Stability Conditions

9. Stability conditions must operate on a fixed collection of elements.

Don't worry, this one's not as rigid as it sounds. Lerdahl perhaps over-generalizes much in his discussion of this constraint: "... an element of a collection need only be perceived categorically". What he's advocating is composition with categories of sounds and techniques. This is a proven technique of composition, from orchestral writing which breaks the orchestra into "choirs" to Pierre Schaeffer's categories for sonification. A beautiful example is Parmegiani's De Natura Sonorum composed with oscillators and sampled bowls and wine glasses.

Risset's works show what beautiful music can be made if someone carefully breaks these rules. He's aware of the categories involved and plays with our perceptions by composing sounds that fill in the spaces between these categories. Risset is not the only composer who's done this, and there more ways to do it than his.

10. Intervals between elements of a collection arranged along a scale should fall within a certain [perceptible] range of magnitude.

This is a bit obvious. Pitches within the range known as a JND (Just Noticeable Difference) will not be noticed. Pitches above 20000 Hz will not be noticed, as well as those below the threshold of hearing.

11. A pitch collection should recur at the octave to produce pitch classes.

Lerdahl's stronger statement carries implication that composers must compose with pitch classes. The weak statement of this constraint is: For a pitch collection to produce pitch classes it should recur at the octave.

Did I screw up? Clue me in!

Lerdahl's Constraints Tuning and Temperaments