A fun way to improvise without knowing any harmony on a regular keyboard is to stick to the black keys. This is basically a pentatonic scale and doesn't have any big dissonances.
In some sense, on an equal temperament piano a major 7th is less dissonant than a major 3rd. But major 7th can’t be played using black keys and major 3rds can.
Check the table in 12 tone equal temperament > Comparison with just intonation section here [1].
Major 7th and major 3rd are both harmonics of the root frequency, so larger differences between JI tuning and 12TET tuning for them cause noise.
In JI, theres a sense where both major 3rd and major 7th are both perfectly in tune with the root frequency. If you play the 3rd two octaves up, all of the harmonics match with all of the harmonics in the root frequency. Same if you play major 7th three octaves up.
The 2 octaves up major 3rds harmonics are 5,10,15,20,… multiples of root. 3 octaves up major 7th are 15,30,45,… multiples of root. The roots harmonics are just 2,3,4,5,6,7,8,9,… so there’s no new frequencies.
If you play square waves with these notes, in a sense you aren’t even playing a chord, just changing the timbre from a square wave to something else.
Kind of tongue in cheek cuz there are other ways of looking at dissonance. This is just an illustration of some ways you might not have seen before!
