There is an old paper where a musician claims to have used an oscilloscope to measure a particular trumpet tone and proved it was a pure sine wave. There is no date available but probably late 50s, the company was started in 1956. So we're talking whatever scope technology would have been available then.

I've always been a bit skeptical about the claims because there are some other aspects that don't make sense to me.

However, my question is about how you would use a 1950s era scope to determine a sine wave or the degree of harmonics present. Most musical tones have a series of harmonics above the fundamental that add the characteristic tone.