Within each level of space, a step is considered perceptually close. Chromatic space makes sense, each half-step is very close in frequency. Likewise at the diatonic level, our concept of scale steps fits well here. Less obvious is triadic space – a step up from Eb is G – and fifth space has one step between Eb and Bb. The distance between two pitch classes is calculated by the horizontal and vertical steps needed to traverse from one to another, by the shortest path possible. It takes five steps to the right from Eb to C in diatonic space, but only two steps to the left, so the shortest horizontal path is two steps. Vertical steps are measured to get to the lowest level of the most salient pitch. A is found only at Level e, G is found at Level c. So the horizontal distance between these two pitches is 2. A to Eb is four vertical steps. Fred combines the horizontal and vertical distances to measure the distance from each pitch to the tonic pitch. Fb goes to the left to Eb and then up the four vertical levels (1+4 = 5), E goes to the right to F, then up a level, then to the left to Eb, then up three levels to root space (1+1+1+3=6).
So the closest pitch to the root is Bb, the fifth. The furthest pitches from the root Eb are Bbb, the flat fifth scale degree; B, the sharp fifth scale degree; and Db, the flat seventh scale degree. This last pitch relationship is the odd one to me. I totally agree that chromatic alterations of all-important Sol is moving us far away from the tonic, but Te is much closer. Fred has a solution later by shifting from major diatonic space to minor diatonic space, but even as a simple chromatic alteration Te seems more like a 5 than a 7 (to pull a number out of my keister).
Thus far we have been dealing with pitches in melodic relationships. Next week we will move to chordal relationships.