The Longnow Bell 3D printed in metal

Lab 22 CSIRO is focussed on 3D printing directly in metal and the focus of my specific research in the Synapse program has been to discover the tuning effects of a known cast bell sound when the bell design has been 3D printed directly in metal.


Types of direct metal printing include using metal powders (titanium, stainless-steel and bronze amongst the most usual materials) placed in electron beam or laser heat sources to fuse the metal particles layer by layer. Alternative methods include accelerating particles to speeds high enough that they fuse with metallic layers already printed and the use of robotic arms and temperature-controlled environments in which electric arc (mig) welding continuously builds layers of fused metal.


Dr Daniel East, Gary Savage and I wanted to see the results of printing process offered in the US by Exone Company using a system where stainless-steel powder is printed in layers with a resin to form a resin bound stainless-steel form which is placed in a kiln and has bronze powder added. At temperatures above 1011 Celsius the resin is burnt out and replaced with liquid bronze.  We ordered one Longnow Clock bell design in the materials 316 stainless-steel and a tin bronze of Cu 90% Sn 10%, and another in the materials 420 stainless-steel and the tin bronze, with a 60 % stainless to 40% bronze ratio.


I include pictures of both bells and note that both bells hold the partial frequency array of cast bronze bells, with both bells generating a difference tone, that is a pitch with a psychoacoustic effect of sounding one octave below the lowest actual partial frequency, its fundamental, sounded in the bell. I believe these to be the first ever 3D direct metal printed bells, and so it seems right that their design be of the newly invented Longnow Difference-tone Bell. Danny Hillis of the Longnow Foundation gave his blessing to this research using the Longnow bell design.


More recently, Lab 22 has printed a 95mm mouth diameter difference tone bell design in titanium using the Electron Beam Printer and this bell also retains the same partial frequency array as a cast bronze bell at the same scale. There are plans to print a larger titanium bell at Lab 22, and some of the small Mathematician Instrument Sculptures I designed whilst in residency at La 22.


Although I have now completed my wonderful Synapse Residency at CSIRO I feel sure that a research relationship with them will endure. I cannot thank ANAT and CSIRO enough and of course everyone at Lab 22 Clayton for allowing me the amazing experience of working in that research environment. The residency has been inspirational for me and has enlarged my vision of what is possible in orders of magnitude I can but hope to demonstrate with my ongoing research into the history, tradition, sound and technology of bell (and sound) design in public-space.

Lab22 titanium printLab22 titanium bell printExone printed bells Exone printed bronze-stainless bellsclose up of printed bell surfaceGary Savage examining bell print

Practical and useful mathematical instruments

Working at Lab 22 CSIRO Material Technology has introduced me to scientists and mathematicians working in fine precision and exact language. It has inspired a desire in me to make a number of instruments of ‘mathematical analysis’ as helpful (!) aids in their calculations. I am imagining hand-held titanium, 3d printed, calculation instruments, as kinds of Swiss Army penknives, hung on their belts, ready for intellectual application.

I have been looking at the founders of the craft of numbers, the ancient Greek philosophers, and thinking about the sort of mathematical tooling they might have fashioned had they access to the high-powered, digital, rapid-prototyping equipment available at Lab 22.

For example, Archimedes of Syracuse developed ideas about infinitesimal forms that predate the development of calculus by Leibniz and Newton. All three considered the convergence of infinite sequences that underwriting ever-finer measurement of change. How helpful would it have been for Archimedes to have fashioned ‘Archimedes Infinity tool’ so that may have fallen into the hands of Newton and Leibniz at the moment of need?  Here is that instrument.


Other examples of the Mathematical tool set include the puzzle of doubling the cube, a mathematical proof Plato set his students. In this ‘Plato’s Gamble’ instrument I have trapped one cube within another, with the inner cube a dice. Entry into the Academy put students in the way of Plato’s gamble. I also love that Euclid unravelled the golden ratio of proportion, and at 1.618, it is the absolute and final ‘cut-off’ point for beauty. Appropriately, ‘Euclid’s Golden Scissor’ can serve this function in aesthetics.

euclids golden scissorIMG_3708

Mention should be made of another useful tool of mathematics. This is the ‘Pythagoras Musical Triangle’ in which his famous proof of the relationship between sides of a triangle has been altered to include a musical scale, another of his revelations.

plato's doublecube gamble

These small artworks will be laser printed when the opportunity arises, but for the moment our focus is on creating 3D printed directly in metal, musical bells.

