If you ask any great musician "Which is more important, notes or rhythm?", most of them will invariably answer "rhythm." (Mozart, in fact, went even further and said that the silence between the notes was the most important thing. As I write this, I'm realizing that one aspect of what he meant was in fact "rhythm.")
Yes, rhythm is paramount. Here's a joke you can tell your friends:
Have a friend ask you "What's the secret of great comedy." As they get halfway through the question, interrupt them by loudly saying "timing!"
Yes, your timing, or rhythm, will be off, and that's what makes this joke effective. You're claiming that timing is all-important while actually saying the word at the wrong time. It's irony, truth, and comedy all rolled into one joke.
Any lounge piano player knows that they can play all the wrong notes they want and no one will notice. But mess up the rhythm, and everyone looks in your direction.
Rhythm is key.
I once read a book about an American drummer who went to Africa to study rhythm. He said that in the traditional way of learning, a young percussionist would be given a big dum, and their job was to play only on the downbeat of each "measure." They'd play the downbeat and then listen to all the other percussionists play intricate rhythms for the rest of the cycle, and then they'd play the next downbeat.
This went on for a year or so.
Can you imagine??? Would any of us have the patience to only play downbeats for a full year?
I don't think many of us would.
But here's the thing: After a full year, the youngster would have a solid sense of rhythm for the rest of their life. In fact, they'd have a better sense of rhythm than most American musicians, even most professionals.
Rhythm is life.
It's worthwhile to take some time (pun intended!) and focus on developing our sense of rhythm. Play drums on your lap while listening to a favorite recording. Play simple chords on the piano and try to keep an absolutely steady beat. Improvise, and pay attention to the exact moment when your tempo speeds up or slows down. Or play different rhythms in each measure to challenge yourself in that way.
There's an alto trombonist, Michael Lake, who's made a nice video about learning jazz rhythm. As pianists, sometimes it's helpful to get the perspective of a musician who plays another instrument and as you'll hear, Michael has an absolutely beautiful sound on the alto trombone.
You can check out the video here:
Take a few days (or a month, or a year) to work on your rhythm. It's well worth the effort!