Two topics I discuss a great deal in my lessons are ear training and the overtone series.
Here is an exercise you can use on your own.
Play the following chord
Play this through all 12 keys.
After playing through all 12 keys: Play the chord again and then play a random pitch with your eyes closed and try and determine the note played.
One of the revealing aspects of playing the first 7 partials of the overtone series is that non-diatonic pitches will feel closer no matter how far apart in register.