In 1894, Olaus Henrici (1840-1918) of London devised a harmonic analyzer for determining the fundamental and harmonic components of complex sound waves. It consists of multiple pulleys and glass spheres, called rolling-sphere integrators, connected to measuring dials. The image of a curve (for example, a phonodeik tracing of a sound wave) is placed under the device. The user moves a mechanical stylus along the curve’s path, tracing out the wave form.

This photograph shows a three-dimensional representation of sound using paper. The spectrum (frequencies from low to high) is represented by an arrangement of single strips of paper, with lower frequencies in the foreground. The changes in the spectrum over time are visible as variations in the profile of the paper strips, if read from left to right. Such paper models were used at the Technische Universität Berlin in the 1960s to represent the sounds of speech (phonetics) and music (acoustics).

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.

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.