I started making musical instruments for fun in the late 1980s while completing a PhD in Physical Chemistry. In 1989 I co-formed the artist collective GongHouse and made many tuned percussion ensembles and installations (see History). In the mid 1990s I learnt computer modelling of vibration to obtain more control over the acoustical properties of instruments. The Federation Bells project In 1999 enabled me to work with Advea Engineering to use their optimization algorithms to design the world's first harmonic bells. Since then I have been developing new harmonic percussion ensembles that can be affordably produced for schools, communities and professional musicians. This work has resulted in a suite of new patented inventions for the joint venture company, Harmonix Instruments Pty Ltd.

Key publications that describe this work include:

  1. N. McLachlan, B. Keramati Nigjeh and A. Hasell, (2003). The Design of Bells with Harmonic Overtones. Journal of the Acoustical Society of America, 114 (1), p 505-511.
  2. N. M. McLachlan (2011). The design of a harmonic percussion ensemble (L), Journal of the Acoustical Society of America, 129, 3441-3444.
  3. N. M. McLachlan, R. Adams and C. Burvill (2012). Tuning natural modes of vibration by prestress in the design of a harmonic gong, Journal of the Acoustical Society of America,131, 926-934.
  4. N. McLachlan (2011). Educating amateurs: New technologies and models to enhance music participation in Western societies. In N. Rickards and K. McFerran (ed), Lifelong engagement in music: Benefits for mental health and well-being. Nova Science Publishers: Melbourne.
                                            

These tubular brass chimes and spun steel gongs were installed in the Children's courtyard in the Museum of Victoria and are typical of percussion instruments I made in which only the lowest frequency partial of each note were tuned. This is also typical of Indonesian gamelan instruments - the graphs on the right show spectra of three gamelan instruments compared to three western instruments. The partials (peaks in spectral amplitude) of the western instruments are equally spaced at harmonic (or integer multiple) relationships to the lowest frequency partials. In contrast the gamelan partials are much wider apart, and in gongs form closely tuned clusters. Western musicians find it hard to locate the pitch of gamelan instruments, but gamelan musicians don't, suggesting that pitch processing is learnt according to cultural conventions (see Auditory Neuroscience).

Wind and string instruments naturally produce harmonic overtones because their vibrations travel along one dimension. Western musicians have learnt to hear pitch and harmony for harmonic sounds. But percussion instruments vibrate in three dimensions, and must be carefully designed to produce harmonic partials. The first percussion instrument to have more than the first two partials
harmonically tuned were the harmonic bells that I designed for the Federation Bells Project.
           
    
The image on the left shows three harmonic bell designs ranging from 110 Hz to 330 Hz fundamental frequencies (A2 - E3). On the right are the wave shapes of the first four partial frequencies of a harmonic bell. The amplitudes of the first three of these modes are largely constrained to the rim of the bell, so these waves are propagating around the rim like pseudo-one dimensional waves on a ring. Consequently they are approximately harmonically tuned. Notice also that the amplitudes of the first mode propagate further up the wall of the bell. This means that its frequency can be altered by changing the stiffness of the bell near its top without affecting the frequency of the other modes. So each mode could be fine tuned by varying the stiffness of the bell wall at different heights. Finally the last vibratory mode also has substantial amplitudes near the center of the bell and could be simultaneously tuned to the fourth harmonic. I designed bells with up to seven harmonics by this principle. In European bells modes with amplitudes near the center of the bell (like mode 4 shown above) are interspersed with circumferential modes and so prevent harmonic tuning.


"Opening" by Neil McLachlan commissioned by the Melbourne International Festival of the Arts for the launch of the Federation Bells in 2002 - a sampled sequence of the bells

The images above show the Federation Bell Installation, quarter tone harmonic handbells, and 2001 harmonic handbells being played at the Sydney Myer Music Bowl in celebration of Australia's Centenary of Federation. Any-one can go online and write music for the Federation Bell Installation and the handbells can be borrowed from the Museum of Victoria for community festivals and events. To date they have been used in welcoming ceremonies for Queen Elizabeth II and the Dalai Lama, and for the commemoration of the Black Friday bushfires and the beatification of Saint Mary McKillop.


These images show Tine and Tide Bells that I designed with UK sculptor Marcus Vergette being installed at Appledore on the Devon coast (left), and at Trinity Warf in the Thames in London. These bells were produced to produce six notes depending on where they are struck by the action of the waves and tides. Another bell has been cast and installed by Marcus on the Isle of Skye.


Casting and machining is expensive, and it seemed possible to make harmonic bells and gongs cheaply by forming sheet metal. The image above shows harmonic bells and gongs with constant wall thicknesses that were designed on the computer, and then manufactured by metal spinning. However metal forming causes residual stresses when the metal springs back after forming. Another example of residual stresses is the stretching of guitar strings to tune them. Residual stresses have a dramatic effect on the frequencies of vibration, and in the case of the bells and gongs, the changes in frequency were very difficult to predict and manage. Residual stresses can be removed by annealing, but this was difficult to do reliably and resulted in a very dull sound. So I went back to the drawing board (or computer models) and designed harmonic bells and gongs that could be folded from sheet metal without adding uncontrolled residual stresses. I also designed a harmonic key for vibraphones and xylophones.


The image above shows the three new harmonic percussion instruments that I designed for Harmonix Instruments. The bell and key rely on their geometry to tune the partials to harmonic frequencies (as shown in the spectra), but the gong design exploits the controlled addition of residual stresses through the forming of dimples at a location that increase the frequency of the higher modes relative to the fundamental. This engineering innovation is currently being evaluated for stiffening airframes without adding extra weight!


Four octaves of gongs ranging from 65 Hz (E2), three octaves of metalophones from 110 Hz (A2) and 1.5 octaves of bells ranging from 220 Hz (A3) have been made for a prototype diatonic ensemble for use in classroom music education. Musical skill and comprehension of primary school children increased dramatically over a 6-week trial using the ensemble without any measurable loss of motivation or enjoyment across the class. The images above shows adults and children using the ensemble in a workshop that is based on the way Indonesian gamelan is taught traditionally in villages; socially and without anxiety! Our bass metalophone has been used extensively in concerts by the popular musician Gotye.


The above images show pre-production prototypes and concept designs for modular harmonic percussion instruments currently being developed by Harmonix Instruments. We hope to build six new ensembles in 2012 to run extended workshops in over 20 schools of widely varying socio-economic status around Australia.