On Friday, January 11, 2019 at 9:07:33 AM UTC-8, wrote:

Some time back I wanted to use the mains power as a frequency standard
when adjusting a generator. I was worried about connecting my 'scope
directly to 125 volts so I used a 12 volt out step down xmfr. The
wave form was really distorted.

That can happen because of saturation and remanence: the addition of a load on
the low voltage side (like, a light bulb) will help greatly. The best small-signal
audio transformers are potted in protective shells, in order to prevent
strain on the magnetic laminations (which makes the magnetic core
do those nonlinear things).