Caleidocicli musicali (Musical Kaleidocycles). Simmetrie infrante dei suoni, Milano, Rugginenti, 2005

Review by Carmine Emanuele Cella
in "Musica theorica Spectrum", 15/51, settembre 2006, pp.38-39

It is not easy to identify the various approaches to musical creation by composers during the historical evolution of music, without the risk of superficial cataloguing. Some of them undoubtedly wrote music simply by means of what could be defined as instinct or maybe creativity. Some others rather filtered and directed their creativity through a strange ‘intellectual monster’ generically named technique. On the other hand, some others often pretended to create their music only thanks to instinct, but then used a technique ‘secretely’ (if the periphrasis can be used) .
It is true that the union creativity/technique has accompanied musical creation practically since this discipline originated. It may be useful to mention Kircher’s Tabula Mirifica or Ockeghem’s giddy counterpoint techniques or, more, the amazing quadruple-counterpoint machines probably used by Bach himself (even though there is no certainty of them). Finally, it may also be useful to mention Ligeti’s mensural techniques for the organization of his continuously changing chords or his complex analytical functions for the organization of rhythm (for example in L’Escalier du diable). When a composer writes music, he/she has to menage with a technique (in the most general sense): tonality, dodecaphony or more complex and different serial combinatorial systems. In these cases, technique has had the role of pre-composing system, or of a free ground where to set /frame musical creativity. A set of rules to menage with, and probably to break.
Thus, in all of these cases, technique has become number; a musical creation can be ultimately thought of as a complex numerical system. For instance, an algebraic system, where the elements to use are the whole numbers from zero to eleven: twelve symbols able to represent the semitones of the twelve-tone scale. Even at the half of last century several theoricians/composers tried to formalize the structure of musical pitches by means of algebraic and set procedures; one of the earliest was undoubtedly Milton Babbitt, who wrote, among the others, three important articles highlighting some properties of the twelve sounds, the so called invariances, as fundamental for the composition. Besides, some other paramount contributions were given by (just to mention a few) Donald Martino, Allen Forte, George Perle, Robert Morris, until David Lewin’s transformational theories and Guerino Mazzola’s geometrical ones.
It is in the path of this rich tradition that composer and theorician Luigi Verdi’s original text may be placed – this writer is already known to Italian (and not only Italian) readers thanks to the by-now classical text “Organizzazione delle altezze nello spazio temperato” (Organization of pitches in tempered space”. In this work, Verdi conceives a complex technique of organizing pitches based on geometrical figures built on the twelve vertexes of an imaginary dodecagon (meant as a graphic representation of the chromatic scale) and used to check transformation of sound-groups according to predetermined cycles. Even though other attempts linked to cyclicity (or periodicity) were made and described by composers as Xenakis (theory of cribles) , Perle, Schat (tone clock) or Vieru (modal theory), Verdi’s work shows its original approach also thanks to the use of a particular “graphism” (however meant as a really practical instrument for computing and not as mere visual delight) which is expressed by graphic representations, tables and colour drawings.
In the first chapter of the book, there are the basic elements of the theory: in fact, it shows how to represent any note-set on the dodecagon and how to transform it according to simple or complex modules (consecutive transpositions by different intervals) until it completes its period (that is to say when the note-set returns to its original form). In the next two chapters Verdi proposes the most original part of his text, by describing the musical kaleidocycles, that is the transposing cycles to which chords – meant as note-sets – are “applied”. Then, the kaleidocycle shows its real nature, a set of sets of which Verdi knows all properties: possible configurations, relations between modules and applied chords, common notes between a chord and its transpositions (this property was also analysed by Skrjabin in his late works).
What’s more, in the fourth chapter, meaningfully bearing the title of “composing with kaleidocyles”, Verdi investigates into the field of composing design (in Morris’s sense) and manages to shows the creative skill of his own machines. In fact, there are many musical examples from the writer’s own works (let’s not forget that first he is a composer and then a theorician) which make the most interesting properties of kaleidocycles explicit, like for example, those linked to the various forms of canons: inverted, double, triple, complementary or rhythmic ones; in this view, Luigi Verdi, who has a Bolognese musical training seems in the ideal path of Father Martini’s Bolognese old musical school, as the latter was not only a music historian, theorician and composer, but he was also one of the most productive canon writers in the history of music.
The most original feature of Verdi’s work is from the point of view of the technical/composing aspect: he does not deal with the issue from the point of view of analysis but, courageously, from the point of view of composition. It is a relevant effort, which is often unfortunately missing today. Finally, the book ends with a useful catalogue of some possible kaleidocycles and with an appendix containing various tables of the hexachord properties, presented by means of original graphics named “chequered”. The book is also complete with three relevant critical contributions by Renzo Cresti, Giovanni Guanti and Moreno Andreatta.
In such a complex period as today, when almost total distrust in today’s composition and music is felt, such contributions as Verdi’s are invaluable. His intellectual honesty when explaining his works, thus permitting to grasp their inner procedures, is admirable and worthy of respect; his attitude will be able to stimulate many young composers and will maybe regain confidence to the art of music, which is important to man as air itself.

Carmine Emanuele Cella