[Smt-talk] Classical Form and Recursion

[Daniel Wolf]

There are a number of examples of recursion as a compositional device in  
twentieth century music which might be noted.   John Cage's "square root  
form" in which the formal proportions of the whole are repeated locally as  
rhythm, is one example.  The mapping of interval ratios onto rhythmic  
proportions, in works by Cowell (Quartet Euphometric, Quartet Romantic),  
Tenney (the Harmonium Series, Crystal Canon for Conlon Nancarrow), and  
Johnston (Knocking Piece, among many others), are examples.  Further, in  
the formula-based works of later Stockhausen, both large-scale and local  
structures are generated from the formula.

Of course, the question of the relationship between such compositional  
applications of recursion and their perception is an open and interesting  
one.

Dr. Daniel Wolf
composer
Frankfurt