I recently obtained an inexpensive plastic recorder and am amazed that it’s possible to play a chromatic scale on it across two octaves. Many of the fingerings seem magical to me - as in, how did anyone figure out that combination X leads to note Y?
That got me wondering more generally how the size and position of recorder holes were determined. There has to be some physics at play here to figure out how the hole positions change the frequency of the notes. But it’s not as simple as “uncovering the next hole moves up a half step or whole step,” since many of the note fingerings involve closing previously opened holes.
What was the process by which the modern recorder finger hole positions and associated fingerings were invented?