Formula is:
(Speed of Sound / 2x the frequency) minus 0.6 radius equals the hole distance from the embouchure or fipple edge.
Reality is:
You have to tune the hole carefully by sanding it larger. There's some room for error, but not much.
Lower keys are more accurate than higher keys.
It's better to start with a separate mouth piece and then to make one tube per note.
Each tube will then be a standard for the note that it blows when attached to the mouthpiece.
As long as the tubing is consistent, the notes will be too.
Notebook (under construction):
3-TET A3 5 hole flute
4-TET A3 7 hole flute
5-TET A3 4 hole flute
5-TET A3 6 hole flute
6-TET A3 5-hole flute
7-TET A3 6-hole flute
8-TET A3 7-hole flute
When we get to 9-TET we have more notes (9) than a simple flute or recorder has tone holes, so now we have to use step patterns to know what notes are in and what notes are out. I'm no scholar, but I suspect this has something to do with the popularity of 6, 7, and 8 tone scales.
9-TET A3 8 hole flute (for giggles) 1-1-1-1-1-1-1-1-1