I've been doing this thing lately where I randomly pick a note on the piano, and use that as the starting note of whatever melody I'm playing, every time I do this I'm in a different key. I find this is great practice for figuring out intervals by ear. I'd rather not look at the piano keys and even attempt to think of the scale.
I'm trying to mimic humming/whistling where you don't need to know the scale in order to play. when was the last time you whistled a tune and thought of a scale? see, it's not required. so I'm thinking the piano should be the same way, where the only skill needed is physical memorization of the sounds of intervals, from any note to any note.
The problem I found isn't the melody, it's the harmony. In order to harmonize my melody without knowing the scale. I usually just play a chord that has the melody note as one of the three notes of chord (1-3-5) and do this visually. So I assume that the the chord has the melody note within it, which I found to be the case most of the time anyway even when knowing the scale. But this isn't really efficient. I'm still thinking of other ways. Another way I found is the melody notes tend to outline the chord they're using just by the physical space they occupy. Another way is to play 2 note chords and opposed to 3 as it lessens the options. I'd like to eventually get to the point where I could do it by ear, and just match the right chord with the melody instantly, but I'm not there yet.
But what other techniques could I use for harmony, without knowing the scale, or is that about it? Any other instruments feel free to answer. this isn't necessarily just a piano thing.