The Grand Bow

The occasion: A string trio. Serena McKinney (violin), Katie Kadarauch (viola) and Arnold Choi (cello), who had recently performed at the famed Carnegie Hall. As we sat spellbound listening to the meticulous vibrations of the strings on a Nicolaus Gagliano violin (circa 1760), a Giovanni Grancino viola (circa 1695) and a Carlo Tononi cello (circa 1725), we were transported to magical moments outside of time. One point is, however, strikingly clear: without the bowing of the strings — without the grand bow — there would be no musical tones or harmonics. As in music, so in spiral galaxies do we encounter waves with the full complexity of modes.

No bowing of the strings of the cello, of the violin, of the viola … no grand bow … no music. Sitting at the National Gallery in Canberra, what we visually saw was each musician bowing their different strings, but what is actually happening is that multitudes of different sound waves of different frequencies are being produced in the auditorium. It is not a static, but a highly dynamic, interplay. To describe this interplay from a mathematical point of view, one can say that the shape of any bowed string can be represented in terms of an infi nite number of waves or modes.