There is a good discussion of turntable speeds and record diameters for microgroove recording in this Wireless World 1951 June article “Gramophone Turntable Speeds – What is the Best Speed for Microgroove Recording?” by G.F. Dutton of EMI.
WW 195106 Turntable Speeds.pdf
Here is the summary from that article:
Summarizing, it can be stated that:
(a) 12in records can be played at either 33 or 45 r.p.m. with good quality to 18 minutes. At 45 r.p.m. the 10 inches per second limit is reached at just over 20 minutes: at 33 r.p.m. this limit is extended nearly to 22 minutes. The rise of distortion is illustrated in Fig. 9(a).
(b) 10in records can, in the extreme, be played to 14½ minutes at either speed, but the last 4 minutes of playing will have noticeably better quality on the 45-r.p.m., record. The lower distortion in the latter case is indicated in Fig. 9(b).
(c) For smaller records, the higher turntable speed is unquestionably better: by this means popular 5-minute recordings can be made comfortably on 7in discs. The advantage is clearly shown in Fig. 9(c).
The conclusions were well-backed by maths and graphs.
One could say that notwithstanding the non-technical factors that led to the appearance of two microgroove record speeds in the late 1940s, in fact having two speeds was technically justified for the range of record diameters commercially needed, and that the two used were each adequately close enough to the numbers that would have been derived from ab initio calculations.
There was an earlier thread on 16⅔ rev/min records, see:
https://www.vintage-radio.net/forum/...d.php?t=141257.
This article, “The Fourth Speed”, from Popular Electronics 1957 August provides quite a bit of background. Therein it was stated that at the time, the frequency response went to around 9 kHz, although improvements were expected.
PE 195708 The Fourth Speed.pdf
Cheers,