An important part of my practice as a sculptor has been to invent helpful objects and instruments for the cutting and dicing of ideas. As a young sculptor, I produced a set of philosophical tools including ‘Kant’s Reality Tester’ and Schopenhauer’s Religion-Scissor’. This was followed by “Instruments of Psychology’, a series of sculptured doctor’s bags with constructions on their opening to might illuminate the central paradox each particular psychologist grappled with in their theoretical musings.

Instruments of Philosophy 1979

My practice developed definite themes in the early 1990s around finding ways through image, form and sound, of ‘tuning’ in country around Mia Mia, where I live. Seeking resonant frequencies that catch to rhythm and beat of the Australian landscape which continues to be slightly unfamiliar, even strange and threatening, to the non-indigenous amongst us. I mention this because some of the works made over the years to explore these ideas are instruments and ‘tools’ of various kinds which will better illuminate my attraction to ‘useful’ sculpture (the definition of sculpture, when I was a student, rested, unconvincingly to my mind, on being objects that were useless).

This program of enquiry, now 35 years in the making, has developed in three parts. The first part’s task was to devise a metaphorical method to let all of us see the country with fresh eyes, as if for the first time. The second part was to follow the example of Ludwig Leichhardt and to encourage our leaving the coastal hinterland and travel to the interior. The third, and I think final part, asks the question, how can we sustainably live in our country beyond exploitation, that is, how are we to live in tune with the visual, sonic and visceral patterns of experience of our country?

In 1994, I made sculptures and bells, prints and drawings imagining fishing trawlers leaving Port Lincoln with citizens on board bound for the Great Southern Ocean. I made a group of life-sized diving suits (as if fabricated in someone’s shed) to be used to lower people into the freezing and darkening sea to a depth at which they could only-just feel their bones, and so embrace the reality of their mortality, to arrive in the moment, to become present. When pulled up into the light and ‘born again’ upon the trawler deck, and taken back to Port Lincoln, surely, people would feel the eucalyptus tree’s strange indifference to their presence and, for the first time, ‘see’ that this is a country not scaled to human domestication, but operating at orders of magnitude that are ineffable to suburban dreaming. We might then tune into the ‘resonant frequency’ of the country, and be able to resist urges to shape the landscape patterned to ideas fashioned overseas.

The second part of this project was to draw people from the coast inland. The simple and overwhelming truth for Leichhardt was that there was an inland sea, that he would be irresistibly drawn to it, and after a frolic in its waters he would make the traverse to the regions of Perth. In 1848, he set out and we await his return. Meanwhile, I determined to make more suitable navigational instruments for his further use. Each instrument I invented for him is kept in proper adjustment through its connection to the landscape. The Lunar Navigational instrument tracks the shifting glint of the moon across a bronze orb in a small water container, and by marking that journey throughout the night the instrument leaves a curve scraped in the sand. Some rudimentary calculus of the curvature directs the pathway forward. There is a ‘Solar Navigational Instrument’ and ‘Over-the-horizon Sonic Navigation Instrument which sounds a small harmonic bell and collects its echo through an elaborate ear piece. Close to the continental centre there is the ‘Inland sea Shell Navigational Instrument’ which is a cast bronze shell with ear piece on a bearing turntable allowing one to turn and listen for the loudest archetypal crash of waves, and an arrow to point out where this is coming from.

