When, and by what means, were music instrument craftsmen able to determine with any precision the exact frequencies of the musical pitches?
I know it’s a loaded question, but I’m interested in knowing about efforts before electronic instruments were in use.
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For most of musical history, they didn’t. And it didn’t matter. It’s possible that in some cases, the resonances of particular buildings etc. influences intonation. But there’s no evidence that they even perceived “F”, for example, as being anything other than the note between E and G. Certainly not anything suggesting that “F should sound like …”
The invention of the tuning fork, in the mid-18th century, changed things. This was a fairly inexpensive and transportable item, which holds its pitch almost perfectly. Once such a product existed, standardisation was an inevitable result.
(FWIW, most of our knowledge of what pre-tuning fork pitches were set at comes from surviving organ pipes from a particular place & time, which provide a fixed frequency.
Here’s a previous related thread:
One person who meant a great deal for the understanding of our perception of tones was the German scientist Hermann von Helmholtz. He studied how we perceive overtones, and made some startling discoveries.
(For example: Take a tone, and add a series of overtones. It still sounds like the same tone, but ‘fuller’. Now remove the base frequency, and it still sounds like the same tone, although a bit ‘tinny’. As an example, take a base frequency of 100Hz, and add a number of overtones, 200Hz, 300Hz and so on. Even if you remove the 100Hz tone, it still sounds like 100Hz!)
I was once at a lecture where the lecturer used some of Helmholtz own instruments to illustrate this!