Spiegel's 1981 taxonomy of twelve pattern-transformation classes underpins algorithmic pattern libraries

In ‘Manipulations of Musical Patterns’ (1981), Laurie Spiegel listed twelve classes of pattern transformation — Transposition, Reversal, Rotation, Phase Offset, Rescaling, Interpolation, Extrapolation, Fragmentation, Substitution, Combination, Sequencing, Repetition — as tried-and-true operations from the musical tradition that computer musicians should implement, plus a thirteenth open category, ‘The Great Unknown’, for patternings not yet discovered. Magnusson and McLean use this taxonomy as a framework for evaluating live-coding pattern systems, and stress that Spiegel’s descriptions are strikingly open to interpretation: each class stands for a huge range of possible implementations. The ‘Great Unknown’ signals that no pattern library is ever complete.

Examples

TidalCycles maps onto some classes: rev (Reversal), rot (Rotation/Phase Offset), fast/slow (Rescaling), cat/append (Combination/Sequencing). Others have no direct built-in and require custom functions.

Assessment

List Spiegel’s twelve pattern classes; give the TidalCycles equivalent for Reversal, Rotation, and Rescaling; and say what ‘The Great Unknown’ implies about the completeness of any pattern library.