or the interplay of aleatory structures within one harmonic tone; electronic music. The title is an anagram of the word ALEA (Latin for dice) with two letters transposed to EL (for electronic). The sound material consists exclusively of pure tones (sine waves) whose frequency scale forms an arithmetic progression with the constant difference of 25 Hz between consecutive tones. The collection of these tones may be interpreted, then, as the harmonic series of one base frequency of 25 Hz. Unlike in natural tones, the partials are independent of the fundamental and extend upwards to the 400th harmonic (10 000 Hz).

Similarly to the pitch scale, the time scale is uniform throughout the piece. It is a logarithmic scale formed by a geometric progression with common ratio of 1.3 and an initial value of 1 second. Each successive tone is 1.3 times longer than the previous one, so that every degree of the scale can be calculated as an = 1.3n sec. The lowest term is 1, 3-11 ≈ 0.056 sec, and the highest 1, 311 ≈ 18.4 sec.

The whole work consists of nine structures that are variations on the same material. Each of these variations is governed by a different vertical structuring principle (combinations of multitones and so forth), different temporal and dynamic structures. To each of the structures, the composer applied an arbitrary system of “rules of the game” (algorithms defining the way and range in which each musical parameter is formed). Conversely, all the details, such as the choice of individual frequencies, durations, volume levels, and directions in stereophonic sound reproduction, were determined randomly, that is by throwing dice, choosing from a shuffled card deck, and so forth, in accordance with preconceived codes which assigned musical parameter values to specific numbers or cards.

The specific order within each structure was established by a number of draws. Draws were not repeated, nor were the obtained values adjusted in any way. The composition was produced (using the traditional technique of tape recording and editing) at the Polish Radio Experimental Studio in Warsaw between January 1969 and June 1970. The resulting tape, just as the work’s printed score, contains only one of many possible interpretations of this work. The rules of the game, formulated as algorithms and notated in a mathematical language such as Algol, can become the basis for an automated production of the music by a computer combined with a suitable converter. The computer must be equipped with a random number generator, and the converter should have an appropriate number of channels (about 70).

The existing version is a little less than 11 minutes long.

*Włodzimierz Kotoński*

*(from the 1970 Warsaw Autumn programme book) *