Her compositional method is based on the idea of first subdividing the octave into twenty-four steps. These are not tones in equal temperament, however, but rather the 24th to 47th harmonic partials of a fundamental of 18.333 cps. It follows, therefore, that the 24th partial is 440 cps. The 48th partial is, of course, the octave of this, and the steps within the octave are separated by equal numbers of cycles per second. Consequently, the scale is linear rather than logarithmic with large scalar steps in its low range and with smaller and smaller steps as the pitch increases. Second, Mother Padberg associated a letter of the alphabet with each note of this scale, doubling up V and W and associating Y with either I or Z. Third, she defined a tone row by means of any 12-letter meaningful phrase and further defined ways of developing rhythms from ratios of consonants to vowels. With the addition of further rows for dynamics and voicing or orchestration, she was then ready to write computer programs for generating compositions based on these schemes. Mother Padberg first wrote a computer program in FORTRAN for an IBM-1620 computer to enable her to write a canon for two or four voices. Later, however, she was able to expand and generalize this idea by writing a more generalized program for an IBM-7072 computer. This later program permitted her to generate canons in two or four voices based on one to three tone rows with the further option of producing a “free fugue.” The construction of this “free fugue” was based on the idea that a tone row and its transformation constitute a “group” to which transformations of group theory are applicable. The result is a Canon and Free Fugue which has since been converted into sound by Max Mathews.

Mother Padberg concludes that while her “computer-composed” Canon and Free Fugue may be lacking in aesthetic appeal, it nevertheless has qualities traditionally associated with both absolute and program music. It is “a logically conceived, unified composition integrally bound to its ‘title’ in melody and rhythm and not dependent on outside connotations for its explanation or development.” It might be noted that, if the project seems willful and arbitrary, it is certainly no more so than many other compositional schemes being used today. It is hardly necessary to point out that mathematical permutations of sets of numbers are considered quite proper when done in the name of serial composition. Moreover, the association of names of notes with words or anagrams has long been used to provide musical themes and mottos. This seems already to be a realization of a way of composing music based on written messages proposed by Cazden in what are apparently meant to be satirical essays [“Staff Notation as a Non-Musical Communication Code,” “How to Compose Non-Music” and “The Thirteen-tone System”].

Lejaren Hiller