Cutting the chimes to length

The mimphonium uses a different length of copper pipe for each note it can play. These cut and drilled pipes are what we call chimes. If you are making your own mimphonium, then cutting the chines to length is one of the earlier steps, If you don’t know how long the chimes are, then you don’t know how big the mimphonium will be, you do’t know how tall the upper chime supports need to be, and you don’t know where to drill the holes in the back board for the lower chime supports.

You probably already know that for a given chime material, shorter chimes produce higher notes than longer chimes. You can see that in action in a xylophone. How do you know exactly how long to cut the pipe?

David Lapp gives us this equation:

\(f_{n} = \frac{\pi v K}{{8L^{2}}}{m^{2}}\)

This equation has a number of obscure constants, some of which are in turn made up from other obscure constants, many of which I couldn’t find for copper plumbing pipe from my local DIY shop. However, we can simplify this equation to:

\(f=\frac{C_m}{L^2}\)

where f is the frequency of oscillation, L is the length of the pipe, and Cis the immodestly named mimphonium constant for the material you are using. Where do you get the mimphonium constant for your copper pipe? You simply cut a random length piece of pipe, measure it’s length, hit it, measure the frequency it rings at, and plug the frequency and length into this equation:

\(C_m = f L^2\)

That is if you measure the frequency at which one piece of pipe rings at, you can calculate all the others from that.

I must admit at this point, that this method has its limitations. If your chimes are relatively long, as they would be if you were making the Big Ben mini mimphonium, this method works very well. However, if you were making a larger instrument, then you will find little errors creeping in that make the tuning quite inaccurate as the notes get shorter. My guess as to the main source of error is that the cutting process does not create perfect square ends. The solution to this is to cut the long chimes first, and keep re-measuring and recalculating as you cut the shorter ones.

Here are a few practical tips:

  • Use a dedicated pipe cutter. This is so much easier to use than a hacksaw. It is very easy to get a neat perpendicular cut. It does not create messy little metal filings.
  • If you cut a piece wrong, you can recycle it for one of the shorter chimes.
  • Start with the long chimes and work your way up to the short ones. That way you stand a better chance of hiding your mistakes. You will also get practice using the pipe cutter. At the long end, you can tolerate a millimetre or so of error. At the short end, you really need to be within half a millimetre or the chime will be noticeably off frequency.
  • Let the pipe reach room temperature before using it. If you cut everything in a cold shed, and bring it into a warm house, it won’t sound as in tune as it could have. Similarly, if you ignore my advice about the pipe cutter, and use a saw or sand paper, then let the pipe cool down. It can get quite hot.
  • When measuring the oscillation frequency, hold the pipe vertically about ¼ of the way down. The right place to hold it is actually 0.224 of the way down, but within the tolerance of the width of your your finger and thumb, 0.25 is near enough.
  • Hit the pipe using the plastic handle of a screwdriver.
  • Measure the frequency of the note using an app on your phone. The one I use is called Pano Tuner. It has a nice clear interface, and the adverts that allow them to keep it free are not too intrusive.
  • If you are making a large mimphonium, it is handy write on or to stick little labels onto the chimes.

 

Here is a spreadsheet with all of the equations already typed in.