1. The musical surface must be capable of being parsed into a sequence of discrete events.
If I can't break a piece down into sections or components at all it is just one sound, and if I want to create a relationship between more than one sound I have to include outside sounds into the piece. That is not to say that music composed of long, continuous timbral transformations (like Ligeti's Lux Aeterna or Lucier's Music on a Long, Thin Wire) are not pieces of music (in spite of Lerdahl's suggestion). When we listen to them we may break them down into the stages along their processes, or into processes and inputs. In all likelihood, though, we break them down into discrete events.
2. The musical surface must be available for hierarchical structuring.
"It does not suffice that the input organization to be structured hierarchically...it is the relationship to the listening grammar that matters." (p. 104)
This is certainly valuable advice. Simply put, Lerdahl is suggesting to us that when we compose it would be useful to take into account what listeners are capable of hearing. The converse could be taken as implicit in this advice. That is, while "cognitively opaque" music is not terribly interesting to listen to, "cognitively transparent" music is just about as boring. Music that takes advantage of the ambiguities in between the two extremes holds a listener's attention.
3. The establishment of local grouping boundaries requires the presence of salient distinctive transitions at the musical surface.
Granted, these are ill-defined words; when is a transition distinctive or salient? Is that the same for every listener? The composer only has recourse to her ears and what she knows of others' ears. She would do well to keep those ears in mind, though.
4. Projection of groups, especially at larger levels, depends on symmetry and on the establishment of musical parallelisms.
Well, this may seem a bit overstated. The number of classical sonatas that are truly symmetrical is actually small in number. It is an interesting area for compositional investigation, though. Is it possible, for instance, to compose the illusion of symmetry in asymmetry, or asymmetry in symmetry? How much does the composer want the listener to be cognizant of this illusory nature of the piece?
5. The establishment of a metrical structure requires a degree of regularity in the placement of phenomenal accents.
Let us overlook the tautological nature of this statement. "A degree of regularity" doesn't yet tell us WHAT degree of regularity. This is left as an exercise for the composer, and what an exercise! Once again we may assume that extremely high and low "degrees of regularity" may lead to accents we find boring. What if we were to create hierarchies of phenomenal accents? Patterns of accents that are different yet related?
6. A complex time-span segmentation depends on the projection of a complex grouping and metrical structures.
"since 'events' in music are usually pitch events, event hierarchies are normally pitch hierarchies." (p. 107)
Here Lerdahl offers us even more exciting areas for exploration. What are the effects of non-pitch hierarchies on the construction of event hierarchies? Any other event hierarchy like contour hierarchy, timbre hierarchy, metrical hierarchy is fair game here! If you feel really ambitious (or really cocky), you might explore combinations of these and how they interact.
7. The projection of a time-span tree depends on a complex time-span segmentation in conjunction with a set of stability conditions.
"Imagine the pitches of Le Marteau plugged into the rhythms of Beethoven's Fifth Symphony. The hierarchical time-span segmentation would largely be erased by the lack of any concomitant pitch articulation ... the absence of stability conditions would prevent the inference of any pitch hierarchy." (p.107)
We actually tried this, and it appeared that the original "time-span segmentation" was replaced by a different one rather than being out and out destroyed. A time-span tree is a hierarchical representation of the time-based relationships in the music. Creation of one, obviously, requires that there be perceivable relationships in existence.
8. The projection of a prolongational tree depends on a corresponding time-span tree in conjunction with a set of stability conditions.
What does this mean? It means that the creation of large scale structures is built by using "Stability conditions" to evaluate the relationships between groups of smaller structures.
Lerdahl's Constraints
Stability conditions