To have 1st, 2nd, 3rd, etc. overtones in a closed or open-air column, do you need to have a longer tube length (than the one that produced the fundamental)?
The overtones of an air column are defined as frequencies that can be produced from the same tube length. To produce the overtones you simply need to force there to be a node/antinode at certain positions along the column.
Alternatively, the fundamental of a column half as long as the original column will be its first overtone, so if anything it would have to get shorter.