No, you're incorrect. Here's why.
I collect electronic music, and have for close to 25 years--I have things that qualify as electronic music, analog electronic music, in my collection that go back to the 30's. This recording is the first instance of a computer being used to produce sound. Digital sound. Before this, there was no digital sound synthesis of any kind; computers were, for all intents and purposes, silent.
This work was produced at AT&T Bell Labs by a researcher named Guttman, who was tasked (among other things) with finding a way to replace human telephone operators with computers. Guttman had to start somewhere, so, he hooked up a transducer to the system he had access to.. Which, if I remember correctly, was an IBM 603. He found that he could use a computer to produce tones by varying the duty cycle of a circuit which was tied to the transducer he attached. From there, he was able to map differing duty cycle amounts to correspond to particular notes. From there, it's a short step to composing music, in that all the program is doing is procedurally modifying the duty cycle of the circuit to match given frequencies at the right times..voila, music.
Digital sound synthesis eventually developed in parallel with analog sound synthesis for the next 20 years or so. By the end of the 70's, the first digitally-controlled frequency-modulated synthesizers became available, and growth in that area became pretty explosive. Just compare the sound quality of a typical arcade game from 1980 versus one from 1984, and you'll see what I mean.
As far as computers went, digital sound synthesis became a feature in home computers by the early 80's. You had computers like the Commodore 64 which had surprisingly sophisticated sound capabilities for its time, which led to the emergence of things like SID and MIDI files, the ancestors of modern MP3s. As sound hardware improved throughout the 80's, other formats emerged, like MOD, which basically enclosed the score along with FM sample data. That, as well, continued well into the 90's, and was replaced by the next generation of hardware, capable of reproducing CD-quality audio, 16-bit per channel, 44 KHz sample rate. By the mid 90's, PC hardware had become capable of both producing as well as decoding realtime decoding of MPEG audio, and the MP3 era was born. You can thank Fraunhofer in Germany for that advancement.
Each evolutionary step in that process can be drawn back to Guttman's work at Bell Labs in New Jersey in the late 50's.