any number of instruments arranged in groups of four
Aldebaron, Betelgeuse, Capella, Deneb, El Nath, Fomalhaut, Gacrux, Hadar, Hydra R, Indus Alpha, Kaus Australis, Lupus Phi, Mirfak, Nunki, Octans Beta, Pollux, Procyon, Rasalhague, Schedar, Taurus Gamma, U Geminorum--the names of twenty-one stars--are also the names of the twenty-one, four-part canons (rounds) of Radif II. Each canon is based on a different collection of 4 or 5 notes from the time-honored "Guidonian" hexachord (C D E F G A) (there are 21 such collections), each has a different canonic property (imitation by delay, and/or inversion, and/or retrograde), and each plays a different rhythmic game within a quick 36 pulse cycle. The canons are material for arranging a version of Radif II which can be for any combination of instruments and last any amount of time. A performance may use one, some, or all of the canons, and be played alone or with versions of Radif I and/or Radif III.
The name "Radif" is taken from traditional Iranian classical music where it denotes an entire corpus of music consisting of 12 interrelated parts (Dastgah) each containing a multitude of sub-parts (Gushe). The Radif is also the register of stars in Arabic astronomy.
My Radif series was written in 1975-6. The three parts of the series are open works, amenable to different uses and occasions. All three parts are based on the Guidonian hexachord and on the cycle of 36 pulses mentioned above. Radif I is a set of five melodies that undergo continual transformation and can be played as a canon by four instruments. Radif II is the collection of canons just described. Radif III is a set of drones based on any of 176 six-note sequences.
In 1993 I made a version Radif II for a computer music system. The system automatically sequences, orchestrates, transposes, and dynamically modulates the canons so that every performance of Radif II will be unique. There is no predetermined time length for the system; in principle it can run forever without repeating itself. The system has three modes: (a) Radif II is played with one of the 176 drone-sequences of Radif III; (b) Radif II is played alone; (c) Radif II is played alone but each canon is played in a different key.