Caleidocicli musicali: Simmetrie infrante dei suoni (Musical Kaleidocycles. Sound Broken Symmetries), Prefazione di Renzo Cresti e Giovanni Guanti. Postfazione di Moreno Andreatta, Milano, Rugginenti 2005, 230 pp. Nuova edizione (2010)

Reviews:
Amadeus, XVIII, 8 (201) agosto 2006, p.66 (Giuseppina La Face Bianconi)
Musica theorica Spectrum, 15/51, settembre 2006, pp.38-39 (Carmine Emanuele Cella)


In investigating the various possibilities of connecting any chord with its transpositions circa 1980, a numerical sequence that indicates the number of notes in common between one particular chord and its own transpositions iw identified (Verdi 1998).  When a reference note (fundamental) of the chord is identified, a series of numbers that repeat cyclically (module) indicate the sequence of transposition levels. The application of the chord to the deriving cyclical series (base module) gives shape to a new structure this I termed “kaleidocycle,” in analogy with some graphic themes in Mauritz Cornelius Escher’s drawings. A kaleidocycle is the result of a vertical structure changing into a horizontal structure. It is a type of regular division of sound space. I also have used the kaleidocycle in the composition of a series of musical excerpts based on a unique chord that connects with itself according to prearranged transposition levels. This chord is often accompanied by its own inversion or by its own complement, creating a superchord including both versions.

LIST OF CONTENTS

Preface
Purity of number, by Renzo Cresti
Polyedricity by Giovanni Guanti

MUSICAL KALEIDOCYCLES
Theory of interval-cycles
Application of chords
Numerical vector of common notes
Composing with kaleidocycles
Various types of musical kaleidocycles
Conclusion

POSTFACE
The Beauty of structure by Moreno Andreatta

Appendix
Cycles originated by meter2
Graphics of some compound-cycles
Transpositional diagrams of all exachords
Graphics of exachordal common note vectors

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