Caleidocicli musicali: Simmetrie infrante dei suoni (Sounds broken simmetry), Con saggi di Renzo Cresti, Giovanni Guanti, Moreno Andreatta, Carmine Emanuele Cella, Nuova edizione, Milano, Rugginenti 2010, 264 pp.

Review by Benedetta Saglietti, in Il giornale della musica, n. 287, dicembre 2011, p.25

Cyclical harmonic modules - that is to say patterns identifying chord relations at regular interval distance - have been used by many 20^th century composers (Ravel,  Stravinsky, Szymanowski, Bartók, Skrjabin), even if without developing a systematization. Domenico Alaleona had already observed that a chord dividing the octave in equal parts may belong to as many tonalities as the pitch belonging to it and had noticed the tendency to the periodical repetition of musical elements, characterized by ambiguity and suspension, tending to return to the initial position. Starting from these remarks and investigating upon the different possibilities to link one chord to itself, Luigi Verdi develops an original musical composing technique with recursive features named ‘kaleidocyclical’ (similarly to Escher’s graphical procedures). Hence, Verdi identifies each chord’s typical modal families coming out of common notes in its transpositions, and he represents them graphically by means of vectorial representation. The text describes theory and practice of the composing technique, from a visual perspective as well, thanks to geometrical representation. The musical examples can be found on the publisher’s web site. This book will certainly appeal to Douglas Hofstadter’s fans.