|Acoustics of the clarinet
Notes are the written pitch.
Here, the C4 may be considered as produced by a variant of the C#4 fingering, with considerable cross fingering to make it flatter. The A#5 is produced by the third peak in the impedance spectrum, which one could consider as the third resonance of a modified fingering for F#3, with the open key acting as a register hole.
A two-note multiphonic requires the superposition of two standing waves (whose frequencies, which are not in harmonic ratios, determine the pitches). Usually, this is achieved by opening one (usually small) tone hole in a series of closed tone holes. The wave travelling downstream from the reed is partially reflected at the open tone hole, which makes one standing wave. The rest of the energy in the incident wave continues down the bore, until it reaches the first in a series of open tone holes. Here it is reflected to make the second standing wave.
For this situation to apply, the frequencies of the notes have to be such that the effect of the inertia of the air in the open tone hole is large enough to allow some transmission past the hole, but small enough to produce some reflection. For low-pitched notes, the tone hole is usually small.
Sound spectrum of a Bb clarinet played using fingering for the multiphonic C4 with A#5.
For more explanation, see Introduction to clarinet acoustics
You can hear the multiphonic C4 with A#5 played.