How to remedy the singing effect dimming lights produce?

For a dimmable circuit you should always use regular incandescent light bulbs to get the best smoothest effect and use a quality dimmer. Light bulbs wok by a filament heating up to produce light at varying intensities that result from varying voltages produced by the dimmer that is just a variable resistor.

There are "chokes" in the dimmers which are filters that filter out electrical noise but sometimes cause a modified sine wave of electricity to actually vibrate the wire filaments in the bulb causing this singing.

Cheap bulbs and cheap dimmers usually cause this.

I think that sound is coming from the dimmer. It indicates that the dimming switch was built with cheap components, lacking filters, and lacking potting compound in its coils. The solution is to get a good quality new switch.

I have halogens too and have never heard any sounds from them, just from the dimmer.

I have a high quality dimmer (installed by an electrician) and experience the same noise. Unfortunately, it's over my kitchen table, so I have to keep it on full brightness to not get the sound. I look forward to hearing of another's remedy.

drop the halogens; a waste of money, as 90% of the energy they use is produced as heat.