# How to calculate the size of a xylophone bar according to its pitch

I am new to StackExchange, and I have a question about a school project I'm working on involving constructing an instrument. I am building a xylophone-glockenspiel-mash kind of thing, but I wanted to save some money on materials and I need to know: If I have the right material, and I know the current length and the current pitch in Hz when struck, can I calculate the length it needs to be to reach a specific note (in this case, F4)? The current length is 3ft or 91.4cm, and currently it hits 218.2Hz when struck. I have found nothing in my searches on the internet so far, although this may be because I don't know the proper terminology to search for. Thank you for reading, and thanks in advance for helping.

• It will depend entirely on the type of material used for the bars, a certain metal alloy or type of wood. And if it is wood, it will vary with the density of the grain of the wood, its age, or its moisture content. I don't think you can easily generalize. You'll certainly end up having to mill or cut blocks and carefully cut them to tune them by hand and by ear. – user1044 Mar 31 '14 at 7:54
• There are other criteria you may want to take into account, especially harmonicity. I’ll try to find my old musical acoustics notes, but I have little to no hope. – Édouard Mar 31 '14 at 17:00
• Usually the length isn't even that important. In many instruments the lengths are chosen in an aesthetically pleasing way, but you can do a lot by tuning them, see e.g. here: youtube.com/watch?v=5PesHXkN2M8 – flawr Jun 10 '17 at 9:39

This question is more suited to physics stackexchange but anyway..

This shows you to calculate frequency of vibrating bars, rods and tubes:

http://fiziks.net/physicsmusic/Experiment%2010.htm

This is a paper on building a copper tube Xylophone:

http://users.df.uba.ar/sgil/physics_paper_doc/papers_phys/lapp.pdf

If you have any further questions check out physics SE

• fiziks.net appears to be 404 – buildsucceeded Jan 18 '18 at 23:54

Eq. 4.39 of H. Olsen, Music Physics and Engineering 1967 gives the equation for the fundamental frequency of a free bar. For this problem, where you have the same material and the same cross-sectional shape, the frequency is proportional to 1/(length squared)

I think that rote numbers will not work. Wood is not a material of homogenous resilience, and xylophone bars are hollowed out for best resonance (and as part of tuning). So you need to figure in some waste material for experiments.