According to Wikipedia the first synthesizer is from 1876.
History
The first electric synthesizer was invented in 1876 by
Elisha Gray [1], who is best known for his
development of a telephone prototype. The "Musical Telegraph" was a chance by-product of his telephone technology. Gray accidentally discovered that he could control sound from a self vibrating electromagnetic circuit and in doing so invented a basic single note oscillator. The Musical Telegraph used steel reeds whose oscillations were created and transmitted, over a telephone line, by electromagnets. Gray also built a simple loudspeaker device in later models consisting of a vibrating diaphragm in a magnetic field to make the oscillator audible.