It is said that conical bore instruments, like the sax, oboe, etc, overblow at an eigth, or octave, while cylindrical bore instruments such as the clarinet, overblow at a twelfth. The flute appears to be cylindrical, so why does it go up in octaves ?

The reason is that the clarinet is a stopped pipe but the flute, like the recorder, is open because of the embouchure hole.

The description is correct. The Frequency Resonance curve of the tube is the same. If you looked at the tube's resonance peaks they are at Hz 100, 300, 500, etc. The dips are at 200, 400, 600 etc.

Clarinet as a stopped pipe at one end is operated therefor by the peaks (which make it an octave lower also) Flute, open at two ends, operates at the minimums which is also why it is an octave higher.

200-400 is a doubling, hence the octave as in flute
100-300 is a twelfth as in clarinet.

Conical Like saxophone also operates at the maximums but the bore shape changes the resonance to octaves.. 100, 200...etc...

If you take a flute headjoint and stop up the open end, it will fall and octave and then if you overblow, it will be close to a twelfth- like clarinet..Make a flute headjoint fit a clarinet and it will be an octave higher and play octaves.

Fun stuff..

Joe B

Contra and JBunky, many thanks for your helpful replies. I still have some memories of my schoolboy physics, so your replies made sense. Thanks again.