As an artist deeply embroiled in my practice, two singular moments of inventive success stand out from the mass of small inventive iterations that constitute my work. The first of these delightful moments was on returning from observing bell casting in Japan in 1998 and seeing the world’s first harmonic bell, as a virtual design, that Professor Josef Tomas had optimised in his FEA software ‘ReShape’ based on the polystyrene coffee cup I had proposed as the starting point for his work. The other magical moment took place on a hot and sweaty day tuning a bell in my workshop in 2014 when, after months of grinding fragments of bronze test bells by hand to shift partial frequency ratios into their desired order, on striking the bell it sounded, for the first time ever, a ‘difference-tone’, that beautiful, elusive psychoacoustic pitch an octave below any actual frequency of the bell. This was the difference-tone that the ‘Reshape’ virtual bell model had predicted, but had failed to produce when the design was cast into bronze. I immediately sent the bell’s sound file to Danny Hillis and Zander Rose at the Longnow Foundation in great excitement and joy, knowing that this discovery would be as thrilling to them as it was for me.
I am now able to tell the story of the invention of the difference-tone bell and the casting and tuning of the ten difference-tone bells for the 10,000 Year Clock project currently underway in West Texas.
The background for this work was the collaborative work of myself and Neil McLachlan, along with many other people, to create the Federation Bells Projects between 1998 and 2002. We collaborated with Professor Josef Tomas and his ‘ReShape’ Finite Elements Analysis (FEA) software to invent the Harmonic bell design and other new bell designs in 1999-2001. The harmonic bell design, in its various iterations, was the central bell design used for the Federation Bells Carillon in Melbourne. This carillon celebrates the centenary of the Australian Federation in 2001 (for more, see www.federationbells.com.au). Australian Bell was granted a US Patent on this bell design/sound. The three Federation bell projects Australian Bell was commissioned to undertake were the Federation Bells Carillon in Birrarung Marr Park, Melbourne, the 2001 harmonic handbells in 60 two-octave sets of 24 bells, and a two-octave set of larger harmonic bells for the Melbourne Symphony Orchestra.
In 1999 Danny Hillis asked Brian Eno for help with the bells for the clock and Brian suggested that the Longnow Foundation’s Clock design use 10 bells ringing in a different order each day, following the ‘change-ringing’ tradition. Possible numbers of different ring patterns for 10 bells approximate the number of days in a 10,000-year period.
‘ .
Brian Eno was familiar with Australian Bell’s work on bell design and introduced Danny Hillis to Australian Bell’s director, Dr Anton Hasell. In 2013, Danny Hillis began a discussion with me on the possibility of inventing a new bell design that would generate a ‘difference-tone’ when rung. Organ makers have long used the psychoacoustic principals of difference-tones in the design of their organs. Whereas the pitch C65 Hertz requires an organ pipe 64 feet in length, that very low note can also be achieved by sounding a 32-foot C130 Hertz pipe simultaneously with its perfect fifth G pipe. The difference-tone generated by the two pipes suggest to the listener’s ear that they hear the pitch C65 Hertz, when in fact, this is a pitch that is an octave below the 32-foot pipe’s sound compass. Danny Hillis had asked traditional bell founders if such a bell was possible and they thought not.
The attraction of a difference-tone bell design was that the bell would be half the scale of a traditional bell of the same pitch, (just as the 32-foot organ pipe is half the length of the 64-foot organ pipe) allowing Brian Eno’s Mixolydian musical scale for the ten bells, with the lowest pitch at C 65 Hertz, to fit inside the clock structure, which is itself fitted inside a vertical tunnel bored into the mountain.
I agreed to undertake a research project to find out if such a bell design was possible. In collaboration with Ryan Adams using ‘ReShape’ software, and starting with a conical harmonic bell design as the initial virtual profile (the choice of the virtual model is critical to successful FEA operations, as shown with the invention of the harmonic bell), and the software optimised a bell shape that predicted a difference-tone bell design.
This virtual shape was 3D printed as a foundry pattern and used to cast a sample bell in silicon bronze. Disappointingly, the cast bell did not sound a difference-tone. I sent this bell casting and a similarly scaled conical harmonic bell cast in 316 stainless-steel to Danny Hillis in San Francisco and visited Danny, Alexander Rose and Stewart Brand at their San Rafael workshop in 2015 to discuss which of the two bell designs we should develop for the project. Danny Hillis asked me to continue to try to get the bronze bell design to sound a difference-tone. That is, to find the bell profile that did sound a given pitch exactly one octave below the bell’s lowest actual frequency. Over a 3-month tuning period, through a process of carefully removing metal from several test bells (to their point of ‘tuning’ destruction) and mapping the subtle shifts in partial frequency ratios with each slight profile change, I was able to make a tuning map of the bell design. I used this map to tune a third casting and put its partial frequencies into the exact ratio needed to generate a difference-tone, psychoacoustic pitch. This ‘eureka’ moment was achieved in the Australian summer of 2015.
We were all delighted, of course, and a bit surprised at how effective the difference-tone bell was at creating the aural illusion of a pitch an octave below the bell’s actual frequency. This did allow a bell to sound its pitch at typically half the scale of other bell designs sounding the same pitch. This invention would not have been possible without ‘ReShape’ Finite Element Analysis software generating a bell profile within the ball-park needed to find the exact bell profile.
After inventing the bell, Australian Bell was then commissioned to design, cast and tune Brian Eno’s musical set of the ten bells required for the Longnow Foundation’s Clock project. These bells were produced in both Australian Bell’s’ Mia Mia bell foundry and in collaboration with Billmans Foundry in Castlemaine between 2015 and 2016. The bells, responding to the resonant frequency of the space they inhabit, range from G 392Hertz (difference-tone G 196Hz) with a mass of 21Kilograms to C 130.8 Hertz (difference-tone C 65.4Hertz) with a mass of 566 Kilograms. As the bells were cast and tuned they were crated and transported from Australia to San Rafael USA, with the first bell shipped mid 2015 and the largest bell shipped late 2016.
The Clock is still under construction and testing and the bells were installed in the Clock in 2019 as part of its 55,000 lb chime generator. The chime generator will ring the ten bells in a different sequence each time they chime over the next 10,000 years. Australian Bell remains the owner of the intellectual property the difference-tone bell design has generated.
Being invited to work with legendary inventors and thinkers on such an exquisite and sublime project has been an extraordinary privilege for me. The Clock is visionary in both its modelling of long-term thinking, fundamental for a sustainable civilization on our planet, and the technological ambition and inspirational design aesthetics we might expect from considerate ancestors. Projects of this brilliance are exceedingly rare and I truly appreciate, and treasure the opportunity to make a small contribution offered to me.
