The math isn't hard AT ALL!! I will walk you through it.
There are pictures through this, so you can see what I've done. You can duplicate or do your own way.
I used 2 inch diameter PVC. There are also 2 inch black pipes that work perfectly well, I just liked the white better. I'm thinking of putting a bunch of stickers all over the pipes. I suggest also using 2 inch because of the math. It's much easier with 2 inch.
Tools I use:
*chromatic tuner (piano isn't quite good enough, see if you can
borrow one, or buy one for about $30, they are good to have around if you play other instruments)
*Pipe Cutter (there are expensive so borrow one if you can, they are about $50)
*Flip Flops (these are great for playing the instrument)
*Chop Saw (for fine tuning)
*Sand Paper (takes the sharpness off the edges and the lettering off the tubing)
The very first thing you must do is get a really long 2 inch tube, 3 feet is good. And a coupling. You'll need a coupling for each tube, those keep the tubes from falling through the shelf or table you'll mount the whole thing on. You need to do all measurements with the coupling on as tight as you can get it. If you put the couplings on last, all the tuning will be off. Buy the coupling and measure with them on. They are currently .49 each. The 10 foot of tube is $5.35. The bends you see are $1.80. Those are the expensive things.
So, you have the long tubing and a coupling. You need to put the coupling on and use the tuner to see what you've got in the way of tuning. You want an A under middle C. This note vibrates at 220 and we need to have this perfect in order to do the math. Perfect A.
So, what's the math?
It's NOT hard, it's all done on the regular calculator.
Okay, after you have the perfect A, measure the tube with coupling (always with coupling, did I mention that?) and get it to the nearest 1/16th inch. We need this to be really close.
We are looking for the speed of sound. It's not the same everywhere. The speed of sound is different inside and outside your house. It's different from Tampa, FL to Denver, CO. You need the speed of sound for your area. We find it with the perfect A and the tube length of that perfect A.
Speed of Sound (SS) = (tube length - tube diameter/2) X 2 X Frequency
For this the frequency is 220 (that perfect A)
my math looked like this: SS = (29.25 - 1) X 2 X 220
SS = 28.25 X 2 X 220
SS = 12430 This means for my area, Denver CO, the speed of sound is 12430 somethings per minute.
The next math will generate tube lengths for you, but you have to find what each note frequency is. They are not linear. If you subtract one from the next, you do not get the same amount between each note, you will have to do each note's math. You can find this info on the internet, just Google 'Music Note Frequency' and you'll get lots of tables of info.
One thing I did find is that the lower notes sound much better in PVC than higher notes. I made my instrument up to an F above Middle C and will go no higher, since it sounds a bit bad in PVC above that. But you can experiment with higher if you like. Now is the time to determine how wide a range you want to do. You can get one octave per 25 feet from F down to G. The lower the note, the longer the tube has to be.
So, tube length. Since you have the speed of sound for your area, you will need to find out tube lengths for your notes.
The math is: Tube length = speed of sound/2 X Frequency + tube diameter/2
So, my math looked like this: TL = 12430/2 X 233.08 + 1 (for G#)
TL = 12430/466.16 + 1
TL = 27.664 inches (to find 1/16 inch, 664 X 16 = 10624 or 10.624 which is 11/16 rounded up)
I cut my tube just a bit longer with the cutter and used the chop saw to cut blade widths off and check it to my chromatic tuner. Be sure to clean out the inside before trying to tune, it might make a difference.
That is the math you'll need to do for each note you use in your range. Remember, do the math twice so you only have to cut once.
These are the high notes on my instrument.
Longest is 30ish inches and G# and the shortest is an F above middle C. I did make the A#, just not pictured here. Each one has a coupling so they hang well. You'll see that in another photo.
Okay, from here you will need to do math, cut, tune, chop, tune etc. After the G# above, I knew that the G natural would be too long to keep straight. From here it would be time to bend and weave the next notes. I needed to see them hang so I used a long box from long ceiling lights and cut holes in it and hung the finished tubes.
This is the musicians side of the instrument.
The couplings keep the tubes from dropping through the 2 inch holes in the cardboard.
This is the audience side.
So as the tube lengths get longer, they will have to go somewhere, like up and over. I've seen YouTube vids of instruments that look like two Giant Squids roman greco wrestling and I don't want mine to look like that. I also want to be able to port it places, like my son's Cub Scout meetings. So it can't sit on the floor at all. New notes will have to go up and over and around and around. . .
Here are two new notes, G and F# and you can see how I'm going to do this. The F# is on top. They won't hang funky like this on the finished instrument, the cardboard doesn't hold them up very well and they will have supports behind them to make them stable.
This is all I have for now, I am out of elbows so I need to hit Home Depot for more of those. And I'll have to look around for what I want to use as the top and base. I can't keep them on the chairs!
More in a few days, email me with questions at firstname.lastname@example.org for more info.
Thanks for looking!
Here is a sneek peak at the almost finished instrument: