One of the classes I'm in this semester is all about physics in the arts. One of our final projects is to make an instrument and, as a euphonium player, I decided to make a serpent. I've made the body out of pvc piping and gotten it to about the right length, but I know that it isn't perfect. My question is, how do I find the right placements for the finger holes before making any holes? I don't have extra pvc piping to play around with, so I kinda need to get these right the first try

Have you found https:serpentwebsite.com? It mainly deals with wooden construction, but a lot of the principles apply.

Playing a serpent is extremely hard work. I built their squorm, but it does not resonate like a brass instrument and does not behave like a recorder either. It exhibits the worst of both brass and woodwind instruments. Good luck!

• This is because brass instruments, where the pitch is set by the vibrating lips of the user, produce near-square wave output, and that waveform gets destroyed by the changes in impedance at each open hole of the serpent family. (as opposed to a single tube length of a brass instrument) Commented Nov 28, 2022 at 15:00

The pitch is determined by the position of the holes and the size of the holes (as well as by all of the lower holes as well). So place the holes so that they are comfortable to finger. Then start with the lowest hole and a small drill and hope that the resulting note is too low (else the drill was too thick (or the position too high), so really start with a small drill. Then gradually enlarge the hole until to pitch is right. Then proceed with the next hole.

The holes produced this way will not be acoustically perfect (for this you’d want them to be around the diameter of the tube), which would require keys and mathematically optimal positioning.

• As this is a physics project, I think the 'mathematically optimal positioning' is precisely what @Michael Gardner is asking about! Commented Nov 27, 2022 at 10:38
• @Laurence No, I would not think so. Optimal tone holes would require keys and mechanics, both of which is not within the scope of a physics project.
– Lazy
Commented Nov 27, 2022 at 14:01
• If jointing pipe and cutting holes is 'in scope', why isn't making keys? There's always going to ne engineering involved in a practical physics project. Commented Nov 27, 2022 at 19:00
• Hole position and size are strongly related to the equations of Helmholtz resonators Commented Nov 28, 2022 at 15:01