The Gum and the Teeth Behave As A System
Gums can be considered a functional element in their own right and studied as such, but we will consider them as part of a compound oscillator for the purpose of clarity in this exposition. The function of the gum is to shape the vibrational behavior of the rods to be united in a global oscillation (but not radiating). The rods must be firmly connected with the gum in order for them to behave as clamped rods, and therefore the gum becomes part of a compound oscillator.
It is the gum, with its weight and rigidity, that gives the rods their specific tension and wavelengths, creating a new compound oscillator. The fact that the gum is contributing a new function, gathering and accumulating the vibrations of the rods could make it a subject of study on its own, and we could consider it as a completely different functional element. It is true that the Baschet implemented the gum as a new acoustic functional element, since it carries on a complicated acoustic impedance transformation. If we hold a gum tightly between our hands while the rods are vibrating, we won’t be able to stop the vibration; this allows for the formation of standing waves in the gum and has a deep impact on the overall behaviour and dynamic potential. We could also argue that the Baschets’ high impedance innovations brought a new functional element to the system of acoustics, a radical innovation in hundreds of years of evolution of organology.
In addition to the essential functions of oscillation, activation, radiation, and the optional functions of gamut articulation and resonance modifiers, there is the optional function of acoustic impedance transducer, or sound accumulator. But for now, we will consider the gum as a part of a compound oscillating system that features complex vibrational relations sharing mechanical energy in subtly intertwined ways. We don’t intend to be exhaustive on this issue and can save it as a topic for further discussion. For the purpose of this discussion let’s just say that some gums can be heavier and more powerful, and some can be lighter and less powerful, but even when the impedance relations are not as remarkable as in the Baschet pieces, we would like to consider every sound device based on clamped oscillators to be an odontophone and consider the system created by combined rods and gum as one, the same way we would suggest considering the tongues and the bridge of kalimbas as one compound oscillating system, noting the commonalities of all those mountings as a feature of odontophones in general. Since their oscillators are all clamped to some sort of accumulator, the basic idea of the odontophone could apply to other sound devices not created by the Baschets.
The gum, our sonic accumulator, must be heavy and rigid to serve this purpose. François Baschet wrote that the weight of the gum should be at least the same as the weight of all the clamped elements (oscillators) combined. The heavier the gum, the bigger the acoustic impedance, and thus more capacity to store vibrational energy as well as more clarity of the vibrational modes forced on the clamped elements.
To allow this vibrational behaviour to function efficiently, it is generally necessary to insulate the gum and oscillators (the whole complex oscillating system) from the supporting frame to avoid the vibrational energy leaking into any other element other than the coupled radiators. To achieve this acoustic isolation, the Baschets often suspended the gums with ropes from external frames or used padding materials, such as rubber pipes, to support the gum and oscillators. The subject of acoustic insulation is a complex matter in itself, so we have not addressed it deeply in this exposition. Where relevant or particularly interesting, we have described methods of suspension for acoustic isolation in the examples.
For the odontophone to produce its sounds, the oscillators must be tightly clamped to the heavy gum, typically passing through it and protruding from both sides. Each side of a clamped oscillator vibrates independently, since the great tension created by the nuts against the gum produces an artificially forced nodal point, with huge inner pressure and practically no amplitude for the soundwaves, defining one end of the wavelength.
A rod that is clamped at any point along its length (typically though a gum) can appear as two segments (one on each side of the gum), with two different wavelengths vibrating independently. This is partially true in the sense that each length behaves according to its own structural features and tensions, but let's not forget that every element connected to the gum becomes a part of a complex compound system of oscillation in which each part mutually reinforces the others’ resonances, like the teeth of a comb in a massive music box.33 In a Baschet gum all the parts receive a flow of vibrational energy when any of the individual parts are stimulated. The propagation of acoustic waves inside metals like iron, steel, and aluminium is incredibly fast, even when they are compound systems. This means that all the parts of the system, even when they are not directly stimulated, become added resonators for the other elements, adding their potential energy sympathetically and behaving like formant filters. Some will resonate more or less, adding prominence to some overtones or dampening others.
It is quite challenging to study these structures. In each case there are different complex behaviours taking place. The oscillating behaviour of a single rod is already hard to understand and preview in its multiplicity of vibrational modes. It is so much more complicated to consider all the different interactions of all of the parts of an entire system of clamped rods. Not only can a single clamped rod have complex behaviour, but the system formed by many of them clamped to a heavy gum generates new emergent properties. We could poetically say that the individual rods are transformed when connected to a gum, and the gum can be transformed by the addition or subtraction of a single rod. Sometimes adding a new rod to a system can change the way the other clamped rods behave. Every element influences every other.