|Acoustics of the clarinet
Notes are the written pitch.
Observe that, unlike the curves for the notes below D#4, these curves have only two strong harmonic peaks. The sound still has several strong odd harmonics (particularly when played forte, as here), but apart from the first two they are not much assisted by resonances of the bore.
For general comments about the throat register, see E4
Sound spectrum of a Bb clarinet played using fingering for G#4.
For more explanation, see Introduction to clarinet acoustics
You can hear G#4 played.