A tonometer consists of a series of steel cylinders that resonate at specific frequencies upon being struck with a metal hammer. They are used as standards for high frequencies, in the same manner as tuning forks. The transverse vibrational frequencies (i.e. fundamental and harmonics) of a given cylinder depend on the length, elastic modulus, and linear density of the metal.

Invented by John Shore in 1711, the tuning fork was initially used by musicians. After Chladni’s studies of its vibrations, however, it was also extensively employed by acousticians, who praised the purity of its sound. Hermann von Helmholtz, especially, based his experiments with beats, combination tones, and simple tones on tuning forks attached to resonators that enhanced their suitability for experimentation.

Koenig’s flame analyser was, next to the sound synthesizer, one of the clearest expressions of Hermann von Helmholtz’s theory that complex sounds were made up of a spectrum of elemental or pure tones. The adjustable resonators covering a range of 65 notes from sol1 to mi5 (96–1,280 Hz), could each be rendered visible with a connection to a manometric flame capsule. The resonators were connected to a gas-filled capsule with a rubber tube. If activated, the distinctive pattern would appear in the rotating mirror.

This specific array of precision tuning forks are highly-specialized experimental forks that relate directly to Koenig’s long-standing disagreement with Helmholtz on the nature of combination tones. Some of them date back to Koenig's display at the 1876 Philadelphia exposition.

Videos:

The history of the tuning forks in the Koenig collection

The sound synthesiser was Helmholtz’s clearest instrumental expression of his theory of timbre, or sound quality. Whereas his spherical resonators dissected compound sounds (vowels or musical sounds) into elemental frequencies, the synthesiser did this by building up complex sounds from simple frequencies. In 1857 he went to the instrument maker Friedrich Fessel of Cologne to turn this idea into reality. The initial instruments used a combination of electrically driven tuning forks, resonators and piano keys to synthesise compound sounds.