15. Any but the most primitive stability conditions must be susceptible to multidimensional representation, where spatial distance correlates with cognitive distance.
This seems an odd constraint. Shouldn't the analytical methods conform to perception, not the other way around? What in fact Lerdahl goes on to propose is a complementary pitch space that has a reductional rather than a geometric format. For more information consult Deutsch and Feroe "The internal representation of pitch sequences in tonal music" from vol. 88 of Psychological Review. In general, the difference between the reductional and geometric models are that in the geometric model distances don't necessarily correlate to hierarchies. there is only one "state" or "level" to the geometric model. The reductional model presents levels of detail, reducing the amount of information at each level.
16. Levels of pitch space must be sufficiently available from musical surfaces to be internalized.
This refers to the ability to hierarchically relate pitch classes. An example is from Krumhansl's study of tonal music in which listeners rated the context-bound stability of chromatic scale degrees.
Krumhansl postulated that this was most likely produced by the amount of repetition of these pitches in music. It is worth noting that maintaining certain distributions of pitches throughout a work will probably aid listeners in internalizing their relationships.
17. A reductionally organized pitch space is needed to express the steps and skips by which cognitive distance is measured and to express degrees of melodic completeness.
By this Lerdahl is saying that a hierarchically reduced pitch space allows for the cognition of different 'leaps' as steps at higher hierarchical levels.
Lerdahl's Constraints