If you mentally spin a cube, you are visualising.
If you mentally traverse a diatonic scale, you are AUDIATING.
I suspect this is of great importance for musical fluency and also acquisition of perfect pitch.
Here are some basic exercises.
1. Audiate a note, then sing it out loud. How close are you? Can you even detect whether it is a match or not?
2. Hear a note. Audiate it. Now sing it back.
NOTE: this is completely different from pitch-matching. In pitch-matching you are singing as you are hearing the reference note, and listening for 'constructive interference' (for want of a better term).
3. Hear a note. Audiate a particular interval above it. Sing that!
4. Go through a melody, alternately singing / audiating each bar
It gives a better training if you pay random notes between rounds, to prevent relative hopping.
Bruce Dalby writes (here):
The goal is to play the instrument is an extension of the mind's inner audiation instrument.
He is talking about playing an instrument. I consider this a second step. The first step is to harness the voice as an extension of the mind's inner audition instrument.