ENTRA

 

 

 


The History of Set Theory from a European point of view, in "Perspectives of new music", vol. 45, n. 1 (Winter 2007), pp. 154-183.

The attitude to use whole numbers to point out notes in the twelve-tone chromatic scale dates back to about a century ago. Although the trend to quantify and to catalogue has always been present in Western music, it was with the dissolution of the tonal system that this trend became urgent, especially among those composers who were looking for new forms of expression. InEurope , the first steps in this direction were made especially towards the subdivision of scales dividing the octave into equal parts. Ferruccio Busoni and Joseph Mathias Hauer may be considered as the beginner of the European set theory. In 1907 Busoni developed the idea of Synthetic scale and worked out one early and pionieering classification of scales, while at the beginning of the Twenties, with the trope theory, Hauer made the first example of a complete survey of all exachords and of their combinatorial properties, developing also the concept of harmonic field, meant as a collection of notes including the features of scale and chord, regardless of  the horizontal or vertical order. In the Fifties, a few outside theorists, such as Edmond Costère, from France, and Heinrich Simbriger, from Bohemian Germany, moved towards this direction.
In the Seventies, original research developed in Eastern Europe, almost contemporarily and without any apparent exchange of ideas: Alois Pinos with Tonove Skupiny (1971) in Czechoslovakia, Maciei Zalewki with Harmonia  Teoretyczna (1972) in Poland and Anatol Vieru with  Cartea modurilor (1980) drew similar conclusions. These authors’ research has substantially led to the same outcomes reached by the American set theorists at the beginning of the Eighties. In particular, Vieru’s work has remarkably echoed, especially after mathematician Dan  Vuza’s further working out.
Only during the last decade has research in Europe remarkably accelerated, with the original contributions like Guerino Mazzola,’s whose theorical formulations are universally acknowledged as a model.

Click here to request the complete text 

 

Index | Studies | Compositions | Music Writings
 Cultural Promotion | Orchestra Conduction 
Exhibitions | Lectures | Festivals
| Links

Via Pontevecchio 16, 40139, Bologna (Italia)
Tel. 051 546682
E-mail

© Copyright 2002 Luigi Verdi