The students actively worked, composing the polyrhythmic polyphony – new interesting examples constantly appeared, and some young musicians were especially fascinated by the polyphony exercises. The entire material of the exercises was naturally based on the fragments of the sound lines. There occurred separate remarkable experiments, in particular, one piece appeared, completely built on the basis of a fragment from line No. 2. It applies numerous techniques of the imitation polyphony and theme transformations. Let's consider it in detail.
Mathematical music as a new means of developing compositional skills
The Eighth Essay
This piece, entitled “The Joke Invention” for three wind instruments (clarinet in B, bass clarinet and bassoon), was composed according to the rules of working with a computer sound line. The musicians applied all possible transformations of the theme – increase, decrease, inversion movement; imitations and canons were introduced.
In the reprise of the piece, even the elements of the theme reversal were allowed, which was not supposed to be done with a computer line, since this fundamentally changed the sounds of the line from which the theme of the Invention was built. But since the piece carries the name “The Joke Invention”, then light “deceptions” and “incorrectnesses” could be admitted to an insignificant extent. The musicians who were well aware of this, themselves “confessed" about this transformation of the theme. The theme of the invention was taken from the computer sound line No. 2:
The fragment of the sound line has a huge range of 6 octaves, therefore, without changing a single sound of the line, it was necessary to transpose the sounds up and down several octaves, thanks to which this fragment ended up in the middle register. And only then, after the rhythmic modification of the fragment, the theme of the invention was composed. The theme possesses rather sharp intonations and whimsical rhythm.
The Invention is built in a three-part polyphonic form with a small developmental part and a reprise. In the exposition, all three introductions are given in the main key, since the answer cannot be held in the dominant key, insofar as unnecessary sounds cannot be introduced into the computer sound line. The third entry (bassoon) does not begin with an ascending sixth, but with a descending third – this is required by the range of the instrument.
In the middle part of the Invention, the theme passes twice in the inversion movement, first at the bass clarinet (measure 10), and then at the clarinet (measure 12). Small imitations and canons appear in the interludes. In the reprise, the theme is given to the bassoon in an increase, and at the same time it sounds in a decrease in the clarinet performance.
The authors of the Invention demonstrated their work to S. Filatov-Beckman, to E. Sokolovski and to the students. All of them became convinced of the realization of the possibilities of the computer line in the field of polyphony. “Brilliant!” – such was the summary of the listeners after viewing the notes, analyzing the creation and getting acquainted with the sound recording of this piece. Here is its musical text and the computer sound recording.
