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FEDERATION BELLS  

CONTEXT

The use of large round mouthed temple bells spread across Asia with the movement of Buddhism from Northern India around 600BC. These bells evolved into quite culture specific shapes and sounds in various parts of Asia and across the European continent. While there is evidence of shared influences in Asian bell traditions to this day, the European and Asian traditions have remained separate for almost a millennium. With the use of very recent computer modeling of vibration we can better understand the relationships between physical shapes and the sounds they emit. Our project is unique in that we seek to bridge between these ancient traditions, and in so doing use the most advanced technology and acoustic knowledge currently available to reinvent the bell. To produce bells which are uniquely Australian and reflective of a community in which Asian and European cultural traditions co-exist and merge.

The Federation Bell Installation in Birrarung Mar, Melbourne, Australia

DESIGN

The installation is a set of musical bells like a carillon, but dispersed across a small field rather than hidden in a tower. Our primary impetus is that the bells are also sculptural forms to be seen and approached. Being able to see the different shapes and hear how they sound is fundamental to the aural/visual aesthetic of the project and the underlying concept of integrating the various traditional bell forms. Naturally the bells sound very different when you are standing in the middle of the installation to when you are 100 metres away at the edge of the park.

The installation is a public musical instrument. The bells are struck by computer controlled hammers programmed to play MIDI compositions. On a daily basis (8.00 am and 5.00 pm) sequences composed for the bells by 7 Australian composers play, allowing people to wander amongst the bells for an exhilarating experience or sit nearby and enjoy their clear and gentle musicality. While bells were once amongst the loudest sounds people would normally hear, they are now often drowned out by traffic and amplified music. These bells can usually be heard within about 100 metres in the relatively quiet riverside park. The sequencing of the bells uses standard musical software and the bell sounds can be downloaded from this site, allowing composers from anywhere in the world to write works for the bells and send them as MIDI files over the internet for performance.

The installation was designed in collaboration with Swanney Draper Architects in Melbourne, Australia. The plan shown below has been adapted from the installation plan designed by Swanney Draper in collaboration with Australian Bell.

INSTALLATION PLAN
SOUND
#
TYPE
FUND. FREQ/S
RATIO
1
Harmonic
74
1
2
Harmonic
110
3/2
3
Harmonic
147
1
4
Harmonic
165
9/8
5
Harmonic
184
5/4
6
Harmonic
220
3/2
7
Harmonic
257
7/4
8
3 tone
293, 367, 489
1, 4/3, 5/3
9
2 tone
293, 469
1, 8/5
10
2 tone
293, 513
1, 7/4
11
2 tone
293, 528
1, 9/5
12
2 tone
293, 704
1, 6/5
13
2 tone
293, 733
1, 5/4
14
2 tone
293, 821
1, 7/5
15
Harmonic
293 - 1173
As above
27
Harmonic
293 - 1173
As above
39
Harmonic
293 - 1173
As above

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

THE OPENING

The Federation Bells installation was opened by Sir Gustav Nostle on the 26th January 2002. Seven Australian composers wrote 5 minute pieces for the opening. Their music can still be heard onsite at 8.00am and 5.00pm every day in the following order (and then repeated once).

  • Neil McLachlan
  • Terry McDermott
  • Anne Boyd
  • Brenton Broadstock
  • Constantine Koukias
  • Anne Norman
  • Garth Paine

 

The crowd walking around the bells at the opening

THE BELLS

The installation comprises 39 bells of up to 1.2 tonnes mass. Seven of these are polytonal bells with a fundamental pitch of D4, and the remainder are harmonic bells ranging from D2 to D6. Since this installation seeks to draw attention to relationships of sound and form, the bells have been just tuned, requiring composers address the particular qualities of this instrument, rather than apply generic musical ideas or old musical materials. Just tuning is also the most consonant tuning possible for the harmonic and polytone bell timbres. The following table sets out the bell tunings.

JUST TUNING RATIOS
OCTAVE
1
. 9\8 .
6\5
5\4
4\3
7\5
. 3\2 .
8\5
5\3
7\4
9\5
15\8
. 2 .
D2 (73-146 Hz)
H
 
 
 
 
 
H
 
 
 
 
 
 
D3 (146-293 Hz)
H
H
 
H
 
 
H
 
 
H
 
 
 
D4 (293-586 Hz)
H
H
H & P
H & P
H & P*
H & P
H
H & P
H & P*
H & P
H & P
H
 
D5 (586- 1173 Hz)
H
H
H
H
H
H
H
H
H
H
H
H
H

 

Where H means a harmonic bell pitch, P are the second pitches of two-tone polytone bells with a fundamental pitch at D4, and P* are the pitches of the three-tone polytone bell.

