Vinyl Speeds
If I remember correctly, there used to be four (approximate) speeds that various turntables had used: 16, 33, 45 & 78. What are known as '45s' were typically, but not necessarily, about 7 inch diameter discs. I'm sure there were 10 or 12 inch discs out there at some point as well. The only 33s I ever saw were 12 inch discs, but I've heard about 10s. I've never seen a disc that was recorded at the 16 RPM speed, but I have used a turntable that had that speed setting. It's funny to listen to a 78 on 16 speed, but even funnier to listen to a 33 on 78 speed; it's like Alvin & The Chipmunks. I'm guessing the speeds were determined by the need for a manufacturing standard, so once the manufacturing of the hardware was generally standardized, the mathematical relationship of one speed to another (16 X 2 = 32 [which is pretty close to 33]; 33 + 16 = 49 [which is not far from 45]; and 45 +33 = 78 [which is, of course, exact]) was probably a function of, through switching, applying four different voltages to the drive motor to get the different speeds. I'm guessing that the 16 speed was created to get a longer recording on a smaller disc to save on the cost of recording materials. The faster speeds were probably implemented to improve the sound quality by approximating a higher audio 'resolution' of sorts.