alignment kernel. The successive control groups create successive misalignments of the iso-regular groups in the alignment kernel. The profound point is this:

Mechanical CAD. The iso-regular groups, , loaded into the alignment kernel, are the shape primitives (cylinder, sphere, cube, etc.).

Music. The iso-regular groups, , loaded into the alignment kernel, are the anticipation hierarchies.

In other words, what have been called features in mechanical CAD (e.g., the cylindrical hole or rectangular block) correspond to the metrical and melodic anticipation hierarchies in music. Therefore our theory of feature attachment in mechanical CAD, becomes equivalent to our theory of composition in music. That is:

Theory of Musical Composition Musical composition proceeds by successively adding new iso-regular groups (anticipation hierarchies) into the alignment kernel, and positioning the command group for each new instance in the appropriate wreath position within the unfolding group corresponding to the inheritance hierarchy of the structure.

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