An electronic instrument capable of producing a variety of sounds by generating and combining signals of different frequencies. A modern digital synthesizer uses a frequency synthesizer microprocessor to calculate mathematical functions, which generate signals of different frequencies.

There are three main types of synthesizers, which differ in operation: analogue, digital and software-based. Synthesizers create electrical signals, rather than direct acoustic sounds, which are then amplified through a loudspeaker or set of headphones.

Synthesizers are typically controlled with a piano-style keyboard, in which each key functions as a switch to turn electronic circuits on and off. Although keyboards are the most common control interface, other devices such as saxophone-style wind controllers, MIDI-equipped electric guitars, drum pads or computers are used to control synthesizers. Synthesizers can produce a wide range of sounds, which can either imitate other instruments or generate unusual new timbres.

The first electric synthesizer was invented in 1876 by Elisha Gray. By the 1960s, there were a number of synthesizers which could be played in realtime, but were usually confined to studios due to their size. Most early synthesizers were experimental modular designs.

In 1964, Robert Moog created a revolutionary synthesizer which could be used by musicians, being much smaller and more intuitive - and hence less of a machine and more like a musical instrument. Other early commercial synthesizer manufacturers included ARP, who also started with modular synthesizers before producing all-in-one instruments.

In 1970, Moog designed an innovative and popular synthesizer called the Minimoog, with a built-in keyboard and without modular design. The analogue circuits were retained, but made interconnectable with switches in a simplified arrangement called normalisation. Although less flexible than a modular design, normalisation made the instrument more portable and easier to use.

In the 1970s, the development of miniaturised solid-state components allowed synthesizers to become self-contained, portable instruments, which made them easier to use in live performances.

By 1976, the first true music synthesizers to offer polyphony had begun to appear. The first practical polyphonic synth, and the first to use a microprocessor as a controller, was the Prophet-5 introduced in late 1977. For the first time, musicians had a practical polyphonic synthesizer that allowed all knob settings to be saved in computer memory and recalled by pushing a button. The Prophet-5 was also physically compact and lightweight, unlike its predecessors.

The Fairlight CMI (Computer Musical Instrument) was the first polyphonic digital sampling synthesizer, designed in 1978. It gave musicians the ability to modify volume, attack, decay and special effects like vibrato. Waveforms could also be modified on a computer monitor using a light pen. It rose to prominence in the early 1980s and competed in the market with the Synclavier.

The Kurzweil K250, first produced in 1983, was also a successful polyphonic digital music synthesizer. It was noted for its ability to reproduce several instruments synchronously and also had a velocity-sensitive keyboard.

Most new synthesizers since the early 1980s have been digital, strongly influenced by Japanese manufacturers such as Yamaha and Casio and largely aimed at the home organ market. Yamaha's third generation of digital synthesizers, consisting of the DX7 and DX9 (1983) was a great commercial success. The DX7 was the first mass-market all-digital synthesizer and became indispensable to many music artists of the 1980s. 

Another important innovation was the development of MIDI (Musical Instrument Digital Interface), which made it easier to integrate and synchronise synthesizers with other electronic instruments.

In the 1990s, complex synthesizers no longer required specialist hardware and began to appear as PC software, often as hardware emulators with on-screen knobs and panels.