Is there any musical instrument which produces sounds from pure electrical circuits? Wherein there is no pre-recorded sounds from other instruments...

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    Most certainly, this is how many synthesizers work. The theremin would be another example. This question is probable better suited for the Music: Practice & Theory or Sound Design SE's. Commented Jul 26, 2015 at 14:39
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    Agreed. Most people don't realize that the common electric guitar is also one of these instruments: the passive electromagnetic pickup does not record nor amplify the sound of the guitar. The pickup has a magnet that creates a magnetic field, when the string is plucked it disrupts the magnetic field, the pickup detects that disruption and converts it into an electronic signal, that signal is relayed to the amplifier. The amplifier decodes the signal and amplifies it. Commented Mar 26, 2016 at 7:10

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Yes, certainly. This is the definition of "analog synthesizer". There have been many analog synthesizers going back to the theremin, circa 1928. There were a large number of analog synthesizer instruments coming to market in the 1960s and 1970s. It was not until the early 1980s that there were electronic musical instruments that used digital samples of instrument sounds and waveforms. But since the 1960s there have always been new musical instruments coming to market which create their sounds through analog synthesis.

Furthermore, there are digital synthesizers which do not make use of sampled sounds or waveforms. The first commercially successful digital synthesizer was the Yamaha DX7, circa 1983. There are still many new digital synthesizers today, in hardware and as software virtual instruments that run on a computer.

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