Leichhardt's navigation instruments, 2011Leichhardt's mapcase and instruments of navigation, 1996

The ‘Water finding navigational Instrument’ is cleverness itself, if the psychology of birds is ever clever. Three magnifying glasses are aligned to make an adjustable telescope and two cast bronze budgies are perched upon it in splendid colour. At dusk, the flock is attracted (especially to the blue budgie) and visit with our decoys, only to, eventually, bore of their stiff company and wheel away toward the nearest waterhole. By following the line of sight with the telescope, one then merely follows by foot to the water. So, all the tools (there are more but it is too tiring to tell) that are needed and maps too! But not European drawn maps that can’t work in so flat and featureless plain repeated across Australia. Instead, beautiful maps beaten out against the anvil earth in copper sheet, taken along for the purpose. Here every scrape and mark of the earth itself is transferred to each map, including the marks of previous and ongoing occupation, and in this way the subtle topology of a plain is captured as no eye can discern. Only the touch of a finger can read the braille of Australia.

My current research is making a study of naturally occurring patterns; of the shifting distribution of birds on bodies of water, the ratios of rock and tree arrays in their placement on the ground as well as the rhythmical swirls of water flows coursing through creeks. Patterns that I suspect might be read as a kind of ‘sheet-music’, with which we can penetrate the surface and appearance of things to really ‘site-read’, or otherwise sense, feel and hear the orchestral truth of our Australian experience, that we belong to it, not it to us, and that we serve its song-line needs rather than have it serve those tuneless needs of our own.

Leichhardt's map of the interior 2004

I am also making a series of cast bronze and fabricated stainless-steel tuning-fork instruments intended to amplify the ambient soundscape of the bush, to distinguish those resonant frequencies that generate the landscape’s background ‘hum. An interesting report in the AGE newspaper (Sunday 10th December from the Washington Post titled ‘Deciphering the Earth’s mysterious hum’ (pp8), reports that the “earth is ringing like a bell all the time”, and that sea movement, volcanoes and earthquakes are vibrating the planet at frequencies between 2.9 and 4.5 milli-hertz. I have experienced that sublimated ‘hum’ in the active silence of Uluru in Central Australia, and have heard reports of a whooshing sound across Antarctica as trapped air continually escapes ice.

Making useful tooling for mathematicians and engineers falls naturally to hand.

My next blog will concentrate on the work of 3D printing forms in metal.

Casting a Difference-Tone Bell into a 3D print mould

Watching the Voxeljet VX1000 patiently print sand moulds in the print box, layer upon layer, becomes a kind of meditation. Many readers will have become entranced watching the continuous thread of a PLA 3D printer, for example, being spun into form, from virtual to actual object. The Voxeljet has this similar power of hypnosis, sand layer, print, sand layer, print and so on.

Having modelled the Difference-Tone Bell in SolidWorks software, and then modelled the 2-part sand mould required to cast this bell form, the Voxeljet printed the sand mould sections are ready to be cast into. Before casting the mould surfaces need a graphite-based foundry paint to be applied and set alight. This both hardens the casting surfaces and drives residual moisture away from them. This is usually completed as the metal is being melted in the furnace. The warm mould sections are assembled and clamped together, ready to receive the molten metal.

The negative space inside the mould is filled with liquid bronze, which runs like water at the temperature of 1100 degrees Celsius.

When the mould has cooled the sand can be broken away leaving the casting free to be cleaned, and then fettled (that is, to have its in-gate and airing systems cut away).

The second half of casting a bell is the tuning process. If the design calculations are accurate the bell will be cast close to its desired tuning, with hopefully a small amount of metal needing to be removed to fine-tune the partial frequencies to put them into the necessary array.

The array of partial frequencies, especially the 5 or 6 lowest frequencies, that combine together when the bell is rung, produces the dominant sustained sound of the bell. The art of tuning a bell is to get those partial frequencies into their proper array. The proper array is a function of the bell’s profile given uniform metal density.  In a harmonic bell the harmonic array of partial frequencies support the dominance of the lowest frequency (often called the hum) of the bell through octave and the perfect fifth (generating a difference tone at the lowest frequency) interaction with the lowest frequency (fundamental partial frequency).

In the case of the Difference-Tone bell frequency array, the relationship between the fundamental partial frequency and its perfect fifth partial frequency is critical to the bell generating the difference tone effect (of sounding a psychoacoustic pitch an octave lower than the fundamental frequency of the bell).

