I am trying to find some kind of formula for cutting stainless steel pipes to a proper length for a xylophone. I see some examples on line but the pipes are different diameters. I did find where I can buy a note reader for fine tuning. That will be a big help. My stainless pipe is 1" od by .o65 wall thickness if that matters. I am hoping for something that wil start in the 18" range if possible.
The progression of frequencies through the chromatic scale, taken one half step at a time (e.g. C, C#, D, D#, etc.) is by the twelfth root of two. From a given starting note, taking twelve of these intervals will result in doubling (or halving) its frequency and thus give an octave. This will apply to the length of pipe – double or halve the length, change the tone one octave. Going up in pitch, each adjacent note (half step) will be approx. 5.95%* higher in pitch than its predecessor.
Therefore, measure the note of whatever length of pipe you have, then compute the length you need for the notes desired.
*The twelfth root of two.
Let’s not forget just intonation, or the other possible tuning systems. But yes, this is the simplest way to do it. I even used an app back in the late 90s that would, given the thickness and width of a pipe, tell you what length to cut it so it would produce your desired pitch.
Do you know what that app might be called today? I am not sure if I did the formula right or not, I took the number 2 and did the square root 12 times on it. I come out with a very small number. Almosy looks like I will need to cut them and shave each one for proper tune. I have zero music knowledge.
Here’s how:
- Pick the length of your shortest pipe.
- After cutting the pipe to the desired length, measure it and multiply the length times the square root of 2.
- Cut your next pipe to that length. It will be slightly longer.
- Multiply the length of your longer pipe by the square root of 2.
- Cut your third pipe to THAT length. It will be slightly longer, as was the previous pipe than the one before it.
Keep going until you have your desired number of pipes.
I’ll see if I can dig up that app, but you won’t need it unless you’re planning to play your instrument with other pitched instruments.
Here is a page with lots of tables for chime lengths. You can choose different scales, like the pentatonic scale, which is a good one for beginners, or just go with the regular 12-note scale. For your purposes, all the tuning advice for chimes is the same as for a xylophone (xylophones are generally made of wood, but whatever).
I found a calculator that will make it real easy as long as I tune the first piece properly. I have good 1" stainless so it should be consistent. Thanks for your help, that calculator made it very easy.
Technically, xylophones’ bars are always made out of wood. So I suppose this is a metallophone.
Once I started reading I became more interested in the wood. I will likely build both.
Well, since rosewood is so expensive these days, many cheaper instruments are now made of a nylon and ceramic resin called kelon. They don’t sound as good as rosewood, but they are cheap, utterly resistant to humidity (unlike wood–I’ve seen a rosewood xylophone go almost a half-step flat from being in a non-climate-controlled space in a humid climate after a few decades), and really tough. Granted, the old-growth rosewood xylophones and marimbas from the early 1900s have incredibly hard bars after a century of aging. However, those instruments are really expensive these days, and hard to come by.
We have a wood in the U.S. called osage orange, denser specimens are very similar to rosewood. It is a domestic wood but is ore like the tropical as it is high in oils and latex. I plan to use that. About the hardest wood in America and beautiful yellow new ages to a very very dark brown but ages gradually. I make archery bows from it.
Padauk is the most common wood besides rosewood for xylophones. Let us know how the Osage orange sounds, though. I’m curious.
From what i know about making archery bows both rosewood and paduak are what we call low hietrisis woods. We have acouple of domestics that are also low histerisis and have similar elastic properties as the rosewood and paduak, One is a light semi hardwood called cherry and the other is a hard heavy wood called black locust. Both grown localy. The locust is not commercially available but easy to find and cut. I would need some dry and cure time though.
You want the 12th root of two, as Gary T said, not the square root of two. The square root of two will give you very bad results.
The 12th root of two is roughly 1.05946. So if you start with a 10-inch pipe, your lengths will be:
[ul]
[li]10[/li][li]10.5946[/li][li]11.2245[/li][li]11.8919[/li][li]12.5989[/li][li]13.3480[/li][li]14.1416[/li][li]14.9824[/li][li]15.8732[/li][li]16.8170[/li][li]17.8169[/li][li]18.8762[/li][li]20[/li][/ul]
That’s one octave. This assumes, of course, that all your pipes are the same diameter.
One disadvantage of making them all the same diameter is that you have to keep doubling in length. Your next octave will end at 40 inches, then 80, then 160. You’ll end up with a xylophone that looks like a grand piano. That’s why xylophone makers will typically resort to using multiple diameters. (Even piano makers resort to different types of strings.)
Whoops. I never was great at math. LOL
Xylophones generally have the same width of bar for the whole instrument, though. Marimbas do not. Tubophones (or whatever you want to call them) are so rarely made, and so limited in range, that I don’t know of any standards of any kind re:graduated diameter for them.
I will do a video when I get done and post a link here.
The hardest wood in America would surely be the Eastern Hornbeam, otherwise known as ironwood, otherwise known as musclewood. But it’s very difficult to make anything at all out of that, as it has an unfortunate tendency to dull the tools used on it.
To clarify on that, hysteresis (note spelling) is the property of materials to not only respond to current conditions, but to “remember” previous conditions. One most often encounters the term with respect to magnetic materials: Iron, for instance, will magnetize in the presence of an external magnetic field, but will retain (some of) that magnetization even after the external field is removed. In this context, I expect that it refers to the deformation of the wood under stress: Any wood will deform somewhat when stressed, but a low hysteresis wood will resume (mostly) its original shape as soon as the stress is removed.
You might find one of these useful: Snark tuner. Clips on and reads vibes.
I work with hop hornbeam as well, most of mine comes from canada, it is very hardwood but not as hard as osage. Worst wood I have found for dulling tools is persimmom, it tends to suck up silicas into the wood. The iron wood refers to the specific gravity of woods that will sink in water. Hop hornbeam is actually about .80 when dry.
That’s fine for string instruments, but this is a simpler project. Cut it right, and it will be in tune, until the material itself fails or is damaged.