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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.

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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

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

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

This is a paper on building a copper tube Xylophone:

If you have any further questions check out physics SE

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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)

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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.

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