I’m linking here to a terrific bit of advice, 10 Ways to Be a Musical Family by Nancy Salwen. Nancy runs workshops for kids and adults and her focus seems to be on helping non-musical adults bring music into their homes for their kids.
One aspect of family music-making that I think is very important is that your children get to see you – the infallible grownup – learning, fumbling a bit, making mistakes. Not always hitting the right note but persevering and having fun along the way. If we jump in like this we get to model what we’re always telling them to do in their classrooms and extracurriculars: don’t worry about not being good right away, have fun, keep learning, keep trying, and keep practicing.
Too often we stop trying new things as we get older, and stick to activities that we’re already good at. Our kids only see us playing sports or making art or playing instruments that we have some proficiency at. They may conclude that we never have difficulty with things like they do*, and this could feed their frustration when they attempt new activities with a significant learning curve.
Personally, I think every parent should take up a brand new musical instrument or difficult sport when their child hits about age six or seven, and is coping with new challenges daily!

I also think there is value in demonstrating the enjoyment of being an amateur at something. Just because a person doesn’t have Broadway-calibre talent doesn’t mean they can’t enjoy singing or dancing. These days any interest in the arts for the young seems inextricably linked to a pursuit of excellence and stardom – winning competitions and clawing your way to the top. It’s always valuable to re-emphasize the fun, camaraderie and joy of making music.
To put my money where my mouth is… we’ve been in our new house for almost a month now, and this afternoon I WILL unpack and assemble my looooong neglected drum kit, which I am spectacularly inept at playing. Woo hoo!

not my drum kit
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* Of course I’m talking here about the younger years, pre-adolescence. Once our kids hit twelve or thirteen they know for a fact that we can’t do anything right.