It should also be pointed out that in my previous experiments the bubbles were only vibrating in one plane - up and down. Seen from above they remain circular and vibrate in accordance with a particular order of spherical harmonics, as shown below (figure 78).
Furthermore, a bubble is only a spherical membrane. What would a sphere look like, what patterns would emerge if it were to vibrate in three dimensions?
A globe of water in space, excited by a gust of air (figure 79). What patterns would emerge if it were sonically vibrated?
No amount of boffining can conjure up zero gravity in my living room, and elastic spheres are difficult to come by for experimental purposes. So it is difficult to conceive how to pursue the project.
Indeed even the notion of a sphere vibrating harmonically is contentious. The acousticians I’ve talked to dismiss the idea out of hand stating that a sphere when sonically vibrated would only adopt what is termed a breathing mode, contracting and expanding - not taking on polyhedral forms. Nevertheless I’ve come across intriguing material which would seem to support my grandiose harmonic pipe dream.
The students of Buckminster Fuller evidently conducted an experiment by immersing a sonically vibrated balloon in liquid dye resulting in symmetrical patterns appearing on the surface of the balloon at the vibrational nodes, forming traceries of platonic solids. However, I have yet to replicate this experiment.
Furthermore, researchers at Clemson University have published experiments in which droplets levitated in an ultrasonic field can be induced to asssume polyhedral shapes at different harmonics of the droplets resonant frequency (figure 80).
Also, I’ve read that if a spherical air cavity is incited to vibrate radially, that is from the centre outwards, then this would be akin to assembling many cones at their apex so as to form a sphere as in figure 81 below but more closely packed.
Now since a conical air column, like that of a saxophone, vibrates harmonically, it follows that the air cavity would also, in this mode of vibration.
Another interesting example which appears to substantiate the claim is the case of overtone singing, where the rounded nature of the mouth cavity encourages the production of distinct harmonics of a fundamental tone.
The matter at present remains inconclusive and I’m loath to force an elegant theory on the issue if the experimental evidence is lacking.
If we could see the vibrational pressure patterns in the air around us, what would emerge in a spherical room like Stockhausen’s spherical concert hall in Osaka (figure 82) or the interior of Etienne-Louis Boullee’s proposed mausoleum for Isaac Newton (figure 83)?
A way forward may be through modelling the wave forms with computational fluid dynamics, though the renderings I’ve seen are rather disappointing - a pale imitation of real patterns I’ve managed to capture on film.
Another potential avenue may be to develop a means to visualize the vibrational patterning of sound waves within a spherical air cavity. The process used in the design of a laser microphone as shown in the video below (figure 84), where the wave patterns in a smoke-filled cavity excited by sound are analysed by a laser, could perhaps be elaborated upon.
Where I envisage this project heading ultimately is a form of multimedia performance where there is a formal correspondance between the music being played and the visuals displayed.
Imagine a three dimensional sphere projected, say, within the dome of St. Paul’s which could be scaled and sliced and which vibrated not merely as an accompaniment to the music but as a direct proportional reflection of it.
Would the spherical architecture in any way correlate with Johannes Kepler’s nested platonic solids as shown in figure 86; Kepler’s concept of the Music of the Spheres may be fanciful hyperbole but the prospect of the music of a sphere promises to be no less enthralling.