12. There must be a strong psychoacoustical basis for stability conditions. For pitch collections, this entails intervals that proceed gradually from very small to comparatively large frequency ratios.
It seems likely Lerdahl's point here is that intervals proceed graduallyfrom small frequency ratios to larger frequency ones rather than suddenly. The classic Just diatonic scale does this and, to a lesser extent, so does the Pythagorean scale.
13. Division of the octave into equal parts facilitates transposition and reduces memory load.
This is one of the constraints that Lerdahl acknowledges "... can be variously jettisoned." (p. 114), which certainly seems plausible given that people presumably did enjoy music before equal temperament came into practice.
So when should one jettison this constraint? It would seem plausible that someone who wishes different key areas to have distinct timbral qualities may find various Just tunings valuable. On the other hand, if a composer desires to write tonal music in which modulations occur often without any structural importance, this constraint may be heeded to good effect.
14. Assume pitch sets of n-fold equal divisions of the octave. Then subsets that satisfy uniqueness, coherence, and simplicity will facilitate location within the overall pitch space.
This is entirely derived from an article by Gerald Balzano in which he uses set-theory to find various relationships between different scale types. This is a fundamentally different approach to the cognition of pitch space which assumes that our scales are derived from tuning theory and the harmonicity of fundamental frequencies.
Lerdahl's Constraints
Pitch Space