Interesting topic. I was mostly raised by my Grandma, who was born in 1900. She and my Grandpa adopted my mother, who was born in 1936. By the time I came around in 1956, there were just about 2 generations between my Grandma and me.
Fortunately, the home and car radios were on WOWO most of the time, unless there was a local event on local station WRSW, Warsaw, IN. I say fortunately because WOWO, even though it was the full-service news, info and farm voice, the music it played was top 40...even stuff like the Doors and Jefferson Airplane. The exception was during The Little Red Barn. I don't remember a lot about my Grandmother's musical taste. She had several Hawaiian albums (Martin Denny particularly). I seem to remember Herb Alpert's "Whipped Cream and Other Delights" in the house. My Grandmother did not like seeing all those black faces on her TV, so "Soul Train" was out.
My mother graduated in 1954, and immediately married my bio-father, who I never met. From what I was told, he was a very religious man who "didn't allow no music in here". My mother handed a lort of 45s she had down to me, and I have a special place in my heart with Domenico Modnugo's "Nel Blu Dipinto Di Blu" which was one of them.
My Mom married my step-dad, and they had a variety of greatest hits albums, some which were sold at tire dealerships. I remember one of them having The Leaves version of "Hey Joe". When my Dad was driving, he listened to country station WMGS, Bowling Green, Ohio.
We moved to Western Ohio when I was 10, still with a strong signal from WOWO but there was a different station being played at the pool--Fun Radio 8 CKLW (shortly after becoming The Big 8). About that time I got my first transistor radio. Mom and Grandma called my music "wang wang". Grandma was on record as hating "Somebody to Love" by Jefferson Airplane. Our family vacation for several years was to a town called Fremont, Michigan, which had a small lake. I was shocked when my parents turned on CKLW somewhere in Michigan and kept it on until it suffered interference from an 810. Maybe it was because it was the strongest station on the dial. They also turned on WLS for awhile on the way back.
In adulthood I had the opportunity to take my (step)dad to see Conway Twitty at an outdoor venue in extreme Northeast Indiana.
I think my Mom would have liked the Music of Your Life format later in life.