Why do turntables do 33.33 RPM?
By 1920 turntables (both Gramophones and Edison’s phonograph) were being powered by electric motors which ran at 3600 RPM with a gear ratio of 48:1, bringing the platter speed down very close to 78 RPM (78.26, to be exact).
The downside of the 78 was that based on its diameter (10 inches), number of grooves per inch (i.e. how tightly packed they could be cut) and the rotational speed, the maximum length of the spiral groove that stored the music was restricted to 270 feet. That works out to about four minutes of music. Not good if you want to listen to an entire symphony with no interruptions.
In 1931, RCA introduced a new type of 12-inch record just as movies with sound were spreading around the world. Motion pictures came on standard reels featuring 1,000 feet of film. Based on the speed that film was fed through a project, each reel provided 11 minutes of viewing.
To match up the film with sound, a company called Vitaphone introduced a system that used a standard 3600 RPM motor to rotate a soundtrack disc. To make the audio last the same 11 minutes, the maths dictated that the motor be geared down to 108:1. That gives us a rotational speed of 33.33 RPM.