Whether it be Chladni plates, dishes of water, bells or drumheads, the vast majority of vibrating systems in nature are anharmonic, that is to say that their overtones do not correspond with the harmonic series. Harmonic systems such as the stretched string are very much the exception.
In respect to this project then, is it possible to find a vibrating system that is both harmonic and displays the wealth of dynamic patterning that we saw with vibrating dishes of water, since a vibrating string holds limited appeal as a visual counterpart to harmonic music.
Are we any closer to a meaningful musical correspondence with the vibrating forms of water dropets? Indeed, since we can negate the problematic issue of boundary inconsistencies we encountered earlier with the walls of dishes and because it transpires that the vibrational modes of a water droplet match those of the circular membrane of a tuned drum.
Here we can see the analogous forms of a drum head on the left and a water droplet on the right. To use the categorization I mentioned before, the first pattern is (2,1), having two nodal diameters and one nodal ring. Followed (3,1) with three nodal diameters and one nodal ring….(4,1)….(5,1)…(2,2) with two nodal diameters and two nodal rings and (3,2) with three nodal diameters and two nodal rings.
A more extensive frequency sweep of droplets of different proportional sizes produces this grid (figure 72). The y-axis shows the different droplet sizes ranging from 4 to 16mm in diameter, while the x-axis plots the frequency. The different coloured bars mark the different nodal diameters (symmetries). Note how the (3,1) form (first red bar from left) as it occurs at proportionally higher frequencies as the droplet becomes smaller – on the left lit from above and the right lit from the side to highlight the three-dimensionality.
As with the patterns in dishes of water, the progression of water droplet forms shows elements of harmonicity. While in the former this was evident in the successive nodal ring multiples of patterns of the same symmetry, in the case of water droplets it is manifest in the successive symmetries of forms with the same number of nodal rings. We can see and hear this with the 6mm droplet. The coloured bars of the different symmetries are evenly spaced and a harmonic series is audible in the sequence of forms with both one and two nodal rings.
Another important observation is that these forms do not appear at frequency pinpoints, but rather like the channel bands of an analogue radio, they cover wide ranges of frequency. So, with a 5mm droplet this fourfold symmetry covers a range of 30Hz until this twofold pattern emerges. This makes the cymatic patterning more malleable to musical interpretation.
When I visited Dr Peter Guy Manners, the sound healing pioneer who collaborated with Hans Jenny, I asked him about Jenny’s experimental methodology. It transpires that the extraordinary images were created with a surprisingly unsophisticated setup, hardly rocket science; but to move forward with this project, perhaps rocket science is just what is needed.
The astronaut Don Pettit conducted a series of entertaining popular science presentations from the International Space Station. Here, he sonically vibrates water droplets with a didgeridoo improvised from the space station’s vacuum cleaner.
Now due to zero gravity, water droplets are always hemispherical, unlike the different sized droplets I investigated (figure 74) which are not uniform in shape due to gravity and surface tension.
While in my experiments there was no clear relationship between the symmetries of different sized droplets, perhaps there would be if the droplets were all hemispherical. Incidently, a group of scientists from Cornell University who have explored the physics of vibrating water droplets actually came second in a NASA competition to choose a research project for the ISS.