A register hole suppresses odd harmonics while leaving even ones intact

Evidence

Toneholes can also act as register holes—for example, opening a tone-hole halfway along a flute kills the C4 fundamental having an antinode there, and likewise quenches all of its odd harmonics, yet it barely affects the even harmonic C5, which has a node in the center. The flute will jump to C5. — Eric J. Heller, Why You Hear What You Hear- An…, 1597