Automatic Tubular Bells

This instrucuable explains the main steps I followed, to build the first prototype of a set of Automatic Tubular Bells I built in 2006. The automatic musical instrument features are:
- 12 chimes ( 12 tubular bells )
- Each chime plays one note, so it can play a full octave ( from C to B, including sustains )
- It can play up to 4 simultaneous notes ( so it can play 4 note chime chords )
- It is controlled through PC serial port (standar RS-232)

The instrument is composed of the control unit box and three towers. Each tower contains 4 chimes and two motors, every motor strikes two of the four chimes. All the towers are connected to the control unit box through a 10 wire-bus. The control unit is the responsible of powering each motor with the precise energy and speed to hit each chime, playing the notes that the software in computer sends to it. It is internally composed of three boards. The first board contains the microcontroller, which is an Atmel ATMega16, and the RS-232 communication elements. The second one contains the motor driver circuits, and the third one, the motor position controllers.

It took me nearly half year to finish this project. Next steps are general steps, with the most relevant information of the project construction process, minor details can be viewed on the pictures.

A video of the Automatic Tubular Bells:

Project main page:
Automatic Tubular Bells home page

Step 1 Building the chimes

First step was finding a good and cheap material to build chimes. After visiting some stores and doing some tests, I found that aluminium was the material which gave me the best sound quality vs. price relationship. So I bought 6 bars of 1 meter of length each one. They had a 1,6cm outer diameter and 1,5 cm inner diameter ( 1mm thickness ) Once I had the bars I had to cut them at the proper length to get the frequency of each note. I searched on the internet and found some interesting sites which provided me lots of interesting information about how to calculate the length of each bar in order to get the frequencies I wished (see links section). Needless to say that the frecuency I was looking for was the fundamental frecuency of each note, and as happens in nearly all instruments, the bars will produce other simultaneos frecuencies appart of the fundamental. This other simultaneous frecuenices are the harmonics which are normally multiple of the fundamental frecuency. The number, duration and proportion of these harmonics is the responsible of insturment's timbre.

The relationship between the frequency of one note and the same note in the next octave is 2. So if fundamental frequency of C note is 261.6Hz , the fundamental frequency of C in the next octave will be 2*261.6=523,25Hz. As we know that Western European music divides an octave into 12 scale steps ( 12 semitones organized into 7 notes, and 5 sustained notes), we can calculate the frequency of next semitone by multiplying previous note frequency by 2 # (1/12). As we know that C frequency is 261.6Hz and the ratio between 2 conescutive semitones is 2 # (1/12) we can deduce all notes frecuencies:

NOTE: the # symbol represents the power operator. For example: "a # 2" is the same that "a^2"

Note Freq
01 C 261.6 Hz
02 Csust 261.6 * (2 # (1/12) ) = 277.18 Hz
03 D 277.18 * (2 # (1/12) ) = 293,66 Hz
04 Dsust 293,66 * (2 # (1/12) ) = 311,12 Hz
05 E 311,12 * (2 # (1/12) ) = 329.62Hz
06 F 329,62 * (2 # (1/12) ) = 349.22 Hz
07 Fsust 349.22 * (2 # (1/12) ) = 369.99 Hz
08 G 369.99 * (2 # (1/12) ) = 391.99 Hz
09 Gsust 391.99 * (2 # (1/12) ) = 415.30 Hz
10 A 415.30 * (2 # (1/12) ) = 440.00 Hz
11 Asust 440.00 * (2 # (1/12) ) = 466,16 Hz
12 B 466,16 * (2 # (1/12) ) = 493.88 Hz
13 C 493.88 * (2 # (1/12) ) = 2 * 261.6 = 523.25 Hz

Previous table is only for information purpose and it is not necessary to calculate the bars length. The most important thing is the relationship factor between frequencies: 2 for the same note in the next octave, and (2 # (1/12) for the next semitone. We will use it in the formula used to calculate the length of the bars. The initial formula which I found on Internet (see links section) is:

f1/f2 = (L2/L1) # 2

from it we can easily deduce the formula which will lets us calculate the length of each bar. As f2 is the frecuency of the next note we want to calculate and we want to know next semitone frequency: f2 = f1 * (2 # (1/12))

f1/(f1*(2#(1/12)))=(L2/L1)#2
...
L1*(1/(2#(1/24)))= L2

the formula is:

L2=L1*(2#(-1/24))

So with this formula we can deduce the length of the chime which will play next semitone, but obviously we will need the length of the chime which plays the first note. How can we calculate it? I don't know how to calculate the length of the first chime. I supose that exists a formula which relates the physical properties of the material, the size of the bar (length, outer and inner diameter) with the frequency it will play, but I don't know it. I simply found it by tuning it with the help of my ear and guitar ( you can also use a tuning fork or a PC sound card frecuencemeter to tune it ).

Comments

[Oimi]

Awww, come on! You could have at least played the Tubular Bells song (well known because of the Exorcist film).

[pepsigood]

i was thinking te same thing

[Oimi]

Yeah, hopefully that will come along some time soon.

[hammer9876]

Now I wish I had gotten into the electronics classes. Looks like a lot of fun to muck around with!

[Goldtechnic]

DUDE. could you give me the title of the backgroud music? real dope man =D

[Tolaemon]

The song is Mellotron from The Youngsters

[GorillazMiko]

Nice job! Step four looks incredibly messy/ difficult.