The research paper co-written by Dr Anton Hasell, Australian Bell and Dr Daniel East, CSIRO on the acoustic outcomes of a known musical, traditionally cast, bronze bell with the same bell design now 3D printed in several different processes and differing metal materials has been accepted for publication by Leonardo. The datum bell design chosen was the ‘difference-tone’ bell designed by Anton Hasell for the Longnow Foundation’s 10,000-year Clock project. The Foundation, through Danny Hillis, asked if it was possible to invent a ‘difference-tone’ bell where the array of partial frequencies of the bell generated a difference-tone. A difference-tone is a psychoacoustic pitch effect in which the listener’s ear recognises a pitch one octave below the lowest actual pitch (the fundamental partial frequency) sounded in the bell. The effect of a difference-tone bell, if it could be invented, would be to half the scale of a bell at any given pitch. Working with Ryan Adams using Professor Tomas’ ReShape optimising software starting with a harmonic bell virtual profile model, the final optimised bell profile produced by the software was then translated from its virtual space into a real object through 3D printing in plastic. This plastic bell form was used as a foundry pattern to cast a replica silicon bronze bell. This cast bell did not sound a difference-tone when rung, against the prediction of the software optimisation. Months were spent with several other cast bronze test bells to manually tune the bell and map its partial frequency ratio shifts with small removals of metal in specific locations on the bells. The resulting mapping of ratio shifts allowed a final test bell to be tuned to sound a difference-tone when rung. This bell profile was used by Australian Bell, working with Billmans Foundry in Castlemaine, to cast the 10 musical difference-tone bells currently being installed within the Clock mechanism inside a mountain in Texas (see www.longnow.org).
A number of test difference-tone bells were 3D printed using laser fusion in titanium at the CSIRO’s Lab 22 in Clayton Victoria where Dr Daniel East is the director, and two difference-tone bells were printed in the USA using EXONE’s processes, one bell printed in 316 stainless-steel/tin bronze and another printed in 420 stainless-steel/tin bronze. The results of our analysis show that so long as the profile is maintained exactly in the various 3D printing direct-metal processes, the difference-tone effect was replicated in the printed bells. Given differing densities and elasticities of the metals used, the bells had differing pitch generations for the same sized bell. The full test results are soon to be available to interested researchers through the Leonardo publication.