It is hard to find information on how modern day people selling solfeggio tuning forks and the like know which exact frequencies to use. I liked this article below but as I have just joined I apparently couldn't comment as yet ? Does anyone have an answer for this? I have searched the net but it is just a given that certain frequencies align with certain notes when there is no way to measure what pitches 11th century monks were singing.
TL;DR: 11th-Century monks did not sing according to a standardized reference pitch.
In 1955, the International Organization for Standardization adopted 440Hz as A4. Prior to that, there was an ongoing process of standardization, and, prior to that, there was essentially no agreement. (For more, see What is the origin of the notation A4, B3, F5, etc. (i.e. ))
The tuning fork itself was invented in 1711 (Source).
Before then ... Wikipedia summarizes the lack of consistency in reference pitch:
Until the 19th century, there was no coordinated effort to standardize musical pitch, and the levels across Europe varied widely. Pitches did not just vary from place to place, or over time—pitch levels could vary even within the same city. The pitch used for an English cathedral organ in the 17th century, for example, could be as much as five semitones lower than that used for a domestic keyboard instrument in the same city.
Even within one church, the pitch used could vary over time because of the way organs were tuned. Generally, the end of an organ pipe would be hammered inwards to a cone, or flared outwards, to raise or lower the pitch. When the pipe ends became frayed by this constant process they were all trimmed down, thus raising the overall pitch of the organ.
The oldest extant pipe organs are from the 1400s (Wikipedia), so even those would have nothing to say about the 11th century.
A modern tuning fork is calibrated against a known pitch, such as a tuner of some sort.
Back in the day, exact tuning didn't seem to be that important, as orchestras and bands were parochial - they didn't travel far, so an orchestra from one place could easily have a different tuning from that of another, even in the same country.
It didn't really matter much, as long as all the players were in tune with each other. As far as standardisation is concerned, that came much later, when there was far more movement between venues for musos, but even then, it would be the local organ that had to be the datum point - it would be set at whatever the maker felt was the 'correct' pitch. Even now, that 'correct' pitch varies from place to place in the world!