one :) To play a semitone I change only the angle from which I blow (and maybe also cover the hole a little bit by a bottom lip).</p><p>If you are good player you can go even three tones lower than the basic tone of the pipe. So I would had to bend it very much to do it.</p><p>I've noticed that if you have a round bulb with a hole it is possible to play an octave range by just blowing from different angles and making the hole smaller by covering it with your bottom lip.</p>
<p>Please its very important that I have your name, or at least your sources so i can get their name</p>
Honestly, I don't understand why you need to know my name...<br>However, I suppose you're asking for the sources of information about the data and the formulas used. As I clearly state, my main sources are Wikipedia, Google and an old textbook of physics that I used when I was in high school (since then I've sold the textbook, and I don't remember the title; I'm italian, and so it was the book).<br><br>There is something I'm missing? Because for as long as I can think about, I don't seem to find a reason to give you my name.
<p>If you don't mind me asking, may I please have your full name so that i can use this information in an essay I'm writing?</p>
<p>Hi, I seem to be having a problem with calculating the length. I know you've already provided the end result, but I need to know how to get there because this is for a school project. Your formula is length (which unit?) = speed of sound (in m/s?)/ 4* frequency (in Hz?)</p><p>I keep getting very small results, like .15 for C4, and I think i'm missing something but I can't tell what. Please help me! How can I find the length in centimetres and not get this: length = 345 (my local speed of sound)/ 4*440 = .196</p>
<p>Hi again, i've re read some of the comments below and apparently the speed of sound needs to be in centimetres per second! I see in hind sight how I should have guessed it but I'd appreciate it if next time you would mark you units properly so I and others like me don't get so lost again. </p>
<p>Actually, the speed of sound should be in m/s, and the resulting length is in meters, so 0.15 m = 15 cm, as expected.</p><p>The formula works for any kind of units system, as long as you keep them consistent for all your calculation; replacing each variable with its unit you can easily see that fact:</p><p>1. [meters] = [meters/second]/[1/second]</p><p>2. [centimeters] = [centimeters/second]/[1/second]</p><p>3. [yards] = [yards/second]/[1/second]</p><p>4. [inches] = [inches/second]/[1/second]</p><p>and so on...</p>
<p>I see! Thank you for your reply, this will her very useful information!</p>
<p>Hello I wanted to ask you if the diameter of the pipes would change the frequencies of the note and if so I wanted to ask how I would be able make the length of the pipes using the formula. Thx in advance.</p>
<p>Hi! The diameter of the pipes will not interfere with the frequency: as you can see, the frequency f is related only to the speed of sound v and the pipe length l.</p><p>If you know the frequencies you need you can just plug those values into the formula along with the speed of sound, and you'll have all the length you need.</p><p>You can also use the spreadsheet I've prepared that will make al calculation for you. You can reach it from the last step.</p><p>Regards!</p>
<p>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!</p>
<p>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.</p>
alright, thank you so much
Thanks for the information on tuning. I was able to apply that when I made my pan flute paldrun.
<p>Wow! It looks awesome! I'm glad to have helped.</p>
<p>Would it be okay if divide the pipe pieces in half, to make the pan pipe smaller? </p>
<p>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</p>
<p>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</p><p>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.</p>
<p>Correction:</p><p>For pipes with significant flange: L=nv/4f -0.4d</p><p>For unflanged pipe: L=nv/4f -0.3d</p>
<p>Thanks for this remark, I should have mentioned before!</p><p>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).</p><p>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.</p><p>But again, thank for pointing out!</p>
Does the sound differ if you use metal or plastic pipe?
<p>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.</p>
<p>For the panflute I need a F4 to F5 instrument please help.</p>
<p>You can obtain the data you need from the formulas in step 1. However, I made those calculation for you.</p><p>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.</p><p>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.</p><p>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.</p><p>Hope this helps!</p>
<p>Hi <a href="https://www.instructables.com/member/Drako84" rel="nofollow">Drako84</a>,</p><p>I want to made a 22 tubes pan flute in G1-G4. Could you help me please? I need the tube length for that.</p><p>Thanks in advance and best regards</p><p>Florian</p>
<p>Hi there!</p><p>First of all, just to be sure, you only need the &quot;white notes&quot; 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!</p><p>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:</p><p>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</p><p>or, if you prefer:</p><p>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.</p><p>I must say that&rsquo;s quite a big pan flute!</p>
<p>hi Drako84,</p><p>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:</p><p><a href="http://www.beautifulflute.com/Panflute_Gallery.php" rel="nofollow">http://www.beautifulflute.com/Panflute_Gallery.php</a></p><p>the first pipe has maximum 26cm length</p><p>Could you help me please?</p><p>Thanks in advance</p><p>Regards Florian</p>
<p>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?</p><p>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.</p><p>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.</p>
<p>Thanks for your help. The calculator is very useful. </p><p>Best regards Florian</p>
<p>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? </p><p>34029 = speed of sound in cm/s</p><p>34029/(4)(261.6) = 32.52cm, not 31.69cm.</p>
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 &quot;real&quot; 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.<br><br>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.
<p>I am going to try making one of these. Hopefully it works well. :) </p>
<p>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?</p>
<p>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!</p><p>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.</p>
<p>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?</p>
<p>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?</p>
<p>Thank you!</p><p>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.</p><p>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.</p><p>The diameter counts only when you try to make some holes for fingering, but this will make things very complicated...</p><p>Hope this helps!</p>
Superb instructable! :) <br>I have one question though: <br> <br>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?
Thank you! <br> <br>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!!!<br><br>One advise: Maybe it would be &quot;safer&quot; 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. ;-)
I think you meant physicist, not physician.
One more thing added to my to-do list<br>also, you could use epoxy to bind the tubes together
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. <br><br>Thanks :)
Brilliant instructables.&nbsp; I like the theory as well as the practical explanation.&nbsp; We've just made one out of the plastic coated mild steel handles of 3 floor brushes that we got from the poundshop!<br /> Our first attempt just used insulating tape to close one end of the tubes - this didn't work at all.&nbsp; We then tried stiff cardboard held in place with insulating tape which worked perfectly.<br /> <br />
Neat Instructable, but a video of you playing them would really add to it.<br /> 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.<br />
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...<br /> After all, Stradivari was an excellent violin maker, but a poor violin player.<br /> <br /> The way Andes performers play their instrument is very interesting, I'd like to see them in action.<br />
Good point about Stradivarius.&nbsp; I've never seen a video of him playing anywhere ;&not;)<br /> I can't find a video of the alternate blowing either.&nbsp; We get a few Andean bands busking in the High Street during the year and one of them explained and demonstrated the technique once.&nbsp; Since then I've seen others do it.<br />
&nbsp;Lovely! &nbsp;My family used to participate in Renaissance Faires (well, they still do, but I don't!). &nbsp;Using instruments was&nbsp;incorporated&nbsp;heavily into our character designs.<br /> <br /> My stepmom played the fiddle and a mouth harp.<br /> <br /> My dad played the Tabor Drum, the fife, the flute, and a dozen other random instruments.<br /> <br /> I also played the flute. &nbsp;(I liked juggling better than musical instruments)<br /> <br /> We performed with an Irish Stepdancing group. &nbsp;It was quite fun!<br /> <br /> This would be great for those who can't find a pan flute. &nbsp;(I'm also excited for your tin whistle!)<br /> <br /> Very nice job!<br />

About This Instructable




More by Drako84:Folding spoon-and-fork Simple cardboard folder Homemade well tuned pan flute 
Add instructable to: