Some of my home-made pitched cylinders created with double-walled drain pipe,
shipping tubes, PVC pipe, fluorescent light protectors, hollow table legs, & electrical conduit
|Illustration depicting Pythagoras demon-|
strating harmonics from Franchino Gafori,
Theorica Musice (Milan, 1492)
I always cut my material slightly long and then trim it to fine tune, using reference pitches or an electronic tuner (available as a phone app). Be warned that if you cut a cylinder too short, it will be impossible to correct, and you will have to simply cut the piece shorter for a different, higher pitch.
Depending on the material you're using, you will need an X-acto knife, small saw, or paring/pocket knife to cut and trim. I used a paring knife to fine tune my boom pipes (large white example above) because the plastic is surprisingly soft. Warning: PVC dust is harmful to your health, so take your measurements to the hardware store and have them do most of the cutting; then wear a mask if you need to fine tune.
If you have a limited amount/length of material, simply create a limited tone set such as a pentatonic scale or only the tonic and dominant of a key for use as a bordun.
OK, here's how to figure out the lengths you need:
(1) Find or create your fundamental note (prime, tonic, 'do') by comparing a long but musical-sounding length of your material to a reference pitch or use an electronic tuner (or phone app). Determine what note it is. It will likely be flat or sharp and need trimming. (Remember: longer = lower; shorter = higher.) The note you identify can be the fundamental pitch of your set, or you can trim the cylinder to be the tonic of the key you want. (Hint: middle C is often about 25" long, and the C below is usually around 51".) Note: as with Boomwhackers, if you cap one end, the pitch will drop one octave.
(2) Once your fundamental note is in tune, measure its length carefully (centimeters is best). Divide this measurement by the decimals below to determine the lengths of additional notes.
Scale Interval Ratio Divide by Tempered
do Prime 1:1 1.0 (1, 1)
re Major second 8:9 1.125 (1.22, 1.125)
mi Major third 4:5 1.266 (1.260, 1.250)
fa Perfect fourth 3:4 1.333 (1.335, 1.333)
so Perfect fifth 2:3 1.5 (1.498, 1.5)
la Major sixth 3:5 1.688 (1.682, 1.667)
ti Major seventh 8:15 1.898 (1.888, 1.875)
do' Octave 2:1 2.0 (2, 2)
BTW, I'll be posting instructions for making a variety of instruments this summer (while I and other teachers have a little more time to explore).