Here's a synopsis of how the different record speeds came into being, introduced by Edison and then degraded into an RCA/Columbia corporate battle.
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Thomas Edison’s first phonographs were hand cranked, which made a single standard speed virtually impossible. The listener cranked the machine at whatever speed sounded right, which usually worked out to around 80 RPM. That was slow enough to get five minutes of material (the average length of a popular song) onto one of Edison’s five-inch cylinders, and fast enough to provide what passed in those days for decent fidelity.
When the first disc record was introduced in 1888, it was designed to meet the loose standards of the Edison cylinder — five minutes of playing time at 70 to 80 RPM. Formal standardization — at 78.26 RPM — didn’t come until 1925, when the phonograph was married to the speed of a common, mass-produced electric motor fitted with equally common gears.
Around this same time (1925) the original acoustic method of recording was made obsolete by the far superior electric system. The fidelity possible at 78 RPM could now be had at a much slower speed — 33-1/3, thus yielding more playing time from the same size disc. But since radio had been introduced around this time, there was little appetite among the public to incur the cost of converting record standards. So, through the twenties and thirties, the new 33-1/3 process was used only in studios and radio stations.
In 1931, RCA Victor badly bungled an attempt to put a cheap, imperfect 33-1/3 system on the mass market, and no one tried it again until 17 years later (1948), when Columbia Records introduced a new system, shrewdly pitching the new “Long Plays” to classical musical collectors, pointing out that the listener could now settle back and enjoy an entire movement of a symphony without the annoyance of changing the disc every five minutes.
In a pure marketing move, RCA created an entirely new patented system — 45 RPM — on the market. It offered the same five minute playing time as the 78 with somewhat improved fidelity and the dubious advantage of being more “convenient” because the discs were smaller. In presenting the 45, RCA came up with marketing B.S. about how 45 RPM was the "optimum speed" for sound reproduction, but actually had told its engineers to come up with any old speed so long as it wasn’t compatible with Columbia’s 33-1/3 system. The big hole in the 45 was apparently supposed to make the two types of records even more incompatible.
And that's how the 3 different record speeds came into being.
The linked article talks about subsequent "standards" infighting between RCA and Columbia, with each eventually licensing the other's technology (RCA owning 45 and Columbia owning 33.) As an interesting aside, the whole concept of optimum turntable speed had been marketing BS since the turn of the century...at a constant turntable speed, the velocity of the grooves moving past the stylus decreases as the record plays. Some systems sprung up that spun the turntable at a variable speed for Constant Groove Velocity, but that quickly died. I wonder if the European records with the small spindle hole with the 45 knock-out wasn't to make the records compatible no matter which company prevailed in the standards battle.