Think of Barkhausen's curves when the filament is operated on DC.

There is no change over time.

Now, think real hard about Barkhausen's curves when the filament is operated on AC.

That is a dynamic situation, constantly changing over time, according to the AC waveform.

Doubt that? Then look at this . . .

Part of the time, the voltage differential along the filament is Zero Volts (0, 180, 360 degrees)

Part of the time, the voltage differential along the filament is at 1/2 of Peak Volts (30, 150, 210, 330 degrees)

Part of the time, the voltage differential along the filament is Peak Volts (90, 270 degrees)

Perhaps with the above dynamic differential voltage along the filament from the AC, there might be sidebands occuring on musical notes and harmonics.