It can be a slow process to change the bell’s profile carefully to shift partial frequencies into their proper relations.


Casting the bell print box  Printer bed Printer screendifference-tone bell mould with graphitebell cast



Synapse Alumni Meeting

It was fantastic to meet so many of the Synapse staff, board members and participating researchers, past and present at the Alumni Network gathering in Adelaide last week. Two interesting projects were presented by the artist/scientist collaborators, making clear the potential for discovery that these kinds of collaborations make possible. Both projects demonstrated how a shared interest and curiosity each participant brought to their joint inquiry illuminated new possibilities in the field of their investigation.  What was most clear to me was the common ground that artists and scientists share in creative and agile thinking and taking joy in problem-solving. The digital wave being surfed by artists and scientists alike is washing away the silo mentality that fields of enquiry can tend to forge. Rapid change is upon us, and opportunity abounds for those prepared to partner with divergent and alternative approaches to investigation.

The great truth is that scientists and artists are aimed toward similar ends, to imagine and model the forms and structures of existence from within its turbulence. Penetrations of the ineffable are surprising and, coming thick and fast from both scientific and artistic endeavour, stand as testament to the civilising of our intellect and imagination.


My own recent collaboration has been to work with Gary Savage in Lab 22 to 3D print sand moulds using the Voxeljet VX1000 sand printer. We are exploring alternative ingate systems to fill sand moulds with molten metal that is free from oxide-boundary ingress, as well as developing new shapes for cast bronze vibrating forms. These forms are designed across several 3D design software packages and sent to the Sand Printer as STL files.


The voxeljet VX1000 uses catalyst (sulphonic acid) coated silica sand grains which are continuously layered thinly (300 microns or 0.3mm) above each print-head deposit of Furan resin (like an inkjet printer), slowly building up 3D models in the sand box as each resin printed sand layer is lowered by 300 microns, and a fresh layer of sand is spread over the printable surface.  The printed layers are set hard by the catalyst in the sand. When the sandbox is filled after thousands of sand layers have been deposited, the un-catalysed sand is removed to expose the catalysed furan sand moulds with very fine surface details intact.


Currently I have designed steel frames to support the 3D sand prints for casting in bronze, and these are being laser cut. I will post pictures of the sand moulds and their casting soon. The opportunity to have deep and technical discussion with the brilliant staff at Lab 22 about sound, the vibrating forms that produce it and the complexity of casting and printing such computer designed forms at the highest levels of accuracy is both satisfying and a privilege I truly appreciate. Thank you to the SYNAPSE program and the wonderful people associated with it.

Printing bells in metal

The opportunity to undertake research into metal 3D printing and 3D printed resin sand moulds to explore new bell designs printed in a variety of metals at CSIRO’s Lab 22 Materials technology is just wonderful.

I need to outline a brief history to bell tuning to make the research I am undertaking at Lab 22 sensible.

Since an interest developed in Europe’s Middle Ages to refine the musicality of bells (from adding bells to bell towers and so generating musical pitch intervals between these grouped bells), there has been an ongoing quest by campanologists to exert control over the partial frequency ratios that together make up the sound of a bell and constitute the clarity of pitch this sound generates.

A bell is in tune in two separate ways. The pitch of a bell is given by its scale, such that a bell exactly scaled to half its size will sound exactly an octave higher and a bell scaled twice its size will sound an octave lower. The particular pitch of a bell within an octave is therefore a mathematical ratio of the bell’s size between the scale doubling or halving, regardless of intonation (such as equal temper, just tuning or any other musical scale chosen for the octave).

