A transverse, side-blown flute is a cylindrical aeroacoustic resonator whose playable pitches arise from selective shortening of the effective air-column length through tone-hole venting, modified by embouchure geometry, end correction, chimney height, and head-end boundary conditions imposed by the cork.
The main takeaway is that the note is set by the effective vibrating length of the air column, which must resonate; within reason* [A]; in accordance with the wavelength of the note in equal temperament (12-TET) — and that the tone holes shorten that column by allowing air to escape.
- Base tube length for the fundamental
For an open cylindrical tube, the ideal relationship is: