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