The more difficult tuning of a bell is to find a bell profile (its inside and outside shape) that puts the lowest seven or less partial frequencies that the bell generates into a harmonic array. When a profile is found that achieves this, the dominant partial frequencies generated in the bell support the lowest (called the fundamental) frequency, giving the bell’s ring a distinct clarity of pitch to the ear of the listener.  The human ear seeks harmonic sounds in the world and has great subtlety in finding them as the human voice, a column of vibrating air, naturally produces harmonic overtones (partial frequencies). Most musical instruments use the natural harmonics of vibrating strings or vibrating air columns to generate harmonic pitch with great clarity.Hasell hand chipped European Bell

The quest to harmonically tune the bell started with bell founders chiselling their cast bell, sometimes finely, but often quite crudely in an attempt to better control the frequency array of the bell. The chipping and filing are attempts to change the shape of the bell’s profile to shift partial frequency ratios and so improve the clarity of its pitch when rung. The inventive step to use a lathe to scrape metal from the surface of the bell, usually internally where it doesn’t show, to tune the partial frequencies and put them in as best a harmonic array as possible was made (and subsequently) forgotten in the Netherlands of the 1600s and again in Europe around 1900. Apart from the ‘Foreign note’ of a minor third partial frequency locked into the European bell due to its profile, the bell founders managed by foundry iteration to tune the European bell to a harmonic sequence of partial frequencies.Hasell Lathe tuning bell John Taylors Bell Foundry 2006

In the middle 1980s Dr Lehr at Royal Eijbouts Bell Foundry collaborated with Eindhoven University of Technology to use Finite Element Analysis vibrational engineering software to develop a series of new bell designs. They attempted a fully harmonic bell to finally remove the minor third ‘foreign note’ partial frequency, with their virtual model starting at a traditional European bell profile. The computer result, a unique solution, was carefully cast as an actual bell, but only to discover the bell started at one pitch and finished at another.

Commissioned to undertake the Melbourne International Festival’s Federation Bell Projects in 1998 Australian Bell collaborated with RMIT University’s Aeronautical Engineering Professor Tomas whose Finite Element Analysis software ReShape was used to optimise a number of new musical bells including a fully harmonic bell, found using a cone profile as the virtual model.

In 2014 Australian Bell was commissioned by the LongNow Foundation to invent, cast and tune 10 ‘Difference-Tone’ bells for the 10,000-year Clock project being constructed to be installed inside a mountain in Texas, and designed to operate, and ring, for the next 10,000 years. Collaborating with ADVEA Engineering using ReShape software a bell profile was optimised that, when cast using 3D plastic prints as foundry patterns, did not ring a difference tone, but made its discovery possible with a careful and very slow manual tuning process of a cast bronze bell taken from the 3D print pattern. A ‘difference-tone’ is generated when a fundamental partial frequency is sounded with its perfect fifth partial frequency. The resulting pitch has the psycho-acoustical effect in the ear of the listener to generate a pitch that is an octave below the fundamental (lowest) frequency of the sounding instrument. This bell design allowed a bell four times smaller than ordinarily needed to sound the very low pitch of C 65 Hertz, which was perfect for the confined spaces inside the clock, inside the mountain. Hasell last four of the LongNow difference tone bells 2016

These bells are digitally designed with great accuracy and to transfer the virtual information unmolested into an actual cast bell required the accuracy of 3D printing of foundry patterns and the use of resin sand moulds.Hasell 3D printed Difference tone bell with cast in bronze taken from it, 2014

My research at Lab 22 is to explore bell designs, particularly the Australian invention of the ‘Difference-Tone’ Bell design, as direct metal 3D prints. The vagaries of sand moulding and hot metal casting can be eliminated through this process and bells can be manufactured at the highest levels of accuracy. After all, the distinguishing feature of casting bells throughout history compared to regular foundry work has always been the high levels of accuracy required to preserve the exacting musical demand being made on bells. Early on this kept bell foundry work hidden in the monasteries, and later, in the secretive world of the few specialist bell foundries making musical bells.

Danny Hillis, the founder of the 10,000-year clock project, has given his blessing to this research to print the world’s first ‘Difference-Tone’ Bell and like him, I cannot wait to hear the printed bell ring.

It is a great privilege to work with Dr Daniel East and other researchers at Lab 22 on this project. Dr Anton Hasell Australian Bell.Hasell casting a Difference tone bell Billmans foundry Castlemaine 2016