What vibrating matter seems most conducive to harmonic enquiry? Many have investigated and classified the vibrational patterns of metal plates - Ernst Chladni, the French mathematician Sophie Germain and most comprehensively Mary E. Waller.
I’ve chosen to begin by experimenting with vibrating water. This is because of the sheer range of different vibrational patterns to explore and also because these patterns, unlike the static formations of sand on vibrating plates, are dynamic, ebbing and flowing periodically over time, which makes them suitable for musical accompaniment.
When the water is vibrated by a low frequency sine wave certain distinct steady states of vibration are achieved, dependent upon the amplitude of the signal. So in figure 60 a tone of 20 Hz is slowly increased in volume causing the water to adopt two steady ring states before the pattern evolves into an intricate dynamic form with thirteenfold symmetry.
Figure 60 (click to play)
One issue which is immediately apparent concerning the possible cross-fertilisation between music and visual pattern is the mismatch of scale. The dynamic process of figure 60 has in fact been slowed down about 20 times. The realtime speed is shown in figure 61 where much of the subtleties of form development are lost in the blur of motion.
Figure 61 (click picture to start video)
Added to this, the tone which created this patterning can hardly be called musically complex - intricate dynamics emerge from very simple sonic impulses - and it is not the most captivating of musical experiences listening to a 20 Hz sine wave which has all the musicality of an idling bus engine.
Furthermore the cymatic patterning of more complex musical sound tends to be visually unintelligible; witness figure 56 where Mozart is played to vibrate a dish of water. Any apparent visual patterns are more the result of the music’s dynamics rather than its harmonic content. This I think is also the case with Alexander Lauterwasser’s attempts to bring music and cymatics together; as the musician plays the sound is fed directly into the dish of water which splashes about rhythmically.
However, while any viable one to one realtime correspondance between the visual and the musical on a creative level appears impossible, the two can still be brought together meaningfully. In the same way as a bass line underpins harmonic movement so the visual element can be conceived as a shadowing of the shifting sonic landscape.
To what extent, however, do the dynamic symmetries which the vibrated water adopts conform to harmonic principles? Figure 63 is an interactive graph of the symmetries resulting from vibrating a dish of water with a sine wave over the range of 6-37 Hz. The y-axis marks the symmetries the x-axis the frequency.
Figure 63 - Click to enlarge
If we follow the sequence of each symmetry horizontally we can hear that the frequencies which produce the steady vibrational states adhere to some extent to the harmonic series. So for example in the case of the patterns with sixfold symmetry we can hear that they coincide with the 5th through to 12th harmonic of a harmonic series. However while the behaviour of the water may hint at harmonicity, there seems no way of explaining how the different symmetries interconnect from a harmonic pont of view.
When dealing with the harmonic nature of vibrating strings we noted that doubling the length of the string halved the resultant frequency. Is there any similar proportional correlation with the vibrating liquid media?
Figure 64 shows the vibrational states of three dishes of water which are proportionally related. Graph (a) corresponds to a dish with 95mm diameter filled with 25ml of water, graph (b) represents the same dish with twice the depth of water (50ml) and graph (c) shows a dish with twice the diameter (190mm) and four times the volume of water (100ml), thus having the same depth as the water in the dish shown graph (a).
The yellow lines on each graph highlight the stable vibrational states which correspond with the 4th harmonic for each symmetry.
As with the doubling of string length so with the doubling of the dish’s diameter from (a) to (c), the resultant frequency appears to be roughly halved: the 4th harmonic of the 5 symmetry in (a) occurs at 16.8 Hz while in (c) it occurs at 8.4 Hz. However, there seems to be no meaningful harmonic link between (a) and (b) when the volume of water in the same dish was doubled.
In conclusion, while vibrating dishes of water with sound certainly brings forth an array of fascinating dynamic figures as can be seen on the gallery pages and provide a wonderful visual accompaniment to my first attempts at harmonic music in the videos I have produced, they only offer intimations of harmonicity - to find a closer correlation between
harmonic music and the visual patterning of vibrating media we must look elsewhere.