Mathematical link?

[Bonzo 2000]

Is there any link between the numbers 33 and 45?  The most obvious application is the rev speed of old vinyl records. Why were they set at these specific speeds?  However, 33 and 45 also seem to come up in other areas, such as dilution rates etc.  Is there some sort of link?

[EssJay1]

Don't know, but there used to be a speed of 78 for vinyls. LPs should play at 33 1/3 rpm. 78 - 45 = 33
Very unhelpful.

[Hippy]

The first flat disc records were made and played by purely mechanical means. The speed of these early discs varied between 65 and 100 rpm However, the 78 rpm standard was decided around 1900, from an early attempt at 80 rpm This speed was chosen as a compromise between length of play per side of disc (fast = less time), groove and needle size (big = less susceptible to damage and bad sound), and fidelity of playback (fast = better reproduction).

When, around 1925, electrical recording took over from the mechanical system driven by falling weights and governors, synchronous motors were used. The speed of rotation of such motors is governed by the frequency of the mains. At 60 Hz (USA) such motors spin at 3600 or 1800 rpm, and at 50 Hz (UK) 3000 and 1500 rpm. By using a gearing that reduces speed by 46 times in the USA we get 78.3 rpm and in the UK a reduction of 38.5 gave 77.9 rpm. Near enough. The later (nominally) 45 and 33.3 rpm speeds were chosen for similar reasons of groove size, length of play and gearing from a synchronous motor.