Date: Fri, 28 Oct 1994 20:06:00 +48000
From: toyoji
To: didjeridu list processor

From: Matthew Newby didjeridu@varese.mills.edu
Date: Fri, 28 Oct 1994 08:28:47 -0700 (PDT)

Hello all,

Several months ago, I asked on rec.music.makers.builders, and in
the didjeridu digest, what the measurements were for making your own
didjeridu. With the leads you provided, and the help of a couple of
physics books, I worked out the formulas for calculating the length of
a pipe to produce a fundamental of a specific note. I then obtained
some 2" Schedule 40 PVC piping and was able to make some decent
sounding instruments. I borrowed a chromatic tuner to validate that
my calculations were correct, and was pleasantly surprised to find
out that they were right on. After a little bit of effort learning
the instrument, I've mastered the basics enough to feel comfortable
playing as a solo didj in our ensemble at church (raised a few
eyebrows in the process! :-)

Formulas:

Here's the measurements that I worked out for plastic pipe didjeridus.
The formula for calculating the length of a tube, given that you want
it to resonate at a specific frequency is as follows:

1. The speed of sound
V(sound) = 340 m/s at sea level
(my measurements are in inches, so we have to convert the speed
to in/sec by multiplying 340 m/s * 1/0.0254 in/m)
V(sound) = 13385.826 in/s

2. Frequency
The frequencies listed in the chart below are calculated by
this formula:
F(note - 1 semitone) = F(note)/(2^(1/12))
(that's the 12th root of 2 in the denominator)
Where F(A) = 220 Hertz

3. Effective Length vs Actual Length
The formulas for calculating the resonant frequency of a pipe
were in three catagories: both ends closed, both ends open, and
one end closed. The didjeridu is in the last category. This
means that one end is where the pressure disturbance is created,
and is sealed to the atmosphere around it. The other end is open
to the atmosphere and the pressure must drop to atmospheric
pressure very shortly after leaving the end of the tube. How far
out does the pressure node go? Well, it extends beyond the end of
the tube at a distance roughly equivalent to the interior radius
of the tube. With the pipe I was using, this is a little short of
2 inches.
L(eff) = L(actual) + DeltaL(radius of the tube)

Figure 1
Single End Closed Pipe

|<----------------Length of Pipe---------------- |
|<-------------Effective Length of Pipe------------ |
Delta Length -- | |<--

+------------------------------------------------+
| :-\
<- (lip reed blows here) : |
| :-/
+------------------------------------------------+

4. The Final Formula...
Length = (V(sound) / (2*freq)) + interior radius of the tube

The Chart:

Note | Freq (Hz) | Length (in) | Made
------+-----------+-------------+------
G | 97.999 | 69.296 | Y
G# | 103.826 | 65.463 | N
A | 110.000 | 61.845 | Y
A# | 116.541 | 58.430 | N
B | 123.471 | 55.206 | Y
C | 130.813 | 52.164 | Y
C# | 138.591 | 49.292 | N
D | 146.832 | 46.582 | Y
D# | 155.563 | 44.024 | Y
E | 164.814 | 41.609 | Y
F | 174.614 | 39.330 | Y
F# | 184.997 | 37.178 | N
G | 195.998 | 35.148 | Y
G# | 207.652 | 33.231 | N
A | 220.000 | 31.422 | Y

Equipment:

I borrowed the use of my friend's Makita power mitre saw. I find it
indispensible in cutting the PVC. It slices cleanly through the pipe,
leaving almost glass-smooth perpendicular angles on the pipe and lots
of coconut-like confetti all over the floor (FUN!). The saw plus a
tape measure and a pencil and you should be in business. My first
attempts a cutting the pipe required a hack saw. This works, in the
sense that the pipe gets cut, but leaves a very imprecise edge.
Precision is important in the construction of my set of didjs. I
also checked the pitch by observing the display of my friend's
chromatic tuner.

Construction:

1. Mouthpiece
I deviated from the traditional method of forming a mouthpiece with
wax, and chose to construct interchangeable mouthpieces from two or
three couplers, also made out of PVC. I used a coupler that dropped
from an exterior diameter of 2" to an exterior diameter of 1.5". I
then inserted another coupler into the 1.5" side that further tightened
the interior diameter to 1". I find that this arrangement is
comfortable for playing all the didjs lower than the D#. I got ahold
of two other inserts to go from 1" to 3/4" and from 1" to 1/2". These
allow me to play the higher pitched instruments with ease. The side
advantage is that they are removable and interchangeable so they are
extremly easy to clean and convenient for sharing with other players.

Figure 2
Mouthpiece

+-------+
+-+-----+-+
| | | |
+-+- - -+-+
/ +-----+ \
/ \
+- - - - - - - -+
| |
+---------------+

2. Pipe construction
I did not make multiple didj's of full length. I purchased some 2" to 2"
connectors and cut the didj's as follows: I made two solid "base units"
which produce the 220Hz A. Then I cut the other pipes so that, when
attached to the "base unit" with one of the connectors, the overall pipe
length is as displayed in the chart. Except for the 98Hz G didj, all the
other pipe pieces are smaller than the A "base unit". This makes for a
much smaller load to carry when transporting them. (Since I also play a
small conga, harmonicas, melodica, clave, shakers, etc., and soon will be
playing a djembe, portability is very important to me!)

This method of construction also lets me haul out the two "base units"
along with two extensions and another player and play didjchords!

3. Cost
I don't think I've ever made a cheaper instrument. I can pick up 10'
of the 2" PVC piping for $2.41 each. The couplers and connectors are
a little more expensive individually, but overall, my entire didj set
probably didn't set me back more than $20.

Conclusions and Questions:

I've had a blast with these things so far. PVC is so inexpensive that
even a novice like me can afford to make mistakes in construction, and
not feel guilty about throwing away my flubs. I've found that Acetone
does an admirable job of taking the pink lettering off the pipe without
damaging the plastic in the process. I haven't had the time to explore
decorations yet, so if any of you have any idea what kind of paint would
adhere to the plastic, please let me know. Also, do you have any leads
on where I can find some "appropriate" designs to paint on the tubes, as
well as some indication of what the designs mean to the Aboriginals?

I've also started constructing my didj's with some PVC traps and larger
couplers allowing me to put a right angle bend in the pipe and get the
"business end" of the didj pointed back at me. This is very nice to
have when you've got an electric guitar amp on one side, a bass amp on
the other, a drum set behind you, and a bank of monitor speakers in
front. Let's face it, the didj isn't inherently as loud as the
electrically amplified instruments. It also allows me to point my head
up instead of down while playing so that I can see our worship leader.
The larger couplers are put together to make a kind of bell about 4"
across that slightly amplifies the sound produced when playing.

While the PVC version of the Didj doesn't produce as warm or mellow of
tones as a "genuine" Austrailian Aboriginal Didjeridu, its cost, and
the ease of working with it make it an excellent choice for beginning
players. For the non-discriminating ear of those who haven't been
exposed to wooden didj's, I've found that many people recognize the
characteristic sounds my plastic didj's produce, and can even cite
movies and advertisements where they've heard the sound before.

If you are just starting out, I recommend you get ahold of some
instructional tapes, and invest in a little PVC to learn the basics.
You can go a long way with plastic before you decide you want to
spend the money for a wooden didj. I hope this article gives you
the information you need to get started with this wonderful instrument.

Happy Didj'ing!

Matt Newby