The actual frequency of the just ratios can be determined by multiplying the fundamental by the given ratio. Since Western music was based on similar consonant intervals many of these ratios are close to the notes of the chromatic scale. However because the ratios are not equally spaced only limited modulations of melodies and chords can be achieved in just tuning.

MUSICAL INTERVALS
JUST
. 1 .
 
9\8
6\5
5\4
4\3
7\5
3\2
8\5
5\3
7\4
9\5
15\8
2
CHROMATIC (from D)
1
min 2nd
2nd
min 3rd
maj 3rd
4th
aug 4th
5th
min 6th
maj 6th
dom 7th
dom 7th
7th
octave
DIFFERENCE
1
 
+3.9
+15.6
-13.7
-2
-17.5
+2
+13.7
-15.6
-31.2
+17.6
-11.7
0

 

where the difference (just - chromatic) is in cents, (percent of one semitone).

Note that there are two possible dom 7th intervals. Apart from the 15/8 and 9/8 intervals this tuning includes all the possible consonant intervals for ratios with denominators up to 5. There are 3 series of intervals based on the denominators 3, 4 and 5, with the series based on 4 extended by the illusion of the 9/8 and 15/8 intervals. These intervals are included due to their importance as melodic steps.

The 3 based series is included in one bell; the polytone bell with intervals, 1, 4/3 and 5/3.

The 4 based series includes the intervals 1, 9/8, 5/4, 3/2 (6/4), 7/4, and 15/8.

The 5 based series includes the intervals 1, 6/5, 7/5, 8/5 and 9/5.

Two notes with the same denominator will produce a consonant interval (simple ratio) due to the mathematics of dividing fractions (eg. 7/5 divided by 6/5 equals 7/5 times 5/6. The 5's cancel leaving the ratio 7/6).

COMPOSING MUSIC

The bell recordings have been down sampled to 11025 Hz. For people interested in writing music for the bells the following table shows the midi note allocations for each bell. The bell sound files can be downloaded individually (they are 150-200Kb each) or as a compressed folder from the following link (allbells.zip -4.4Mb). These recordings were made prior to installation of the bells and are only a guide to how the final peice will sound in the park.

In your midi sampler sequentially map each bell to a different note starting at C0 (a software sampler called VSamp can be downloaded for trial or purchase from WWW.Kagi.com -click on "order now" and search site for VSamp). The samples will then be played back without any pitch shifts from the tuning system devised for the bells. A midi sequencer can then be used to write music for the bells (eg. Vision DSP can be downloaded from WWW.opcode.com for trial or purchase). Mac users will also need to install OMS (also available as free download from WWW.opcode.com). PC users can find a virtual sampler and midi sequencer at WWW.polyhedric.com/software as well as necessary support applications. If you hear pitch doubling of the bell samples try mapping the sampler starting at C1 -there appear to be some inconsistencies in these applications!

MIDI MAP FOR BELL SAMPLES

C
C#
D
D#
E
F
F#
G
G#
A
A#
B
0
b1
b2
b3
b4
b5
b6
b7
b8
b9
b10
b11
b12
1
b13
b14
b15
b16
b17
b18
b19
b20
b21
b22
b23
b24
2
b25
b26
b27
b28
b29
b30
b31
b32
b33
b34
b35
b36
3
b37
b38
b39
 
 
 
 
 
 
 
 
 

To help your memory, the top 2 octaves of bells (b15 to b39) are all harmonic bells at intervals that map as follows.

D D# E F F# G G# A A# B C C#
Just ratio of top 2 octaves of harmonic bells
1
9/8
6/5
5/4
4/3
7/5
3/2
8/5
5/3
7/4
9/5
15/8

Bells 1 to 7 are harmonic bells with intervals that map as follows.

C C# D D# E F F#
Just ratios of lowest 2 octaves of harmonic bells
1
3/2
1
9/8
5/4
3/2
7/4
Bell number
1
2
3
4
5
6
7

Bells 8 to 14 are polytonal bells with a fundamental at D4 (equivalent to b15) and second and third tones at intervals that map as follows.

G G# A A# B C C#
Just ratios of polytone bells
4/3 & 5/3
8/5
7/4
9/5
6/5
5/4
7/5
Bell number
8
9
10
11
12
13
14