Opera singers often are taught to visualise a note as an angle. Base notes at -45 degrees (say) middle C level, and higher notes upwards. Each note has an unique angle. It gives a nebulous concept like "the note" another, more tangible, handle. Maybe they even point their eyes in the right direction.
It probably has to be taught but there must be books on the subject. Those pitch pipes will come in handy. This will help people keep the the same key because they will soon notice the average angle has shifted. But it is all down to practice, to build up the muscle memory. Mr Atlas (after all) was a 9 stone (126 pound) weakling until the "sand in the face incedent".
Tape recording, and singing in private (car journeys)helped me, though I did get there fairly quickly. Breathing is important because if there is not enough air to finish the phrase you tend to alter the pressure which alters the control necessary over the note, so it can change. I was taught by Bill Long to breath from the diaphragm, not the ribs. (Bill runs Chipping Norton FC 2nd Mon Fox Hotel).
Some people actually see notes as colours - a condition called synasthesia I think. Hope this strikes the right note. **groan**